Carbon Chain Molecules: Production and … Chain Molecules: Production and Spectroscopic Detection...

Carbon Chain Molecules:Production and Spectroscopic Detection

Inaugural-Dissertationzur

Erlangung des Doktorgradesder Mathematisch-Naturwissenschaftlichen Fakultat

der Universitat zu Koln

vorgelegt von

Guido W. Fuchsaus Polch

UNIVERSITÄT

ZU KÖLN

Koln 2002

Berichterstatter: Prof. Dr. G. Winnewisser

Prof. Dr. J. Jolie

Tag der mundlichen Prufung: 18.2.2003

Abstract

In this work the production and detection of carbon chain molecules in laboratory andinterstellar space are presented. The work is divided into three parts.

Part I, the production of reactive molecules. The availability of efficient molecularsources are of great importance for absorption and emission experiments. Hence, theircharacterization and optimization is indispensable for the success of these kinds of ex-periments. Molecular sources can be very specialized concerning the species produced.The excimer laser ablation source used in Cologne is highly efficient in the productionof pure carbon molecules, i.e. carbon clusters. However, the carbon cluster yield in therange from C10 to C60 is still not satisfactory. For an improvement of the productionrates new methods have to be tested. In the course of this thesis a excimer laser ab-lation is compared with Nd:YAG laser ablation. For that purpose a quadrupole massspectrometer has been used to characterize the Nd:YAG laser ablation source. Investi-gations on a slit nozzle discharge source have been performed. This type of moleculesource is able to produce pure carbon clusters but was originately developed for theproduction of hydro-carbon molecules. Both kinds of molecule sources, i.e. laser abla-tion as well as slit nozzle discharge sources, produce a plasma which causes significantproblems when recording mass spectra. Therefore, a mass spectrometer specially de-signed for plasma applications in combination with the discharge slit nozzle was testedin Lichtenstein/Balzer. Cations as well as anions could be detected but no signal ofdischarge related neutrals were found. In addition to the mass spectroscopic studies alsoinfrared (IR) absorption experiments have been performed. In the course of this thesisthe Cologne carbon cluster experiment has been rebuild. In particular, the precedingIR diode laser spectrometer has been replaced by a new one which has been largelyimproved by using a liquid nitrogen dewar for the laser diode, new detectors for the2000 cm−1 frequency region, stable optical setup and the development of new data ac-quisition and calibration software. First measurements are presented.Part II, measurements of CnN radicals. At the Harvard Laboratory AstrochemistryGroup measurements have been performed on mono-substituted C3N isotopomers (cya-noethynyl) in a supersonic molecular beam using Fourier transform microwave spec-troscopy. A detailed spectroscopic characterization of 13CCCN, C13CCN, CC13CN andCCC15N including their hyperfine spectra is given in this work. The rotational and lead-ing centrifugal distortion constants were determined to high accuracy by using micro-wave data between 9.5 - 38.4 GHz and previously measured millimeter data. The Fermicontact b(14N), dipole-dipole c(14N), and the nitrogen quadrupole hyperfine couplingconstants for 13CCCN, C13CCN, and CC13CN have been determined and the previ-ously published b(13C) and c(13C) values were stated more precisely [McCarthy et al.,J.Chem.Phys. 103, 7820 (1995)]. The magnetic hyperfine coupling constants of the pre-sented 13C isotopic species of C3N differ from those of the isoelectronic chain C4H, butare fairly close to those of the isoelectronic C2H, indicating a rather pure 2Σ electronicground state. The CCC15N b and c magnetic hyperfine constants follow the expected

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values derived from the 14N species. In addition two new cyano radicals, linear C4N andC6N were analyzed. C4N, C6N are linear chains with 2Π electronic ground states andboth have resolvable hyperfine structure and Λ-type doubling. At least four transitionsin the lowest-energy fine structure component Ω =1/2 were measured between 7 and 22GHz and, at most, 9 spectroscopic constants were required to reproduce their spectrato a few parts in 107. Although the strongest lines of C6N are more than five timesless intense than those of C5N, owing to large differences in the ground state dipolemoments, both new chains are more abundant than C5N. Searches for C7N have so farbeen unsuccessful. The absence of lines at the predicted frequencies requires that theproduct of the dipole moment times the abundance (µ · Na) to be more than 60 timessmaller for C7N than for C5N, suggesting that the ground state of C7N may be 2Π, forwhich the dipole moment is calculated to be small.Part III, CnN radicals in the interstellar space. Astrophysical investigations of C3Nisotopomers are compared with laboratory data presented in this work. Possible misas-signments of 13CCCN lines towards IRC+10216 are investigated. Finally, a search forC2N has been performed towards the envelope of the late-type star IRC+10216 using theIRAM 30m telescope at Pico Veleta, Spain. Three lines in the frequency bands at 154,224 and 248 GHz have been detected at transition frequencies of C2N and preliminaryassigned to C2N as a carrier. Thus, a rotational temperature as well as a column densityof C2N could be estimated. The results are in agreement with estimations deduced byprevious observations (Guelin & Cernicharo [74] ). Further astronomical measurementsare necessary to confirm this tentative detection.

Kurzzusammenfassung

In der vorliegenden Arbeit werden die Produktion und die Messung von Radikalen imLabor sowie im Weltraum an ausgesuchten Beispielen vorgestellt. Die Arbeit ist in dreiTeile gegliedert. Teil 1 befaßt sich mit der Charakterisierung von Molekulquellen. Die inKoln verwendete Excimer-Laserablationsquelle ist hoch effizient in der Erzeugung vonreinen Kohlenstoffmolekulen, sog. Kohlenstoff Clustern. Zunachst wird eine Excimer-Laserablation mit einer Nd:YAG- Laserablation verglichen. Dabei wurde ein Quadrupol-Massenspektrometer zur Charakterisierung der Nd:YAG-Ablationquelle eingesetzt. Des-weiteren wurde eine Schlitzdusen-Entladungsquelle untersucht die neben der Produktionvon Kohlenwasserstoffen und anderer kohlenstoff-basierter Molekule auch reine Kohlen-stoffcluster erzeugen kann. In beiden Molekulquellenarten entsteht ein Plasma, daß zuerheblichen Schwierigkeiten bei der Aufnahme von Massenspektren fuhrt. Ein speziell furPlasmen vorgesehenes Massenspektrometer wurde in Lichtenstein/Balzer mit Hilfe derSchlitzdusen-Entladungsquelle getestet. Erste Ergebnisse werden vorgestellt. Zusatzlichwurde am Kolner Kohlenstoff Cluster Experiment das vorhandene IR-Dioden Spektro-meter erneuert. Wesentliche Verbesserungen wurden erreicht durch den Einsatz einesFlussigstickstoff-Dewars fur die Kuhlung der Laserdioden, nachweisempfindlichere De-tektoren fur den Frequenzbereich um 2000 cm−1, einen stabileren optischen Aufbau,

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sowie die Entwicklung neuer Meß -und Kalibrationssoftware. Erste Meßungen werdenvorgestellt.In Teil 2 dieser Arbeit werden Messungen an einfach-substituierten C3N Isotopomeren so-wie Untersuchungen an C4N und C6N vorgestellt. Die Messungen an 13CCCN, C13CCN,CC13CN und CCC15N fuhrten zur detailierten spektroskopischen Charakterisierung derRadikale und wurden an einem Fourier Transform Mikrowellen Spektrometer der Har-vard Laboratory Astrochemistry Group vorgenommen. Die linearen, mit 13C und 15Nsubstituierten C3N Molekule wurden mittels einer elektrischen Entladungsquelle mit an-schließender adiabatischen Expansion hergestellt. Mit den gemessenen Mikrowellendatenzwischen 9.5 und 38.4 GHz und den zuvor bekannten Millimeterwellen-Daten konntendie Rotations- sowie die fuhrenden Zentrifugalverzerrungsterme sehr genau ermittelt,die Fermikontakt- sowie die Dipol-Dipol Wechselwirkung der 13C-Isotope prazisiert unddie magnetische Wechselwirkung der 14N bzw. 15N-Isotope erstmals ermittelt werden.Zusatzlich wurden zwei neue Cyan-Radikale, lineares C4N und C6N, untersucht. Ba-sierend auf Messngen der Ω=1/2 Zustande zwischen 7 und 22 GHz [121], wurden dieMolekulparameter der sich im 2Π elektronischen Grundzustand befindenden Radikaleermittelt. Beide Spezies zeigen eine Hyperfeinstrukturaufspaltung und Λ-Verdopplung.Die in dieser Arbeit bestimmten neun Molekulparameter je Radikal ermoglichen eineReproduktion der Spektren bis auf wenige kHz Genauigkeit.In Teil 3 werden astrophysikalische Untersuchungen an linearen C3N Isotopomeren mitden in dieser Arbeit gewonnenen Labordaten verglichen. Eigene Arbeiten umfassen dieSuche nach C2N in der Sternenhulle von IRC+10216 mit Hilfe des IRAM 30m Teleskopsam Pico Veleta, Spanien. Es wurden drei Linien in den Frequenzbandern um 154, 224und 248 GHz beobachtet, die mit Rotationsubergangen von C2N ubereinstimmen undeine vorlaufige Zuordnung dieser Linien zu C2N erlauben. Weitere astrophysikalischeMessungen sind jedoch notwendig um eine eindeutige Detektion von C2N in IRC+10216sicherzustellen.

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”Jedermann sieht die Grenzen seiner eigenen Vision alsdie Grenzen der Welt an.”

by Arthur Schopenhauer (1788 - 1860)

For my parents Agnes and Werner Fuchs

Contents

Abstract / Kurzzusammenfassung i

Zusammenfassung ix

1 Introduction 1

I Characterization of Radical Sources 7

2 Molecule Source Characterization 9

2.1 Ablation Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.1.1 Excimer Laser Ablation . . . . . . . . . . . . . . . . . . . . . . . 14

2.1.2 Nd:YAG Laser Ablation . . . . . . . . . . . . . . . . . . . . . . . 17

2.2 Discharge Plasma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.3 Conclusions and Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3 The Cologne Carbon Cluster Experiment: The New Setup 33

3.1 The Cologne Carbon Cluster experiment . . . . . . . . . . . . . . . . . . 34

3.2 The New Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35


II C3N Isotopomers, C4N, and C6N 39

4 Experimental Setup 41

4.1 The Production of CnN Radicals . . . . . . . . . . . . . . . . . . . . . . 44

4.1.1 The Precursor Gases . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.1.2 The Discharge Nozzle . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.2 Adiabatic Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.3 The Fourier Transform Microwave Spectrometer . . . . . . . . . . . . . . 63

5 Linear CnN, Cyanide Radicals 69

vi Contents

6 Theoretical Considerations 776.1 Pure Rotation of Linear Molecules . . . . . . . . . . . . . . . . . . . . . . 79

6.1.1 Selection Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

6.2 Fine Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

6.2.1 Hund’s Coupling Cases a) and b) . . . . . . . . . . . . . . . . . . 83

6.2.2 Λ-type Doubling, and l-type Doubling . . . . . . . . . . . . . . . 86

6.3 Hyperfine Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

6.3.1 Magnetic Hyperfine Structure . . . . . . . . . . . . . . . . . . . . 88

6.3.2 The Electric Quadrupole Interaction . . . . . . . . . . . . . . . . 91

6.4 Matrix Representation of the Hamiltonian . . . . . . . . . . . . . . . . . 93

6.4.1 The Matrix Representation of the 2Π-Radicals . . . . . . . . . . . 93

7 Measurements and Analysis 977.1 The C3N Mono-Substituted Isotopomers . . . . . . . . . . . . . . . . . . 98

7.1.1 CCC15N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

7.1.2 13CCCN, C13CCN and CC13CN . . . . . . . . . . . . . . . . . . . 103

7.2 C4N and C6N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

7.3 The Search for C7N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123


III Linear CnN Chains in Space 125

8 CnN Chains in Space 1278.1 The Search for Interstellar C2N . . . . . . . . . . . . . . . . . . . . . . . 134

8.1.1 Observation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

8.1.2 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

8.1.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

8.1.4 Conclusions and Prospects . . . . . . . . . . . . . . . . . . . . . . 141

IV Appendix 143

A Linear CnH 145

B The HQ Matrix Elements 147

C Molecular Constants of C13CCN and CC13CN 151

D Tables: Interstellar C3N ,C5N, and C3N Isotopomers 153

Bibliography 157

List of Figures 173

Contents vii

List of Tables 175

Acknowledgments 177

Beglaubigung 179

Publication List 179

Curriculum Vitae 181

viii Contents

Zusammenfassung

Interstellares Gas, sowie von kalten Sternen ausgestoßenes Gas, zeigt eine große Vielfaltan beobachteten Molekulen, in der Kohlenstoff als viert haufigstes Element im Univer-sum eine zentrale Rolle spielt. In der vorliegenden Arbeit werden die Produktion unddie Messung von Radikalen im Labor sowie im Weltraum an ausgesuchten Beispielenvorgestellt. Insbesondere wird die Produktion von kohlenstoffhaltigen Radikalen wie rei-ne Kohlenstoffcluster Cn oder Molekule der Form CnN erlautert. Die Anwendung derhier vorgestellten Techniken kann aber auch zur Produktion anderer Molekule eingesetztwerden, z.B. von SinCm, NCnN, HCnH, HCnN, etc. .

Effiziente Molekulquellen sind von zentraler Bedeutung fur die Entdeckung und Struk-turbestimmung neuer Molekule mit Hilfe der Emissions- und Absorptionsspektroskopie.Die Charakterisierung und Optimierung von Molekulquellen ist daher wichtig in Hin-blick auf zukunftige Erfolge auf diesem Gebiet der Forschung. Die in Koln verwendeteExcimer-Laserablationsquelle ist hoch effizient in der Erzeugung von reinen Kohlen-stoffmolekulen, sog. Kohlenstoff Clustern, und ermoglichte die Entdeckung von linearemC8 und C10 [61, 14]. Die Detektion von großeren Clustern erscheint jedoch zunehmendschwieriger, sodaß einer Erschließung neuer Produktionstechniken eine wachsende Be-deutung zukommt. In dieser Arbeit wurde zunachst eine Excimer-Laserablation mit einerNd:YAG- Laserablation verglichen. Der seperate Aufbau einer Testapparatur erlaubteden Einsatz eines Quadrupol-Massenspektrometers zur Charakterisierung der Nd:YAG-Ablationquelle. Desweiteren wurde eine Schlitzdusen-Entladungsquelle untersucht dieneben der Produktion von Kohlenwasserstoffen und anderer kohlenstoff-basierter Mo-lekulen auch reine Kohlenstoffcluster erzeugen kann. Bei beiden Quellen, d.h. bei Ent-ladungs- sowie bei Ablationsquelle, entsteht ein Plasma, das zu erheblichen Schwie-rigkeiten bei der Aufnahme von Massenspektren fuhrt. Diese lassen sich jedoch durchVerwendung geeigneter Energiefilter beheben, wie Testmessungen an einem Plasmamo-nitor der Firma Inficon AG gezeigt haben. In dem Entladungsplasma konnten dannKationen sowie Anionen nachgewiesen werden. Neutralteilchen sind allerdings wesent-lich schwieriger nachzuweisen.

Neben der Optimierung der Quellen ist eine gesteigerte Nachweisempfindlichkeit derverwendeten Spektrometer essentiell. Wesentliche Verbesserungen des vorhandenen IR-Dioden Spektrometers wurden durch den Einsatz eines Flussigstickstoff-Dewars zurKuhlung der Laserdioden erreicht. Die Verwendung von InSb-Detektoren statt der bis-her verwendeten HgCaTe Detektoren fuhrt im Frequenzbereich um 2000 cm−1 ebenfallszu einem Gewinn im Signal-Rausch-Verhaltnis. Ein stabilerer optischer Aufbau, sowiedie Entwicklung neuer Meß -und Kalibrationssoftware fuhrten zu einer Verbesserung der

x Zusammenfassung

Systemstabilitat sowie zur prazisen Frequenzzuordnung der Mess-Signale. Erste Messun-gen belegen dies auf eindrucksvolle Weise.

Desweiteren werden spektroskopische Untersuchungen an Kohlenstoffkettenmolekulenmit einer Nitrilgruppe CnN im cm-Wellenlangenbereich vorgestellt. Im einzelnen sinddies vier C3N Isotopomere sowie die Kettenmolekule C4N und C6N.Die Messungen an 13CCCN, C13CCN, CC13CN und CCC15N fuhrten zur detailiertenspektroskopischen Charakterisierung der Radikale und wurden an einem Fourier Trans-form Mikrowellen Spektrometer der Harvard Laboratory Astrochemistry Group vorge-nommen. Die linearen, mit 13C und 15N substituierten C3N Molekule wurden mittelseiner elektrischen Entladungsquelle mit anschließender adiabatischen Expansion herge-stellt. Mit den gemessenen Mikrowellendaten zwischen 9.5 und 38.4 GHz und den zuvorbekannten Millimeterwellen-Daten konnten die Rotations- sowie die fuhrenden Zentri-fugalverzerrungsterme sehr genau ermittelt, die Fermikontakt- sowie die Dipol-DipolWechselwirkung der 13C-Isotope prazisiert und die magnetische Wechselwirkung der 14Nbzw. 15N-Isotope erstmals ermittelt werden. Die magnetischen Kopplungskonstanten der13C enthaltenden C3N Radikale unterscheiden sich von denen der isoelektronischen C4HKetten, liegen aber nahe an denen von C2H bekannten Werten und lassen somit auf einenfast reinen 2Σ Grundzustand schließen. Die CCC15N magnetischen Hyperfeinkonstantenfolgen den von den 14N-Radikalen theoretisch abgeleiteten Werten.Zusatzlich wurden zwei neue Cyan-Radikale, lineares C4N und C6N, untersucht. Basie-rend auf Messungen an jeweils vier Rotationsubergangen im unteren Ω=1/2 Zustandzwischen 7 und 22 GHz [121], wurden die Molekulparameter der sich im 2Π elektro-nischen Grundzustand befindenden Radikale ermittelt. Beide Spezies zeigen eine Hy-perfeinstrukturaufspaltung und Λ-Verdopplung. Die in dieser Arbeit bestimmten 9 Mo-lekulparameter je Radikal ermoglichen eine Reproduktion der Spektren bis auf eine Ge-nauigkeit von ca. 107. Obwohl die starksten Linien von C6N etwa 5 mal schwacher sindals die entsprechenden C5N Linien, was auf einen großen Unterschied im Grundzustands-dipolmoment zuruckzufuhren ist, liegen beide neuen Kettenmolekule in einer großerenHaufigkeit als C5N vor.Es wurde im Verlaufe dieser Arbeit auch versucht C7N spektroskopisch nachzuweisen.Trotz guter Vorhersagen konnte jedoch keine der in den beobachteten Spektren enthal-tenen Linien auf C7N zuruckgefuhrt werden. Das Fehlen der erwarteten Linien setztvorraus, daß das Produkt aus Dipolmoment und Haufigkeit (µ · Na) mehr als 60 malkleiner fur C7N als fur C5N ist, sodaß C7N wahrscheinlich nicht im 2Σ sondern im 2ΠGrundzustand vorliegt. Berechnungen ergeben, daß das zum 2Π Grundzustand gehorigeDipolmoment sehr klein ist.

CnN Radikale sind auch im Weltraum schon nachgewiesen. In Teil 3 werden astrophy-sikalische Untersuchungen an linearen C3N Isotopomeren mit den in dieser Arbeit ge-wonnenen Labordaten verglichen. Eigene Arbeiten umfassen die Suche nach C2N inder Sternhulle von IRC+10216 mit Hilfe des IRAM 30m Teleskops am Pico Veleta,Spanien. Es wurden drei Linien beobachtet, die mit Rotationsubergangen von C2Nubereinstimmen und eine vorlaufige Zuordnung dieser Linien zu C2N erlauben. DieSaulendichte konnten abgeschatzt werden und steht in Einklang mit theoretischen Vor-

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hersagen von Millar & Herbst [132]. Weitere astrophysikalische Messungen sind jedochnotwendig um eine eindeutige Detektion von C2N in IRC+10216 sicherzustellen.

xii Zusammenfassung

1 Introduction

“ I ask you to look both ways. For the road to a knowledge ofthe stars leads through the atom; and important knowledge of theatom has been reached through the stars. ”

Sir Arthur Eddington (1882 - 1944), Stars and Atoms

Interstellar gas and gas ejected into space by cool stars are known to contain a richcollection of molecules [123]. After Hydrogen, Helium and Oxygen, Carbon, the fourthabundant element in space with its plurality of possible bondings unclose a whole zooof different carbon bearing molecules, ions and radicals. An important feature of thecarbon atom is that it easily builds long carbon chain molecules. Many of the organiccompounds are familiar to the terrestrial chemist and can be found in a standard chemicalstockroom like formaldehyde, ethanol, and methyl formate but a large part of the knowninterstellar molecules, as seen in Tab. 1.1, are entirely new species. A closer look onthese species reveals that while two-thirds of the diatomic molecules and one-third ofthe triatomics are inorganic there exists no inorganic molecule detected in space withmore than 5 atoms indicating that future discoveries of large molecules are likely toexclusively comprise organic compounds.The particularity of the carbon chains foundin space is that most of them are highly unsaturated and therefore represent a form ofmatter which is explosively unstable through polymerization even at moderate densitiesand difficult to study on earth. It is for this reason that laboratory detection laggedbehind the astronomical discoveries of new radicals for a long time. There are twodifferent types of carbon chains: those which carry a permanent electric dipole momentand those that are nonpolar. Most of the molecules found in space are polar compoundswhich can be detected with radio- or microwave techniques. Today, modern laboratoryspectrometers like FTMW spectrometers or advanced mm-wave to THz-spectrometerscan achieve a high sensitivity and frequency accuracy of 2 kHz in the 10 GHz region up to50 kHz in the 1 THz region. Application of these powerful spectrometers on supersonicmolecular beams in the mid 1990’s resulted in an avalanche of new detected moleculesmost of which are candidates of future astronomical discovery like long carbon chains,chains attached to rings, silicon-carbon rings, and protonated molecular ions. In the gas

2 1 Introduction

phase, rotational transitions and low lying bending vibrations can be observed and yieldin an unambiguous identification of molecules. Large telescopes with a high signal-to-noise ratio can achieve frequency accuracies of one part in 107 [179]. This connectionbetween laboratory spectroscopy and radioastronomy yielded already results in the early1960’s with the detection of the hydroxyl radical [192] in ’63, followed by ammonia [39]and water [40] 5 years later. In principal an unambiguous identification of moleculesin space is also possible in the optical or UV frequency region like it happened for CH,CH+ and CN in the early 1940’s [195]. The majority of discoveries, however, have beenmade in the frequency region between 100 and 300 GHz (1-3 mm region). Nonpolarspecies which are equally important for astrochemistry than polar molecules have nopure rotational spectrum and can therefore not be detected by radio astronomy. Thisshortcoming has been partially overcome by the onset of infrared astronomy. Moleculessuch as CO2, C2H2, CH3, C3 or even C5 have been identified in this frequency region byro-vibrational absorption or by emission from hot gas as for example in the case of H2

[50]. Beside asymmetric stretching modes in the mid-infrared region many carbon chainmolecules exhibit infrared active, low-energy bending vibrations. All pure carbon chainmolecules Cn with n > 2 are expected to display bending vibrations in the range 30 -150 cm−1, i.e. in the far-infrared region. C3 for example has already been detected inthe interstellar space by KAO (Kuiper Airborne Observatory) near 2 THz [59]. Furtherspectroscopic data in these frequency region will be essential for future missions, suchas SOFIA (Stratospheric Observatory For Infrared Astronomy) and Herschel, a 3 mtelescope space mission. Because of the success in detecting more than 120 molecules sofar and the prospect of finding many more, the interest in carbon bearing molecules isstronger than ever.

Considering a spiral galaxy like our Milky Way, the interstellar medium consists about75% of hydrogen and 24% of helium which leaves only 1% of the total interstellar massfor all other chemical elements [179]. ”It is one of the paradoxes of interstellar chemistrythat unsaturated carbon should be so conspicuous in a regime where hydrogen is thedominant chemically active element by more than three orders of magnitude” ([123],p.178). A hydrogen-helium chemistry by its own is very poor, however, 80% of theremaining gas is consisting of C, N, and O which have a reach chemistry. Following thisargument it comes as no surprise that molecules containing C, H and N like HCnN, CnHor CnN play a key role in the chemistry of molecular clouds or circumstellar envelopes,as can be seen in Tab. 1.1. 73% of the detected interstellar molecules contain carbon,66% hydrogen, 34% nitrogen and 28% oxygen. It is a remarkable fact that in certainsources in space a large number of reactive organic compounds often exist in comparableabundances with stable compounds of the same size.

Although big progress has been made in theoretical astrochemistry, this science is stillheavily dependent on pure fact gathering. New chemical models like those of Millar &Herbst [131] or Doty et al. [48] include as much as 407 molecules, ions and radicalsconnected by 3851 reactions [132], and most of these species are still not detected inspace.

It can be seen as disadvantage of modern chemical network models, though, that they de-

3

pend on such large numbers of parameters and reaction coefficients which are not alwaysknown to high precision and which in turn allow for a certain flexibility in predictions.By new astronomical measurements, these parameters can be refined and the models canbe tested. Radicals like Cn or CnN which play an important role in the production ordepletion of cyanopolyynes are a sensitive probe for such models. To make spectroscopicwork contribute optimally to astrophysics, it is advantageous to examine molecules ofsmall or medium size which contain C, H, or N. Therefore in this thesis radicals likelinear isotopic C3N, C4N and C6N, have been investigated and first measurements onC7N and C8N have been started but did not result in any detection so far.

The main task of laboratory spectroscopy concerning its contribution to astrophysicsis to make accurate frequency predictions available for species yet undetected. Underthis considerations a spectroscopic characterization is said to be complete when it pro-vides either measured transitions to high precision or calculated transitions from thederived spectroscopic constants to an accuracy similar to measurements. For open shellmolecules as presented in this work not only the rotational and leading centrifugal dis-tortion constants have to be determined but also several constants which characterizethe hyperfine structure as well as the Λ-doubling caused by the unpaired electron. How-ever, the first detection of linear C3N in the gas phase has not been done in laboratorybut with a radio telescope by Guelin and Thaddeus [78, 79] in 1977. Today, the study ofthe HC3N-C3N pair is of great importance to test and refine photochemical models e.g.of carbon-rich stars like IRC+10216 [38]. C5N has first been measured in laboratoryby Kasai et al. [99] and then in the dark cloud TMC-1 by Guelin et al. [77]. A detailedstudy of the electronic structure of C3N is also worth undertaking because this radicalis isoelectronic with C4H, a well-studied molecule in which an extremely low-lying A2Πelectronic state strongly interacts with the X2Σ+ ground state [121]. Owing to largezero-order mixing between the two states, the 13C hyperfine coupling constants of C4Hat each substituted position along the chain [37] differ significantly from those of theclosely related chain CCH [120]. Determination of the analogous constants for isotopicC3N should provide an unambiguous comparison of the electronic structure and chemicalbonding for these two isoelectronic radicals.

Even-membered CnN chain radicals may play important roles in interstellar chemistryand soot formation [48, 81]. So far, CCN is the only member of this group that hasbeen detected in the gas-phase. Like CN, the electronic spectrum of CCN was observedmore than twenty-five years [128] before its pure rotational spectrum was measured [142].Laboratory detection of longer C2nN radicals has proven to be difficult because they, likeCCN, are expected to have 2Πelectronic ground states and small dipole moments [144].Non of the CnN molecules with n even have yet been detected in space. Recently, thefeasibility of C2N detection in space was proposed by Mebel & Kaiser [127]. Therefore,in the course of this work a search for linear C2N towards the late-type star IRC+10216has been performed.

If it is said that the distribution of more complex and reactive molecules in space remainslargely unknown and that many have been observed in only a single or few sources, thesame is true for the terrestrial ”sources” of these species. For a long time, production of

4 1 Introduction

highly reactive molecules in laboratory was a main obstacle in their detection. So far,only application of sensitive spectrometers in combination with supersonic molecularbeams seem to be particular effective for the study of reactive carbon chains. Here therotational spectra of the radicals are greatly simplified at low rotational temperatures ofa few degree Kelvin which can easily be achieved in supersonic expansions. In this work,different kinds of production methods have been investigated (Chapter 2). Excimerlaser ablation sources achieve high production rates of pure carbon molecules Cn orsilicon-carbon molecules SinCm. The Cologne carbon cluster experiment consists of ahighly sensitive IR tunable diode laser spectrometer (Chapter 3). Radicals like linear C8

and C10 have been observed with this spectrometer for the first time [61, 14]. Anothermethod to produce radicals is the usage of discharge nozzles. In this work, two kindsof discharge nozzles have been applied, a slit nozzle and a pinhole nozzle. The first onehas been used to examine a discharge plasma by the usage of a plasma monitor andthe latter one was needed for the production of C4N, C6N and C3N isotopomers. Thecomplete production method as well as the FTMW spectrometer used for the detectionof the CnN radicals is decribed in Chapter 4. Chapter 5 provides a brief introductionof spectroscopic properties of CnN radicals known so far. Main aspects of the theory ofradical spectroscopy are summarized in Chapter 6. Measurements and analysis of theC3N isotopomers, C4N and C6N radicals are discussed in Chapter 7. The role of CnNchains in the interstellar medium and their detections so far as well as the search for C2Ntowards IRC+10216 performed in the course of this thesis is described in Chapter 8.

5

Table 1.1: Known Interstellar and Circumstellar Molecules (Dec 2002), [31]

Number of Atoms (2-7)2 3 4 5 6 7

H2 C3 c-C3H C5 C5H C6HAlF C2H l-C3H C4H l-H2C4 CH2CHCNAlCl C2O C3N C4Si C2H4 CH3C2HC2 C2S C3O l-C3H2 CH3CN HC5NCH CH2 C3S c-C3H2 CH3NC HCOCH3

CH+ HCN C2H2 CH2CN CH3OH NH2CH3

CN HCO CH2D+? CH4 CH3SH c-C2H4O

CO HCO+ HCCN HC3N HC3NH+ CH2CHOHCO+ HCS+ HCNH+ HC2NC HC2CHOCP HOC+ HNCO HCOOH NH2CHOCSi H2O HNCS H2CHN C5NHCl H2S HOCO+ H2C2O l-HC4HKCl HNC H2CO H2NCNNH HNO H2CN HNC3

NO MgCN H2CS SiH4

NS MgNC H3O+ H2COH+

NaCl N2H+ NH3

OH N2O c-SiC3

PN NaCN CH3

SO OCSSO+ SO2

SiN c-SiC2

SiO CO2

SiS NH2

CS H+3

HF H2DSH SiCNHD AlNCFeO

Number of Atoms (8-13)8 9 10 11 12 13

CH3C3N CH3C4H CH3C5N HC9N C6H6 HC11NHCOOCH3 CH3CH2CN (CH3)2COCH3COOH? (CH3)2OC7H CH3CH2OHH2C6 HC7NCH2OHCHO C8Hl-HC6H

6 1 Introduction

Part I

Characterization of Radical Sources

2 Molecule Source Characterization

“ ...one or two atoms can convert a fuel to a poison, change acolor, render an inedible substance edible, or replace a pungentodor with a fragrant one. That changing a single atom can havesuch consequences is the wonder of the chemical world.“

P. W. Atkins, ”Molecules”

In this thesis, it will be shown how radicals can be produced and detected by differenthigh resolution spectroscopic tools like IR spectroscopy and FTMW spectroscopy. Theaim is to determine as many molecular properties as possible like moment of inertia,electronic structure, vibrational motions, hyperfine interactions, etc. Well known pro-duction methods in combination with spectrometers of extreme high sensitivity allowfor the detection of molecules and radicals up to linear C13, HC13H or HC17N [62, 123].However, detection of more complex radicals or molecules of even larger sizes seem to beimpaired by the effectiveness of the production methods. For example, for the detectionof C13 with a vibrational dipole moment of ∼2 Debye, a particle density of ≈ 1010 cm−3

is required to record the rotationally resolved IR spectrum of an asymmetric stretchingmode. In future, molecular sources have to produce even higher yields to allow for thedetection of molecules with smaller dipole moments or unfavorable partition functions.For the same reason, it is advantageous to produce molecules with low rotational temper-atures because the spectra simplify and gain intensity of low lying transitions. Anotherimportant requirement of molecular sources is the stability of their production yield.When spectrometers work at their limit of sensitivity the signal has to be integratedmany times in order to increase the signal-to-noise ratio. Therefore, it is apparent thatconditions have to be stable over the whole integration time. Furthermore, the charac-terization of available molecule sources is an important step towards the development ofnew production techniques.

Out of many techniques to produce radicals, two particularly important methods havebeen chosen which are the laser ablation and the discharge nozzles technique. Both areapplicable to the Cologne IR-Carbon Cluster experiment but due to advantage of laserablation sources to only produce pure carbon molecules Cn this technique is predom-inantly used. It has resulted already in a number of first detections of linear carbon

10 2 Molecule Source Characterization

Frequency [nm]

rela

tive

Sca

le

Figure 2.1: Spectra of C2 at 516 nm measured in Basel. A laser ablation source (top)and and discharge nozzle (bottom) was used to produce the C2 radicals.

clusters like C8 and C10 [61]. The detection of C13 [62] has shown that even highermembers of linear Cn chains can be detected with this type of ablation source. Thismolecule source is particularly valuable for the production of iso-atomic molecules likeCn, Sin or Men with n=2,3,4,... but also for other species like CnSim when using appro-priate target materials. The Cologne IR experiment will be described in Chapter 3. Theused ablation source is in principle similar to the Smalley type ablation source [169, 41].However, important improvements have been done to adapt this technique to laser spec-troscopical needs which led to a tremendous success in the production of radicals. Theimproved design has been described in [186, 58, 14]. Details will be discussed furtherdown. So far an excimer laser with 25-50 ns pulses and typical pulse energies of 270 mJwas used as a strong laser light source at repetition rates of 50 Hz. It is evident thatlonger pulses with higher energies increase the amount of ablated material. However,the main question is whether the ablated material is available in a molecular form orwhether it immediately builds grains and soot. For molecular spectroscopic reasons itis desirable to have a broad mass distribution of ablated material in a molecular formwith high abundances of particles containing between 3 and 30 atoms. As an alternativeto the excimer laser, a Nd:YAG laser was used with pulse energies up to several Joulesand pulse lengths of 0.1 to 1 ms. A new experimental setup was built to characterizethe ablated material by means of quadrupole mass spectroscopy (QMS).

11

Figure 2.2: C60 optimized mass spectrum. a) mainly small carbon clusters are produced.By changing the flow rate of the buffer gas larger clusters were produced (b). Forcertain laser and source conditions the production of C60 can drastically be enhanced(c). [80]

Laser ablation is not unique in producing radicals or iso-atomic molecules. There areseveral other techniques like sputtering, electric arcs, the use of ovens, etc. which could inprinciple as well be used but which have proved in praxis to be less efficient. Consideringthese alternatives the discharge nozzle technique appears to be quiet comparable to thelaser ablation technique and was therefore also taken into account in the experiment.The applied discharge slit nozzle was developed by the Basel group [111, 135]. Theconceptual design of a discharge nozzle will be described in more detail in Section 2.2as well as in Chapter 4.1.2. Between each of the described production methods, thereare principle differences concerning the conditions under which the molecules can bedetected, i.e. pressure, temperature, chemical composition, jet boundaries and layers.Properties of molecular beams, i.e. supersonic jets, will be discussed in Chapter 4.2.

As an example, two spectra of C2 are shown in Fig. 2.1 which were recorded using twodifferent molecular sources. Both sources are able to produce C2 in sufficient amountsfor cavity ringdown spectroscopy in the visible region but the rotational temperatures


of the molecules are different for both techniques. The laser ablation spectrum has arotational temperature of about 10-20 K whereas for the discharge spectrum, Trot is inthe order of 100 K. For an extended spectroscopic analysis of molecules it is importantto produce molecules under different physical conditions, e.g. different temperatureswhich is possible by using the appropriate molecule source. A detailed understanding ofdifferent types of production methods is thus indispensable.

For this purpose, a diagnostic tool is needed that focus on yield and relative mass dis-tribution of molecules or radicals produced by different types of molecule sources ratherthan their structure or other intrinsic properties. Mass spectrometers, for example,have an extremely high sensitivity compared to other spectrometers but do not allowfor any information beyond pure mass-per-charge distribution. Beside this restriction,they can provide valuable information on chemical reaction mechanisms. Broad scanscovering molecules of nearly every size allows for source controlling which can supportthe production of certain species. A famous example is the discovery of the Buckminsterfullerene C60 in 1985 by Smalley, Curl, and Kroto [108, 41, 169] 1. For this, a laserablation source was monitored by a mass spectrometer so that experimental conditionscould successfully be varied in order to yield C60 in huge amounts (see Fig. 2.2).

1In 1996, Kroto, Smalley, and Curl have won the Nobel prize in Chemistry for their discovery of C60.

2.1 Ablation Technique 13

36003400 3800 4000 4200 4400 4600 4800

0.1

1

10

100

Temperature (K)

Pre

ssu

re (

AT

M)

Liquid

Solid

Vapor

Triple PointLiquid−Vapor

Figure 2.3: Pressure-temperature diagram of graphite [106, 155].

2.1 Ablation Technique

Laser ablation can be described as removal of material by applying an intense light pulseof high energy onto a target in order to vaporize solid or liquid materials. Under atmos-pheric pressure graphite is solid and has a transition to the gas phase at temperatureshigher than 4000 K, see Fig. 2.3. Laser ablation can achieve high temperatures andhigh gas phase carbon densities and is therefore an ideal tool for spectroscopy on carbonclusters and other carbon bearing radicals.

The effect of intense laser light on solid material such as graphite results in lattice vibra-tions, electronic excitations or direct ionization which causes bonds to break. Dependingon the laser power irradiated, the material vaporizes or liquefies. With beam intensitieshigher than 108 W/cm2, more material is vaporized while consequently less is liquefied[86]. The produced vapor does not condense immediately on the surface but flows offthus perturbing the conditions of a local thermodynamic equilibrium. The number ofablated carbon atoms depends on the irradiated laser wavelength, laser power and theevaporation heat of graphite. Only a small fraction of the radiation is directly absorbed.

If n denotes the real and κ the imaginary part of the complex refraction index, than

reflectance R for a perpendicular irradiation on graphite is R = (n−1)2+κ2

(n+1)2+κ2 . The value of R


cap

UV−pulsplasma

rotating

rodgraphite

pulsed heliumsupply

plasma

excimerUV−pulse248 nm

10 barHe

vacuumjet

reaction channel

graphiteGV

adiabaticexpansion

Figure 2.4: The Cologne Laser Ablation Source

is between 0.1 and 0.5, depending on the orientation of the light in respect to the graphitestructure [18], yielding a fraction A ≡ 1−R of absorbed radiation. However, the powerof the laser light is also an important factor in the absorption process [70, 86]. If the laserpower exceeds a threshold value of 108 W/cm2, a plasma is built on the graphite surfacewhich almost completely absorbs the laser power and partially transfers the energy to thematerial. This energy transfer takes place due to radiation in the visible and ultravioletspectral range [86] or via compression waves [70] where the plasma pressure can easilyachieve 100 kbar. For the ablation source discussed here, typical ablations of 30-50 ngcarbon per pulse are achieved, which corresponds to roughly 1.5 · 1015 carbon atoms [7].

A graphite rod of 1 cm in diameter was used as target which consisted to more than99.5% of 12C at a density of 2.25 g/cm3 (Goodfellow/Cambridge). While being exposedto the laser beam, the graphite rod is slowly rotated to ensure a stable and uniformablation process.

2.1.1 Excimer Laser Ablation

The standard technique to produce pure carbon clusters at the Cologne IR experimentis to use a pulsed excimer laser beam at 248 nm wavelength which is focused onto arotating graphite rod. Thereby, a plasma consisting of carbon particles is producedwhich accelerates the ablation process. Helium at a backing pressure of 10 bar flushesthe vaporized graphite in an adiabatic expansion into the vacuum chamber causing fastcondensation of single atoms to small carbon clusters. Within a few µsec the temperatureof the carbon vapor drops down from several thousand Kelvin plasma temperature to afew Kelvin rotational temperature of the condensed clusters. A total amount of 1013–1014

clusters of different sizes are produced with every single laser pulse [58]. A two stageroots blower unit and a vacuum rotary pump keep the chamber pressure below 10−1

mbar. Carbon clusters with up to 13 atoms have been produced in sufficient amountsfor infrared absorption detection [60].

Carbon clusters seeded in a flow of buffer gas usually readily separate down stream, mostlikely due to differing formation times. It is thus possible to clearly distinguish betweenclusters of different sizes, i.e. small clusters come first while larger ones come later.


Figure 2.5: Jet produced by excimer laser ablation technique. The molecular proberegion for spectroscopy is 1-2 cm downstream the source exit. Left: Side view of theablation jet with a sketch of the source. The jet dimensions are roughly 17 cm bothin height and length. A compression zone caused by the edge next to the source isvisible at the lower boundary of the jet. Right: Top view of the jet. Jet width isroughly 1-3 cm.

For the Cologne IR experiment, a KrF excimer laser (Lambda Physics, LPX200) is used.This laser can operate at repetition rates of up to 50 Hz with pulse lengths of 25-50 nsand pulse energies up to 500 mJ. For the production of carbon cluster pulse energies of200 mJ result in an optimal yield. The evaporation heat of graphite is λ = 716.9 kJ/mol[155], i.e. the maximal number of particles that can be ablated is 1.7 · 1017, assuminga total absorption of laser power in the vaporization process. The excimer laser has a’square’ beam profile. When the light is focused by a MgF2 lense (f=50cm), the beamhas a size of 0.45 x 0.05 mm2 on the surface of the graphite rod (see Fig. 2.8). Energydensities of 1 · 109 W/cm2 are therefore achievable. The laser ablation source is madeof stainless steel and consists of two parts, the main body and the cap, as can be seenin Fig. 2.4 (left). At the rear side, a solenoid valve can be attached and a hole of 2 x 2mm2 allows for inflow of buffer gas. The gas preexpands into a cross sectional area of 12mm x 1mm at the graphite rod. The visible graphite rod area at the channel surface is70mm2. The source exit consists of a slit like reaction channel sized 12mm x 0.9mm incross section and 8mm in length. The excimer pulse enters the ablation source throughthe exit slit. The square form of the UV beam profile results in a line focus at thegraphite rod. After several hours of operation the reaction channel is clogged by sootand has to be cleaned. The laser ablation process with subsequent adiabatic cooling isshown in Fig. 2.4 (right). First, the valve is opened and a buffer gas (e.g. He) with abacking pressure of 10 - 15 bar flows through the nozzle. During this flow, an excimerpulse is released which causes the formation of a dense plasma of vaporized carbon atoms


density of particles NC mass rel. abundanceparticles nρ per pulse Ci / C3

[#/cm3] [ng]C3 2.3 · 1012 ≈ 1013 0.6 1C9 4.2 · 1010 ≈ 1.7 · 1011 0.03 1/55C13 9.9 · 109 ≈ 4 · 1010 0.01 1/230

Table 2.1: Particle numbers of C3, C9 and C13 using excimer laser ablation

and ions. For each individual measurement, the time delay between the opening of thevalve and the excimer pulse has to be adjusted to achieve optimal jet conditions. Incase of an incorrect time delay the molecule yield drops because of insufficient cooling.The reason for this is that the hot atomic carbon vapor is cooled by the buffer gas atroom temperature and additionally small molecules can form via three-body collisionsin an endothermal process. The formation of molecules and radicals mainly happens inthe reaction channel where the density and pressure is high enough for a condensationprocess. The most efficient cooling process is adiabatic expansion of the gas into thevacuum chamber where the molecules are then available for spectroscopic detection (seeFig. 2.5).

From IR measurements on linear carbon clusters [58] it has been shown that mainly smallmolecules are produced in the excimer jet (see Tab. 2.1). C3 is found to be much moreabundant than C9 and C13. It is remarkable however, that long carbon chains like C13

are also produced in sufficient amounts for IR detection. So far, only linear carbon chains[189] or silicon-carbon clusters [188, 187] have been found. Interest in the detection ofmolecules with cyclic, polycyclic or cage like structure which probably correspond tolarger species is increasing, though. There has never been a mass spectroscopic analysisof the here introduced Cologne laser ablation source and there is no information at handwhether larger molecules are formed in the excimer jet or not 2. These facts led directlyto the question whether it is possible to change conditions in a way to increase the yieldof medium sized to large molecules (e.g. C10 - C60).

Murray et al. [138, 197] employing material research experiments investigated the effectof lasers with different wavelength on graphite targets. They compared pulsed laserdepositions of carbon films using a KrF excimer laser at wavelength 248 nm with pulselengths of 15 ns with those of a Q-switched Nd:YAG laser at 1064 nm, also havinga pulse length of 15 ns. The fluence of the excimer laser at the pyrolytic graphitetarget was 3 J/cm2 while that of the Nd:YAG was 2.7 J/cm2. In a time-of-flight (TOF)mass spectrum positive ions ejected from the target were investigated3. In the Nd:YAGspectrum, many peaks corresponding to carbon clusters C+

n of size 1 ≤ n ≤ 27 appearedwith most intense peaks for C+

11 and C+15. Contrary to that, the TOF mass spectrum

2Fullerenes can also be produced in a laser ablation source [169, 41] but their production has not yetbeen proved in the case of the Cologne laser ablation source.

3No buffer gas was applied.


ionization chamber / ion optics

ion detector

quadrupole mass filter

Quadrupolechambervacuum

Jet

IR beam

amplifier

Nd:Yag @ 1064 nm

pulsed

pulsed

skimmer / orifice

Figure 2.6: QMS experimental setup

for the excimer laser ablation only had significant peaks at C+2 and C+

3 . Murray et al.concluded that “the ejected species [...] are dependent upon the laser wavelength” [138].Since these results are in agreement with the investigations for the Cologne excimer laserablation shown in Tab. 2.1, application of a Nd:YAG laser rather than an excimer laserappeared to be useful for the production of medium sized and large carbon clusters.

2.1.2 Nd:YAG Laser Ablation

For the characterization of a Nd:YAG ablation it seemed desirable to directly investigatethe mass spectrum. For this reason, a new experimental setup had to be build (see Fig.2.6). The Nd:YAG laser (Baasel BLS 700) used for this work operates at a wavelengthof 1064 nm with pulse energies of up to 15 Joule. The laser has no option of Q-switchingand thus has pulse widths from 0.1 to 1 ms instead of 25 - 50 ns. Important technicaldata of the Nd:YAG and the excimer laser are given in Tab. 2.2. As detection device, aquadrupole mass spectrometer was applied that works in two modes, the first of whichhas a mass range of 1 - 100 amu with high mass resolution while the second worksbetween 100 - 400 amu. This mass spectrometer had previously been used to analyzethe electric arc spectrum of graphite and is described in [58]. It is designed to detectneutral species and contains an electron impact ionizer, a quadrupole mass filter and an


ion detector. The ion source works with an adjustable emission current between 0.04and 5 mA and electron energies of ∼ 90 eV. The ionized molecules are mass selected ina mass filter which consists of four rods with 4 mm diameter and 200 mm length. Fieldradius of the latter is 3.45 mm 4. Mass resolution m/∆m at mass 100 is better than100 for the first modus (1 - 100 amu) and 50 for the second modus (10 - 400 amu) 5.A multiplier is used as ion detector with an output current between 10−6 and 10−12Awhich is subsequently amplified and transformed into a voltage signal which is then sendto a computer.

The first question to answer was whether a 0.1 -1 ms Nd:YAG laser pulse ablation ontoa graphite target without the use of buffer gas results in a similar mass spectrum asreported by Murray et al. [138], i.e. can clusters of the size C11 and C15 be found ornot? Murray et al. had looked for the ionic species and found that C+

n clusters producedby Nd:YAG laser ablation have kinetic energies less than 5 eV. In a plasma the meankinetic energies of neutral species is usually well below those of the corresponding ions.The potential settings - which are important for the guiding of the ions through thequadrupole - were well adjusted for particles with kinetic energies of less than 1 eV butcould not be adjusted to arbitrary potentials. A mass spectrum of a Nd:YAG ablationis shown in Fig. 2.7. The hydro-carbon molecules in the spectrum originate from theinteraction with the rest gas, i.e. with H2O. Other species like OH and O are produced byfragmentation processes in the electron impact source due to the high electron energies.Since ionization potentials of pure carbon chains Cn with n=3-25 are between 7 - 12 eV[189] a mean kinetic electron energy Ee of 20 eV would probably have been sufficient.Nevertheless, Ee was kept at 90 eV. A lot of soot was produced during the experimentand a protection glass in front of the IR mirror became polluted very quickly 6. Thereforethe vacuum chamber had to be opened regularly. As a consequence, it was not possibleto let the vacuum chamber be evacuated over a longer time, e.g. several weeks, toachieve background pressures below 10−8 or 10−9 mbar which would have been useful toavoid interaction of the ablated material with the rest gas during measurements. Themeasurements reveal the predominance of atomic C while C2 was less abundant by afactor of 10 and C3 was already close to the detection limit. Larger clusters could notbe detected. The relative abundance C:C2:C3 was found to be 100:6.6:2.4.

A comparison of different kinds of carbon cluster sources reveals significant differencesconcerning the amount and distribution of produced carbon molecules as can be seenin Tab. 2.3. Typically, usage of laser ablation sources results in a broad distribution ofcluster sizes in the lower mass region from C1 to C10 [11, 107] with abundances thatallow for absorption spectroscopy.

Gas aggregation sources like thermal vaporization of graphite (vaporization in an oven)[193, 53, 198] or the Langmuir-method (surface method, electric arc) [89, 168, 54] produce

4The field radius denotes half the distance between the rods.5The mass resolution is dependent on the operation frequency and dc- and ac voltage of the mass filter.

As a first approximation it can be said that the better the mass resolution the lower the sensitivity.Details are given in [58]

6Mirrors can be protected with a Helium flow but this feature was not implemented.


excimer (KrF), Nd:YAG, Baasel BLS 700Lambda Physics LPX 200 (not Q-switched)

wavelength 248 nm 1.064 µmpulse duration 25 - 50 ns 0.1-1 msrepetition rate single pulse - 50Hz single pulse - 100 Hzpulse energy max. 500 mJ max. 15 Jouleaver. power max. 8 W max. 50 Wbeam diameter/size 5-12 x 23 mm2 6 mmbeam divergence 1 - 3 ≤ 6 mrad(full angle)mode multi mode multi mode

Table 2.2: Technical data of applied ablation lasers.

soot in large abundances but nearly no small carbon molecules (see Tab. 2.3).

Using these schemes, the Nd:YAG laser ablation process resembles more a thermal orelectric arc process than an typical laser ablation process. This can be explained by thefollowing considerations. Nd:YAG laser can produce long laser pulses with high pulseenergies which increase the ablation rate while the intensity, i.e. the power per area,decreases. If a laser does not exceed an intensity of 108 W/cm2, the ablation process isnot dominated by direct sublimation but rather by melting-vaporization processes. Q-switched Nd:YAG or excimer laser have pulse widths of 15-50 ns and thus high intensitiesat the focus point. The target material absorbs the energy during a time interval thatdoes not allow for heat conduction effects. Thus, most of the energy is directly usedfor sublimation. If the pulse width of the laser is increased, heat conduction dominatesthe energy transfer and melting occurs. The intermediate step through a liquid phasecan be very efficient in terms of ablation yield, however, most of the material is ejectedas soot rather then in molecular form. To gain more insight into these processes, theablated material was investigated under a microscope (see Fig. 2.8 and 2.9). Aluminumhas been used to determine the focus size of the Nd:YAG laser beam. The beam focusarea is about 3 · 10−5 cm2 in the case of the Nd:YAG laser and roughly 2 · 10−3 cm2 inthe case of the excimer laser. If a pulse energy of 200 mJ with a pulse length of 100 µsis applied, maximum intensity at the target can reach 7 · 107 W/cm2 which is still belowthe threshold value of 108 W/cm2. If instead the excimer laser with a 200 mJ pulseenergy is applied, the intensity is 1.8 · 109 W/cm2. As Fig. 2.8 (e,f) and 2.9 (e,f) show,melting of graphite is much more emphasized by using a Nd:YAG laser compared to anexcimer laser. This indicates that much more soot is produced using a Nd:YAG laserinstead of an excimer laser. However, meltings occur in both cases as the small carbonblebs indicate. Graphite is difficult to analyze under an optical microscope because ofits low contrast and strong light absorption in the visible frequency range. Therefore,differences concerning ablation processes can better be investigated if silicium or glassare used as target materials rather than graphite. The melting zone of an silicium wafer


Figure 2.7: Mass spectrum of Nd:YAG laser ablated graphite rod. Background pressurewas 1.4 · 10−5mbar.

after being exposed to a Nd:YAG laser pulse is clearly visible in Fig. 2.9(d) whereas thesame energy applied by an excimer laser shows no sign of melting.

Ablation of graphite without the use of buffer gas is of no use for absorption spectroscopysince the molecule yield is not high enough for that purpose. Therefore, as a next step theNd:YAG laser irradiation had to be combined with a buffer gas flow in order to achievehigh molecule production rates. The attempt to record a mass spectrum of an ablationjet by using a Nd:YAG laser together with Helium as buffer gas failed completely. Thiscan be explained by two reasons. 1) If no buffer gas is used, the pressure in the vacuumchamber (about 10−4 - 10−5 mbar due to the use of a turbo molecular pump with 1500l/s) changes to maximal 10−3 mbar which can still be handled by the mass spectrometerwithout the need of using a skimmer 7. If a buffer gas is used, even at moderate backingpressures of 1 bar a skimmer is absolutely necessary to avoid damage of the secondaryelectron multiplier (or channeltron) as well as to avoid collisions and interactions ofthe ions in the mass filter. Furthermore, a skimmer is needed to avoid turbulences ofthe gas flow in front of the hole. Turbulences cause collisions and thus a change inthe chemistry of the jet which is undesired. On the other hand, the introduction of askimmer brings in certain difficulties and disadvantages. For example, the skimmer has

7This type of experiment resembles more a drift experiment in which the ablated species have time tointeract with the rest gas in the vacuum chamber before they are ionized and detected. Therefore,also species like C2H and C2H2 can be found (Fig. 2.7).


Laser thermal electric arcC-Cluster [11] [107] [175] [53] [89] [168] [168]

C1 37.0 56.0 99.0 22.2 35 100.0 100.0C2 31.4 35.0 74.4 62.5 13 20 35-48C3 100.0 100.0 100.0 100.0 100.0 61 7-10C4 2.13 2.5 14.5 3.8 . . 0.6-1.0C5 7.9 1.6 31.6 5.7 . . .C6 0.413 . 26.1 . . . .C7 1.11 . 34.7 . . . .C8 0.19 . 11.0 . . . .C9 0.11 . 0.9 . . . .C10 0.32 . . . . . .

Table 2.3: Relative C-cluster concentration of different production techniques. Valuesof 100.0 in each column indicate clusters with largest abundance whereas all otherentries were set in relation to those. [133]

to be perfectly aligned with respect to the molecule flow and the ionization chamber ofthe mass spectrometer. Since the opening diameter of the skimmer has to be chosensmall, i.e. of the order 100 -200 µm this can be very difficult. In addition to that, thesupersonic gas flow is not stable, i.e. might have slightly different shapes or internalstructures. Therefore, proper alignment is not easy. In first approximation, loss ofintensity due to usage of a skimmer is primarily determined by a 1/r2 law with r thedistance between skimmer and ionizer. Thus r should best be a few mm to cm 8. In theexperimental setup described here the distance between skimmer and ionization regioncould not be reduced below 15 cm. This results in a loss of signal intensity of two orders ofmagnitude. 2) If a buffer gas is used to form a supersonic expansion, the plasma spreadsfar beyond the focus point of the laser ablation. Although a plasma in its entirenessis neutral, it can cause significant electrical interferences even through a skimmer. Atypical problem was that for masses < 1 a huge artificial signal occurred but no signalwas recorded at other masses. The main goal to characterize a supersonic ablation jetwith the help of a mass spectrometer could therefore not be achieved. It has to be statedthat the mass spectrometer used in the experiment, i.e. the mass filter and ion detector,worked perfectly. Also, laser ablation did not cause principal problems, although therehappened to appear soot depositions on the diagonal mirror. What seemed to be morecritical for the experiment was the device consisting of skimmer and ionizer which wasused to extract the molecules and radicals out of the ablation jet as well as to ionizethem. However, this device serves as a mediator between molecule source and moleculedetection. Consequently, this part of the setup had to be rearranged and optimized. Forthe optimization process it is advantageous to have a stable supersonic molecular flow.Laser ablation technique as it was implemented in this specific setup was not able to

8It seems to exist an optimum distance between skimmer and ionization region as can be read in [165].


serve this purpose.

As a consequence, a slit nozzle discharge source was used in further experiments toproduce molecules and radicals in a supersonic jet. Although the discharge jet wasstable and easy to apply, disturbances very similar to those of Nd:YAG laser ablationappeared. As a result, it was not possible to record mass spectra with the currentexperimental setup. Further improvements were necessary.


Figure 2.8: Excimer laser ablation of different kinds of material. a) and b) showablations on aluminum foil (thickness 10 µm). In a) the whole area of ablation isshown for which 16 shots at 150 mJ were needed to produce the hole. In b) one shotat 450 mJ results in a very sharp edge, no signs of melting are visible. In c) an ablatedglass sheet (thickness 2 mm) is shown. The laser was applied 30 sec at 50 Hz with apulse energy of 400 mJ. Bubbles (diameter 17 - 40 µm) indicate a melting phase. Ind) a silicium wafer after one shot of a 330 mJ laser pulse is shown. For pictures e)and f) a laser was applied to a graphite rod over a period of 10 sec at 50 Hz repetitionrate with a pulse energy of 400 mJ. Left side of e) shows the ablation hole with anestimated width of 190 µm; the bright vertical stripe (44 µm in width) indicates theedge of the ablation hole. f) shows the ablation edge in more detail which marks theborder line of the melting zone to the unperturbed region. The blebs and bubblesindicate a liquid phase during ablation process close to the ablation hole.


Figure 2.9: Nd:YAG laser focused on different kinds of material. Photos a) and b)show ablations on aluminum foil (thickness 10 µm). On the right hand side of a) theeffect of a single laser shot (200 mJ during 100 µs) is demonstrated. The hole on theleft side of a) is caused by the same laser light applied 50 times. In b), 100 shots of a1 ms (230 mJ) laser pulse were applied. In the lower left corner it can be seen thatthe ablation hole is surrounded by a melting zone and a transition zone which has anouter border wall towards the unperturbed aluminum. In c), an ablated glass sheet(thickness 2 mm thick) is displayed. The dark zone at the lower right corner indicatesthe melting zone of the center ablation region. Picture d) shows an ablated siliciumwafer. The square structure in the upper region can be interpreted as focus region ofthe laser pulse (1 shot, 100 µs, 330 mJ). A segment line in the lower left area marksthe border between melting region and unperturbed silicium structure. Pictures e)and f) show an ablated graphite rod. In e), melting of graphite can clearly be seen.In f), 50 laser pulses (1 ms) with an energy of 330 mJ were applied. Small blebs (8-11µm in diameter) surround the edge of the ablation hole.

2.2 Discharge Plasma 25

expansion

pulsed valve

gas

slit (30 x 0.25 mm )

groundedmetal plate

applied potential

gas

enlargement

discharge

insulator

2

(−600 to −1200 V)

Figure 2.10: Discharge slit nozzle

2.2 Discharge Plasma

Discharge nozzles are of great importance for the investigation of molecular species andcan by applied in many spectroscopic fields, see Fig. 2.11. The discharge slit nozzleused for the mass spectroscopic analysis of the described experiment was developed atBasel by Linnartz et al. [111, 135] and is a versatile tool concerning the production ofmolecules, radicals and ions. It has been shown that pure carbon clusters can be formedin such a device (see Fig. 2.1) [113, 136] as well as hydro-carbons of many kinds [110]and ions [112]. In Fig. 2.10, a cross section of the molecule source is shown. The orificeof the slit consists of an insulator, a metal plate, a second insulator and two sharp plateswhich form the actual slit (30mm x 250 µm, 60 exit angle). A solenoid valve is usedfor the inflow of buffer gas and precursor gas with a backing pressure of 2-5 bar and amass flow between 15 and 30 sccm (standard cubic cm per minute). A stable dischargecan be achieved by applying a voltage of 400 - 1000 V (300-400 µs) to the jaws duringthe gas flow. The discharge strikes to the inner metal plate which is grounded 9. Duringthis process, the flow is heated up which causes fragmentation of the precursor gas, andthus new species start to form. During the subsequent expansion the gas is cooled downand can reach temperature as low as 100 K (see Chapter 4.2).

The investigation of the discharge mass spectrum was performed at Balzers/Lichtensteinin November 2000 using a Plasma Monitor PPM 422 (Inficon AG). For this purpose,the electric discharge nozzle, a gas mixing device and precursor gases were implementedinto a setup as shown in Fig. 2.12. The plasma monitor (PM) operates in the massrange between 1 - 512 amu. It is optimized to detect ions in a plasma but is also ableto detect neutrals. The PM consists of an entrance orifice, ion optics, an ion source,energy analyzer, intermediate focus, mass filter and an ion counter. In this test setup

9If the outer plate is grounded and the negative voltage is applied to the inner plate the discharge isinstable and arcing to the solenoid valve occurs.


Figure 2.11: Jets produced by a discharge slit nozzle. The molecular probe regionfor spectroscopy is 1-2 cm downstream the source exit. Left: Angular view of thedischarge jet. Right: Top view showing a broad zone with two diverging areas ofhigh density. In the Cologne Carbon Cluster experiment the IR laser probes the jetparallel to the slit. The resultant absorption length (4-5 cm) is larger than in the caseof the laser ablation source (Fig. 2.5).

the discharge (500 - 600 V) nozzle was used with repetition rates of 1-2 Hz and gaspulses of 1 ms. Discharge duration was less than 300-500 µs. If the PM is used in apulsed operation mode as it is described here, a 103 CPS (counts per second) signal atthe PM corresponds to a sensitivity of 106 CPS in a cw plasma. The average pressurein the vacuum chamber was ∼ 3 · 10−3 mbar (N2 equivalent) during operation. Anelectrically isolated extraction orifice10 instead of a skimmer was used as entrance holeto the PM and placed 2-3 cm apart from the front of the discharge nozzle. Ions aremore easily detected than neutrals because they are guided into the PM by an electricfield, and alignment of the PM orifice with respect to the jet is less crucial. Thus a largeextraction volume can be probed. The detected mass distribution of ions is not effectedby any ionization process as it would be the case for neutral species and fragmentationprocesses are negligible. Kinetic energies of ions in a plasma are in the order of a few tohundred eV. A quadrupole without any energy filter can only handle ions with a certainenergy distribution. It is therefore necessary to first determine the energy distributionof the ions with an energy analyzer (± 500V) and then to select the species of a certain

10Could be pos. and neg. biased or on floating potential.


23.924.0

Ionization Chamber / Ion Optics

Ion Detector

Energy Filter

Quadrupole Mass Filter

Plasma−Monitor

Multi Channel

Jet

Sample Gas

Mass FlowController

Voltage

DischargeSource

ChamberVacuum

Figure 2.12: Experimental setup for mass spectrometry on a molecular beam atBalzer/Lichtenstein, Nov 2000

energy range. For example, if neutral He is ionized in the PM (ion source 70 eV, 1 mA),the energy distribution is Emean= 98 eV with ∆E = 2-4 eV (see Fig. 2.13). If necessary,the PM potentials can be set appropriate to Emean so that even high energy ions (± 500eV) can be detected. The energy filter can select ions within a certain energy range ∆Efor a further mass selection in the mass filter. If only nitrogen was used in the dischargeslit nozzle, Emean was found to be 4.40 eV. In Fig. 2.14 (top), cations of the N2 dischargehave been investigated and nitrogen complexes N+

n with a broad mass distribution havebeen found. The mass resolution m/∆m at mass 55 amu was 23. Acetylene (C2H2)diluted in a buffer gas is a precursor for the production of many radicals and ions likeCnH, HCnH, H2Cn,... . Fig. 2.14 (bottom) shows a 20 sec scan of a discharge using0.5% C2H2 in Ar. The mean kinetic energy of the ions was 4.40 eV. In the lower massregions, ions like C2H

+2 , Ar+, ArH+

3 and C4H+2 could be found but the corresponding

count rates of max. 80 CPS are rather sobering. The signal-to-noise ratio of the ions isbetween 6 - 17 and the ion signals are well resolved. In a second experiment anions havebeen detected. The measurements showed that anions are less abundant than cations.In both cases the detected ion signal was far from being satisfying. Nevertheless, massspectra of positive and negative ions could be obtained.

For measurements on neutral species a multi-channel analyzer was used to allow forintegrations over the relevant time intervals when the discharge was switched on, therebyreducing the noise. Again, the detection of even the faintest rest gas molecules worked


Figure 2.13: Energy distribution of He+ produced in the ion source of the plasmamonitor, ∆E = 2-4 eV.

perfectly but no correlated discharge signal could be recorded. The reason for this failuremight be that the PM was optimized for ion detection and hence no skimmer was usedsince this is less important for ions than it is for neutral species. This lack of a skimmerclearly lowered the chance of detecting neutrals. Another reason may be that the ionoptic precedes the ion source in the PM setup. Therefore, the ion source has a distanceof 3-4 cm to the orifice which corresponds to an intensity decrease in the order of 101-102.


Figure 2.14: Mass spectra of a molecular beam. Top: Discharge on N2 molecules (E=-4.4eV). Bottom: Measurement of cations on a discharge of 0.5% C2H2 in Ar (E=-4.4 eV).


2.3 Conclusions and Prospects

Detection of ions and neutrals in a supersonic jet makes high demands on mass spec-trometers. This is especially true if one considers that the use of a mass spectrometeris intended to monitor conditions within the jet during optimization processes, i.e. withintegration times of max. 5 min or less. The main challenge is the development of aneffective extraction device to probe molecules and ions of a few mbar pressure gas flow.

The most important region to probe the jet is 1 - 3 cm downstream the nozzle exit.Depending on the backing pressure of the buffer gas and the type of nozzle used, pressuresup to 10 mbar may occur in regions where the extraction orifice or skimmer is placed.In this experiment the pumping speed is not high enough to reduce the mean vacuumpressure below 10−1-10−2 mbar during operation with 50Hz discharge/ablation repetitionrates. Mass filter usually require operation pressures of 10−4 - 10−5 mbar. The use of asingle pressure reduction stage can not be sufficient to achieve this pressure drop. To usea mass spectrometer at high repetition rates a second stage pressure reduction is required.The Distance d between the two orifices (or skimmer and orifice) of the reduction stageshould be much smaller than the mean free path of the incoming particles. The exactdistance d depends on the Knudsen characteristics of the extracted beam [165].

It has been shown that there is a difference between the detection of ions and that ofneutrals. Ions require no further ionization process and can be guided by electric ormagnetic fields. Nevertheless it is important to place the ion optics very close to theextraction orifice to enhance the yield. If the focus is on neutral detection, an ionizationsource has to be placed right behind the skimmer (or orifice). Hence it is clear that amass spectrometer can only be optimized on either ions or neutrals. Displacement ofthe ionization source or of the ion optics result in a significant decrease of the signalintensity.

In a pulsed experiment with pulse lengths of a few µs up to several hundred µs, a massspectrometer which intrinsically works in a pulsed mode, like a TOF mass spectrometeris advantageous, i.e. a better duty cycle can be achieved by using a TOF instead of aquadrupole mass spectrometer. This is because a TOF records all masses simultaneouslywhereas a quadrupole can only detect one species at a time. If a mass scan from 1 to 400amu is desired, the effectiveness of the TOF relative to a quadrupole is 400. Anotherprincipal disadvantage of a quadrupole is that the mass range is usually limited, e.g.from 1 - 400 amu in the here described experiment. TOF have no such mass limits. Itis the mass resolution that decreases for higher masses and thus limits the TOF massrange. A quadrupole mass spectrometer needs an energy filter to detect species with highenergies or broad energy distributions. This is not needed if a TOF mass spectrometeris used. The use of an energy analyzer provides additional information on the plasmaconditions. In most cases this information is less important, and TOFs usually make nouse of this possibility because it restricts the mass spectrum to species within a certainenergy range.

For measurements on less stable molecular beams and supersonic jets, i.e. when fluc-

2.3 Conclusions and Prospects 31

tuations between peak times of a beam occur, the use of an additional ion storagequadrupole device can be advantageous. Independent on the kind of mass filter whichis used (i.e. quadrupole or TOF), this device can collect ions for a certain time, e.g. fora time slightly longer than the duration of the plasma pulse, before they are released tothe mass filter section. A precise timing is therefore not as crucial as without using thisdevice.

Mass spectrometers can be used to optimize experimental conditions or they can serveas monitoring devices for experiments which require time consuming searches for certainspecies or long integration times. They can also be applied to develop new molecularsources. Although the nowadays available molecule sources are very efficient, it is verylikely that the production of larger radicals or reactive molecules in their gas phase, e.g.molecules with a carbon chain backbone between C20 and C60, will only be possible ifnew production techniques are developed and tested. This can be of great importance forthe understanding of grain growth or for the identification of larger cyclic or polycyclicmolecules. It seems that even the limits for the detection of linear species can be pushedfurther away to allow discoveries beyond molecules like C13, HC17N, HC13H, H3C12N,C14H, ... [61, 123].


3 The Cologne Carbon ClusterExperiment: The New Setup

Good name in man and woman, dear my lord,Is the immediate jewel of their souls:Who steals my purse steals trash; ’tis something, nothing;’Twas mine, ’tis his, and has been slave to thousands;But he that filches from me my good nameRobs me of that which not enriches himAnd makes me poor indeed.

William Shakespeare (1564 - 1616), “Othello”

Molecules like pure carbon clusters Cn or other species with no permanent dipole mo-ment can only be observed due to their vibrational or electronic properties. C3 andC5 have been astrophysically detected towards the late-type star IRC+10216 [87, 13].The knowledge of the ro-vibrational transitions of small carbon clusters in the IR re-gion is therefore important for future astronomical detections of these species. TheCologne carbon cluster experiment combines an effective excimer laser ablation source(see Chapter 2.1.1) with a sensitive, high resolution infrared tunable diode laser (TDL)spectrometer. TDL’s provide a fairly monochromatic beam which guarantee high spec-tral resolution and high sensitivity, with detection of absorbance as low as 10−6-10−7.Radicals like linear C8 and C10 have been observed with this spectrometer for the firsttime [61, 14]. The experimental setup has previously been described in the work ofBerndt [14], Giesen [60] and Winnewisser et al. [194].

TDL’s are not well suited for large scans over wide frequency ranges. Thus spectralsearches for the asymmetric stretching modes of gas-phase carbon molecules is essentiallyguided by the infrared vibration spectra of cold matrix isolated carbon clusters (see e.g.Shen et al. [166]) and their assignment to asymmetric stretching modes by ab initiocalculations (e.g. Martin et al. [115]). In the recent years the group of Prof. J.P. Maierfrom Basel has developed a novel matrix isolation technique that allows to deposit massselected carbon clusters. The infrared spectra of such a matrix can undoubtedly be

34 3 The Cologne Carbon Cluster Experiment: The New Setup

Figure 3.1: The Cologne carbon cluster experiment.

assigned to a cluster of a certain size. Once the vibrational bands of the radicals areknown an aimed search for ro-vibrational transitions in the gas phase can be conducted.

3.1 The Cologne Carbon Cluster experiment

Fig. 3.1 shows the new experimental setup of the Cologne carbon cluster experiment.A TDL spectrometer with a spectral resolution better than 5×10−4 cm−1 is used torecord the rotationally resolved spectra of asymmetric stretching modes of small carbonclusters. Using a number of different diode lasers the spectral region between 1750– 2100 cm−1, where most of the carbon clusters are predicted to have characteristicIR active vibrational bands, can be covered. The IR laser beam intersects the pulsedcluster jet of a laser ablation source (see Chapter 2.1.1 for details of the source) 10 mmdownstream from the nozzle. An increase in sensitivity is gained by using a multi-passoptics of Herriott type to obtain 24 passes through the jet. Since most of the diodelasers have multi-mode laser performance, a monochromator with 1 cm−1 resolution hasto provide sufficient mode separation. The exiting IR beam is focused on a HgCdTephoto-conductive detector. A fast AC-coupled amplifier allows time resolved detectionof the weak absorption signal on a pair of gated boxcar integrators before storing thedata by a PC. Part of the IR beam is used to monitor the absorption spectrum of a

3.2 The New Setup 35

Figure 3.2: Sensitivity of IR detectors [97]. In this experiment InSb (J10D) detectorsare used in the 5 µm region.

reference gas and fringes of a germanium etalon simultaneously with the cluster signal.The 1m reference cell is used to record Doppler limited lines of a reference gas at lowpressures. Frequency calibration of the data is accomplished by referencing the lines tothe fringe spectrum of the etalon with a free spectral range of 0.016 cm−1.

3.2 The New Setup

Measurements of the linear radicals C13, C10 and C8 have revealed that for the detectionof higher members of the Cn chain further improvements in the sensitivity of the spec-trometer are needed. The main problems occurred from the use of a cold head systemfor cooling the laser diodes, mechanical instabilities in the optical system and electricalinterference of the IR signal with the excimer pulse signal. In the course of this thesis acompletely new experimental setup was build. Important improvements have been doneincluding:

• Laser diodes mounted in a liquid nitrogen dewar instead of using a cryogenic coldhead


Figure 3.3: Frequency calibration using CCCS and Calib. The TDL laser was frequencymodulated at 5kHz.

• The use of InSb detectors for the 2000 cm−1 frequency region instead of HgCdTedetectors

• Enhancement of mechanical stability

• Setting up a new optical system to avoid astigmatism

• Reduction of electrical interferences

• Development of new calibration software

With the new setup a better signal-to-noise can be achieved and the sensitivity is in-creased in the frequency region of 2000 cm−1 where vibrational bands of C10 and C8

occur. In the new setup the laser diodes are mounted in a liquid nitrogen dewar insteadof a cryogenic cold head using closed cycle technique. Mechanical shocks are completelyavoided and baseline fluctuations are significantly smaller. The frequency of the TDL

3.3 Conclusions and Prospects 37

diodes is tuned by temperature and current. In the new setup the minimal temperatureof the diodes can not drop below 77 K so that special diodes are required. The laserpower of these diodes is between 0.1 and 10 mW as it was the case with the previouslyused diodes at temperatures of . 4K. The spectral line widths of these lasers are about30 MHz. A new laser control device and complete new electrical connections of theelectronic devices reduced electrical interference with the Excimer pulse significantly.The optical system has been improved by using stable mountings for the optic compo-nents and by mounting both optics and vacuum chamber on the same optical bench.The arrangement of the optic components is chosen to minimize astigmatism and lossof signal.

The HgCdTe detectors for the reference and etalon signal were replaced by InSb photo-voltaic detectors for the measurements at 5 µm wavelength (i.e. at 2000 cm−1). In Fig.3.2 it can be seen that HgCdTe (J15D12, Judson) detectors have their peak sensitivitybetween 10-11 µm whereas InSb (J10D, Judson) detectors peak at 5 µm.

Reference and etalon signal can be modulated in two modes. Mode one (M1) uses achopper wheel with a modulation frequency at 1.2 kHz whereas mode two (M2) mod-ulates the frequency of the TDL laser (up to 6 kHz). M1 is used for measurementswith the laser ablation source. M2 can be used for fast and high precision frequencycalibration where the lock-in amplifiers operate in the second derivative mode.

The new calibration software CCCS (Carbon Cluster Control Software) is based on thelinux operating system using the in-house program dada as program language. CCCSreceives and converts the data into ascii format and displays the measurement on themonitor screen. The program is nearly self explaining and comprises of help functions.With an additional program Calib the data can be immediately frequency calibrated,see Fig. 3.3.

Test measurements on C3 have been performed. Fig. 3.4 shows the R(28) transition ofC3.


High resolution absorption spectroscopy is one of the most powerful tools to charac-terize small gas-phase molecules. The Cologne carbon cluster experiment has providedhighly accurate data on asymmetric stretching transitions of small linear carbon clustersduring the last few years. With the new setup even more challenging problems can beapproached. At first, searches for hitherto undetected linear chains like C11 and C12 canbe started. The vibrational spectra of cyclic C6 and C8 trapped in a cold matrix havebeen found by Graham et al. [190, 191]. It is thus most likely to find these species in thegas-phase with the Cologne infrared spectrometer. The infrared spectra of combinationbands also provide good predictions for the low bending modes of carbon clusters, whichare as low as 1 - 4 THz.


Figure 3.4: Rovibrational transition of C3 at 2067 cm−1 (left line). The line at the righthand side is probably due to a hot band transition of C3.

Part II

C3N Isotopomers, C4N, and C6N

4 Experimental Setup

“ The principle of science, the definition almost, is the following:The test of all knowledge is experiment. Experiment is the solejudge of scientific ’truth’. But what is the source of knowledge?Where do the laws that are to be tested come from? Experiment,itself, helps to produce these laws, in the sense that it give us hints.But also needed is imagination to create from these hints the greatgeneralizations - to guess at the wonderful, simple, but very strangepattern beneath them all, and then to experiment to check againwhether we made the right guess. ”

Richard P. Feynman, ”The Feynman Lecture on Physics”

The rotational spectra of the molecules presented here were detected in a supersonicmolecular beam by a Fourier Transform Microwave (FTMW) experiment carried out atthe Harvard-Smithsonian Laboratory, Cambridge MA/USA. This spectrometer (Fig.4.1)has been used to detect over 80 new reactive molecules during the past six years [179]and the experimental setup has previously been described in McCarthy et al. [118, 122].

The basic principle of the spectrometer is as follows. A pulsed supersonic molecularbeam of an organic precursor gas heavily diluted in an inert gas is produced by an com-mercial solenoid valve (General Valve Co.). Reactive molecules of many kinds are madeby applying a small electrical discharge in the throat of the supersonic nozzle, prior toexpansion of the gas into the large Fabry-Perot cavity of the spectrometer. As the molec-ular beam traverses the cavity the molecules are irradiated by a short (1 µs) microwavepulse at frequency ν0. The microwave pulse induces polarized resonant transitions of themolecules, ions or radicals. At that time the molecules are under far different conditionsthan they were prior to the expansion. Important properties which have to be consideredare the translational, rotational and vibrational temperatures, as well as the pressure,and density of the molecules. After the polarizing pulse is switched off the polarized gascoherently emits at its resonant frequencies. This free-induction decay (FID) is detectedtime resolved by a superheterodyne receiver and subsequently Fourier transformed to

42 4 Experimental Setup

give the spectrum in the frequency domain. The spectrometer operates from 5 to 40GHz and is fully-computer controlled to the extent that, in spite of the small spectralcoverage of each setting of the Fabry-Perot (< 0.5 MHz), automated scans covering widefrequencies and requiring many hours of integration, can be conducted. Rotational linesof known molecules are routinely monitored for calibration.

The experimental part can be divided in three main sections, i.e. the production of theradicals (see Chap. 4.1) using a gas flow controller and a discharge nozzle, their coolingin an adiabatic expansion (see Chap. 4.2) and the subsequent detection in the FTMWspectrometer (see Chap. 4.3).

43

antennaSignal

liquidNitrogen

filterLow−pass

Polarizationpulseantenna

30 MHz

30 MHzsource

νo − 30 MHz

synthesizerFrequency

30 MHz

δ δ

0 to +90 dB

filter

Bandpass

Fabry−Perot cavity

Pulsed dischargenozzle

Vacuum chamber

+ 30 MHz

PINswitch

+30dB

+ δνo

+ δνo

Mirror

νo − 30 MHz

+20dB

Diffusion pump6

.

70 cm

36 cm

.

νo

3

45

inputGas

7 8

12

PINswitch

trigger

9

Figure 4.1: Block diagram of the FTMW low band system, 5 - 25 GHz with supersonicjet. (1) The control computer sets the synthesizer frequency (5 - 26.5 GHz) to νo-30MHz. (2) The output is mixed (single sideband modulator) with a 30 MHz signalwhich results in a frequency of νo and is amplified (’drive’ amplifier) (3) A 1 µs pumppulse triggered by a ’polarization’ PIN switch enters the FP-cavity via an antennaand (4) polarizes the incoming molecules in the vacuum chamber. The TE00q mode ofthe radiation field is indicated by the dotted lines between the mirrors. At this stagethe molecules have undergone significant cooling due to the adiabatic expansion in thesupersonic jet and rotational temperatures of a few Kelvin can be achieved. (5) Duringthe relaxation process the molecules emit signals at certain transition frequencies νo+δDuring this process the ’polarization’ PIN is switched off to suppress noise from thedrive amplifier. (6) The Free Induction Decay (FID) signal of the molecules is receivedat the signal antenna and amplified (front-end amplifier). (7) It passes a second PINswitch and is then mixed with a νo-30 MHz signal from the synthesizer. The imagerejection mixer has an internal amplifier (+20dB). (8) The resulting δ+30 MHz signalpasses a bandpass filter which discriminates the broadband noise and a second mixertransfers the signal down to the 1-MHz video band using a 30 MHz signal. (9) Thecomputer records the filtered and amplified signal in the time domain.


4.1 The Production of CnN Radicals

Radicals can be produced in many ways [58], e.g. by laser ablation, cw glow discharge,and pulsed discharge followed by a supersonic expansion. In the present work the lattermethod was used and the production of the radicals consisted mainly of two steps. (1) Tofind and produce the appropriate stable precursor gases, which are then mixed througha gas flow controller (see 4.1.1). (2) To choose and build an effective discharge nozzleand optimize the conditions for a maximum radical yield (see 4.1.2).

4.1.1 The Precursor Gases

To achieve an efficient way of producing long carbon chain molecules like HCnN, CH3CnN,H2Cn, and even for open-shell molecules like CnN with n≥3 it is advantageous to usemoderately large organic precursors (e.g. cyanoacetylene and diacetylene), rather thancommercially available gases such as acetylene (C2H2) and nitrogen (N2).

Cyanoacetylene (HC3N) was used for the production of C4N and C6N as well as for theproduction of all 13C isotopic species of C3N (in this case 13C isotopic acetylene had tobe added).

An appropriate synthesis of HC3N has been described in Murahashi et al. [137] andMoravec [134] together with suggestions for further readings. HC3N can be stored at-5 C for several months without evidence of polymerization and a vacuum distillationprocess prior to use was not required. The sample can be produced to a purity of morethan 98% as has been shown by 1H NMR spectroscopy [66].

Once the precursor gases are produced they are heavily diluted in an inert gas likeargon or neon which is necessary to maintain a steady gas discharge and to achieve lowrotational temperatures of 3 K in the adiabatic expansion following the discharge, (seeFig.4.2).

In general there seems to be no ready made recipes for the optimum mixing ratio ofprecursors to yield a certain radical in sufficient amounts; the work has nearly always tobe done by trial and error. In the case of CnN chains the pioneering work was alreadydone by Gottlieb et al. [66, 121] and Ohshima et al. [142] and had only slightly to bechanged. A good mixture for supersonic expansions proofed to be quit different frommixtures used in gas flow cells (see Gottlieb et al. [66]). The best results for C3Nproduction in a glass tube using a glow discharge where achieved by using HC3N andN2 or He with an equal molar mixing ratio at 3.3·10−5 bar (3.3 Pa). For experimentsusing a supersonic expansion the best conditions were found to be the following:

13C-isotopic C3N: In this work the strongest lines of the 13C-isotopes of C3N were ob-tained with a mixture of 0.02% HC3N and 0.07% 13C-enriched acetylene in Ne.The 13C-enriched acetylene is a 50% H13CCH, 25% H13C13CH and 25% HCCHmixture produced by hydrolysis of Li2C2 containing an 1:1 mixture of 12C and 13Cthat was prepared by the NIH Stable Isotope Resource at Los Alamos National

4.1 The Production of CnN Radicals 45

Laboratory [121]. For speed and convenience all measurements on isotopic specieswere done with enriched samples and in the case of the 13C isotopic species anenhancement of the signal by a factor of 2-3 was achieved.

An other, but less effective, way to produce isotopic cyanoacetylene is to use aC2H2/

13CO/inert gas mixture. For the CC13CN species a lot of energy is neededto break the strong C≡N bond in the HC3N precursor. This problem can becircumvented by using HCC13CN as precursor which can be produced using chem-ical reactions like K13CN + H3PO4 → H13CN + other and H13CN + C2H2 →HCC13CN + other.

CCC15N: For the production of CCC15N only a mixture of 0.2-0.3% CH3C15N (Ace-

tonitrile) in Ne was used and for the strongest lines a 6 times stronger signal thanthose of the 13C isotopic species was observed.

C2N: Ohshima et al. [142] used a 0.15% CH3CN or CCl3CN mixture diluted in Arwhere the CCl3CN/Ar sample produced a two times stronger signal. 1

C4N and C6N: For the C4N and C6N production it was sufficient to take 0.05% HC3N inNe. The relation of the signal intensity between CCCN and C4N is ∼15 and underoptimized experimental conditions, the absorption intensities of the strongest linesof the C6N are only two times weaker than those of C4N.

The total mass flow which entered the vacuum chamber was 14 sccm (standard cubiccm per minute) for C4N and 32 sccm for isotopic C3N and C6N.

1C2N can also be produced in a glass tube experiment using a microwave discharge of CF4 withCH3CN as Kakimoto & Kasuya have shown in [98].


23.924.0

1100−1250 V

Ne

2.1%2.4% 95.5%

trigger

on/off

HC N3H CCH13

hot

5−6 mmgas

insulationteflon

4.3 cm

copper electrode3mm thick

Discharge

Voltage

time

oscilloscope

Vacuum chamber

trigger

Current

30 sccm

Mirror

.

.

.

Mass Flow VoltageController

Sample Gas

Jet

DischargeSource

Figure 4.2: The Production of CnN radicals. On the left: precursor gases (H13CCH,HC3N) are mixed with a buffer gas (Ne) and fed to a pulsed discharge nozzle beforeit adiabatically expands into the vacuum chamber. On the top right: the dischargenozzle as it is used for the production of intermediate sized radicals. On the bottomright: The discharge voltage and current is monitored. In most cases an efficientradical production is indicated by a fine fringed current line. The dashed verticalcursor which frame the current line within the 2ms voltage supply marks a separationof 1-1.5 ms.


Gas

Pulsednozzle

Teflonhousing

Teflon spacers

.

.

.

.

electrodescopper

Gas

Pulsednozzle

Teflonhousing

10 mm Teflon

.

.

.

10 − 20 mm Teflon5 − 10 mm Teflon spacer spacer

spacer

.

electrodescopper

Figure 4.3: Nozzle for the production of molecules and radicals. On the left: Dischargenozzle optimized for the production of radicals like C4N. On the right: Dischargenozzle for the production of molecules like HC17N. The left part on each figure is asolenoid valve with an orifice of 1mm.

4.1.2 The Discharge Nozzle

Discharge nozzles similar to the ones used for the here presented experiments were firstdescribed by Schlachta et al. [164] in 1991. Since then many other work groups useddischarge nozzles of the same type to produce radicals and molecules. The first longcarbon chain molecule of astrophysical interest was the cyanopolyyne HC9N observedin the laboratory by Iida et al [92] in 1991. The same group showed that also reac-tive molecules which previously were detected in glow discharges in glass tubes (e.g.C3N, C4H [66], and C6H [146]) can also be effectively generated in supersonic expansiondischarge nozzles.

The basic geometry of the discharge nozzles which were used for this work is as follows.A solenoid valve through which the sample gas enters the nozzle is mounted on a Teflonhousing which contains a Teflon spacer (5-18 mm in length), two oxygen-free high-conductivity copper electrodes (1mm thick) separated by a spacer (4-10 mm) of the samedielectric. In some cases a third spacer is added to function as a reaction channel but thisis usually only the case if long closed-shell molecules are to be studied. The dimensions ofthe electrodes and the insulators are quite critical for the efficient formation of dischargeproducts. Applying a short pulse discharge in a small region between the electrodeswhere the pressure of the flow gas is still high and a subsequent expansion of the gasin a supersonic free jet, where almost no collision occurs, generates a relatively highconcentration of transient species. These conditions are very different to a dc dischargein a flow gas cell system which is far inferior in terms of the plurality of radical productionas known so far. This emphasizes the importance of the right discharge conditions, suchas dimension of the discharge unit, the applied discharge voltage, discharge timing, andas already discussed the composition of the sample gas.


i.d. 3 mm11 mm

1 2 3 4 5 6 7 8Pin

−HV

ground

reaction1 mm 4 mm

.

solenoid

gas

tefloncopper

valve

zone channeldischarge

Figure 4.4: Test nozzle to optimize the geometry of the discharge nozzle. Eight electrodes(PIN) give the possibility to freely choose the distances of the electrodes in use, i.e.the discharge zone can be varied by just reconnecting the electrodes from outside thevacuum chamber. Also the length of the reaction channel is adjustable from 0-30mm.Highly reactive molecules as well as long carbon chain molecules like HC17N can beproduced with this nozzle.

Restricting oneself to the here described geometry of the nozzle there is a possibility tosystematically vary the length of the discharge zone and of the reaction channel duringthe operation of the nozzle. As part of this thesis a test nozzle as seen in Fig.4.4 wasbuild to study the most effective electrode and reaction channel positions and lengths.Two electrodes were used at a time which could be chosen freely out of the 8 electrodesof the test nozzle. The region between cathode and the grounded electrode is calledthe ’discharge zone’ which is followed by the ’reaction channel’, i.e. the space left untilthe flow exits the nozzle. With this nozzle many different combinations of dischargezone lengths and reaction channel lengths can be tested and in-situ electrode changingduring an experiment can be done from outside the vacuum chamber which ensuressimilar conditions for each electrode setting in terms of mass flow, valve opening timesand gas mixing. The testing and optimization usually works by monitoring the signals ofknown species; starting with easily to produce ones like HC5N or C3N and then refiningwith more rare species of the same type. There seems to be a principal difference in theproduction of stable and unstable molecules. In the case of the closed-shell moleculeslike HC9N [141] and HC2n+1N with n=5-8 [118] which have been generated from simplemolecules such as (CN)2 and HC4H (or CH2CHCN and C2H2 as used in [141]) morecollisions are required to form longer carbon chains. This might explain why for suchmolecules a nozzle with an additional reaction channel is favorable. Once an optimumsetting of ’discharge zone’ and ’reaction channel’ lengths is found an easier to assembleand to clean nozzle can be build (see Fig. 4.3, right and Fig. 4.7). For highly reactivespecies such as open shell free radicals it is important to avoid any quenching process onthe surfaces of electrodes, insulators (spacers) and other molecules. Collisions apparently


drive the hydrocarbon chemistry to the more stable closed-shell polyynes [118]. Theoptimal production conditions for the CnN chains were achieved by using no reactionchannel 2 and a 10 mm discharge zone in the test nozzle. This corresponds to a shortnozzle as shown in Fig. 4.3 (left) 3. This nozzle was used with a low-current dc dischargeof 1100-1300 V synchronized with a 300-480 µs long gas pulse at a total backing pressureof 2.5 bar and a total gas flow of 30-32 sccm. The discharge current (see Fig. 4.2 bottomright) was typically 10-100 mA and lasted from 1 - 1.5ms per pulse corresponding toan energy per pulse of the order of 100mJ. For the production of open-shell moleculesthe first (inner) electrode was used as the cathode and the second (outer) electrode wasgrounded, whereas long closed-shell carbon chains were obtained by using the second(outer) electrode as cathode. The strength of rotational lines can decrease by a factorof 2-4 when the polarity of the electrodes is reversed [118]. For radicals the loss factorcan be much higher by changing the polarity. The short discharge nozzle was used forthe measurements of C4N, C6N and the C3N isotopomers (see Fig. 4.5 and Fig. 4.6) andit is also described in [37].

2except the tip of the nozzle3These conditions were found to be similar to those that optimize production of the acetylenic free

radicals CnH.


Figure 4.5: The short ’radical’ nozzle during a discharge. This nozzle was used for themeasurements of C4N, C6N and the C3N isotopes.

Figure 4.6: The supersonic jet expansion of the short nozzle. The picture was takenin Cologne using a pure He discharge at 5 bar stagnation pressure and 10−1 mbarbackground pressure. The straight line in the middle of the picture marks the centerline of the gas flow. The jet boundary is indicated by the upper line which arisesfrom the nozzle exit at an angle of roughly 23 with respect to the exit plummet. Thedashed line indicates the barrel shock. On the right hand side the vacuum chamberwindow limits the further view on the still expanding jet.


Figure 4.7: The long nozzles during a discharge. The pictures were taken in Cologneusing pure He discharges at 5 bar stagnation pressure and 10−1 mbar backgroundpressure. The discharge nozzle has a total length of 55mm (with tip), both electrodeswere separated by a spacer (13mm length, 5mm hole diameter) and the last electrodehas a distance of 29mm from the nozzle exit. At the top: The first (on the very leftwhich can hardly be seen) electrode was grounded and the second (the dark, verticalstripe in the middle of the nozzle) on a negative high voltage. Bottom picture: Thefirst electrode (left to the bright discharge zone) had a negative high voltage and thesecond (in the middle of the nozzle) was grounded. This kind of nozzle is mainly usedin the mode shown in the upper picture and is very effective in the production of longcarbon chain molecules with an electronic close shell structure, e.g. HC17N.


4.2 Adiabatic Expansion

After the precursor gases have passed the discharge region the particles in the gas un-dergo an adiabatic expansion into the vacuum chamber, i.e. they form a molecularbeam. Spectroscopy on a pulsed molecular beam is used in a number of laboratories be-cause the low rotational temperature of the molecules within the beam allows interestingexperiments in the field of Van-der-Waals complexes, clusters and radicals. Comparedwith experiments in glass tubes under room temperature and medium low pressure 4

the spectra of stable and unstable molecules in a beam are very simple since they areusually free of high rotational and highly excited vibrational states.

Although the primal interest is in the molecules created in the discharge the first andmain part of this section deals with the buffer gas atoms which usually contribute tomore than 98% of the flow particles and which set constraints on the flow conditionsin which the molecules of interest are seeded. In the last part of this section the focusis on the interaction of the buffer gas with the molecules and radicals and the spectralbehavior in a supersonic expansion of the latter. The problem is mainly approached ina theoretical way to clarify the basic prosseses. It has to be mentioned that deviationsfrom experiment are known but that up to now no theory comprising jet properties,chemical reactions and spectroscopic properties of certain molecular species is available.

The experiment described here is set up in a pulsed mode with repetition rates of 2Hz which requires smaller and less expensive pumping systems than a cw mode. In thisexperiment a 35cm diameter diffusion pump (Varian) backed by a dual-stage mechanicalpump is used to maintain a background pressure of 2.7·10−9bar (0.27 mPa). Typicalpeak pressures at 2 Hz repetition rate of the nozzle are 6.7·10−8bar (6.7 mPa).

Assuming a perfect adiabatic process one could argue that the properties of the moleculesare mainly determined by the adiabatic equations, like

T

T0

=

(p

p0

) γ−1γ

(4.1)

with T0 ≈ 300 K the stagnation temperature, p the background pressure during theexpansion 5 and p0 = 2.5 bar the stagnation pressure result in a minimum temperatureof Ta & 1.2 K. This however does not consider that the adiabatic expansion happens as a’free jet’, i.e. a supersonic flow which can show complicated features as seen in Fig. 4.8.Free jets have been investigated by many authors and the main reference for this sectionis the ’new classic’ book edited by Scoles ’Atomic and Molecular Beam Methods’ [165],the work of Balle & Flygare [6], and McClelland et al. [124].

Molecular beams with pulses longer than 100µs in a vacuum chamber of 1m length aretechnically rather ”gated” or ”modulated” than pulsed (R. Gentry in [165], p.54), i.e the

4usually in the µbar - mbar region5This is not necessarily the mean background pressure but the lower limit can be set to the achieved

pressure if there is no gas load.

4.2 Adiabatic Expansion 53

Zone ofSilence

ShockReflected

CompressionWaves

Expansion Fan

P ,T0 0

Background Pressure P b

Mach Disc Shock

M=1

Slip Line

M>1

Barrel Shock

Jet Boundary

FlowM>>1 M<1

M<<1

M>1

Figure 4.8: Continuum free-jet expansion [165].

mean free path of molecules moving at a speed of typically 800-1000 m/s is larger thanthe dimension of the vacuum chamber itself. In the further discussion the molecularbeam although pulsed is treated as a continuum free-jet for the time between 500 - 1100µs after the valve has opened and released the gas because in that time it is assumed thatthe beam exposes all important features which characterize a continuum free jet. A gasexpansion from an region with a stagnation pressure p0 into an area with a backgroundpressure pb becomes supersonic if the equation

p0

pb

> G ≡(γ + 1

2

) γγ−1

= 2.05 using γ =5

3for atoms (4.2)

is fulfilled. G is less than 2.1 for all gases and in this experiment the requirement ofEq. 4.2 is easily achieved. A supersonic flow increases velocity as the gas expands andthe Mach number M , with

M ≡ v

vs

(4.3)

where v is the flow velocity and vs is the speed of sound, is a measure of this, i.e thebeam is supersonic if M ≥ 1. Eq. 4.2 ensures that the pressure at the source exit ornozzle ’throat’ is well above the background pressure and the flow is said to be ’under-expanded’. In the subsequent expansion the gas is accelerated so strongly that M canbe much larger than 1, e.g. 40 or even larger which means that the particles in the beamhave a higher velocity than the local speed of sound. On the other hand informationcan only propagate at the speed of sound 6. This means that for a certain region in theflow, the so called ’zone of silence’ (ZOS), the particles in the flow are not influenced by

6Here, information refers mainly to the pressure and density distribution in the vacuum chamber orthe molecular flow.


any external conditions imposed on them like the ambient pressure pb which they haveto meet downstream. The jet over-expands with M continuously increasing in the ZOS.Of course at some point the supersonic flow is adjusted to the boundary conditions viashock waves, which are regions between the ZOS and the rest of the vacuum chamberthat are very thin non-isotropic regions of large density, pressure and temperature. There-compression usually happens as a barrel shock at the sides and the Mach disc shockat the normal to the centerline of the flow, see Fig. 4.8. In this regions the flow becomessubsonic (M < 1) and can react on the background pressure, walls or other obstacles.Assuming that only background gas reacts on the flow the distance nozzle exit - machdisc location xM is given by

xM

d= 0.67

√p0

pb

(4.4)

where d is the nozzle diameter. This formula together with a similar one for the width ofthe barrel shock has proved to give results which are in fair agreement with observationsat the Cologne Cluster Experiment. In this experiment a laser ablation or alternatively adischarge is used where many molecules are optically excited which make the jet visible.In the Cologne Cluster Experiment p0 is 10 bar and pb is of the order 5·10−2 mbar witha clearly visible jet of ca. 17 - 20 cm length within the vacuum chamber which agreeswell with Eq. 4.4. On the contrary because of the very low background pressure as itoccurs in the here described FTMW experiment the location of the Mach disc wouldbe far beyond the walls of the vacuum chamber. The main constrains on the jet aretherefore the walls and mirrors of the vacuum chamber.

The shock wave thickness is of the order of the mean free path λ and for the centerlineregion it can be estimated using

λ(x) =kBT (x)√2σp(x)

(4.5)

with kB the Boltzmann constant, T (x) the temperature at the position along the center-line axis x, p(x) the pressure and σ the hard sphere collision cross section of the buffergas. The distance between the mirrors where the free jet can expand is 70 cm and toestimate the shock front position xS which limits the free jet in the x-direction a detailedknowledge of the flow properties is necessary.

Scoles ([165], p.23, Tab. 2.2) gives numerical formulas for the Mach number M as afunction of (x/d), with x the downstream coordinate along the centerline axis, assumingan isentropic, compressible flow of an ideal gas 7 (see Fig. 4.9). For a pin nozzle andwith (x/d) 1 and gases with γ = 5/3 like He, Ne, Ar, etc. this formulae 8 reduces to

M = 3.232 ·(xd

) 23

(4.6)

This equation is independent of the background pressure and is only valid in the ZOSwhere M > 1. Once the Mach number is known in that region all the other important

7It is also assumed that there are negligible viscous and heat conduction effects.8[165], p.23, Tab. 2.2


flow properties can be calculated if the stagnation values like T0, p0, n0 (particle density)are given and the following equation

T

T0

=

(1 +

γ − 1

2M2

)−1

(4.7)

together with the adiabatic equations, e.g. Eq.4.1, are used, see Fig.4.9.

To get an idea of the numbers involved in the flow process a simple model is appliedto calculate some flow properties, see Fig. 4.10, and a small program was written 9 tocalculate the Mach number, temperatures, pressure, velocity, collision numbers, etc. atvarious points downstream the flow axis. The discharge is not explicitly included in themodel but is assumed to correspond to a higher stagnation temperature T0.

In the simple model the gas pre-expands into the discharge nozzle so that the pressuredrops from the stagnation pressure p0 to the pressure at the nozzle exit pn ∼ 2 mbar 10.This pressure drop can be estimated by assuming a constant mass flow rate m = ρvA,with ρ the density, v the one-dimensional flow speed, and A the cross-sectioned area ofthe flow which then can be used to calculate the increase of the flow velocity, i.e theMach number via ([165], p.19, Eq. 2.9)

An

A0

=1

M

[2

γ + 1

(1 +

(γ − 1

2

)M2

)](γ+1)/2(γ−1)

(4.8)

where An is the flow area at the nozzle exit and A0 the flow area at the valve exit.According to that the flow gains already ca. 97% of is final speed in the discharge nozzleand the temperature drops to ∼20K.

It follows a free expansion into the vacuum chamber. For the calculation of the free jetproperties, as it is summarized in Tab.4.1, the discharge nozzle was now not includedand the free jet starts directly behind the valve orifice 11. The expansion is split into3 zones. The first is the region of continuum flow where all particles can interchangeenergy via collisions and one parameter, the Mach number, characterizes all importantproperties at each point along the flow axis, e.g. the isotropic equilibrium Boltzmanndistribution of the velocity. Because the density of the gas decreases rapidly in the ex-pansion the collision frequency cannot maintain continuum flow and a smooth transitionto free-molecular flow begins (zone 2). The low background pressure in this experimentcauses this transition to happen without any conspicuous continuum shock structure. Ameasure of this transition is the point xF at which only one collision Z ' 1 is left for eachparticle to interact during the rest of the expansion. Usually one collision is sufficient toachieve a transitional relaxation but beyond xF the particles remain in their states andthe temperature TF of the flow does not change after the transition to a free molecularflow so that TF is the lowest possible temperature which can be achieved during the

9based on the formulas [165], Eq. 2.3, 2.4-2.6, Tab. 2.2, and [124], Eq. 410assuming the input values of Tab. 4.111This means that the distances xi given in the Tab.4.1 have no direct meaning to the experimental

setup but are included to estimate the order of magnitude.


Figure 4.9: Top: Mach number along the centerline axis of a free expansion. Bottom:Temperature along the centerline axis of a free expansion.


tubegas

dischargeenergy

dischargenozzle

T p0 0,

A 0A nozzle

1

2

.

.

..

.

..

.

.

.

..

.

..

.

.

.

..

.

..

.

.

.

..

.

..

.

.

.

..

.

..

.free jet

free−molecularflow

backgroundgas

beginning

begin of shock zone

.

.

.

.

.

.

.

.

..

.

.

.

x Ftransition zone

x S

TS

FT

3 4

5T p vn n n, ,

Figure 4.10: Model of flow development. 1. The stagnation region (tube and solenoidvalve). 2. The gas enters the discharge nozzle. The pressure drops to pn (Eq. 4.8)A0 is the entrance nozzle area and Anozzle the exit area. Because of the boundaryconditions enforced by the walls the expansion is strictly speaking not adiabatic butthis fact is neglected here. To calculate the temperature drop Eq. 4.1 is used andTn is the temperature at the nozzle exit. The gas pre-expands in the nozzle and isgaining flow speed. When a discharge is applied the energy of the flow increases toTn,d. 3. Free jet. Isentropic flow region. Many collisions occur. 4. At xF transition tofree-molecular flow. The translational temperature is ’frozen’. 5. Shock waves appearat xS and re-thermalize the flow gas.

expansion. Because of the walls or mirror a shock wave will appear at xS which marksthe transition to zone 3. Unwanted collisions with molecules scattered by the surfacesin front of the expansion re-thermalize or broaden the velocity distribution, i.e heat thebeam, in terms of an effective temperature.

Assuming T0 = 300 K xS can be estimated to be ≈ 58 cm because the mirror distanceis 70cm and at that point the mean free path is of the order of 12cm. The highestpossible mach number would still be M(xF ) ≈ 43, so that a translational temperatureof Ttrans = 0.47K should be achievable. Because the translational temperature changesalong the x-axis the mean temperature between the mirrors should be slightly largerthan 0.5 K.

An alternative approach to estimate the translational temperature based on experimentswith iodine in seeded supersonic beams is given in McClelland et al. [124] where theterminal Mach number can be estimated by

Mt = F (γ)

(Kn

ε

)− γ−1γ

(4.9)


with F (γ) = 2.03 for γ = 5/3 andKn = λ0/d the Knudsen number, λ0 the mean free pathin the stagnation zone 12 , and ε the ’maximum fractional change in the mean randomvelocity per collision’ ( ε(H2, He) = 0.02, ε(Ar) = 0.25, and ε(Ne,D2, N2, CO, . . . ) =0.1− 0.5, [124]). In the case of Ne this results in a minimum translational temperatureof 0.1 - 0.3 K depending on which ε is taken 13 .

The precursors are heavily diluted in the buffer gas and can usually be neglected by thecalculations of the flow properties. From Table 4.1 it can be seen that there are largediscrepancies between the different kind of estimations of the translational temperatureof a free jet, i.e. 30% between TF (xF ) (using Eq. 4.6) and Tt(xt) (using Eq. 4.9)14. Thebuffer gases can not be detected by the Fourier transform spectrometer and an directverification of the here presented flow values is not possible. Instead the translationalvelocity of polar species (precursors or radicals which are created in the discharge, seeSection 4.3) can be measured and compared to the theoretical results as seen in Tab. 4.1,e.g. a velocity of 840 m/s was measured for a molecule which was cooled by Ne atomsin a supersonic jet. If this molecule was in thermal equilibrium with Ne a stagnationtemperature of 343 K has to be assumed, see Tab. 4.1. Because the Ne as well as theprecursor gases were used at room temperature it has to be concluded that it was thedischarge that heated the gas to ca. 50C prior to the adiabatic expansion.

12In McClelland et al. [124] the formula is described with a mean free path at the nozzle throat, whichin Balle & Flygare [6] is interpreted as stagnation value. To calculate λth with the pressure at thenozzle throat p0 has to be replaced by p0/G, ([165], p.15) which yields higher temperatures of afactor 2.

13T0 was assumed to be 300 K. For Ar and He the results are T(Ar)=0.6 K and T(He)=7.3 K respec-tively.

14For comparison also the values Ta derived by using the pure adiabatic equation 4.1 are given in Table4.1. Because Trot(molecule) > Ttrans(molecule) and Ttrans(molecule) ≥ Ttrans(Ne) it is clear thatfor Trot(molecule) less or equal 0.5K (see Fig. 4.11) Ta can not be ∼ Ttrans(Ne). Therefor Ta doesnot correctly describe the physical conditions of the buffer gas in the jet.


Table 4.1: Free jet flow properties for Ne

Experimental / particle parametersγ 5/3 ε ∼0.2 - 0.5mNe [amu] 20.18 σNe−Ne [nm2] 0.24T0,1 [K] 293.15 p0 [bar] 2.5T0,2 [K] ∼ 343 pb [mbar] 2.7·10−6

T0,3 [K] 500 pb,load [mbar] 6.7·10−5

gas mass flow [sccm] 30 repetition rate [Hz] 2d [mm] 1 D [mm] 5Under standard conditions there are ≈ 6.7·1018 particles per pulse.

Jet properties at T0(293.15 K), p0 T0(300 K),p0 T0(343 K), p0

xF [mm] 49 44 42M(xF ) 48.4 47.8 44TF (xF ) [K] ≈ Ttrans,min 0.5 0.47 0.6Tt(xt) [K] ≈ Ttrans,min 0.1-0.3 0.1-0.3 0.18-0.4TZ<5 [K] & Trot,min 1.1 1.68 2.13Ta [K] 1.2-4.3 1.2-4.4 1.4-5.1p(xF ) [mbar] 2.3·10−4 2.4·10−4 3.1·10−4

v(xF ) [m/s] 776.5 785 839.7vt [m/s] 777.1 786 840.5ρ(x = 350) [1/cm3] ∼ 1014

Jet boundariesxM [m] > 4 ∅barrel shock [m] > 2

γ = cp/cv the heat capacity ratio, ε from [124] p.950-951, mNe atomic mass of Ne, σNe−Ne

hard sphere collision cross section of Ne [5], T0,i stagnation temperature i, p0 stagnationpressure, pb = background pressure without gas load, pb,load background pressure withgas load, d diameter of valve orifice, D diameter of nozzle exit,x distance from nozzle exit, xF freezing point with Zr,binary(xF ) ' 1, xt point whereterminal Mach number is reached [124], M is taken from [165], the following tempera-tures T are all translational temperatures, TF (xF ) temperature at freezing point, Tt(xt)temperature corresponding to Mt with Mt as in [124], TZ<5 temperature at point whereonly less than 5 collision remain per particle (a rotational relaxation needs less than5 collisions), Ta as in Eq. 4.1 using pb (first value) and pb,load (second value), p pres-sure at xF [165], xM location of Mach disk, ∅barrel shock diameter of the barrel shock,v flow velocity at x, vt terminal velocity, ρ density at x. It should be xF ≈ xt andT (xS) < T (xF ) ≈ T (xt) < Ta.


Molecular collision rates are important for the translational, rotational and vibrationalrelaxation process as well as for chemical reactions and cause the most important devia-tions from ideal predictions based on the continuum properties. Two-body collision ratesscale with p0d, whereas three-body collisions required to build molecules out of atomsscale with p2

0d. This means that any chemical reaction takes place in the discharge nozzleor shortly after the particles enter the vacuum chamber (x/d) ∼ 1 15 where the densityof the flow is still high. After the radicals have formed kinetic processes, such as energyexchange for cooling of internal states, first decrease and finally ’freeze’, i.e. terminate.The effectiveness of such cooling processes depends on the number of collisions experi-enced by each particle. The total amount of binary collisions Ztot can be calculated byintegrating the collision rates Z(x) from x = 0 to x =∞ and is typically of the order of102 (pin nozzle) to 103 (slit nozzle) collisions. From this number the number of collisionsZr remaining in the expansion at a given point x along the flow axis can be calculatedand gives a measure of the positions of the ’transition zones’ where an average particlewill not experience enough collisions to achieve translational or rotational equilibrium.In the case of the translation relaxation only a few collisions Z ' 1 are required and thistransition often occurs beyond the point where the velocity ratio v(x)/v∞ ∼ 0.98 [165]16, see Tab.4.1 (xF ).

Rotational relaxation of small molecules like C3N need slightly more collisions Z . 5.Simple diatomic molecules may require ca. 104 for the vibrational relaxation. The neededvibrational collision number for large polyatomic molecules and the rotational collisionnumber of most diatomic molecules are of the order 10 to 100 so that the vibrationalmodes of diatomic do not participate in the expansion [165].

It is not only the collision number which determines the effectiveness of cooling but alsothe cross section σ of the energy transfer (e.g. Erot → Etrans, Evib → Etrans) comparedwith Etrans → Etrans. Usually it is

σ(Etrans → Etrans) > σ(Erot → Etrans)

> σ(Evib → Etrans)(4.10)

so that the rotational energy is smaller than the vibrational energy but higher thanthe translational energy. In most cases is σ(Erot → Erot) > σ(Etrans → Etrans) andan equilibrium within the rotational levels is achieved with a temperature Trot. Thepopulation of the vibrational levels usually do not follow a Boltzmann distribution but itis nevertheless standard to speak of a vibrational temperature Tvib which is a temperaturecorresponding to a Boltzmann distribution which has been approximated to the realdistribution. After the expansion the gas has usually the following order of temperatures:Ttrans < Trot < Tvib [43].

The Ttrans, Trot, Tvib values depend on the expansion parameters and are typicallyTtrans < 5 K, Trot < 10 K, Tvib < 100 K (Demtroder et al. [43], 3 bar Ar with 5%NO2 with a d=50 µm nozzle.). Grabow et al. [69] who did measurements on the SO

15see [165], p. 25, Fig. 2.1016For this experiment v(x)/v∞ ∼ 0.99 .


radical (with X3Σ−) reported that the effectiveness of the cooling by a beam expansiondepends inversely on the heights of the energy levels to be cooled. Rotational transi-tions with energy differences of only a few cm−1 are cooled much more effective, i.e. therotational temperatures Trot can be as low as a few degree Kelvin, whereas vibrationalstates where found to have Tvib of a few hundred K.

If for the rotational relaxation only 3 or less collisions are required the rotational tem-perature Trot is expected to be between 0.2 - 2.1 K 17. In Fig. 4.11 a measured C4Nspectrum is plotted together with a theoretical spectrum corresponding to 0.5 K 18.

In the work of Grabow et al. [69] molecules in a beam expansion without a dischargeare found to have transitions with low vibrational energies, e.g. OCS, SO2 or SO,which become much stronger in intensity when the discharge is turned on within thenozzle orifice. This is in agreement with Schlachta et al. [164] who studied a variety ofdiatomic radicals like OH, NH, CN, and C2 and report rotational temperatures of 5-50K, depending on the expansion parameters, and in many cases vibrational temperaturesof several thousand Kelvin when applying a discharge.

The main advantages for the analysis of the spectrum due to the cooling of the moleculesin the jet can be seen by the formula describing the number of molecules in a certainstate νi, Ji

N(νi, Ji) =N0

Z

∏i

(2Ji + 1)e(−ErotkTrot

)e(−EvibkTvib

)(4.11)

, where νi is the vibrational quantum number of the vibrational mode i and Ji therotational quantum number within the vibration νi, and Z the overall partition function:

• The population number N(νi, Ji) reduces to a few ro-vibrational levels, so that thenumber of the absorption lines decreases drastically.

• Because the absolute number N0 remains constant the population of the lowerlevels increase and instead of many weak lines a few strong lines are conceived inthe spectrum, see Fig.4.11

17see Table 4.1 with Tt(xt) = 0.2 K and TZ<5 = 2.1 K.18 It is however not unproblematic to make a straight forward comparison between the measured and

the calculated intensities. Some people including myself believe that to estimate the rotationaltemperature of a molecule measured with a FTMW spectrometer the effect of the Q-factor (seesection 4.3) has to be considered. The result including this effect would be a rotational temperatureof 0.2K.


Figure 4.11: Theoretical intensities of the C4N rotational transitions corresponding to0.5K together with the measured lines as discussed in Chapter 7.2.

4.3 The Fourier Transform Microwave Spectrometer 63

4.3 The Fourier Transform Microwave Spectrometer

The Fourier Transform Microwave (FTMW) Spectrometer at the Harvard/DEAS Spec-troscopy Laboratory exists since 1995 and was build following the classical experimentfrom Balle & Flygare [6, 29] published in 1981. At the moment the FTMW spectrometeroperates in two modes, the low band mode between 5 and 25 GHz and the high bandmode between 25-40 GHz. Both modes were used for the measurements of the radicalspresented in this work. A block diagram of the used FTMW spectrometer in its lowband operational mode is shown in Fig. 4.1. A schematic diagram of the FTMW wasalready published in [122] but Fig. 4.1 reflects some rearrangements which were donesince then and it also shows the cooling of the mirrors. Between 1997 and 2000 thesensitivity could be improved by more than an order of magnitude and the results werepublished in [118].

The spectrometer can only be used within resonant frequencies ν of a TEMmnq mode ofthe Fabry-Perot (F.-P.) resonator 19

ν = ν0

[(q + 1) +

(1

π

)(m+ n+ 1)

cos(1− dR)

](4.12)

with ν0 = c/2d, d the distance between the mirrors, R radius of curvature of bothspherical concave mirrors, c speed of light. The experiment is set up in a confocalarrangement of the mirrors (R=d) with d=70cm and the TEM00q modes which are thedominant modes are therefore

ν = ν0

[(q + 1) +

1

π

](4.13)

and separated by ν0=214 MHz. One of the mirrors, the ’drive’ mirror, can be movedand allows the frequency tuning of the spectrometer. To change the resonance frequencyfrom ν1 to ν2 = ν1 + ∆ν by moving the drive mirror from position 1 with d1 to position2 with d2 = d1 −∆d the Eq. 4.12 transforms to

∆ν =c

2

(1

d1

− 1

d2

)(q + 1)

d1d2≈d2

=c(q + 1)

2

∆d

d2

yielding

∆d =c∆νd2

c(q + 1). (4.14)

At 20 GHz Eq. 4.13 results in (q+ 1) ≈ 90 half wavelength between the mirrors and if afrequency search with step sizes of ∆ν = 500 kHz is desired Eq. 4.14 yields a separation∆d for each step of ca. 20 µm 20.

19nomenclature and formulas of the following section are mainly taken from Balle & Flygare [6]20 This means that also mechanical vibrations can vary the cavity resonant frequency and thereby

contributes to the low frequency noise.


Using separate antennas, i.e the ’drive’ antenna to connect the F.-P. cavity to the os-cillator injecting the 1µs pulse and the ’signal’ antenna to couple the electric field ofthe resonator to the detector circuit, which can be tuned externally and independentlycritically coupling can be obtained. Both antennas are ’L’ shaped and can have differentgeometrical dimensions (varying from 0.5 to 2 cm) depending on the frequency rangethey are used for. Various antenna separations from the mirror surface were tested.During the measurements for the CnN chain molecules two equal antennas specified for9.5 GHz were used and both were separated from the mirror surface by 0.08 mm to yieldan optimum coupling.

An important parameter of the experiment is the Q factor (quality factor) which isdefined as

Q = ωW/P (4.15)

where ω = 2πν is the angular frequency of the radiation, W is the total energy storedin the cavity and P is the power dissipation, i.e. the energy loss per time −dW/dt. In aquasi-optical treatment of a resonator there are mainly two reasons for the power insidethe cell to dissipate. (1) The power can be dissipated by diffracting on the mirrors. Thisproblem can be made arbitrarily small by increasing the radius of the mirrors a. TheFresnel number F ≡ a2

λRwith F&1 is a measure of the Fresnel diffraction and making

F=1, i.e. a =√Rλ insures a good Q because the mirror captures more than 95% of the

wave amplitude at any point [6]. The spectrometer has mirrors with radii a of 36 cmwhich cause a cut-off frequency at ∼5 GHz, see Fig. 4.13. A general discussion of thisproblem is given in the classical work of Boyd & Gordon [21] and Kogelnik & Li [105]21. The upper limit at about 40 GHz is not due to diffraction but is imposed by cut-offsin amplifiers and the high-band PIN switch. (2) Ohmic losses in the metallic mirrors.Based on the assumption that the dissipations are only due to ohmic losses a theoreticalQth can be calculated with

Qth =d

2δ(4.16)

where δ is the skin depth, i.e. the distance in the conductor at which the amplitude of anelectromagnetic wave has decreased to 1/e of its value at the surface. In this experimentthe mirrors are made of aluminum which has a δ of 8.5·10−5 cm at 10 GHz thus resultingin a Qth ≈ 4.1·105. The resonant cavity mode has a Lorentzian line shape and the fullwidth ∆νc at half height is given by

∆νc =νc

Q, or Q =

νc

∆νc

(4.17)

The decay time constant τc of the energy W in the cavity can be obtained by consid-ering that the energy W decays at a rate proportional to W and 1/τc defined as theproportionality constant

W · (1/τc) = −dWdt≡ P

(4.15)=

2πνcW

Q, thus following τc =

Q

2πν

(4.17)=

1

2π∆νc

. (4.18)

21Storm et al. [171] describe a way to circumvent this problem by using a cylindrical resonator tooperate in TE01q modes instead of TEM00q as used in the spectrometer described here.


polarization

signal

1 MHz

Lorentzianlineshape

band width Fabry−Perot

ν

power

Q = ∆ νν

Q2 Q1>

Q1

Q2

νoνpol

400 kHz

Figure 4.12: Cavity mode Lorentzian line shape. The quality factor Q is a measure ofthe full width ∆ν at a given frequency ν of the cavity mode. Different Q’s result indifferent power values for a given frequency. If the mirrors are adjusted for a cavitymode center frequency νo of 10 GHz the bandwidth of the Fabry-Perot is ∼ 1 MHz.The polarization pulse has a 400 kHz offset from the expected molecule emissionfrequency.

In this experiment high-quality factors (Q up to ∼ 104) have been obtained over muchof the centimeter-wave band. The highest unloaded Q0

22 now achieved is 2·105, whichis close to the above calculated theoretical limit of about 4·105. When the cavity iscritically coupled, the loaded QL

23 is about 105. For a cavity with Q=104 at νc = 10GHz the decay time τc is 0.16 µs which corresponds to a cavity band width ∆νc of 1 MHz,see Fig. 4.12. This means that in praxis the maximum frequency region which can berecorded at a time is of the order <1 MHz, i.e. 500-600 kHz. After this frequency regionis examined a new frequency can be set and a computer moves the mirrors appropriatelyto match the desired center frequency with the cavity mode.

Line intensities I are sensitive to the cavity Q. In [6], Eq.(40), a relation between theemitted electric field in the cavity and the Q factor is given in form of a proportionalityE(r, t) ∼ Q, so that I ∼ Q2. However the measurable Qeff , in which also influencesof the detection circuit are considered, is no smooth function of the frequency ν andcan vary rapidly between adjacent frequency regions so that measured intensities candiffer strongly from theoretically predicted. During this thesis many new Q-values cor-

22The unloaded Q, Q0, accounts for power dissipation in ohmic losses23The sum of all dissipative elements defines the loaded Q, QL, i.e diffraction, antenna coupling, etc..


Figure 4.13: Measured Qeff and calculated Qth for the Fabry-Perot cavity. Set 1 - 4are effective Q values including effects of the electrical detection circuits measured bySam Palmer (April 1998). Set 5 was measured during this work. Between 6 and 13GHz the Q-value can change rapidly by stepping to an nearby frequency which is bestseen in Set 5. Therefore a comparison between absolute intensities of even close lyingemission lines is nearly impossible. ’s=1.3mm’ and ’d=203µm’ means that the signalantenna was separated by 1.3mm from the mirror surface and the drive antenna by203µm.’L=1.9cm’ is the length of the antenna and the frequency in brackets is the opti-mum coupling frequency for that antenna. The theoretical Q values were calculated bySam Palmer using the formulae Q = 2πdν

c1α, with αreflectiv = 4π δ

λ= 1.43 ·10−4√νGHz,

δ the skin depth and αdiffractiv = 16π2Fe−4πF = 23.79νGHze−1.893νGHz , F = a2

λdthe

Fresnel number in cgs units.


responding to the used antenna set and frequencies of interest were determined and usedas reference values, see Fig. 4.13.

The essential cavity optics and first-stage amplifier are cooled with liquid nitrogen,thereby reducing the noise equivalent system temperature from 800 K to about 200 K,which is nearly a factor of four better sensitivity 24. Above 10 GHz diffraction losses inthe open resonator are negligible, and roughly two-thirds (110 K) of the receiver noiseis from the cold amplifier and one-third from the 77 K mirrors. Below 10 GHz diffrac-tion from the open resonator contributes significantly to the cavity Q, and the systemtemperature rises to about 400 K. The cooling is done separately for each mirror by con-tinuously flowing liquid nitrogen through a copper coil soldered to a copper disk makinggood thermal contact with the mirror’s back surface. Thermal isolation of the mirrorsis achieved by suspension on epoxy strips. Condensation of gas from the supersonic jetdoes not appreciably degrade the reflectivity of the cold mirrors.

The supersonic molecular beam is oriented parallel, rather than perpendicular as de-scribed in [6], to the Fabry-Perot axis and can be removed via a gate valve assembly toservice the discharge nozzle even when the spectrometer is operated at 77 K.

The transition lines measured by this spectrometer appear Doppler shifted, see Fig. 4.14.The Doppler separation is a measure of the relative speed ±vmolecule of the incomingmolecules with regard to the back and forward traveling microwaves and is symmetricwith respect to the rest frequency νo of the molecules.(

∆ν2

)νo

=vmolecule

c,

Here 0.107MHz/219083.2MHz

·c = 840.45ms

= speed of the molecule. see Fig. 4.14. The line separationand thus the speed of the molecules can differ due to their size or charge, i.e ions arefaster than neutral species.

24 ”The sensitivity of the present liquid-nitrogen-cooled FTM spectrometer is far from the fundamentallimits. Liquid helium cooling of the optics and the first stage of receiver amplification might improvethe sensitivity by nearly an order of magnitude. ” [179]


νo

µ st /

time domain

E

Vµsignal/

= 19083.2139 MHz

frequency ( )400 kHz − νo

11 kHz

∆ν = 107 kHzDoppler

Figure 4.14: Time and Frequency Domains. The computer receives a FID signal in thetime domain and Fourier transforms it into the frequency domain. The moleculesemission frequency νo is the mean value of the two doppler shifted lines. These origi-nate from the el.mag. waves which travel back and forth in the FP-cavity relative tothe molecule’s flight direction. The Fourier transform FID is displayed as a frequencyoffset from the pump frequency νpolarization. The plotted line is an unidentified linemeasured during a 13CCCN survey.

5 Linear CnN, Cyanide Radicals

“ The important thing in science is not so much to obtain new factsas to discover new ways of thinking about them. ”

Sir William Bragg

CnN are open shell molecules, radicals in the technical sense of the term, and thereforeparamagnetic. All members of the even numbered radicals are found in the 2Π electronicground state through theory [144] and experiment (e.g. this work) whereas in the caseof odd membered cyanide radicals there is an expected change from 2Σ to 2Π groundstate for increasing n [99, 144]. Dipole moments have not been measured for any of theCnN chains discussed here, see Tab. 5.1 and 5.2 but instead ab initio calculations havebeen performed [144, 20]. In each series the dipole moment is found to increase steadilywith chain length; given that the radicals have the same ground state.

Other carbon chains like CnH and HCnN which both are readily detected in space areof great importance regarding the CnN chains. The first ones, CnH (or CnCH, withCH playing the role of N), is isoelectronic to the CnN chains and in this work is oftenused for references and comparison of molecular constants and properties like magnetichyperfine constants or electronic energy separations, see Appendix A. The second ones,the cyanopolyynes HCnN are interesting because mainly of two reasons. (1.) The role ofCnN chains in the production and depletion of interstellar cyanopolyynes, see Chapter 8.(2.) On a theoretical point of view the odd CnN chains can be thought of daughtermolecules of acetylenic HCnN by removal of the terminal hydrogen atom which resultsin an π4 σ1 2Σ electronic state for the cyanide radicals with the radical electron localizedat the terminal carbon [144]. An electron transfer from a π orbital into the half-filled σorbital will cause a shift in the charge distribution and generates a nonpolar or in praxisnearly nonpolar 2Π state radical which is close in energy, (see Fig. 5.1 top and bottomright). This causes a principle difference between CnN chains with odd n or even n. Theelectron configuration of even CnN chains can be explained by adding the electrons ofan extra C atom to an odd numbered CnN chain after the π → σ electron transfer, (seeFig. 5.1 bottom).

70 5 Linear CnN, Cyanide Radicals

In the following part a brief introduction to the CnN molecules known so far is given.

The odd numbered CnN (n=1,3,5,...,13) members:

CN Emissions of CN in the violet band first measured in the 1920’s were later (1937 byAdel [2], 1941 by McKellar [126]) rediscovered in the tails of comets (see Herzberg[85]) and in absorption towards the star ξ Ophiuchi (in 1941 by Adams [1]).

The exploration of the µm-wave spectrum of the CN radical was widely promotedby radio astronomical observations. Here CN was first measured by Jefferts etal. [94] in 1970 towards Orion A and W51 and Penzias et al.[149] and Turner &Gammon [184] were able to determine the hyperfine (hf) structure of CN in thevibrational ground state to high precision.

At this point it is worthwhile mentioning that the rotational transition N= 1 → 0at 113 GHz is also of cosmological interest as is shortly described now. In 1964Penzias and Wilson [148] discovered during their work at the Bell Laboratoriesthe existence of the isotropic cosmic background radiation (CBR) which was sooninterpreted by Dicke et al. [44] as the relic of an early stage of our universe whenthe electromagnetic field decoupled from matter. Interpretation of the intensityratios of the R(0) violet transition X2Σ+ → B2Σ+ at 3874.6 A and the R(1)transition by Thaddeus et al.[177] resulted in a rotational temperature [147] thatcame close to the today excepted value for the CBR of 2.725 K [71] and led to theconclusion that CN is thermally excited by the background microwave radiation;an interpretation which is in sharp contrast to the one given in 1950 by Herzberg[83] where it is said that ”the rotational temperature of 2.3 K [...] of course only[has] a very restricted meaning”. This example shows nicely that the relevancy ofobservations can change significantly with the progress of science.

Also vibrational excited states have been investigated. Important work was doneby Skatrud et al. [167], who determined the Dunham coefficients, the spin-doubling, and the hf parameter for the v = 0,1,2,3 states. Johnson et al. [96]have studied the v = 2 state and Ito et al.[93] gave an analysis of the excitedstates up to v = 10. A good overview of this work for states from v = 0 to 7and additional measurements up to the THz region is given in the PhD thesis ofE. Klisch [104].

Isotopic measurements of 13CN have been done by Bogey et al. between 1984-86and included ground state [16] and excited vibrational states ν ≤ 9 [17] as well asa study of the isotopic dependence of the molecular constants.

12C15N was first measured in space with the KOSMA 3m telescope towards OrionA by Saleck et al. [160] and little later spectroscopically characterized by Salecket al. [161] in 1994.

Thomson et al. [180] determined the dipole moment to be 1.45 Debye.

71

Figure 5.1: Top: Schematic diagram of electron configuration of CN π4σ1 (X2Σ).Bottom: CCN σ2π1 (X2Π) electron configuration. On the right: CN changing fromπ4σ1 (Σ) into a π2σ3 (Π) state after electron transfer. (see Engelke [52] and Rajendraet al. [158]).


An important result of the isotopic measurements is that CN as many otherdiatomic molecules like O2, CO, and NO deviate significantly from the Born-Oppenheimer approximation.

C3N The linear carbon chain radical C3N (cyanoethynyl) was first detected in the gasphase with a radio telescope by Guelin and Thaddeus [78, 79] in 1977 in themolecular envelope of the carbon-rich star IRC+10216. The identification wasbased on two emission line doublets at 89 and 99 GHz and the B, D and |γ|molecular constants have been determined. The detection was later confirmedby observations in many other interstellar sources (e.g. [56, 10]) and also the ρ-type doubling and magnetic hyperfine constants were determined by astronomicalobservations [76]. The laboratory detection of C3N had to wait until 1983 whenGottlieb at al. [66] made first measurements in the mm-range.

Mikami et al. [130] studied the ν5 vibrationally excited bending mode state of C3Nby performing measurements at 208 to 278 GHz which resulted in the determina-tion of several parameters including the l-type doubling parameter q.

Sadlej et al.[159] studied the A2Π, B2Π, C2Σ and X2Σ ground state of C3N by abinitio calculations and obtained a dipole moment of 3.0 D.

First measurements on the isotopic species were done by McCarthy at al. [121]in the mm-range (near 250 GHz). These efforts resulted in a detailed knowledgeof the geometry of C3N and also a preliminary estimation of the hyperfine cou-pling constant bF (13C) for the 13CCCN and C13CCN radicals. In the same workBotschwina presented calculations of the vibration frequencies of C3N. Magnetichyperfine structure (hfs) is a sensitive probe of the electronic structure of openshell molecules and in this work a detailed measurement of the magnetic hyperfinestructure of 13CCCN, C13CCN, CC13CN, and CCC15N is presented with the aim ofgetting information on the distribution of the unpaired electron spin density alongthe carbon chain, (see Chapter 7). The electric quadrupole hyperfine structure ofthe 13C-isotopes was also determined.

During a line survey of the C-star envelope IRC+10216 carried out by Cernicharoet al. [34] 10 lines of low intensity were assigned to 3 isotopic species of C3N. Twoout of four lines assigned to 13CCCN are not in agreement with the laboratorywork presented here, (see Chapter 8).

C5N In 1991 Pauzat et al. [144] noted that for odd numbered CnN chains with n>3 achange from 2Σ to 2Π electronic ground state is expected and C5N was predictedto be in a 2Π ground state. In detail this means, that if the energy of the molecularorbital 7σ is higher than that of 3π, C5N should be in a 2Σ ground state. A 2Πstate would apply if the energy of the 3π orbital is higher than that of the 7σ. Highlevel coupled cluster calculations by Botschwina [19] predicted the ground stateto have a 2Σ symmetry. In 1997 Kasai et al. [99] published the first detection ofC5N by Fourier transform microwave spectroscopy between 5 and 17 GHz and theground state was determined to have 2Σ symmetry. Shortly after Guelin et al. [77]

73

detected C5N in the dark cloud TMC-1, (see Chapter 8). Electronic transitions of2Π← X2Σ of C5N in a neon matrix have been measured in the visible by Grutteret al. [72] between 427 and 471 nm.

C7N The absorption bands of the 2Π ← X2Σ electronic transition of C7N have beenmeasured in the visible in a neon matrix by Grutter et al. [72]. They find a ” greatdeal of similarity [...] in the vibrational pattern of the C5N and C7N” and concludethat C7N is probably also in a 2Σ electronic ground state. An ab initio calculationby Botschwina et al. [20] using restricted Hartree-Fock and partially restrictedopen-shell coupled cluster theory yield an opposite result for which C7N has not2Σ but instead a 2Π electronic ground state. During this work a measurementcampaign was started for linear C7N but ended without any result. Our conclusionis that C7N might be in a 2Π ground state because if C7N has a 2Σ ground statewith a dipole moment of roughly -3.1 D to -4.2 D but is less abundant than C5Nit still should have been detected during our search. The dipole moment of theradical in a 2Π state is calculated to be between -0.5 and 1.0 D [20] and could havecaused the emission of the radicals to fall under the detection limit of the FTMWspectrometer, (see Chapter 7.3).

C9N - C13N Grutter et al.[72] published 6K neon matrices measurements of C5N upto C13N radicals in the visible and near IR between 470 and 830 nm. For C9N,C11N and C13N the 2Π← X2Π states were studied with several vibrational bandsincluding the C≡C, C≡N, and C-C stretching modes.

The even numbered CnN (n=2,4,6,8) members:

C2N CCN was first observed in the laboratory by Merer and Travis [128] in 1965. Theexperiment was done with a flash photolysis of diazoacetonitrile and they observedan absorption spectrum of X2Π → A2∆, X2Π → B2Σ−, and X2Π → C2Σ+ inthe region 4710-3480 A. They deduced that CCN is linear in the ground as well asin the excited states. Furthermore they found a Renner-Teller (R-T) interactionfor both X2Π and A2∆ states. Kakimoto et al. [98] reinvestigated the (000)-(000) band of the A2∆-X2Π system through Doppler-limited dye laser excitationspectroscopy and extended this study to the (010)-(010) and (020)-(020) sequenceband [100] in 1984. The experimental R-T splitting measured by Oliphant et al.[143] is ∼ 144 cm−1.

Theoretical work including high level ab initio calculations was performed by Mebeland Kaiser [127], Pd and Chandra [145] and Martin et al. [116] which showedthat CCN(2Π) does not seem to be the most stable isomer but CNC(2Πg) by 3.1kJ/mol [116]; cyclic C2N(2A1) lies 50.7 kJ/mol above CNC, see Fig. 5.2; Mererand Travis also observed CNC [129]. Measurement of laser-induced fluorescencespectra yielding ground state vibrational frequencies at 1923 cm−1 (ν1), 325 cm−1

(ν2), and 1051 cm−1 (ν3) were done by Brazier et al. [23] and Oliphant et al.


Figure 5.2: Calculated geometries of C2N. The bond distances are given in Angstroms,bond angles in degrees for the B3LYP/6-311G∗∗ and CCSD(T)/TZ2P (bold numbers)calculations [116]. The point groups and electronic states are also given.

[143]. Measurements of vibration-rotation spectra were published by Suzuki etal. [173] including hyperfine transitions in the electronic A state by a microwave-optical double resonance technique. Feher et al.[55] measured the ν1 vibration-rotation transitions by infrared absorption spectroscopy using a tunable diodelaser. The first pure rotational spectrum of CCN in the 2Π electronic groundstate was measured by Ohshima and Endo [142] in 1995 by Fourier transformspectroscopy at 35 GHz. They determined the magnetic hyperfine constants a−,b, d, eQq0 and eQq2 and refined the known rotational, centrifugal distortion, andfine structure constants to high precision. Pd et al. [145] and Ohshima et al. [142]gave a nice overview of the field including comprehensive reference tables. The ν2

bending fundamental of the CCN radical in its X2Πr state was studied by Allenet al. [3] using infrared laser magnetic resonance spectroscopy.

C4N Ding at al. [46] suggested that C4N might be the first member among the CnN rad-icals with even n having stable low-lying cyclic isomers with the three-memberedring isomer NC-cCCC only 2.8 kcal/mol higher in energy than the linear CCCCNbut with a larger dipole moment of 0.62 D, (see Fig. 5.3). In this work the firstobservation of the pure rotational spectrum of linear C4N in the 2Π electronicground state (as mentioned in [4]) is presented. Only the Ω = 1

2spin sub levels

were examined. Transitions of C4N with ∆ F = 0,-1 from J=32− 1

2up to J= 9

2− 7

2

were measured and yield precise hyperfine coupling constants due to the nitrogennucleus.

C6N The C6N radical is the largest member among the CnN chains for which the purerotational spectrum was observed. In this work the molecule was found to have aground state with 2Π symmetry as expected and the Ω = 1

2spin sub levels were

examined. Here transitions with ∆ F = -1 from J=92− 7

2to J= 21

2− 19

2were

75

Figure 5.3: Theoretical geometries of C4N. The bond distances are given in Angstromsand the angles in degrees for the B3LYP/6-311G(d) and QCISD/6-311G(d) (in bold)calculations, see [46]. The point groups are written under each structure.

measured.

C8N The effort undertaken during this thesis to measure C8N remained unrewarded. Itwas expected to find a radical in a 2Π ground state with a dipole moment largerthan 0.3 D. The rotational constant B was estimated to be ∼410 MHz.

In contrast to the odd-membered CnN radicals (see Tab. 5.1) where already CN, C3N,and C5N were detected in space none of the even-numbered molecules (see Tab. 5.2) wereobserved so far beside the laboratory. There is no doubt that the detailed informationon the hyperfine structure of C4N and C6N is indispensable for their future astronomicaldetection but the main obstacle is seen in their small ground state dipole moments of0.14 - 0.33 D [144].


Table 5.1: CnN, n odd.

molecule ground dipole exp B value first year Referencesstate moment (predicted) detection

[Debye] [MHz] [astro-source]CN X2Σ+ -1.45 56693.47 astro,visible 1941 Adams [1]

astro,radio 1970 Jefferts [95]lab,mm-µm 1977 Dixon [47]lab,THz 1995 Klisch [103]

C3N X2Σ -2.2 4947.62 astro,mm 1977 Guelin [78]lab 1983 Gottlieb [66]

C5N X2Σ -3.4 1403.08 lab 1997 Endo [99]astro 1998 Guelin [77]

C7N probably 0.8 (583±1) not yet Botschwina [20]X2Π detected

Dipole moments are taken from Pauzat et al. [144]

Table 5.2: CnN, n even.

molecule ground dipole exp B value first year Referencesstate moment (predicted) detection

[Debye] [MHz]C2N X2Π 0.40 11938.58 lab,UV-vis 1965 Merer [128]

lab,µm 1995 Ohshima [142]C4N X2Π 0.14 2422.70 lab,µm 2000 this workC6N X2Π 0.31 873.11 lab,µm 2001 this workC8N X2Π (410±2)∗ not yet

detected

Dipole moments are taken from Pauzat et al. [144] and Pd & Chandra [145]in the case of C2N. * estimated by the author

6 Theoretical Considerations

“Die Uberlegung ist lustig und bestechend; aber ob der Herrgottnicht daruber lacht und mich an der Nase herumgefuhrt hat, daskann ich nicht wissen...”

Albert Einstein, letter to C.Habicht, 1905

Although the history of spectroscopy dates back to the mid 19th century 1 the emissionand absorption of light by atoms and molecules can only be correctly understood ina modern quantum mechanical treatment of the phenomenon. Today the basic theoryof the interaction of particles like atoms, molecules, and radicals with electro-magneticwaves is on wide parts well understood but still not complete. Radicals for instanceare not only difficult to produce in the laboratory but show also special features intheir spectra which make the work with these molecules especially challenging. It isnot simply the rotational and vibrational motions which have to be considered but alsothe electronic and magnetic behavior of these molecules which because of their openshell structure can be very complicate. To demonstrate this a hypothetical energy leveldiagram of an radical in a 2Π ground state is given in Fig. 6.1 including an inlet showing aspectra of several hyperfine components of one rotation transition. Transitions betweenthese energy levels are governed by selection rules and in many cases spin statisticsdetermine the intensity of the measurable lines. As has been seen in Chapter 4 theused FTMW spectrometer has a very high frequency resolution and an extremely highsensitivity so that in many cases even the faintest lines can be detected. For the analysisof a measured spectra all of these lines have to be assigned and labeled by quantumnumbers corresponding to the energy levels. The focus of this chapter is to introducean appropriate Hamiltonian to describe the rotational spectra of linear radicals in a 2Σor 2Π electronic ground state; in particular for the CnN radicals.

The basic references are the standard text books of Bernath, “Spectra of Atoms andMolecules” [12]; Edmonds, “Angular Momentum in Quantum Mechanics” [51]; Gordy &Cook, “Microwave Molecular Spectra” [63]; Herzberg, “Molecular Spectra and Molecular

1In 1859 Kirchoff and Bunsen discovered that each element has its own characteristic spectrum.

78 6 Theoretical Considerations

6B

4B

2B

J=1/23B

J=5/2

5B

J=3/2

J=5/2

5B

J=3/2

e

e

f

f

f

fe

Fine structure

Π1/2

Π3/2

2

Aso

Hund(b) Hund(a)

Hyperfine structure

Π

spectrum

Λ −doubling

Rotation

7B

S=−1/2

S=+1/2

eN=3

N=2

N=1

N=0

fe

F=3/2

F=1/2F=3/2

F=1/2

F=1/2F=5/2F=3/2F=3/2F=1/2F=5/2

frequency

inte

nsity

Figure 6.1: Hypothetical energy level diagram of a 2Π radical including rotational,fine structure, Λ-doubling and hyperfine structure effects. The inlet on the upperright shows an exemplary spectrum of one rotation transition with several hyperfinecomponents.

Structure I & II” [83, 82], “The Spectra and Structure of Simple Free Radicals” [84];Townes & Schawlow, “Microwave Spectroscopy” [181]. Important contributions camealso from papers and works of Brown & Schubert [27], Frosch & Foley [57], Kawaguchiet al. [102], and Klisch [104].

The frequency ν of emission lines correspond to the difference of two energy levels∆E = E ′′ − E ′ = hν. If the energy levels are known all transitions can be computedand frequency predictions can be made. Using the stationary Schrodinger equation theenergies are the eigenvalues of the Hamilton operator H

HΨ = EΨ (6.1)

which reflects the properties of the molecule and also consists of all interactions that mayoccur. Electrons are generally much faster than nuclei and their motion can very oftenbe treated separately. The generalization of this concept leads to the Born-Oppenheimer

6.1 Pure Rotation of Linear Molecules 79

approximation where the wavefunction Ψ of a molecule can be separated in a productof sub-functions each representing a certain motion or property

Ψ ' ΨelΨvibΨrotΨns (6.2)

with Ψel the electron wavefunction, Ψvib and Ψrot the vibrational and rotational wave-function respectively, and Ψns the nuclear spin wavefunction. Each of the sub-functionsis dependent on a certain set of quantum numbers but not necessarily on all, e.g. theelectron wave function Ψel(nLS) only depends on n the principal, L the orbital, andS the electron spin quantum number but not on v the vibrational, J the rotationaland M the magnetic quantum number. Ψ forms a set of basis functions in which theHamiltonian can be written as a sum of sub-Hamiltonians, e.g.

H = Hel + Hvib + Hrot + Hns (6.3)

If only pure rotational transitions are considered the expectation value 〈Hel+Hvib〉 = Eev

can be treated as a constant. In the case of radicals the electrons and nuclei have severalpossibilities to interact with each other or with the overall motion of the molecule whichleads to extra terms in the Hamiltonian. But instead of refining the Hamiltonian 6.3 itis more convenient to re-express the Hamiltonian in the form

H = Hrot + Hf + HΛ,l + Hhfs (6.4)

that is to focus on the structure of the energy levels and to restrict oneself to therelevant terms for the MW- and mm-wave measurements; here Hrot is the rotation term,Hf the fine structure term caused by the electron spin and orbital angular momentum,

HΛ,l representing the Λ- and l-type doubling effect caused by rotation-electron orbit

interaction and effects of the bending vibration respectively, and Hhfs the hyperfinestructure term mainly caused by the nuclear spins and electric quadrupole interactions,see Tab. 6.1. In the subsequent sections the effect of each term of the Hamiltonian 6.4will be explained in more detail with special focus on the radicals relevant for this thesis.

6.1 Pure Rotation of Linear Molecules

As a first approach and if no vibration and electronic effects are considered a linearmolecule can be seen as a rigid rotor where the distances between the nuclei are fixed.The energies resulting out of an end-over-end rotation can be obtained using

Hrot =L2

2I=

h2

8π2IJ(J + 1) (6.5)

with L the angular momentum operator and J the eigenvalues of L obeying L2 = ~J(J + 1).The Hamiltonian can be simplified by introducing the rotational constant BSI = h2

8π2I


Table 6.1: Selection of important interactions and their constants

parameter interaction (IA) Hamilton term/ quantum numbers / energy term / relations

fine structure γ ρ-type doubling HNS = γ N · S (1)

electr. spin - rotation IAN , S

γD distortion constant of γ

λ electr. spin -electr. spin IA HSS = 23λ (3 s2

z − S2)S

Aso electr.spin - orbit IA HSO = Aso (L · S) (1)

S, LAeff Aeff = ASo + γ

Λ and l-type p (= qΛ) Λ-type doubling e.g. EΛ = ±p12(J + 1

2) (2)

doubling rotation - electr. orbit IA for 2Π1/2 in a pure Hund’sR, L case (a)

q l-type doubling El = ±qi 14(vi + 1)J(J + 1)

bending vibration for Π states (2),vi, l

peff peff = p+ 2qpDeff distortion constant of peff

magnetic hf a, a+, a− nuclear spin - orbit IA HIL = aΛI · k (1),I, L a+ = a+ 1

2(b+ c)

a− = a− 12(b+ c)

b, bF Fermi-contact HF = b I · S, bF =b+ c3

(1)

I, S

c, t elect.dipole- nucl.dipole IA H = c (I · k)(S · k) (1)

I, S t = c3

d hyperfine Λ-doubling Hd = d 12(exp(2iφ)I−S−+

(only for 2π1/2-states 6= 0) exp(−2iφ)I+S+) (3)

I, S

CI nuclear spin - rotation IA HCI= CI I · N

I, N

electr. eQqo 1. and 2. order elec.quadr.IA HeQqo

(3)= eQqo(3I

2z − I2)×

(4I(2I − 1))−1

quadrupole eQq2 I HeQq2

(3)= eQq2/(4I(2I − 1))×(exp(2iφ)I2

−+exp(−2iφ)I2

+)1 from Townes & Schawlow [181]; 2 energy term calculated by perturbation theory, the+ sign yields the upper Λ or l -doublet level and the - sign the lower level, see Gordy &Cook [63], energy terms are expressed in MHz, i.e. normalized by 1/h · 10−6 (h Planckconstant); 3 Kawaguchi et al. [102]

6.1 Pure Rotation of Linear Molecules 81

[Joule] to give Hrot = BSIJ(J + 1). It is however customary to express B in MHz (orcm−1) rather than in the SI-units

B =h

8π2I× 10−6 [MHz] . (6.6)

For the rest of this thesis all molecular constants and energies are expressed in MHz (ifnot otherwise indicated). The eigenvalues of Eq. 6.5 can thus be written as

〈Hrot〉 = Erot = BJ(J + 1) (6.7)

so that the energy is expressed in MHz. The molecular spectrum consists of transitionsbetween these energies, i.e.

νE′→E′′ = E ′ − E ′′ = 2BJ ′ (6.8)

with E ′ the upper state energy and E ′′ the lower state energy. However, a molecule is notstrictly a rigid rotor and centrifugal forces have to be considered so that the rotationalenergy is of the form

Erot = BJ(J + 1)−D[J(J + 1)]2 +H[J(J + 1)]3 + ... (6.9)

with D and H the first and second order centrifugal distortion coefficient respectively.Only the centrifugal distortion constant D could be determined for the molecules dis-cussed in this thesis because the FTMW spectrometer has a upper frequency limit of 40GHz which in these cases correspond to low rotational excitations.

6.1.1 Selection Rules

Not every transition between rotational energy levels is allowed. For electronic dipoletransitions with dipole moment µ the transition moment

µ =

∫Ψ′(J ′M ′)∗µΨ′′(J ′′M ′′)dτ (6.10)

determines the intensity and if µ = 0 the transition is “forbidden” or if µ 6= 0 “allowed”with I ∼ |µ2| 2. The transition moment µ depends on the wave functions and thus onthe quantum numbers which determine Ψ′ and Ψ′′ in order that µ 6= 0 or not. Quantumnumbers that yield allowed transitions are determined by so called “selection rules”.There are two types of selection rules: a) the rigorous electric dipole selection rule andb) the approximate electric dipole selection rule. In a) the selection rules are independentof the degree of approximation introduced in the wave function and in b) they are not.

Disregarding the effect of nuclear spin the resulting selection rule for linear moleculesare that only transitions with

∆J = J ′ − J ′′ = ±1 (6.11)

2 Double primes (Ψ”) indicate the lower state and single prime (Ψ’) stands for the upper state .


are allowed 3. This means that measurable transitions should have frequencies of theform

νJ ′←J ′′ = 2BJ ′ −DJ ′3 . (6.12)

6.2 Fine Structure

Any atom or molecule with unpaired electrons reveals some sort of sub-structure to therotational structure. These effects are mainly due to the electronic spin-orbital, spin-spin, and the spin-rotational interaction which are called fine structure interactions. andcan be expressed in the Hamilton term Hf of Eq.6.4 as

Hf = HNS + HSS + HSO . (6.13)

The first term on the right hand side of Eq. 6.13 takes account of the electron spin-molecular rotation interaction

ˆHNS = γN · S (6.14)

which is always present for radicals with an electronic multiplicity of 2S + 1 ≥ 2. Thiseffect can be explained by the electrons participating in the rotation of the moleculeand thus inducing a weak magnetic field which then can interact with the electron spinmoment. In general this induced magnetic field is rather weak and the splitting ofthe HNS energy levels small. On the other hand the spin-rotation interaction is theonly contribution to the fine structure for molecules in a 2Σ state, e.g. C3N and itsisotopomers.

If a molecule has more than one unpaired electron, e.g. O2 or C4, the dominating termof the fine structure is

HSS =2

3λ(3s2

z − S2). (6.15)

This is somehow the corresponding quantum mechanical expression to the classic magneto-statical equations of two interacting dipoles.

If a molecule also has an electronic orbital angular momentum Λ 6= 0 an usually stronginteraction between the spin and the orbital angular momentum occurs:

ˆHSO = ASOS · L (6.16)

Since a molecular electron does not move in a spherically symmetric field (as it is possiblein an atom), torques are exerted on it by the field which in general causes the angularmomentum not to be constant. In a diatomic or linear molecule the fields are symmetricabout the molecular axis and no torque is exerted on a molecular electron about the

3It is also ∆M = 0,±1. Furthermore, there is a (+/-) parity rule found by Laport in 1924. Hereeach energy level is labeled according to its inversion symmetry property with a plus or minus. Thetransition rules are: +↔ −, + = +, −= −. Irrespective of the presence or absence of nuclearspin, this rule is strictly valid for dipole radiation.

6.2 Fine Structure 83

internuclear axis. The component Λ of the electronic angular momentum L is thereforeconstant in this direction (other important angular momenta are listed in Tab. 6.2). Ina Hund’s case (a) the spin S is coupled to the molecular axis and Ω is a good quantumnumber so that the spin-orbit term is separated by the amount ASO in fine structureblocks with Ω = |Λ + S| and Ω = |Λ− S|. The labeling of these blocks are the Ω itself,e.g. a 2Π state has a Ω = 1/2 and a Ω = 3/2 block and a 2∆ state can be split into aΩ = 3/2 and a Ω = 5/2 block. ASO is a constant of a pure electronic interaction andusually much larger than the rotational constant B so that transitions with different Ωusually do not occur in the microwave region due to the big energy gap between the Ω-blocks. This was also the case in this work where only transitions of C4N and C6N weremeasured with ∆Ω = 0. The typical energy ladder BN(N + 1) of rotational transitionsknown from the Hund’s case (b) can not be found in a Hund’s case (a). Instead theenergy levels are widely separated in the two fine structure blocks which both reveal aladder structure due to the rotation.

Only if molecules are considered with Λ ≥ 1 and 2S + 1 ≥ 3 (e.g. in 3Π states) all threeterms of Eq. 6.13 are simultaneously needed. For the C3N isotopes in a 2Σ state onlyHNS had to be considered and also for the 2Π molecules C4N and C6N only one finestructure term (HSO) is needed. The latter is due to a strong correlation between ASO

and γ in a strong Hund’s case (a) so that instead of using ASO and γ separately a newconstant Aeff = ASO + γ can be introduced to describe the structure of these radicals.

6.2.1 Hund’s Coupling Cases a) and b)

Radicals have one or more unpaired electrons and therefore a total spin S 6=0. Inaddition the molecules can have a non vanishing electronic orbital angular momentumand nuclear spins. The rotational energy expression (Eq. 6.9) is not strictly valid forsuch molecules and a systematic way of including the extra angular momenta has tobe found. In 1926 Hund [91] introduced a method to deal with the coupling of angularmomenta which is basically a classification of ideal cases which are very often closelyapproximated by real molecules. The Hund’s coupling cases are often correlated to theelectronic ground states of the radicals which follow the notation

2S+1|Λ| (6.17)

with S the total electron spin and 2S + 1 the electronic multiplicity, here Λ is theelectronic orbital momentum in units of ~, e.g. 0,1,2,3,..., which is represented by thecharacters Σ, Π, ∆, Φ. The used angular momenta are summarized in table Tab. 6.2.The CnN (n odd) radicals have a 2Σ electronic ground state, i.e. Λ = 0 and S = 1/2,and the even membered radicals have a 2Π ground state, i.e. Λ = 1 and S = 1/2.

Hund’s case (a): This case applies if Λ 6= 0 and the electronic spin-orbit (LS) couplingis assumed to be strong, while the coupling of the rotation of the nuclei with the electronicmotion is very weak, i.e. the magnetic field generated by the rotation is small. Ω is thena good quantum number even if R 6= 0, see Fig. 6.2. Ω and the rotational angular


Table 6.2: Angular momenta and their projections

R angular momentum of the end-over-end rotation of the moleculeL resultant electronic orbital angular momentumΛ component (projection) of L along the molecular axis Λ = |ML| = 0, 1, 2, ..., LS resultant electronic spinΣ projection of S along the molecular axis, Σ = S, S − 1, ...,−SN = R + L angular momentum without elect. spinJ total angular momentum without nuclear spinΩ = |Λ + Σ| resultant angular momentum along molecular axisI nuclear spinF total angular momentum (with nuclear spin)

R J

L S

Λ Σ Λ

L

N RJ

J

N

.

case a) case b) case b), molecule in stateΣ

Ω

SS

.

Figure 6.2: Vector diagram of Hund’s coupling cases a) and b). On the left: Hund’scase (a) with only the total angular momentum J fixed in space. The nutation of theinternuclear axis about J is indicated by the blue ellipse; the precession of L and Sabout the figure axis are assumed to be much faster (green dash-dotted ellipses). Inthe middle: Hund’s case(b) in the general case Λ 6= 0. Also here only the total angularmomentum J is fixed in space. The precision of N and S about J (green ellipse) ismuch slower than the nutation of the internuclear axis about N (dash-dotted blueline). On the right: Hund’s case(b) with Λ = 0.

6.2 Fine Structure 85

momentum R result in an angular momentum J . A criterium for a molecule to be in aHund’s case (a) is (Gordy & Cook [63])

2JB |ΛASO| . (6.18)

Hund’s case (b): This case can be best explained in the most prominent case wereΛ = 0 but S 6= 0, i.e. Σ states almost always can be expressed in a Hund’s case (b).Because there is no orbital field the spin moment can not couple to the internuclearaxis. The strongest influence to the spin moment comes from the weak magnetic fieldgenerated by the end-over-end rotation of the molecule which causes S to couple with N(which is the same as R because Λ=0). In some cases it can happen that light molecules,e.g. OH, in a high rotational state J generate a large magnetic field by rotation that isstrong enough that the electronic spin S is rather resolved in direction of J than to theinternuclear axis even for Λ 6= 0. In general the Hund’s case (b) is defined as the idealcase where S is coupled to N to form J as seen in Fig. 6.2.

Examples of the more complicate cases of the coupling of one or two additional nuclearspins are discussed in Chapter 7.

Selection Rules

The distinction in a Hund’s case (a) or (b) involves the usage of different “good” quantumnumbers, i.e. J and Ω or N in which the selection rules can be expressed.

In the Hund’s case (a) the quantum number Σ is a good quantum number and theselection rule

∆Σ = 0 (6.19)

is valid. This rule holds for combinations of the sets of rotational levels of variousmultiplet components. The usage of Ω is more common and thus the selection rules forlinear molecules 4 are

∆J = ±1 and ∆Ω = 0,±1 (6.20)

In the microwave region there are mainly transitions with ∆Ω = 0 to observe (becauseof the higher energies involved in the other types of transitions) but this is not due to aforbiddance of this transitions.

In the Hund’s case (b) the selection rule is

∆J = ±1 and ∆N = ±1 . (6.21)

In the more complicate case where the molecule has atoms with nuclear spin, e.g. I1and I2, the total angular momentum is not J but

F = J + I1 + I2 (6.22)

4and considering only cases of pure rotation


Now the analog of Eq. 6.11 holds rigorously for dipole radiation:

∆F = 0,±1 with F = 0 = F = 0 (6.23)

Because the interaction with J and the nuclear spin is usually very weak the rule 6.11for the quantum number J is still very strong even though not rigorous.

The selection rules 6.19 and 6.21 for N and S do not hold in intermediate couplingcases between (a) and (b). A nicely summarized presentation of this topic including theselection rules for magnetic dipole and electric quadrupole radiation is given in Herzberg[84].

6.2.2 Λ-type Doubling, and l-type Doubling

Λ-type doubling. For radicals with an orbital angular momentum Λ 6= 0 the finestructure energy terms split in doublet states labeled with e and f with reference tothe parity of the wave function Ψ. At this stage of development these doublet stateswould be exactly degenerate but the influence of the molecular rotation on the electronicorbital momentum lifts the degeneracy. This can be interpreted as a decoupling fromthe electron orbital angular momentum from the internuclear axis 5. The bigger theΛ-type splitting the stronger the coupling of L towards R so that the molecule takesan intermediate state between Hund’s case (a) and Hund’s case (d) which would be theextreme case of a L-R vector coupling scheme. The Λ-doubling splitting is significantlysmaller than the fine structure splitting. Perturbation theoretical considerations areleading to the following proportionalities (Landau-Lifschitz [109])

∆EΛ ∼ (me/M)2Λ (6.24)

with me the mass of the electron and M of the molecule. The ratio of masses (me/M)1 and with Λ > 1 the chances of a measurable splitting of the Λ terms decrease rapidly sothat radicals with a ∆ or Φ electronic ground state are of nearly no interest concerningthis symmetry effect. On the other hand the Π states can have quite large splittings. InTable 6.3 the approximate energy Λ-type splitting is given for 2Π states in pure Hund’scase (a) and (b).

In the case of C4N and C6N it was not the Λ-type doubling constant which was fittedbut an effective Λ-type doubling constant peff , with peff = p+ 2q 6 which also includesq the l-type doubling constant.

l-type doubling. Polyatomic linear molecules have vibrational bending modes νi whichcan be excited. If a degenerate bending mode is excited an additional angular momentumpz = l~ about the internuclear axis with l = vi, vi− 2, vi− 4, ...,−vi has to be taken intoaccount and the rotational energy can be written as

Erot = B[J(J + 1)− l2], (6.25)

5In a classical picture this would be interpreted as an effect of the Coriolis force.6p is used here as the Λ-doubling constant irrespective of the applied Hund’s case.

6.3 Hyperfine Structure 87

Table 6.3: Theoretical Λ-type doubling for 2Π state, Gordy&Cook [63].

∆EHund’s splitting of levels approx. theorcase (approx.) coupling constant

(a) Ω = 12

pa(J + 12) pa = 4ASOB

νe

Ω = 32

pb(J2 − 14)(J + 3

2) pb = 2pa

(B

ASO

)2

= 8B3

νeASO

(b) pN(N + 1)

νe represents the transition frequency between the groundlevel and the lowest Σ state; all constants are in frequencyunits.

with J the total angular momentum including l, so that J = |l|, |l|+ 1, |l|+ 2, ... . TheCoriolis coupling force which is proportional to v × ω between the vibrational motion vand the angular rotation motion ω in it’s orthogonal plane, lifts the ±l degeneracy ofEq. 6.25 and a doublet splitting of the rotational lines is produced. For |l| = 1, i.e. avibrational Π state, the l-type splitting is approximately

∆E|l|=1 = q1

2(vi + 1)J(J + 1) (6.26)

where vi is the vibrational quantum number of the ith degenerate bending mode and qthe vibration-rotational coupling constant. In the first excited state the energy splittingsimplifies to

∆E|l|=1 = qJ(J + 1) (6.27)

In most cases q can be approximated to be (Gordy & Cook [63])

q ≈ 2.6B2

e

νbend

(6.28)

with Be the equilibrium rotational constant and νbend the degenerate bending frequency.

6.3 Hyperfine Structure

If a molecule has one or more nuclear spins the spectra will expose a further splittingof the energy levels due to the interaction of the nuclear spins with the other angularmomenta of the molecule. This is most commonly called the hyperfine structure becauseit is usually much smaller than the above discussed fine structure. However, in somecases the substructure induced by the nuclear magnetic moment can be of the sameorder or even larger than the electric fine structure interactions, e.g. the Fermi-contactinteraction in the case of 13CCCN is larger than the electronic spin-rotation interaction.


For the hyperfine transitions different kinds of electromagnetic radiation can be involved.A photon always carries an angular momentum of l~ with l=1,2,3,... which correspondsto a classical radiation field of a 2l-pole. During an emission or an absorption processnot only the overall angular momentum but also the parity has to be conserved in thephoton-molecule system. The transformation properties (~r) → (−~r) of electric andmagnetic multi-pole radiation are not the same, i.e electric multi-pole radiation has a(−1)l parity whereas magnetic multi-pole radiation has a (−1)l+1 parity. A transitionbetween two molecular states with the parity π1 and π2 can only occur if

π1 = (−1)lπ2, for El-radiation

π1 = (−1)l+1π2, for Ml-radiation

(6.29)

is fulfilled. For example: In the Hund’s case (a) the selection rule is ∆J = ±1 and witha nuclear spin ∆F = 0,±1 so that only magnetic dipole (l = 1) and electric quadrupole(l = 2) are allowed and electric dipole and magnetic quadrupole transitions are forbidden[104]. A molecule containing an atom with a quadrupole moment, e.g. 14N in C4N or 13Cin CC13CN, will always have a hyperfine structure in their spectrum. If the moleculehas an open shell structure with S 6= 0 the magnetic dipole (hfs) transitions usuallydominate upon the electric quadrupole transitions in terms of the line intensities. TheHamilton term Hhfs of Eq. 6.4 can be written as

Hhfs = Hmag,hfs + HQ (6.30)

with Hmag,hfs the magnetic interaction term and HQ the electric quadrupole term.

6.3.1 Magnetic Hyperfine Structure

The magnetic hyperfine structure Hamiltonian as it is used in this thesis can be writtenas

Hmag,hfs = HIL + HF + HIS + Hd (6.31)

with HIL the nuclear spin- electronic orbit interaction term, HF the Fermi contact term,HIS the nuclear spin - electronic spin interaction (or short: dipole-dipole interaction),and Hd the hyperfine Λ-doubling term. In general the Hamiltonian for an interactionbetween a magnetic dipole and a magnetic field is of the form H = µ · Hm where Hm

is the magnetic field and µ the dipole, i.e. µI = gIµnI the magnetic spin moment withgI the dimensionless gyromagnetic ratio (g-factor), µn the nuclear magneton, and I thenuclear spin. The magnetic field Hm can be caused by the electronic orbital or spinangular momentum and depending on the direction of the I,L, and S the Hamiltonequation can be written as

HIL = aΛI · k (6.32)

HF = bI · S (6.33)

HIS = c(I · k)(S · k) (6.34)


with k a unit vector along the molecular axis. The expressions Eq. 6.32 - 6.34 applyaccurately only when Λ is a “good” quantum number and holds for Hund’s case (a) and(b). The introduced constants a, b, and c are

a =2µBµI

I

(1

r3

)U

(6.35)

b =2µBµI

I

(8π

3Ψ2(0)− 3 cos2 θ − 1

2r3

)U

(6.36)

c =3µBµI

I

(3 cos2 θ − 1

r3

)U

(6.37)

with θ the angle between the molecular axis and r the radius from the nucleus to theelectron. Ψ(0) is the electron wavefunction at the interacting nucleus. (. . .)U denotesthat the mean value is taken over the unpaired electron. The Eq. 6.32 - 6.34 apply toeach electron in the molecule. It is evident that for electrons in the inner shells and forthose who are paired the terms nearly cancel out each other so that in most cases onlythe unpaired electrons have to be considered.

Nuclear spin - electronic orbit interaction. The quantity a refers only to electronswith an orbital angular momentum. According to the Biot-Savart law the unpairedelectrons with L 6= 0 generate a magnetic field at the nucleus which interacts with thenucleus magnetic moment.

Fermi contact interaction. It is common to use the “Fermi contact” constant bFinstead of b which is defined as bF = b+ c/3 with

bF =2µBµI

I

(8π

3Ψ2(0)

)U

. (6.38)

(Ψ2(0))U is the probability to find the unpaired electron at the nucleus which for anelectron in an p atomic orbit is negligibly small but for a s-type orbit can be quite large.Hence, whenever there is a appreciable amount of s character to the wavefunction ofan unpaired electron the magnetic hyperfine interaction which is proportional to Ψ2(0),may be expected to dominate, i.e. bF > a.

Dipole-Dipole interaction.Because of the (cos2 θ)U angular dependence this interaction cancels for a sphericalelectron density distribution, e.g. s-type orbitals.

Hyperfine Λ-doubling.The magnetic hyperfine interactions discussed so far are all identical for the two energylevels of a Λ-doublet. For a Π state a certain type of electron spin-nuclear spin interactionresults in a different structure for the Λ doublet. Qualitatively this can be explained bestin a Hund’s case (b). The electron wave function has a eiφ ± e−iφ angular dependencewith φ the angle of rotation about the internuclear axis. The probability distributionΨ2 of the electrons is therfore proportional to sin2 φ and cos2 φ. For the lower Λ-doubletstate with a sin2 φ distribution, the field of the electron at the nucleus is parallel to I and


RR

doublet statedoublet state

molecularaxis

rotation ofmolecule

molecularaxis

rotation ofmolecule

φ

s

s

s

I

s

I

lower upperΛ−Λ−

Figure 6.3: Unpaired electron distribution for a 2Π state in Hund’s case (b) for the twoΛ-doublet states.

for the upper state it is directed oppositely to I, see Fig. 6.3. This causes the spin-spininteraction energy to be different for the two Λ states, i.e. the hf Λ-doubling is paritydepending.

For a 2Π state in a Hund’s case (a) the splitting due to the hyperfine Λ-doubling is

∆Ed = ±d(J + 1

2)

2J(J + 1)I · J (6.39)

for the 2Π1/2 state and ∆E = 0 for the 2Π3/2 state. The upper sign in Eq. 6.39 appliesto the upper Λ-doublet state. d is defined as

d =3µBµI

I

(sin2 θ

r3

)U

(6.40)

In all molecules with a nuclear spin there is an interaction between the nuclear mag-netic moment and the rotation of the molecule which can be calculated by Van Vleck-transformations of higher order terms and usually results in a small splitting which isexpressed in the constant CI . This type of interaction was not considered in this workfor the CnN radicals.

Useful references for the definition of the magnetic interaction constants are Frosch &Foley [57] and Steimle et al. [170].


6.3.2 The Electric Quadrupole Interaction

There can also be a hyperfine structure due to electric charge distribution in the nucleus.If the nucleus is not assumed to be a point charge the charge distribution has to beconsidered which may be in motion and produces magnetic fields which gives the nucleusan angular momentum in quantities of I~ (I is an integer or half integer). If V is theelectrostatic potential produced at the nuclear center of mass by all electronic chargesin the atom the electrostatic energy of a nuclear charge ∆q = ρ(x, y, z)∆x∆y∆z, with ρthe nuclear charge density, is ∆W (x, y, z) = ∆q(x, y, z)V (x, y, z). Quantum mechanicalconsiderations on the multi-pole expansion of the electrostatic potential V

V0 + x∂V0

∂x+ y

∂V0

∂y+ z

∂V0

∂z+

1

2x2∂

2V0

∂x2+

1

2y2∂

2V0

∂y2+

1

2z2∂

2V0

∂z2+ xy

∂2V0

∂x∂y+ ... (6.41)

reveal that the nucleus normally has no inherent dipole moment and that also all termsinvolving odd powers of the coordinates will be zero ([181],p.132) thus leaving only aterm which is independed of the nuclear size or shape (i.e. ZeV , with Z= atomic number, e=proton charge) and a term associated with the quadrupole moment of the nucleus.The energy due to the electric quadrupole moment is than

WQ = −1

6Q : ∇E (6.42)

which is the inner product between the quadrupole moment dyadic

Q =

∫(3~r ⊗ ~r − r21) ρ d(3)~r (6.43)

and the gradient of the electric field due to the electrons. Using a coordinate systemwith z in the direction of the nuclear spin all non diagonal terms of Q vanish and theentire quadrupole moment can be expressed in terms of one constant

Q =1

e

∫(3z2 − r2) dx dy dz (6.44)

called “the” nuclear quadrupole moment [181]. For nuclei with a spherical charge dis-tribution Q is zero and the quadrupole moment can thus be seen as a measure of thedeviation from a spherical shape, i.e. if the nuclear charge distribution ρ is somewhatelongated along z then Q is positive; if it is flattened along the nuclear axis, Q is neg-ative. All isotopes with I=0 or 1/2 have a quadrupole moment equal zero because oftheir spherical symmetry. From Eq. 6.42 it is clear that the energy also depends on thegradient of the electric field at the nucleus. In a linear molecule the charge distribution issymmetric around the molecular axis but varies along these axis so that the gradient ofthe electric field depends on the position within the molecule. Nitrogen 14N with I=1/2has a Q of +0.02 ·1024 cm2 [181] but the electric quadrupole energy from C2N is differentfrom that of CNC because of the different ∇E experienced by the nitrogen nucleus. In aquantum mechanical treatment the Hamiltonian can be build out of Eq. 6.42 with Q and


∇E replaced by operators Q and ∇E. Because 32(II + II) − I21 has the same angular

dependence with respect to nuclear orientation as 3~r ⊗ ~r − r21, Q can be expressed as

Q =eQ

I(2I − 1)

[3

2(II + II)− I21

](6.45)

and ∇E can be shown to be 7

∇E =q

J(2J − 1)

[3

2(JJ + JJ)− J21

](6.46)

with q = (JJ |∂2V∂z2 |JJ) depending on J . The energies of the Hamiltonian HQ = −1

6Q :

∇E are therefore of the form

E = −eQq f(J,Ω, I, F ) (6.47)

where eQq is called the quadrupole coupling constant and f(J,Ω, I, F ) a function 8 whichinvolves the coupling of the angular momenta. In the tensor notation the quadrupoleinteraction can be written as

HQ =61/2eQq0

4I(2I − 1)T 2

0 (I , I)− eQq24I(2I − 1)

∑q=±1

e2iqΦT 22q(I , I) (6.48)

with eQq0 and eQq2 the two electric quadrupole parameters and T 2(I , I) a standard2nd-rank spherical tensor with components expressed in the molecule-fixed axis system,see [27]. It is

eQq2 = −3e2Q

(sin2 θ

r3

)T

(6.49)

with the index T indicating that the mean value is taken over the total (i.e. the pairedand unpaired) electrons, see Ohshima et al. [141]. This equation (6.49) together withEq. 6.37 enables an estimation of the non-axial distribution of the wavefunctions. Thematrix elements of HQ in a Hund’s case (a) are discussed in 6.4.1 in more detail.

7Eq. 6.46 is only valid if J is a “good” quantum number.8Under certain assumptions f is the Casimir function but in general Eq. 6.48 has to be applied.

6.4 Matrix Representation of the Hamiltonian 93

6.4 Matrix Representation of the Hamiltonian

For non-singlet states even the rotational Hamiltonian Hrot = BR2 can be significantlymore complicate than in the singlet case because only with the usage of “good” quantumnumbers is the calculation of the energy expression meaningful. If an electronic orbitalangular momentum and an spin is present the Hamiltonian can be written as

Hrot = B(J − L− S)2 . (6.50)

On way to proceed is to re-express Eq. 6.50 as

Hrot = B(J − J2z )2 +B(S − S2

z )2 +B(L− L2

z)2

−B(J+L− + J−L+)2 −B(J+S− + J−S+)2 +B(L+S− + L−S+)2 (6.51)

using J+, J− as lowering (+) and raising (-) operators respectively and L+, L−, S+,S− as raising (+) and lowering (-) operators in the common sense of definition. WithEq. 6.51 it is already evident that in some cases, e.g. 2Π states, a mixing of the statesis necessary to build the correct Hamiltonian. As an example the basis set of a 2Π stateis given here as

|2Π3/2〉, |2Π1/2〉, |2Π−1/2〉, |2Π−3/2〉, (6.52)

which can be written as e/f parity basis functions:

|2Π3/2e/f〉 =|2Π3/2〉 ± |2Π−3/2〉√

2, |2Π1/2e/f〉 =

|2Π1/2〉 ± |2Π−1/2〉√2

(6.53)

with (+) referring to the e parity and (-) referring to the f parity. The rotationalHamiltonian can now be expressed as

|2Π3/2e/f〉 |2Π1/2e/f〉

H =

B[(J + 1/2)2 − 1] −B[(J + 1/2)2 − 1]1/2

−B[(J + 1/2)2 − 1]1/2 B[(J + 1/2)2 + 1]

(6.54)

Every Hamiltonian term in Eq. 6.4 can be written in such a matrix form. For 2Σ statesthe off-diagonal terms in the matrix are very often zero and a matrix representation isnot necessary in such a case but for 2Π states the situation is completely different.

6.4.1 The Matrix Representation of the 2Π-Radicals

The fit of the 2Π radicals C4N and C6N proved to be not as easy as expected and it istherefore useful to examine the 2Π matrix elements in more detail. The matrix elementsof the rotation, spin-orbit, Λ-doubling and magnetic hyperfine interaction of 2Π statesin the Hund’s case (a) are calculated in Brown et al. [26]. The most influential term of


Table 6.4: Matrix with Spin-Orbit, Rotation and Λ-doubling

|2Π±3/2JIF 〉 |2Π±1/2JIF 〉

〈2Π±3/2JIF |...... 12A + AD[(J + 1

2)2 − 1] −B − 12γ − 1

2γD(Z + 2)− 2D(J + 12)2

−12γDZ ∓1

2q(J + 12)∓ 1

4(pD + 2qD)(J + 12)

+B[(J + 12)2 − 1]−DZ(Z + 1) ∓1

2qD(J + 12)3Z1/2

∓12qD(J − 1

2)(J + 12)(J + 3

2)

〈2Π±1/2JIF |...... (Hermitian) −12A + AD(Z + 2)−γ − γD

12(3Z + 4)

+B[(J + 12)2 + 1]−D(Z2 + 5Z + 4)

∓12(p + 2q)(J + 1

2)∓1

2(pD + 2qD)(J + 12)(Z + 2)

∓+ 12qD(J + 1

2)Z

with Z(J)= (J-12)(J+3

2) = (J+12)2 -1

Upper and lower sign choice refer to e and f levels respectively.

the Hamiltonian is one containing the rotational, spin-orbit, and Λ-doubling interactionand the matrix representation is given in Tab. 6.4.

As an example and because of the importance in the fit of the C4N radical the matrixelements of the electric quadrupole interaction is given here.

HQ of Eq. 6.48 in the Hund’s case (a) can be expressed using 3j- and 6j-Symbols 9:

〈ηΛ′SΣJ ′Ω′IF |HQ|ηΛSΣJΩIF 〉 =1

4

(I 2 I−I 0 I

)−1

(−)J+I+F

F J I2 I J ′

×[(2J ′ + 1)(2J + 1)]1/2

[δΛ′ΛδΩ′ΩeQq0(−)J ′−Ω

(J ′ 2 J−Ω 0 Ω

)+

∑q=±2

δΛ′,Λ∓2(6)1/2eQq2(−)J ′−Ω′(

J ′ 2 J−Ω′ −q Ω

)](6.55)

This formula was directly used in the fit program to analyze the C4N and C6N spectra.A disadvantage of this representation is that it is not very intuitive and it is thereforedesirable to express HQ in a matrix of the form 〈2Π±Ω′JIF |HQ|2Π±ΩJIF 〉 as it can beseen in Tab. 6.5. The derivation is given in the Appendix B. In short: 2Π states have Ωor Ω′ values of 3/2 or 1/2 so that Ω’=Ω± 1. For the energy the ∆J = 0 elements were

9see Brown & Schubert [27], Eq. 2

6.4 Matrix Representation of the Hamiltonian 95

Table 6.5: Matrix with electr. hf interaction

|2Π±3/2JIF 〉 |2Π±1/2JIF 〉

〈2Π±3/2JIF |...... eQq0

2 K(F )[274 − J(J + 1)] ± eQq2

4 K(F )[(J2 − 14)(J + 1

2)(J + 32)]1/2

〈2Π±1/2JIF |...... (Hermitian) eQq0

2 K(F )[34 − J(J + 1)]

with K(F ) = 3R(F )[R(F )+1]−4J(J+1)I(I+1)I(2I−1)(2J+3)(2J+2)(2J)(2J−1)

R(F ) = F (F + 1)− J(J + 1)− I(I + 1)Matrix elements in non-parity conserving basis derived by Tom C. Killian and Guido Fuchsfrom Brown & Schubert, [27].

calculated using the basis functions 10

|2Π±|Ω|, J〉 =|Λ,Σ, J,Ω〉 ± | − Λ,−Σ, J,−Ω〉√

2(6.56)

with ± referring to the e/f parity respectively and following the convention of Brown etal. [25]. It was necessary to include the off-diagonal term eQq2 in the analysis of theC4N spectrum to achieve a good fit, see Chapter 7.1.

Another problem appeared when fitting the C6N spectrum. In this case a correlationbetween the magnetic hfs constant a− and eQq0 seemed to jeopardize the analysis. Thematrix for the magnetic hfs is given in Tab. 6.6 in terms of the constants a, bF and cas it appeared in Brown et al. [26]. If only transitions between one of the Π3/2 or Π1/2

states are measured it is advantageous to use a transformation (a,bF ,c) → (a+,a−,b)which separates the magnetic hf constants for the Ω=3/2 and Ω=1/2 states: a

bFc

→ a+

a−b

=

a+ 12(b+ c)

a− 12(b+ c)b

=

a+ 12bF + 1

3c

a− 12bF − 1

3c

bF − c3

The new matrix is given in Tab. 6.7 and it can be seen that a+ is the interaction constantfor Π3/2 states only and a− and d for Π1/2 states only. b can be determined using Π3/2 orΠ1/2 transitions either. The analysis of the C6N spectrum was based on this Hamiltonianand includes only the a− constant, see Chapter 7.2.

Some other than the here mentioned approach from Brown & Schubert [27, 26, 24] tothe theoretical study of the 2Π Hamiltonian are made by Frosch & Foley [57], Kawaguchiet al. [102], Davies et al. [42].

10The matrix elements are in a non parity conserving basis.


Table 6.6: Matrix with magnetic hyperfine interaction

|2Π±3/2JIF 〉 |2Π±1/2JIF 〉

〈2Π±3/2JIF |......R(F )

2J(J+1)[32a+ 3

4bF + 1

2c] R(F )

[(J− 12)(J+ 3

2)]1/2

2J(J+1)[12bF − 1

6c]

〈2Π±1/2JIF |...... (Hermitian) R(F )2J(J+1)

[12a− 1

4bF − 1

6c∓ 1

2d(J + 1

2)]

with R(F ) = F (F + 1)− J(J + 1)− I(I + 1)

Table 6.7: Transformed matrix with magnetic hyperfine interaction

|2Π±3/2JIF 〉 |2Π±1/2JIF 〉

〈2Π±3/2JIF |......R(F )

2J(J+1)32a+ R(F )

[(J− 12)(J+ 3

2)]1/2

2J(J+1)12b

〈2Π±1/2JIF |...... (Hermitian) R(F )2J(J+1)

12[a− ∓ d(J + 1

2)]

with R(F ) = F (F + 1)− J(J + 1)− I(I + 1)

7 Measurements and Analysis

“ The great tragedy of Science - the slaying of a beautiful hypothesisby an ugly fact. ”

Thomas H. Huxley (1825 - 1895)

The production of the C3N isotopomers and the C4N, C6N production has been alreadydescribed in Chapter 4.1. In short: For speed and convenience, all of the C3N isotopicmeasurements were made with enriched samples; with the 13C-HCCH sample. Lineintensities were typically 2-3 times stronger than those of the same lines observed innatural abundance. When the 13C-methylcyanide sample was employed instead, linesof CC13CN were three times more intense than those observed with 13C-acetylene 1. Inthis chapter the results of the measurements are presented and an interpretation of thedata is given.

CCC15N is discussed first because of its relative simple spectrum which is in fairly goodagreement with the theoretical predictions, i.e. the b(15N) and c(15N) values, derivedfrom the CCC14N measurements done by Gottlieb et al. [66] but which had not beenresolved in the CCC15N measurements of McCarthy et al. [121] so that only the constantsB, D and γ were known.

CCC15N as well as the 13C mono-substituted C3N isotopomers have a 2Σ ground statebut in the case of the 13C isotopic species of C3N two nuclear spins have to be consideredwhich causes an extra splitting of the energy levels compared to that of the CCC15Nspecies.

Only the B, D, γ and bF (13C) values were known for the 13CCCN, C13CCN, and CC13CNspecies from millimeter-wave measurements done by McCarthy et al. [121]. In the samework the c(13C) values were not determinable and set to zero. Also the bF (14N) and

1Short summary: 9 GHz antenna set at room temperature, A/D delay around 16 or 20 µs, dischargevoltage of 1100 - 1250 V, general valve opening time 300 - 480 µs, gas entrance pressure of 2.5 atm,total flow rate of 30 - 32 sccm with 9 sccm Ne, 1.25 sccm 0.18 % HC3N in Ne and 0.5 sccm 1.5% H13CCH (statistical mixture), for CCC15N it was 0.5 sccm 5% CH3C15N, 200 - 5000 shots wereintegrated for one spectrum. A “short-nozzle” with a “normal” tip was used.

98 7 Measurements and Analysis

Figure 7.1: Measured CCC15N transition with Zeeman splitting

c(14N) constants were not fitted but assumed to be close to the values for the CCCNradical which were bF (14N)=-1.20(3)MHz and c(14N)=2.84(9)MHz. In this work allrelevant magnetic hyperfine constants could be fitted plus the electrical quadrupoleconstant due to the 14N nucleus.

C4N and C6N do not have a 2Σ but a 2Π electronic ground state and had therefore to betreated separately with a computer program written by John Brown, see Chapter 6.4.1.Both radicals are detected in the laboratory for the first time and no spectroscopic datawere available for this molecules sofar.

7.1 The C3N Mono-Substituted Isotopomers

7.1.1 CCC15N

CCC15N was measured in the 9.5 - 38.4 GHz region corresponding to rotational tran-sitions from J = 1 → 0 up to J = 4 → 3 respectively, see Table 7.1. The analysis

7.1 The C3N Mono-Substituted Isotopomers 99

Table 7.1: Measured Rotational Transitions of CCC15N in the X2Σ+ StateFrequencya O − C b Transition

(MHz) (kHz) N’ J’ F’ N J F

9593.486 −4 1 3/2 2 0 1/2 119195.842 0 2 5/2 3 1 3/2 219195.863 1 2 5/2 2 1 3/2 119213.911 4 2 3/2 2 1 1/2 119243.521 0 2 3/2 1 1 3/2 128798.215 1 3 7/2 4 2 5/2 328798.215 −1 3 7/2 3 2 5/2 228816.243 −2 3 5/2 2 2 3/2 128816.350 −3 3 5/2 3 2 3/2 238400.553 2 4 9/2 5 3 7/2 438400.553 4 4 9/2 4 3 7/2 3a Estimated experimental uncertainties (1σ) are 2 kHz.b Calculated frequencies derived from the best fit constants in Tab. 7.2

was done with a standard Hamiltonian for a linear molecule in a 2Σ electronic groundstate similar to Eq. 7.8 and 7.9 for the 13C isotopic species but with one nuclear spin.The angular momenta coupling scheme was J = N + S and F = J + I(15N). 11 lineswere sufficient to fit 6 molecular constants but for the final fit also the mm-data fromMcCarthy et al. [121] were included, see Table 7.2. Radicals are paramagnetic and reacton outer magnetic fields like the Earth’s magnetic field as can be seen in the spectrumof CCC15N Fig. 7.1 where the J 3/2→ 1/2, F 2→1 transition is split due to the Zeemaneffect. CCC15N is the only one of the isotopic species of C3N which shows a notableZeeman splitting of 20-30 kHz in its spectrum. Helmholtz coils were mounted aroundthe FTMW cavity to cancel outer magnetic fields but was not used during the measure-ments for this work. Unlike the cases of CCCN or the 13C isotopic C3N species therehas to be no electrical quadrupole to be considered for CCC15N.

The bF (14N) and c(14N) values from the mm-measurements [121] could be used to esti-mate the values for the 15N isotope (see Townes & Schawlow, p.196 [181]):

bF ∼µI

I⇒ bF (14N)

bF (15N)=

µI(14N)I(14N)

µI(15N)I(15N)

=µI(

14N)

µI(15N)

I(15N)

I(14N)= −0.7131 (7.1)

so that bF (15N)est. ≈ 1.68 MHz and c(15N)est. ≈ -3.98 MHz using µI(14N)= 0.4036,

µI(15N)= -0.2830, I(14N)=1, and I(15N)=1/2. This prediction was good enough to find

the actual transition lines within 1-2 MHz.

CCC15N obeys Hund’s case (bβJ) which can be seen using the formulas in Townes &Schawlow (p.199) were an estimation of the magnitude for the hyperfine splitting forthe Hund case (bβJ) is given. In the case of a molecule in a 2Σ ground state the formula


Table 7.2: Molecular Constants of CCC15N (in MHz).Data reduction was done by using the Pickett-program [153].

Constanta this workb mm-data onlyc recommendedd

valuesB 4801.2277(5) 4801.2264(4) 4801.2267(1)D ×10−3 0.76(2) 0.7062(3) 0.7064(1)γ −18.218(3) −18.17(4) −18.208(1)γD ×10−3 0.6(2) −0.02(2) ...bF (15N) 1.87(1) 3(17) 1.883(9)c(15N) −4.26(3) 12.(73) −4.30(3)w-rmse 0.43 0.42 0.97a Uncertainties (in parentheses) are (1σ) in the last significant digit.b 11 lines were used, see Tab. 7.1.The uncertainties of the lines is estimated to be 2 kHz.

c 28 lines from [121] were used.The uncertainties of the lines are estimated to be between 22-86 kHz.

d Total fit with all measured 39 lines.e w-rms weighted rms, i.e. rms normalized with uncertainties of measured lines.

(8-10)2 can be reduced to (J=N-1/2):

WJ=N−1/2 =

ξ︷︸︸︷[− b

2N + 1+

c

(2N − 1)(2N + 1)

]I · J (7.2)

with I · J = 12(F (F + 1)− J(J + 1)− I(I + 1)). ∆F=1 with J=J’ and N=N’ determines

the hyperfine splitting ∆Whfs:

∆Whfs = ξ

[1

2(F ′(F ′ + 1)− ...)− 1

2(F (F + 1)− ...)

]=

1

2ξ [(F + 1)(F + 2)− F (F + 1)]

= ξ(F + 1) (7.3)

With I(15N)=1/2 and F=(N-1/2)-1/2 we obtain

∆WJ=N−1/2 = ξN

= − N

2N + 1· b+

N

(2N − 1)(2N + 1)· c, N 6= 0(!) (7.4)

2Townes & Schawlow, p.199


In the case of CCC15N b=bF -c/3=3.3154 MHz so that

∆WJ=N−1/2(N = 1, F = 0→ 1) =1

3(c− b) = −2.54MHz

∆WJ=N−1/2(N = 2, F = 1→ 2) =2

5(1

3c− b) = −1.90MHz

and ...

N →∞ : ∆WJ=N−1/2 = − b2

= −1.66MHz (7.5)

The corresponding formulae for Eq. 7.4 for J=N+1/2 is

∆WJ=N+1/2,hfs =

[b

2N + 1+

c

(2N + 1)(2N + 3)

](F + 1), with F=J-1/2

=N + 1

2N + 1· b+

N + 1

(2N + 1)(2N + 3)· c (7.6)

and thus

∆WJ=N+1/2(N = 0, F = 0→ 1) = b+1

3c = bF = 1.883MHz

∆WJ=N+1/2(N = 1, F = 1→ 2) =2

3(b+

1

5c) = 1.637MHz

and ...

N →∞ : ∆WJ=N+1/2 =b

2= 1.66MHz (7.7)

These estimations are in fairly good agreement with the measurements, i.e. the energyoutput-file of the fit program, and indicates that we have a nearly pure Hund case (bβJ).The energy level of CCC15N is given in Fig. 7.2.


b =1.88 MHzF

N=2

N=3

Rotation Fine−Structure

10

30

50

60

20

0

27.3 MHz

γ =−18.2 MHz

N=1

J=1/2

J=1/2

J=3/2

γ (N+1/2)

J=5/2

J=3/2

splitting x 183 splitting x 13.7EGHz

CCC N15 (X Σ )2

N=0 1.883 MHz

Hyperfine−Structure

1.888 MHz

1.619 MHz

2.518 MHz

1.649 MHz

F=1

F=0

F=1

F=2

F=1

F=0

F=2

F=3

F=2

F=1

c=−4.30 MHz

b F

.

.

.

.

Figure 7.2: Energy level diagram of CCC15N. The rotational transition N 1 → 0 corre-sponds to an energy difference of ∼ 9.6 GHz. The fine structure splitting which is dueto the spin-rotation interaction is approximately γ(N+1/2). For the N=0, F 0 → 1transition the hyperfine structure is solely determined by the Fermi contact interactionand the splitting is therefore a direct measure for the bF . The dotted vertical linesrepresent measured transitions and are sorted in increasing frequency. Only ∆J=∆Ntransitions which are the strongest are displayed here, i.e. not all measured lines areshown here.


Figure 7.3: Measured 13CCCN transitions.

7.1.2 13CCCN, C13CCN and CC13CN

The hyperfine structures of 13CCCN, C13CCN and CC13CN were analyzed with a stan-dard Hamiltonian for a linear molecule in a 2Σ electronic state including the 13C and14N nuclear spins [57]:

H = Hrot + Hf + Hhfs (7.8)

with

Hrot = BN2 −DN4

Hf = γN · S + γD(N · S)N2

Hhfs = bF I(13C) · S + c[I(13C)zSz −1

3I(13C) · S]

+bF I(14N) · S + c[I(14N)zSz −1

3I(14N) · S]

+eQq/4T (2)o (I(14N)) (7.9)

where N is the rotational angular momentum of the molecule, S is the electron spinangular momentum, and I(13C) = 1/2 and I(14N) = 1 are the nuclear spins of therespective nuclei. The z axis is taken to lie along the linear carbon chain. Hrot is the


sβ

R

I(

I(14

Λ

F

N

2 nuclear spinsHund case (b ) C)

13C)

S

L

1F2F

axisquantization

Jβ

L

R

S

I(

I(

F 1

Hund case (b )2 nuclear spins

C)14

C)13

JF

N

axisquantizationΛ

Figure 7.4: Hund case bβs and bβJ with 2 nuclear spins. Hund case bβs (left): Thesubscript β indicates that the nuclear spin is not coupled to the molecular axis but tosome other vector. In this case the nuclear spin I(13C) is coupled with the electronspin S to form F2. J = N + S does not appear, see Townes & Schawlow p.197 [181],instead a new quantum number F1 is used here. Hund case bβJ (right): In this case,which is expected to be more common, the electron spin couples to the rotation N togive J. Then J and I couple to give F1. This coupling scheme was exploited in the fit.

rotation and centrifugal distortion Hamiltonian and Hf is the fine structure Hamiltonian,i.e. the magnetic interaction between the electronic spin and the molecular rotation.Hhfs is the hyperfine structure Hamiltonian which includes the interaction between theelectron spin and the 13C nucleus as well as the interaction between the electron spinand the 14N nucleus in terms of the Fermi contact and the electron-nuclear dipole-dipole constants. The last term is the electrical quadrupole interaction with T

(2)o (I)

the molecule fixed component of the quadrupole moment tensor. Herb Pickett’s [153]program was used to analyze the data and the coupling scheme

J = N + S, F1 = J + I(13C), F = F1 + I(14N), (7.10)

was applied to examine the hyperfine structure of the two here measured 13C isotopicspecies of C3N. For 13CCCN, a more natural choice for the coupling scheme would beF1 = N + I(13C), F2 = F1 + S,F = F2 + I(N) because the 13C hyperfine interactionis larger than that of spin-rotation [181] , see Fig. 7.4. However the fitting program canreadily handle large off-diagonal terms in the Hamiltonian matrix which occur when thecoupling scheme in Eq. 7.10 is used, so, for uniformity, it was adopted for 13CCCN aswell. Some of the observed rotational transitions of 13CCCN are indicated in the energylevel diagram in Fig. 7.5. The data were fitted in two steps.

In initial fits to the carbon-13 Fourier transform centimeter-wave data (see Table 7.6,7.7 and 7.8), the rotational constant B and the centrifugal distortion constant D wereconstrained to the values previously determined from the millimeter-wave data, and thethree nitrogen hyperfine constants (bF , c, and eQq) were constrained to the values fornormal CCCN [66]. The three remaining constants, the spin-rotation constant γ, bF(13C), and c(13C), were varied to fit the lowest-J transitions, yielding a rms of typically


N=2

Rotation Fine−Structure

10

30

40

50

20

0

γ =−18.0 MHz

N=1

J=1/2N=0

magnetic Fine−Structure, I( C)

c=139.5 MHzb =973.5 MHzF

J=3/2

J=1/2

966 MHz

61 MHz

980 MHz

27.0 MHz

J=5/2

J=3/2

45.1 MHz

956 MHz

28 MHz

splitting x 56

N (X Σ )2

EGHz

13 CCC

F =1

F =1

F =2

arbitrary scaling (less than x 0.1)

Hypefine Structure

F=2

F=1

F=1

F=1

F=1

F=1

F=1

F=1,3 F=2

F=3,4

F=1 F=2 F=0

F=2 F=3

F=3F=2

F=2F=0

F=1F=0

F=2

F=0 F=2

F =01

1

1

1

1F =2

1F =3

F =0

F =1

1

1

1F =1

F =21

1.2 MHz

13

Figure 7.5: 13CCCN energy level scheme. The splitting of the order 900-1000 MHz dueto the magnetic interaction of the 13C is much stronger than those of the 14N (or15N). For the low lying rotation transitions the 13C Fermi contact and dipole-dipoleinteraction dominates the energy splitting and is even larger than the spin-rotationinteraction (for N<50). The magnetic interaction of the 14N nuclear spin provides thehyperfine structure in the order of 1 MHz. The dotted vertical lines (on the right)represent measured transitions and are sorted in increasing frequency. Only ∆J=∆Ntransitions which are the strongest are displayed here.

≤20 kHz; subsequently, B and the three nitrogen constants were varied as well, givingan rms comparable to the 2-5 kHz measurement uncertainty. After the centimeter-wave transitions were assigned, global fits including the millimeterwave data [121] weredone. The centimeter-wave lines were assigned a frequency uncertainty of 2 kHz, andthe millimeter-wave lines uncertainties between 15 kHz and 150 kHz, with 25 kHz formost. Each hyperfine line was thus given a weight of about 100 relative to each of the 5-7millimeter-wave lines in the range of N=11 to 29. The final hyperfine parameters derivedfrom the global fits are nearly identical to those calculated from the initial fits, and theglobal rms are comparable to those obtained from the millimeter-wave data alone. Asan example Tab. 7.3 shows the molecular constants of 13CCCN during each of thesesteps; the analogous tables for C13CCN and CC13CN are in Appendix C. In Tab. 7.4the final fits for 13CCCN, C13CCN and CC13CN are summarized. For comparison, thespectroscopic constants of normal CCCN from [66] are also given.

With the 13C hyperfine constants given in Table 7.4, it is possible to make systematiccomparisons between the electronic structure and chemical bonding of C3N, isoelectronicC4H, and isovalent CCH. Such comparisons are appropriate because all three chains


Table 7.3: Molecular Constants of 13CCCN (in MHz).


valuesB 4771.218(1) 4771.2193(1) 4771.2195(2)D ×10−3 0.62(5) 0.6991(1) 0.6993(2)γ −17.96(2) −17.93(2) −17.963(5)γD ×10−3 0.2(7) −0.020(9) ...bF (13C) 980.(4) 973.(3) 973.(2)c(13C) 140.(5) 108.(1) 139.5(3)bF (14N) −1.17(7) −30.(20) −1.26(6)c(14N) 3.1(2) 0.(10) 3.4(1)eQq0 −4.45(4) −6.(52) −4.48(4)w-rmse 0.61 2.720 1.177

a Uncertainties (in parentheses) are (1σ) in the last significant digit.b 11 lines were used, see Tab.7.6. The uncertainties of the lines isestimated to be 2 kHz. c 20 lines from [121] were used. Theuncertainties of the lines are estimated to be between 22-86 kHz.d Total fit with all measured 31 lines. e w-rms is the weighted rms,i.e. the rms normalized with uncertainties of measured lines.

Table 7.4: Spectroscopic constants of the 13C isotopic CCCN species. The fit includedthe MWFT data and the mm-data from McCarthy et al. [121]

Constanta CCCNb 13CCCN C13CCN CC13CNB 4947.6207(11) 4771.2195(2) 4920.7095(2) 4929.0640(2)D×103 0.7535(16) 0.6993(2) 0.7453(4) 0.7497(3)γ -18.744(6) -17.963(5) -18.574(5) -18.648(3)γD ×103 -0.006(11) ... ... ...bF (13C) ... 973(2) 188.6(2) 23.55(2)c(13C) ... 139.5(3) 52.9(1) 2.17(3)bF (14N) -1.20(3) -1.26(6) -1.234(6) -1.182(8)c(14N) 2.84(9) 3.4(1) 2.82(3) 2.88(2)eQq -4.32(10) -4.48(4) -4.331(9) -4.323(8)w-rmsc ... 1.19 1.16 0.77number of ... 11+(20) 13+(28) 32+(12)transitions usedMWFT+(mm)

a Units are MHz. The 1σ uncertainties (in parantheses) are in the units ofthe last significant digits. The spectroscopic constants were derived from thehyperfine-split centimeter-wave transitions in Tables 7.6, 7.7, 7.8 and the mm-wave transitions in [121]. b Ref.[66] c Normalized standard deviation of the fit.


1

NCCC

NCCC

NCCC

NCCC

2

.

.

.

.

34

Figure 7.6: Resonance structure of CCCN

are σ-bonded radicals with 2Σ ground states, and because the hyperfine constants areproportional to important expectation values of the valence electron, providing highlyspecific probes of the molecular wave function. Carbon-13 is particularly useful becauseit probes the wave function at all the substituted positions along the carbon chain. Thereare only two non-zero hyperfine parameters for a 2Σ state: the Fermi-contact term bFand the dipole-dipole term c.

The Fermi-contact constant bF is a useful measure to localize the unpaired electron, ormore accurate to determine the spin density along the carbon chain in σ bonded radicalslike CnN with odd n (e.g. CN and C3N) and CnH with even n (e.g. C2H and C4H).This is because only s electrons have non-zero amplitude at (r=0) 3 and in this case theunpaired electron is expected to have significant s character, see Fig. 5.1. The magneticdipole coupling constant c also provides useful information on the orbital occupation ofthe unpaired electron, because it is a function of both an angular average and the radialexpectation value of 1/r3.

C3N is isoelectronic to C2H and C4H and shows similar behavior in the hyperfine struc-ture. Before comparing these radicals it is worthwhile thinking of a qualitative model forthe Fermi contact interaction along the carbon chain which is basically similar for thesemolecules (e.g. N is replaced by CH in the case of CnH, n=2,4). A description of thebonding in CCCN requires a superposition of several different electronic structures as itis shown in Fig. 7.6. Structure 1, with the unpaired electron localized on the terminalcarbon has the highest stability of all the resonance structures because of it’s four πbonds: two between C(1) and C(2), two between C(3) and N. Resonance structure 2, withthe unpaired electron on C(2), and structure 4, with the electron on N, are less stablebecause they only have three π bonds. Structure 3, with the unpaired electron on C(3),has only two π bonds and is the least stable structure. It is therefore expected thatthe spin density should be greatest at C(1), less at C(2) and N, and least at C(3). As-suming that the electron configuration is identical in all three here relevant isotopomers13CCCN, C13CCN, and CC13CN, then bF (13C) for each isotopomer is a measure of the

3With (r, θ) the spherical coordinates of the electron.


Table 7.5: bF (13C) and c(13C) values

bF (13C)-values / MHz c(13C)-values / MHz13C position → 1 2 3 1 2 3CCH 900.7(6) 161.63(10) — 142.87(3) 64.07(5) —CCCN 973.46(2) 188.513(1) 23.555(23) 139.5(3) 53.0(1) 2.17(3)CCCCH 396.8(6) 57.49(5) -9.54 89.12(1) -1.91(3) 9.84(8)

spin density at carbon C(i). In Tab. 7.4 the bF -values are listed with 973, 189 and 24MHz for C(1) through C(3), which qualitatively is the predicted decrement.

Figure 7.7 shows the magnitude of the two hyperfine constants at different positionsalong the carbon chain for the three radicals. Although bF (13C) and c(13C) are nearlythe same for 13CCH and 13CCCN and for C13CH and C13CCN, the same two constantsare each smaller by about a factor of two or more at the same substituted positions ofCCCCH. The reason for these difference may be the large zero-order mixing between thelow-lying 2Π state and the X2Σ+ ground state of C4H: the 2Π - X2Σ energy separation iscalculated to be 3600 cm−1 for CCH [150, 151], 2400±50 cm−1 for C3N, but only 100±50cm−1 for C4H [121] 4. Owing to strong vibronic coupling between these states, the 2Σground state of C4H probably possesses significant 2Π character, unlike the ground statesof CCH or C3N, which are nearly pure 2Σ.

With simple atomic orbitals [170] it is possible to estimate crudely the fractional 2s and2p character in the 2σ molecular orbital of C3N, on the assumption the unpaired electronis localized on either of the two carbon atoms furthest from the nitrogen. Within a fewpercent, this calculation yields the same unpaired electron spin density on the terminalcarbon atom (74%) and adjacent carbon atom (26%) for C3N as that previously derivedfor CCH [120], and little contribution from the pπ electronic configuration. In contrast,the relative amount of pπ character is estimated by the same calculation [121] to beabout 28% for C4H, a result in good agreement with that of Hoshina et al. [90], whoconcluded on the basis of LIF measurements that the admixture is about 40%.

4The bF (13C) of CC13CCH is -9.54 MHz (see Tab. 7.4) which can be explained by a spin polarizationeffect which arises when the paired electrons in the σ orbital are slightly polarized by the electronsin the nearby p orbitals [30] : bF = 2µBµI

I 〈 8π3 Ψ2(0)〉U + spin polarization.


0

200

400

600

800

1000

1200

0 1 2 3 4 5

CCH

CCCCH

CCCN

Fer

mi c

onta

ct (

b F, i

n M

Hz)

0

50

100

150

200

0 1 2 3 4 5

Dip

ole-

dipo

le (

c , in

MH

z)

carbon atom

Figure 7.7: (Top:) bF -values of different isoelectronic carbon chains. Each number nstands for the position of a 13C-atom within the molecule as seen from the terminalC-atom, i.e. n=2 for the CCCN isotope is C13CCN. In a pure 2Σ ground state theunpaired electron would be completely localized at the terminal carbon atom. For asmall 2Π admixture in the 2Σ ground state the spin density is highest at the terminalC-atom and decreases with increasing n which is reflected by the decreasing bF -values.CCCCH has more 2Π character in the ground state and hence a smaller |〈Ψ(0)〉|2 whichresults in smaller bF compared with the more pure X2Σ species CCH and CCCN.(Bottom:) c-values of isoelectronic carbon chains.


Table 7.6: Measured Rotational Transitions of 13CCCN in the X2Σ+ State.Frequencya O − C b Transition

(MHz) (kHz) N’ J’ F’1 F’ N J F1 F

9528.817 1 1 3/2 2 3 0 1/2 1 29542.475 −3 1 3/2 1 2 0 1/2 0 1

19073.604 −2 2 5/2 3 3 1 3/2 2 219073.886 −1 2 5/2 3 4 1 3/2 2 319084.532 −3 2 5/2 2 2 1 3/2 1 119084.612 3 2 5/2 2 3 1 3/2 1 219085.382 0 2 3/2 2 3 1 1/2 1 228617.158 2 3 7/2 4 5 2 5/2 3 428626.762 1 3 7/2 3 3 2 5/2 2 328626.796 4 3 7/2 3 4 2 5/2 2 328627.817 −3 3 5/2 3 4 2 3/2 2 3a Estimated experimental uncertainties (1σ) are 2 kHz.b Calculated frequencies derived from the best fit constants in Tab. 7.3

Table 7.7: Measured Rotational Transitions of C13CCN in the X2Σ+ State.Frequencya O − C b Transition


9829.369 −1 1 3/2 2 2 0 1/2 1 19830.396 1 1 3/2 2 3 0 1/2 1 29839.603 −1 1 3/2 1 1 0 1/2 0 19840.701 −2 1 3/2 1 2 0 1/2 0 1

19672.508 6 2 5/2 3 3 1 3/2 2 219672.780 −5 2 5/2 3 4 1 3/2 2 319681.164 −7 2 5/2 2 3 1 3/2 1 219681.175 3 2 5/2 2 2 1 3/2 1 119684.220 1 2 3/2 2 1 1 1/2 1 119684.755 2 2 3/2 2 3 1 1/2 1 229521.725 3 3 7/2 3 4 2 5/2 2 329521.758 1 3 7/2 3 3 2 5/2 2 229626.764 −4 3 5/2 3 4 2 3/2 2 3a Estimated experimental uncertainties (1σ) are 2 kHz.b Calculated frequencies derived from the best fit constants in Tab. 7.3


Table 7.8: Measured Rotational Transitions of CC13CN in the X2Σ+ State.Frequencya O − C b Transition


9847.713 −3 1 3/2 2 2 0 1/2 1 19848.755 2 1 3/2 2 3 0 1/2 1 29853.055 5 1 3/2 1 1 0 1/2 0 19853.282 8 1 3/2 1 2 0 1/2 0 19873.604 2 1 1/2 1 2 0 1/2 1 2

19706.620 3 2 5/2 3 3 1 3/2 2 219706.889 2 2 5/2 3 4 1 3/2 2 319706.914 3 2 5/2 3 2 1 3/2 2 119709.044 −7 2 5/2 2 2 1 3/2 1 119709.080 5 2 5/2 2 3 1 3/2 1 219723.673 3 2 3/2 2 3 1 1/2 1 219726.516 −3 2 3/2 1 2 1 1/2 0 129564.843 0 3 7/2 4 4 2 5/2 3 329564.907 −3 3 7/2 4 3 2 5/2 3 229564.970 2 3 7/2 4 5 2 5/2 3 429566.119 −3 3 7/2 3 3 2 5/2 2 229566.174 5 3 7/2 3 4 2 5/2 2 329568.747 −6 3 7/2 3 2 2 5/2 2 229580.140 −2 3 5/2 3 3 2 3/2 2 329581.389 −3 3 5/2 2 2 2 3/2 1 229582.300 −8 3 5/2 3 3 2 3/2 2 229582.480 3 3 5/2 3 2 2 3/2 2 129582.569 1 3 5/2 3 4 2 3/2 2 329583.673 0 3 5/2 2 2 2 3/2 1 129583.913 5 3 5/2 2 3 2 3/2 1 229584.491 1 3 5/2 2 1 2 3/2 1 139422.912 −5 4 9/2 5 5 3 7/2 4 439422.990 1 4 9/2 5 6 3 7/2 4 539440.879 −1 4 7/2 4 4 3 5/2 3 339440.986 0 4 7/2 4 5 3 5/2 3 439441.702 −2 4 7/2 3 3 3 5/2 2 239441.785 6 4 7/2 3 4 3 5/2 2 3a Estimated experimental uncertainties (1σ) are 5 kHz.b Calculated frequencies derived from the best fit constants in Tab. 7.3


0 20 40 60Frequency [GHz]

The

oret

ical

Inte

nsity

21,72 21,74 21,76 21,78 21,8Frequency [GHz]

The

oret

ical

Inte

nsity

Figure 7.8: C4N stick spectrum calculated for Trot=3K.

7.2 C4N and C6N

For the first time the linear cyano radicals C4N and C6N could be measured in thelaboratory. The spectra were observed between 7.2 and 21.7 GHz for C4N and 7.8 and18.3 GHz for C6N, i.e. at least four rotational transitions of each radical fall withinthe frequency range of the used spectrometer. The measured laboratory frequencies forthese molecules are given in Table 7.11 and 7.12, and typical lines are shown in Fig. 7.9and 7.10. Searches for the rotational spectra of C4N and C6N were guided by ab initiocalculations of Pauzat et al. [144]. The rotational constants for both molecules wereestimated by scaling these ab initio rotational constants by the ratio of the experimental

7.2 C4N and C6N 113

B value to that calculated at the same level of theory for C2N, C3N, and C5N. Rotationaltransitions predicted in this way turned out to be quite accurate - to within 0.25% forC4N and C6N.

The present identifications are extremely secure: (i) the two new molecules are al-most certainly radicals because their rotational transitions are separated in frequency byhalfinteger quantum numbers, and their lines exhibit the expected Zeeman effect (i.e., afairly modest broadening owing to the small magnetic g factor of a 2Π1/2 state) when apermanent magnet is brought near the molecular beam; (ii) the carriers of the observedlines are nitrogen-bearing molecules because the lines disappear when cyanoacetyleneis replaced with diacetylene, and because characteristic hyperfine structure from thenitrogen nucleus was observed in all of the assigned spectra; (iii) impurities from con-taminants in the gas samples and van der Waals complexes with the buffer gas canalso be ruled out, because the lines were produced with acetylene plus cyanogen as theprecursor gas, and when Ar replaced Ne as the buffer gas; and (iv) the identificationsof C4N and C6N are also supported on spectroscopic grounds by the close agreement ofB and D with those estimated by scaling from the ab initio geometries and the CnHchains of similar size. In addition, the Λ-doubling constant p + 2q in the 2Π1/2 ladderof C4N and C6N can be predicted to within a factor of two by scaling from CCN [142]on the assumption of free precession. The nitrogen hyperfine constants a− (b+ c)/2, b,and d also smoothly decrease in magnitude from CCN to C6N, as one might expect ifthe unpaired electron is delocalized along the chain; a similar decrease in the hydrogenhyperfine constant a−(b+c)/2 has been observed in the odd-numbered acetylenic chainsup to C13H [64]. Under optimized experimental conditions, the strongest rotational linesof C4N were approximately 15 times less intense than those of C3N, but were still ob-served with a signal to noise of approximately 25 after one minute of integration; thedecrement in peak signal strength from C4N to C6N was only about a factor of three.

An effective Hamiltonian for molecules in a 2Π electronic state used in the presentanalysis is expressed as

H = Hrot + HSO + HΛ + Hhfs

were the terms on the right side of the equation are the rotational energy, the spin-orbitinteraction, the Λ-type doubling interaction, and the hyperfine interaction, respectively,see Chapter 6.3.1. The hyperfine structure term includes the magnetic and the electric-quadrupole interaction due to the 14N nucleus. Unlike in the case of C2N the spin-rotation interaction was not needed to result in a good fit. Instead of the pure ASO spinorbit constant Aeff = ASO + γ was used for the fit, see Chapter 6.2.

The lowest rotational transitions of both C4N and C6N in the ground 2Π1/2 fine structureladder are split into six components by Λ-doubling on the scale of 2-5 MHz and thenby hyperfine structure from the nitrogen nucleus which is generally smaller by aboutan order of magnitude (i.e. on the scale of 0.2-0.5 MHz). Rotational transitions fromthe higher-lying X2Π3/2 ladder were not observed, because this level lies at least severaltens of Kelvin above the X2Π1/2 level and is apparently not appreciably populated inthe generally rotationally cold molecular beam (Trot = 0.2 - 3 K). The fits were done


Figure 7.9: Measured C4N transition. Shown are the ∆F=∆J transitions at 12094.384MHz and 12094.480 MHz with F 5/2 → 3/2 and F 3/2 → 1/2 respectively.

Figure 7.10: Measured transition of C6N. Shown are the transitions F 17/2→15/2 andF 15/2→13/2 at 13086.043 MHz and F 13/2→11/2 at 13086.146 MHz.

7.2 C4N and C6N 115

quantization

axis

Λ

L

FJ

R

I(14

N)

S

Σ

Hund case a1 nuclear spin

Figure 7.11: Hund’s case a with one nuclear spin. In the case of C4N is L=1, S=1/2,R=0,1,2,... , and I(14N)=1/2.

with the HUNDA program written by J. Brown [27] which is based on the effectiveHamiltonian of Brown et al. [26, 24] in the strong Hund’s case (a) with 2JB |ΛASO|,see Fig. 7.11. The spin-orbit constant Aeff = ASO +γ was constrained at 40 cm−1 (∼ 1.2THz) because no information of the Π3/2 states was available and it was assumed thatASO +γ from C4N and C6N is of the same order of magnitude than that from C2N [142].At most nine spectroscopic constants: the rotational constant B, centrifugal distortionD, two Λ-doubling constants p + 2q and (p + 2q)D, and five hyperfine constants, thediagonal term a− = a − (b + c)/2, the off-diagonal term b, the parity-dependent termd, the electric quadrupole term eQq0, and the nonaxially symmetric quadrupole termeQq2 were required to reproduce the 29 measured lines of C4N and the 42 of C6N tobetter than 2 kHz. If eQq2 was constrained to zero in the C4N fit, the rms increases bymore than a factor of five. In Fig. 7.14 the energy level diagram of C4N is shown. Withthe spectroscopic constants for C4N and C6N as listed in Table 7.9, precise frequenciesfor the astronomically interesting transitions can be calculated to very high precision.Fig. 7.8 shows a stick spectrum with a calculated intensity distribution correspondingto a rotational temperature of 3 K. For both radicals the strongest lines are found for∆F = ∆J transitions (mainly with F’=J’+1). In the case of C4N transitions with∆F = 0 and ∆F = −1 could be observed but ∆F = 0 transitions of C6N are very weakand only ∆F = −1 transitions could be measured. That resulted in a strong correlationbetween the a− and the eQq0 of ∼1 in the fit for the C6N radical. The eQq0 is nearlyconstant for all known CnN chains, with n<6, and was fixed to -4.38 MHz to avoid thatcorrelation.

The CnN, n=2,4,6, are isoelectronic to CnH, with n=3,5,7 and with the exception ofC7H there are already some data at hand concerning their magnetic and electronicquadrupole hyperfine structure. The Frosch & Foley hyperfine parameters a, bF , c, andd give information about the unpaired and total electron distribution 〈1/r3〉, 〈sin2 θ/r3〉,〈3 cos2 θ − 1/r3〉, and 〈ψ2(0)〉. Unfortunately, it is impossible to obtain a complete set


Table 7.9: Spectroscopic Constants of C4N and C6N in the X2Π State.

Constanta C4N C6NAeff 1200000b 1200000b

(40 cm−1) (40 cm−1)B 2422.6963(1) 873.11224(6)D [× 10−6] 90(3) 11.5(7)P eff 4.5525(8) 1.939(5)PDeff [× 10−3] 5.23(2) 0.066(2)a− 15.005(1) 8.7(5)b(14N) 16.2(1) 7.4(10)d 22.4254(9) 13.23(1)eQq0 -4.389(1) -4.38b

eQq2 5.6(3) ...transitions ∆ F = 0,-1 ∆ F = -1no. of lines 29 33exp. uncert. 2 kHz 2 kHzrms 1 kHz 3.6 kHzw-rms 0.614 1.803

a Units are in MHz. The 1σ uncertainties (inparentheses) are in the units of the last significantdigits. bfixed value

of these parameters, owing to lack of data for the a+ = a+ (b+ c)/2 constant for whichΩ3/2 transitions are needed. Ohshima et al. [142] showed how it is possible to use somesimple assumptions concerning the missing constants and to estimate the molecularparameters. It is mainly the fact that the ratios a/d and −c/d should be in the rangesof 0.70-0.75 and 0.52-0.54 respectively for these kinds of radicals. For the C4N and C6Nthe molecular parameters could be calculated by scaling the C2N value appropriate tothe notation of [181, 142], i.e. using Eq. (6.35), (6.37), (6.38), and (6.40). The results forthe CnN chains are listed in Tab. 7.10 together with the values for the isoelectronic CH,C3H, C5H radicals; some of them are plotted in Fig 7.2. The d and the eQq2 constantsare associated with the non-axial symmetry 〈sin2 θ/r3〉 of the electron distribution in theradical. The difference between both constants is that d refers to the unpaired electrons(U) and eQq2 to the total electrons (T). In the case of C2N 〈sin2 θ/r3〉U ≈ 〈sin2 θ/r3〉Twhich means that the non-axial distribution is mainly caused by the unpaired electron.For C4N the situation is different because 〈sin2 θ/r3〉T − 〈sin2 θ/r3〉U = 6 · 1024cm−3 andit is therefor not the unpaired electron that dominates the non-axial term. A comparisonwith other 〈sin2 θ/r3〉T -values from higher members of the CnN (n even) chains wouldbe desirable but for C6N no eQq2 was determined and higher members are not detectedso far.

7.2 C4N and C6N 117

-2

-1

0

2 3 4 5 6 7

log

(rel

ativ

e ab

unda

nce)

number of carbon atoms

CnN radicals

n=3

4

5

6

Figure 7.12: Relative abundances of the CnN radicals per gas pulse in the supersonicmolecular beam as a function of chain length.

Lines of C4N and C6N are readily observed in the supersonic molecular beam, eventhough both radicals are calculated ab initio to possess rather small dipole moments- 0.14 D for C4N and 0.31 D for C6N [144]. In FTM spectroscopy, line strengths areproportional to the first power of the dipole moment µ, not µ2, as in classical absorptionspectroscopy; rotational lines of small µ molecules are therefore relatively much moreintense in FT spectroscopy than in conventional spectroscopy. Bauder and co-workers,for example, have detected a number of deuterated hydrocarbons [157] using the presenttechnique; many with dipole moments in the range of 10−1 - 10−3 D.

Relative abundances (see Fig. 7.2) of the nitrogen-bearing carbon chain radicals hereto one another and to C3N and C5N were determined from intensity measurements onlines as close in frequency as possible to minimize variations in instrumental gain. Thesewere converted to absolute abundances by comparing line intensities with those of the


2 4 6n

0

0,1

0,2

0,3

0,4

0,5 |⟨

Ψ(0

) ⟩ | /

1024

cm

-3

CnN, n=2,4,6 (positive)

Cn+1H, n=2,4 (negative)

2 3 4 5 6n

0

2

4

6

8

⟨1/r3

⟩ / 1

024cm

-3

CnN, n=2,4,6

Cn+1H, n=2,4 (scale x40)

2 4 6n

0

1

2

3

4

5

6

⟨ sin

2 ϑ /r3 ⟩ U

/ 10

24 c

m-3

CnN, n=2,4,6

Cn+1H, n=2,4 (scale x25)

(x40)

(x25)

Figure 7.13: Molecular constants 〈1/r3〉, 〈sin2 θ/r3〉, and 〈ψ2(0)〉 of CnN, n=2,4,6 andCn+1H, n=2,4 as estimated in Tab. 7.10

rare isotopic species of OCS in a supersonic beam of 1% OCS in Ar in the absence of adischarge, taking into account differences in the rotational partition functions and dipolemoments. As Fig. 7.2 shows, the two new chains here are more than a factor of twomore abundant than C5N.

The formation of carbon chain radicals in our molecular beam is apparently differentfor chains with odd and even numbers of carbon atoms. Although the abundance datafor CnN is much less complete than for CnH, it is worth noting that the plot in Fig. 7.2is similar to that previously derived for the acetylenic radicals (see Fig. 2 of Ref.[64]),implying similar, if not common, formation mechanisms in the discharge. Most of theC2n+1H and C2nN chains are more abundant than the corresponding C2nH and C2n+1Nchains. If nonpolar carbon chains C2n+1 are more abundant than even-numbered chainsC2n, for example, subsequent reactions involving the radicals C2H or CN (produceddirectly via cleavage of the central C-C bond of either HC4H or HC3N) may produce theodd-even alternation that is observed. Evidence to support this formation mechanism isthe mass distribution of a diacetylene discharge which exhibits an even-odd alternationin abundance for chains beyond C9, with the odd chains being more abundant [156].

7.2 C4N and C6N 119

2B

J=1/23B

J=5/2

5B

J=3/2

J=5/2

5B

J=3/2

7B

e

e

f

f

fe

Fine structure

F=3/2

F=3/2

F=1/2

F=1/2

F=3/2F=3/2

F=1/2

f

eΠ

1/2

Π3/2

2

Rotation

∆so

Hund(b) Hund(a)

Hyperfine structure

−(a +d)=37 MHz

(a −d)=7 MHz−

eff

Π

F=1/2

F=5/2

W =

F=5/2

∆e transitions with F = 0

∆f transitions with F = −1

∆f transitions with F = 0

∆ F = −1

effp (J+1/2)

p = 4.5 MHz

A = 40 cm −1

−doublingΛ

N=3

N=2

N=1

4B

6B

N=0

S=−1/2

S=+1/2

e transitions with ef

fe

14 MHz

∆ q (J −1/4) (J+3/2)W = D2

Figure 7.14: Schematic C4N energy level. The dominating splitting in the energy leveldiagram is due to the spin-orbital interaction which separates the Π3/2 and Π1/2 states.Transitions involving a Π3/2 state have not been measured and the energy separationis assumed to be 1.19 THz according to other similar species like C2N, see [142]. Incontrast to a Hund’s case (b) as it is plotted on the left with (2N)B spacings the fit wasdone in Hund’s case (a) and the rotational energy levels are now (2N+1)B separated.The Λ-doubling components are labeled by the e/f parity. The hyperfine structure isdue to the nitrogen magnetic and quadrupole moment.


Tab

le7.10:

Hyperfi

ne

and

Molecu

larC

onstan

tsof

Carb

onC

hain

Rad

icals

Hyperfi

ne

Param

eters(M

Hz)

Molecu

larC

onstan

ts(10

24

cm−

3)

Rad

icala

bF

cd

eQq2

〈1/r3〉

U〈(3

cos2θ−

1)/r3〉

U〈sin

2θ/r

3〉U〈sin

2θ/r

3〉T〈Ψ

2(0)〉U

C2 N

34a

11.4-25

b46.8

-9.25.9

-2.95.5

5.60.24

C4 N

16.3a

12.2-12

b22.4

5.62.8

-1.42.6

-3.4c

0.25C

6 N9.6

a1.7

-7b

13.2-

1.7-0.8

1.5-

0.04

C3 H

d12.3

-13.828.3

16.2-

0.15580.2389

0.1368-

-0.0208C

5 H8.3

e-21.8

f19.1

g10.9

h-

0.110.16

0.09-

-0.03

The

calculation

sw

eredon

eusin

gE

q.(6.35),

(6.37),(6.38),

and

(6.40)w

ith2µ

0µ

I(14N

)I(14N

)=

5.7208an

d(

µI(H

)I(H

))/(

µI(14N

)I(14N

))≈

13.84.a

calculated

asin

[142]w

itha/d

=0.70−

0.75;b

calculated

asin

[142]w

ith−c/d

=0.52−

0.54;c

same

-3e2Q

asin

[142];d

constan

tstaken

from[67];

eestim

ationfrom

a(H

)w

itha/d

=0.76

likein

the

caseof

C3 H

.f

theb

value

isderived

fromth

eC

5 Db-valu

e[88]

with

b(H)est

=2µ

H

µDb(D

)an

db(C

5 D)

=−

4.32MHz.bF

isth

anestim

atedw

ithbF

=b+c/3;

gestim

ation

fromc(H

)w

ithc/d

=1.75

likein

the

caseof

C3 H

.h

constan

ttaken

from[35];

7.2 C4N and C6N 121

Table 7.11: Measured Rotational Transitions C4N in the X2Π1/2 State.

Transition Frequency a e/f b O − C c

J ′ → J F ′ → F (MHz) Λ Comp. (kHz)1.5→ 0.5 1.5→ 1.5 7234.345 f 1

2.5→ 1.5 7247.840 e -11.5→ 0.5 7249.186 e 02.5→ 1.5 7255.402 f -11.5→ 1.5 7256.628 e -10.5→ 0.5 7257.124 e 00.5→ 0.5 7261.707 f 01.5→ 0.5 7271.774 f -1

2.5→ 1.5 2.5→ 2.5 12073.322 f -11.5→ 1.5 12084.411 f -13.5→ 2.5 12085.235 e 11.5→ 0.5 12086.839 e 03.5→ 2.5 12091.162 f 22.5→ 2.5 12094.262 e 22.5→ 1.5 12094.384 f 11.5→ 0.5 12094.480 f 01.5→ 1.5 12094.777 e 0

3.5→ 2.5 4.5→ 3.5 16921.368 e -13.5→ 2.5 16921.448 e -12.5→ 1.5 16922.195 e 04.5→ 3.5 16926.823 f 13.5→ 2.5 16928.186 f -12.5→ 1.5 16928.220 f 0

4.5→ 3.5 5.5→ 4.5 21757.146 e 24.5→ 3.5 21757.171 e -13.5→ 2.5 21757.636 e 05.5→ 4.5 21762.464 f -14.5→ 3.5 21763.210 f -13.5→ 2.5 21763.220 f 2

a Estimated experimental uncertainties (1σ) are 2 kHz.b Designation of e and f levels is based on the assump-tion that the hyperfine constant d is positive.c Calculated frequencies derived from the best fit con-stants in Table 7.9.


Table 7.12: Measured Rotational Transitions C6N, HUNDA-fit

Transition Frequency a e/f b O − C c

J ′ → J F ′ → F (MHz) Λ Comp. (kHz)4.5→ 3.5 5.5→ 4.5 7851.036 e -1

4.5→ 3.5 7851.047 e 03.5→ 2.5 7851.318 e 05.5→ 4.5 7853.245 f -34.5→ 3.5 7853.677 f 03.5→ 2.5 7853.677 f -4

5.5→ 4.5 6.5→ 5.5 9596.072 e 25.5→ 4.5 9596.072 e -24.5→ 3.5 9596.260 e 06.5→ 5.5 9598.199 f -15.5→ 4.5 9598.474 f 34.5→ 3.5 9598.474 f 2

6.5→ 5.5 7.5→ 6.5 11341.066 e -16.5→ 5.5 11341.066 e -25.5→ 4.5 11341.203 e 07.5→ 6.5 11343.149 f -16.5→ 5.5 11343.336 f 05.5→ 4.5 11343.336 f 0

7.5→ 6.5 8.5→ 7.5 13086.043 e -17.5→ 6.5 13086.043 e 06.5→ 5.5 13086.146 e 08.5→ 7.5 13088.099 f 17.5→ 6.5 13088.233 f 06.5→ 5.5 13088.233 f 2

8.5→ 7.5 9.5→ 8.5 14831.011 e 28.5→ 7.5 14831.011 e 47.5→ 6.5 14831.085 e -19.5→ 8.5 14833.047 f 38.5→ 7.5 14833.145 f -17.5→ 6.5 14833.145 f 2

9.5→ 8.5 10.5→ 9.5 16575.958 e -19.5→ 8.5 16575.968 e 18.5→ 7.5 16576.024 e -110.5→ 9.5 16577.985 f -29.5→ 8.5 16578.057 f 08.5→ 7.5 16578.068 f 3

10.5→ 9.5 11.5→ 10.5 18320.906 e -410.5→ 9.5 18320.916 e 39.5→ 8.5 18320.973 e ...

11.5→ 10.5 18322.929 f 110.5→ 9.5 18322.986 f -29.5→ 8.5 18322.990 f -2

a Estimated experimental uncertainties (1σ) are 2 kHz.b Designation of e and f levels is based on the assump-tion that the hyperfine constant d is positive.c Calculated frequencies derived from the best fit con-stants in Table 7.9.

7.3 The Search for C7N 123

7.3 The Search for C7N

Laboratory searches were also undertaken for C7N using experimental conditions and gasmixtures that optimize the production of either C5N or C6N, or both molecules simulta-neously. Searches were based on a high-level coupled cluster calculation by Botschwina[20], and covered frequency ranges that correspond to ±1% of the predicted rotationalconstants. Two searches, one assuming a 2Σ ground state with rotational lines separatedin frequency by integer quantum numbers, and one assuming a 2Π ground state with ro-tational lines separated in frequency by half-integer quantum numbers, were performed,but no lines which could be attributed to C7N were found in either survey. The absenceof lines requires the C7N line intensities to be at least 60 times less than those of C5N,which is readily observed in the molecular beam with a signal to noise of better than 25in one minute of integration. The failure to detect C7N may indicate a 2Π ground statefor this molecule. Botschwina concluded on the basis of RCCSD(T)/cc-pVTZ calcula-tions [20] that the ground state of C7N is 2Π (µ = 0.96 D), but that a 2Σ+ state (µ =3.86 D) is very close in energy, lying only 250 cm−1 above ground at the highest level oftheory. If we assume the same abundance decrement from C5N to C7N as from C3N toC5N (a factor of 17) and a 2Π ground state, the C7N lines would be 180 times less intensethan those of C5N, i.e. three times below our present upper limit. If the ground stateis 2Σ+ instead, the expected decrease in line intensity is only a factor of 45. In eithercase, significant rovibronic interaction may occur between these two low-lying electronicstates, a factor which could hinder spectral analysis and assignment regardless of thesymmetry of the ground state. Detection of C7N may still be possible: with furtherimprovements in instrumentation and production efficiency a factor of five or more insensitivity may be within reach.


Without a further improvement of the sensitivity of the FTMW spectrometer the detec-tion of higher members of the CnN chains, like C7N or C8N seems exceedingly difficult.For the same reason measurements on C5N, C4N, and C6N isotopomers, i.e. to deter-mine the exact bonding length or the spin density distribution in these radicals, appearless feasible. However, additional isotopic spectroscopy using 13C-enriched samples ofcyanogen, cyanoacetylene, methylcyanide, etc. may allow the distribution of carbon inthe discharge source to be determined, providing clues to the chemical processes at work.This could turn out to be an important tool for a molecule production improvement.

It is known that also non linear structures are build in a discharge jet [123]. Low-lying isomers of C4N and C6N may be amenable to laboratory detection with presenttechniques. Ding et al. [46] recently calculated the potential energy surface of C4N,and concluded that 13 isomers, some with unusual ring, branched, and caged structures,probably exist. The isomer of the most immediate laboratory interest is the ring-chainanalog to c-C5H, with the CCH group replaced by a nitrile group. This isomer is


predicted to have considerable kinetic stability towards isomerization and dissociation,and is calculated to lie only 2.8 kcal/mol above the linear chain. Because it is alsopredicted to possess a substantial dipole moment (µ = 0.63 D), and because c-C5H hasalready been detected with the same discharge source [4], detection of c-C4N may succeedwith dedicated searches. Other lowlying polar isomers of C4N such as CCCNC (23.4kcal/mol; 1.38 D) may also be within reach. The electronic spectra of C4N and C6Nare completely unknown. Both radicals probably possess strong 2Π - X2Π electronictransitions at visible or near infrared wavelengths, like the shorter chain CCN [142] andmost of the acetylenic chains CnH up to C10H. Many of these have now been studiedby sensitive laser techniques (see e.g., Ref. [110]), including LIF, cavity ring-down laserabsorption spectroscopy (CRLAS), and most recently, resonant two-color, two-photonionization spectroscopy (R2C2PI) combined with time-of-flight mass detection. All ofthe species up to C6N have abundances near the throat of the discharge nozzle of > 109

molecules per pulse - an adequate number density for all three techniques - but thebest choice would appear to be R2C2PI because the optical spectrum of linear C3H issignificantly broadened owing to rapid internal conversion [45], and because REMPI ismore sensitive than CRLAS and is mass selective as well.

Up to now there is also a lack of ro-vibrational data even if one considers only linear CnNradicals. In the case of C2N - the first member of the linear CnN chains - the A2∆-X2Πelectronic transition of the CCN free radical has been observed by Oliphant et al. [143]in emission with a high-resolution Fourier transform spectrometer. Spectroscopic con-stants were derived including the ground-state vibrational frequencies, ν3=1050.7636(6),2ν3=2094.8157(18), and ν1=1923.2547(69) cm1. But for the C3N radical the vibrationalfrequencies have only been investigated by ab initio theory. Botschwina [121] using cou-pled cluster calculations RCCSD(T) determined the asymmetric stretching vibrations tobe at ν3= 2311.8 cm−1 and ν2 = 2116.6 cm−1. There is no verification of these numbersby gas phase experiments so far, whether in the IR nor in the visible spectral range.For the C4N radical the vibration frequencies are calculated to be at ν2=1995 cm−1 andν1=2186 cm−1 by Ding et al.[46]. C3N and C4N are therefore good candidates for a IRgas phase detection, e.g. using the Cologne IR experiment.

Part III

Linear CnN Chains in Space

8 CnN Chains in Space

Remember, too,That the whole sky is revolvingWith its constellations, its planets.I have to force my course against that-Not to be swept backwards as all else is. [...]

Even if you were able to stick to the routeYou have to passThe horns of the Great Bull, the nasty arrowsOf the Haemonian Archer, the gaping jawOf the infuriated Lion,...

Ted Hughes, ”Tales from Ovid”, Phaethon

Presently there are more than 125 gas phase molecules found in space. The speciesrange in size from 2-13 atoms. They are typically found in dense interstellar cloudswith tremendous sizes of 1-100 light years, average gas densities of 102-103 cm−3, andtemperatures in the range 10-60 K 1. On the other hand many of the organic moleculesare detected in extended circumstellar envelopes of cool, old stars that are carbon richlike CW Leo/IRC+10216 or in the somewhat ’special cases’ of molecular clouds TMC-1and TMC-2.

The large abundance of highly unsaturated carbon chains and radicals, most of whichare linear, is a characteristic feature of IRC+10216 2 and except TMC-1 3 no othersource in the sky shows such a wealth of long linear chains [34].

1Both, higher temperatures and higher gas densities are found in localized regions where star formationis occurring.

2 IRC+10216 belongs to the stars with initial masses in the range from about 1 to 8 M. When thesestars “evolve off the main sequence, they go through several stages of evolution in which mass lossplays a crucial role [. . . ]. For such stars the mass loss usually occurs as a cool, low-velocity wind.During the asymptotic giant branch (AGB) evolutionary phase, mass loss rates may reach 1 × 10−4

M yr−1. The resulting high density of such winds near the star and the low temperature of thestellar photosphere assure that most of the ejected material is in molecular form.“ [15].

3 TMC-1 (Taurus Molecular Cloud 1) is a star forming region with low temperatures (T= 6 - 10 K).

128 8 CnN Chains in Space

Figure 8.1: The molecular clouds in the plane of the Milky Way, as seen in the 1-0rotational transition of CO. So far, most of the over 120 astronomical molecules havebeen detected in a small number of locations, sometimes only one or two. IRC+10216is one of the reaches molecular sources in space and CN, C3N and C5N have beenfound in this object. [179]

So far, detection of CnN radicals succeeded for the odd members C3N and C5N whereasnon of the even membered cyano chains, e.g. C2N, could be observed in the interstellarspace.

C3N was first found in the circumstellar envelope of IRC+10216 by Guelin & Thaddeus[78]. Since then it has been found in many other sources like IRAS 15194-5115, the protoplanetary nebulae (PPN) CRL 618 and CRL 2688, and the molecular clouds (MC) TMC-1, TMC-2 and HCL-2. A list of astronomically measured lines is given in the appendix(Tab. D.2). C3N can best be seen in IRC+10216 were it has a rotational temperatureof Trot ≈ 20 K.

So far, only one survey has been undertaken in which isotopes of C3N were detected(Cernicharo et al. [34], see appendix Tab. D.1). Unfortunately not all astronomicallyobserved transitions match the predictions obtained from the newly presented laboratorydata. The astronomical survey reveals that C3N isotopomers have very weak intensitiesand are hardly to be recognized. The discrepancy in the line assignment could thereforebe due to a misinterpretation of astronomical data. In Fig. 8.2 a detail of the linesurvey is shown. On the left side of the picture are three lines indicated by arrows.The left (L1) and middle (L2) line are assigned to 13CCCN and the right one (L3) tothe U152681 unidentified line. The problem is that non of the laboratory measuredtransitions corresponds to the left line (L1). If the lines L2 and L3 are assigned to13CCCN instead of L1 and L2 all disagreements between laboratory and astronomicaldata are solved. However, an other misassignment at 143104.0 MHz (which can not beseen in Fig. 8.2) remains4.

The next larger member of the odd CnN chains C5N was first detected in TMC-1 andIRC+10216 by Guelin et al. [77]. C5N appears to be two orders of magnitude less

4 Other unidentified lines in the survey at 142831.1 ± 10 MHz and 143575.8 ± 15 MHz do not matchto laboratory transitions at 143129.47 MHz and 143136.22 MHz.

129

J. Cernicharo et al.: 2-mm survey of IRC+10216 197

Fig. 2. continued

Figure 8.2: 13CCCN detection in IRC+10216 by Cernicharo et al.[34]

abundant than the related molecule HC5N, i.e. N(HC5N/C5N)' 200. In comparisonthe HC3N to C3N abundance ratio is of the order of 20, i.e. N(HC3N/C3N)= 19. Itis assumed that the rotational temperature of C5N is the same as from HC5N, i.e.Trot ≈ 29K.

In 1991 Pauzat et al. [144] analyzed the feasibility of linear CnN detection in spaceand concluded that due to the small dipole moments all even CnN members in their 2Πelectronic ground state would be poor candidates for interstellar detection. Recently,in a theoretical work Mebel & Kaiser [127] examined the formation of interstellar C2Nisomers via neutral-neutral reactions in the interstellar medium like

C(3Pj) +HCN → C2N +H(2S1/2) . (8.1)

The formation of the C2N isomers is calculated to proceed without any barrier, butreactions forming CCN, CNC, and c-C2N are found to be strongly endothermic by 52.7,59.0, and 99.6 kJ mol−1, respectively. Considering this result it seems to be highly un-likely that C2N can be synthesized in cold molecular clouds where average translationtemperatures of the reactants are only 10-15 K. The physical conditions in circumstellarenvelopes of late type stars like IRC+10216, are different. Close to the photosphere ofthe central star temperatures can reach 4000 K and the elevated velocity of the reac-tants in the long tail of the Maxwell-Boltzmann distribution can overcome the reactionendothermicity to form CCN. These type of environments represent ideal targets forhitherto undetected C2N in the infrared as well as in the microwave region.

Unfortunately, a simple reaction (see Eq. 8.1) is not a realistic scenario for complexenvironments like the IRC+10216 envelope, PPN, molecular clouds or other interstellarmolecule sources. In this situation, astrochemical models specified for the environmentin question can be helpful for estimations of molecule abundances. Nowadays thesemodels are of great complexity and it is often not easy to determine the most importantsynthesis of a species. Especially, if one considers the fact that reaction rates dependon the density, temperature, and radiation which in turn are functions of the positionin the circumstellar envelope or cloud it is clear that the synthesis of a specific speciesis also a function of time and position. Because of the importance of IRC+10216 as a


C H3N

C H 22 C H2

C H 24 C H4

C H 26 C H6

HC N3

HC N5

HC N7

C N3

HC N9

C H2

C H2

C H2

C H 2

2

C H5C H

22

CN HCN

CN HCN

CN HCN

C N5N

Figure 8.3: Major pathways to cyanopolyyne formation in IRC+10216. Although C3N isprobably build by photo-destruction of HC3N it seems to play an important role in theformation process of HC5N and consequently for all higher cyanopolyynes. [131],[38]

major molecule source with great diversity a short description of the Millar & Herbst[131, 132] astrochemical model of its circumstellar envelope is given here.

The gas around IRC+10216 is assumed to expand in a spherically symmetric outflow5 with a velocity of 14 kms−1 and a mass-loss rate of 3 × 10−5 M yr−1. The modelfollows the chemistry from an inner radius ri = 1 × 1016 cm to an outer radius of 1018

cm. At ri parent species (H2,He,CO,C2H2,CH4,HCN,NH3,N2, and H2S) are injected intothe outward flow. The choise of an inner radius is governed by the onset of the photo-chemistry [132]. As the parent molecules flow outwards they are dissociated into reactivedaughter products by the incident interstellar ultraviolet radiation field6. For molecules,the average time to travel from the inner to the outer radius takes approximately 10 000years. The number density of the gas follows an r−2 distribution, while the temperatureprofile T(r) in K is assumed to be T (r) = 100(r/ri)

0.79 but never to be less than 10 K.In this way, the temperature never decreases below 10 K. The rates of photodissocia-tion and photoionization as well as the strength of the un-extinguished radiation fieldis included in the model. The model network contains 407 species connected by 3851reactions 7. In this circumstellar model, as opposed to the interstellar models, neutral-neutral reactions and photo-destruction are very important especially for the formationof larger hydrocarbons.

In the distance of 3·1016 cm where much of the chemistry takes place the major formation

5This smooth outflow is a oversimplification since observations [117] have revealed that the envelopeconsist of discrete, concentric shells.

6that is by UV radiation coming from far outside IRC+102167Hydrocarbons with more than 23 atoms are not included in the network.

131

mechanism for C3N (cyanoacetylene) seems to be the photo-destruction of HC3N. Thelatter is formed mainly via the two reactions

CN + C2H2 −→ HC3N +H (8.2)

HCN + CCH −→ HC3N +H (8.3)

On the other side the major depletion mechanism for C3N is photo-destruction to formC2 and CN. C3N is also an important constituent in the major pathways to cyanopolyyneformation in IRC+10216, as can be seen in Fig. 8.3. Similar to C3N the next member ofthe CnN (n odd) chains C5N seems to be formed by photo-destruction of HC5N which isproduced similar to Eq. 8.2 and 8.3, i.e. by CN+C4H2 → HC5N + H and HCN + C4H→ HC5N + H.

The main question for CnN (n even) astrochemistry is how likely the detection of C2Nis. Following this model a list of theoretical and observed column densities includingthe precursor molecules HCnN and CnH is given in Tab. 8.1 and plotted in Fig. 8.4.C2N has probably a two magnitudes smaller column density than C3N so that it canhardly be seen in normal line surveys. The column density ratios 8 NL(HC3N/C3N)and NL(HC5N/C5N) are of the order of 10. If this is also valid for NL(HC2N/C2N) anastronomical search seems to be reasonable. The parent molecule HC2N has alreadybeen observed towards IRC+10216 and the column density of C2N is expected to be lessthan 3.6 · 1012 cm−2 which should hence be detectable as well. For comparison: WhenHC11N was unambiguously detected in TMC-1 in 1997 by Bell et al. [8] 9 the signalcorresponded to a column density of 2.8 ·1011 cm−2 at Trot=10 K. Assuming a rotationaltemperature similar to C3N (Trot = 20 K) the best frequency range to search for C2N isbetween 150 and 180 GHz with the transitions J 6.5→5.5 and 7.5→6.5.

8Not to be confused with the abundance ratios mentioned earlier in this chapter.9The 1982 detection in IRC+10216 by Bell et al. [9] was probably incorrect


theor. observedmolecule Trot Tex Col.Dens. Col.Dens. Frac. abund.

[K] [K] [cm−2] [cm−2] N(X)/N(H2)HCN - 1.7 1016 2.8 1016

HC2N 12 1.2-1.8 1013

HC3N 26 1.8 1015 0.8-1.7 1015

HC5N 25-35 7.1 1014 1.3-3.7 1014

HC7N 26 2.2 1014 1.3 1014

HC9N 12-23 5.8 1013 2.7-4.0 1013

C2H 20 16 5.7 1015 4.6-5.0 1015 7.1 10−6

C3H 8.5 1.4 1014 5.6 1013

C4H 35 15 1.0 1015 2.4-3.0 1015 4.3 10−6

C5H 25 27(Π1/2) / 39(Π3/2) 8.7 1013 0.4-2.9 1014 6.3 10−8

C6H 35 35(Π3/2) / 46(Π1/2) 5.8 1014 0.6-1.7 1014 7.8 10−8

C7H 35 4.5 1013 2.2 1012 3.1 10−9

C8H 52 1.1 1014 1.0 1013 1.4 10−8

CN 8.7 1.0 1015 6.2 1014

C2N 3.6 1012

C3N 20 15 3.2 1014 2.5-4.1 1014 3.5 10−7

C4N 8.2 1009

C5N 35 1.4 1014 6.3 1012 9.0 10−9

C7N 7.8 1012

Table 8.1: Molecular column densities in IRC+10216, observed values are taken fromCernicharo et al. [34] and Kawaguchi et al. [101]. Theoretical values are from Millar& Herbst [132].

133

02

46

810

n

1e+

09

1e+

10

1e+

11

1e+

12

1e+

13

1e+

14

1e+

15

1e+

16

column density [cm-2

]

obse

rved

(n o

dd)

theo

r.

(n e

ven)

theo

r.

02

46

810

n

1e+

12

1e+

13

1e+

14

1e+

15

1e+

16


]

obse

rved

(n o

dd)

theo

r.

(n e

ven)

theo

r.

02

46

810

n

1e+

13

1e+

14

1e+

15

1e+

16

1e+

17


]

obse

rved

theo

r.

HC

nN

CnH

CnN

HC

2N

Fig

ure

8.4:

Col

um

nden

siti

esof

CnN

,C

nH

,an

dH

CnN

inIR

C+

1021

6,se

eTab

.8.

1.


T (K)A*.

Figure 8.5: Possible C2N transition towards IRC+10216 at 248 GHz. The left lineappears at the C2N 248 GHz transition frequency with µ2S=1.2 - 1.9 D2. The dottedline results from a line shape fit for molecules in a circumstellar envelope. The line atthe right hand side could not be identified. The total integration time was 170 min.

8.1 The Search for Interstellar C2N

In the previous section it has been shown that the detection of C2N may be in reach withthe present day radio telescope techniques. The astronomical search for this moleculewas guided by the use of laboratory data. In 1995 Ohshima and Endo [142] did measure-ments on C2N using a Fourier transform spectrometer in the Microwave region. Theirmolecular spectroscopic constants were used as reference as well as the constants derivedby Kakimoto and Kasuya [98] to calculate the millimeter rotational spectrum of C2N(see Tab. 8.3).

8.1.1 Observation

In September 2002 a search was performed for the C2N radical towards IRC+10216employing the IRAM 30m telescope at Pico Veleta, Spain (see Fig. 8.8). The observationswere done at position (Eq 1950) RA 09:45:14.8 Dec 13:30:40.0 and focused on four 500MHz broad frequency bands with centers at 83 GHz, 154 GHz, 224 GHz and 248 GHzcorresponding to the J=7/2 → 5/2, 13/2 → 11/2, 19/2 → 17/2 and 21/2 → 19/2rotational transitions of C2N, respectively. The integration time was 4 - 4 1/4 hours

8.1 The Search for Interstellar C2N 135

T (K)A*

.

T (K)A*.

Figure 8.6: Possible C2N transitions towards IRC+10216. The C2N transitions appearat 224.5 GHz (with µ2S = 1.9 - 2.3 Debye2 and a total integration time of 265 min.)and 153.6 GHz (with µ2S = 4.2 - 5.8 Debye2 and a total integration time of 250 min.).The dotted lines result from line shape fits for molecules in a circumstellar envelope.The right line in the top picture at 224.7 GHz is C17O (v=0, J 2 → 1). The C2N lineat 224.5 GHz can also be due to a possible upper sideband image of SiC2 at 232534MHz.


Table 8.2: Observational parameters, IRC+10216

molecule transition obs.freq. a Tsys ρ vexp

∫T∗A dν

J (MHz) (K) [km m−1] (K.km s−1)

C2N 21/2 → 19/2(e/f) 248189.9(3) 800 0.49 14.6 0.78(7)[ 19/2 → 17/2(e) 224545.2(12) 650 0.53 14.7 0.12(9) ]c

[ 19/2 → 17/2(f) 224551.2(12) 650 0.53 14.7 0.12(9) ]c

13/2 → 11/2(f) 153644.7(5) 400 0.67 14.7 0.04(1)

U1d - 248291.22(8) 800 0.49 14.0 2.69(7)C17O (v=0) 2 → 1 224714.18(15) 650 0.53 14.7 1.78(3)C2S 11,12 → 11,11 153449.21(5) 400 0.67 13.9 0.81(5)

NaCN 100,10 → 90,9 153557.04(7) 400 0.67 12.7 0.84(5)U2d 153842.29(9) 400 0.67 16.1 0.60(6)

HC5N 31 → 30 82538.835(3) 105 0.80 14.0 0.73(3)

a Rest frequencies (assuming a source LSR velocity of -27 km s−1) in IRC+10216;b The numbers in parenthesis are the estimated uncertainties (1σ);c poss. upper sideband image of SiC2 at 232534 MHz;d unidentified line

and for most of these bands the r.m.s. noise is 9 - 13 mK 10, low enough to reveal linesas weak as 0.01 - 0.04 K. Optically thin lines from the outer shells of the IRC+10216envelope have a U-shaped profile (see Fig. 8.5 and 8.6) where the two horns 11 arisefrom the blue-shifted (front), and red-shifted (rear) polar caps. The emission at thecenter originates from the meridian ring perpendicular to the line of sight. The horn-to-center intensity ratio of emissions coming from spherical shells of constant thickness andconstant radial velocity12 depend primarily on the shell diameter relative to the telescopebeam [73], i.e. for a given frequency we have: the larger the shell, the larger the ratio.The lines at 224 and 248 GHz reveal the typical U-shape which suggests that the carrierof these lines is essentially present in the outer envelope. The measured intensitiesare given in T ∗A, the effective antenna temperature corrected for spillover losses andatmosphere attenuation. T ∗A is related to TMB the main beam-averaged source brightnesstemperature by T ∗a = ρTMB, where ρ = ρ(ν) is the 30m telescope beam efficiency, seeTable 8.2.

10scale is in T ∗A, the effective antenna temperature corrected for spillover losses and atmosphere atten-uation.

11This notion is taken from [73].12see vexp in Tab. 8.2.


8.1.2 Data Analysis

The Grenoble molecular line reduction software CLASS was used to fit the observed linesto an U-shaped line profile. Two lines are observed13 at frequencies of C2N transitionswith integrated line intensities of at least 0.78 and 0.24 K km s−1, and one weaker lineis found at 154 GHz with an intensity of 0.04 K km s−1, see Table 8.2. The frequencyscale is computed for a LSR source velocity of -27 kms−1.

The total molecular column density NT as well as the rotational temperature T areimportant for the unambiguous assignment of the observed transitions to a certainmolecule. There are some formulas needed to calculate this values. The integratedline intensity

∫Tldν is proportional to µ2S, with S the line strength of the transition.

The dipole moment of C2N has been calculated by Pd et al. [145] to be µ=0.425 Debye.The line strength can be calculated from the intensity I of a transition or vice versawith the following formula [154]

µ2S =10IpQ(T )

4.16231 · 10−5 · ν[exp

(−El

kT

)− exp

(−Eu

kT

)] (8.4)

with Ip the logarithm of the intensity 14 ,ν in MHz, µ the relevant component of thedipole moment of the molecule in Debye, Q the partition function [152], El the lowerstate energy and Eu the upper state energy of the transition. For reasons of conformitythe theoretical intensities of the C2N transitions were calculated with the dpfit and dpcatprogram written by Herb Pickett. Here T is set to 300 K 15.

In case of small optical depth 16 the column densityNu in its upper level can be calculatedby 17

Nu

gu

= 1.669813 · 1017

∫TMBdv

νµ2S(8.5)

with gu the statistical weight of the level [196],∫TMBdv the line integral 18 in (K km s−1),

ν in MHz and µ2S from Eq.8.4.

The line width in IRC+10216 of the newly measured transitions are of the order 30 km s−1

corresponding to 20-25 MHz for 248 GHz, see Fig. 8.5.

If C2N is the carrier of the absorption lines many hyperfine transitions remain unresolved,i.e. three lines at 153 GHz, six lines at 224GHz and also six at 248 GHz, see Fig. 8.5

13The line at 224.5 GHz is a possible upper sideband image of the SiC2 line at 232.534 GHz.14The Pickett program uses the logarithm Ip of the intensity I instead of the intensity itself in its

catalog files, i.e. I = 10Ip

15This is a necessary standard procedure because the Pickett program sums over a finite amount oftransitions to calculate the partition function and not over all. Thus differences can occur if an othertemperature is chosen. Q is given in the Pickett filename.out file. For C2N Q(300K) = 5737.4682

16and for Tex hν/k and Tex Tbg, see [196]17 Nu

gu= 3k

8π3

∫Tldv

νµ2S18Some times the line integral is given in K·MHz instead of K·km·s−1. The conversion equation is∫

Tldv [K km s−1]= 10−3 cν

∫Tldν [K MHz] with c the speed of light in [m/s] and ν the transition

frequency in [MHz].


Table 8.3: Line parameters, IRC+10216

molecule transition obs.freq.a calc.freq. o-c Eupper log(Nu)(with Nu

J (MHz) (MHz) (MHz) (K) in cm−2)

C2N 21/2 → 19/2(e/f) 248189.9(3) 248189.1(1) 0.8 68.6 11.0[ 19/2 → 17/2(e) 224545.2(12)c 224545.2(1) - 56.7 10.6 ][ 19/2 → 17/2(f) 224551.2(12)c 224551.2(1) - 56.7 10.6 ]13/2 → 11/2(e) - 153617.9(1) - 27.8 -13/2 → 11/2(f) 153644.70(8)c 153644.70(8) 27.8 -[ 7/2 → 5/2(e) - 82701.63(1) - 9.1 11.2d ][ 7/2 → 5/2(f) - 82743.70(1) - 9.1 11.2d ]

U1 - 248291.22(8) - - - -C17O (v=0) 2 → 1 224714.18(15) 224714.389(3) -0.21 16.2 13.5C2S 11,12 → 11,11 153449.21(5) 153449.774(11) -0.56 53.8 10.2

NaCN 100,10 → 90,9 153557.04(7) 153557.651e -0.61 - -U2 - 153842.29(9) - - - -

HC5N 31 → 30 82538.835(3) 82539.040 -0.21 63.4 9.3

a Rest frequencies (assuming a source LSR velocity of -27 km s−1) and intensities in IRC+10216;b The numbers in parenthesis are the estimated uncertainties (1σ).c In a free fit the rest frequencies have been 224549.64(188) MHz for the 19/2 → 17/2(e/f)transitions and 153642.61(10) for the 13/2 → 11/2(f) transition. Because of the close lyingdoublet components both transitions have been fitted with fixed rest frequencies.d integrated noise, 0.003K · 30 km s−1

e see [34] on-line data

and 8.6. In this case a mean line strength S of the unresolved transitions is computedand multiplied by the number n of these lines to give Ss the summed line strength thatreplaces S in Eq. 8.5.

If several resolvable transitions, e.g. rotational transitions, of a molecule are observed arotational temperature can be assigned by using

Nu

gu

=NT

Q(Trot)exp

(− Eu

kTrot

)(8.6)

where NT is the total molecular column density, Q the partition function, and Eu theenergy of the upper level. Eq. 8.6 can be rewritten in the form

log10

(Nu

gu

)= log10

(NT

Q(Trot)

)− 1

Trot

log10(e)Eu[in K] (8.7)

where Trot and NT19 can be determined by a least-square fit [114]. The result can be

19The partition function for a temperature T has been calculated by Q(T ) = α · T β , where α and βare determined by the Q(Ti) values given by the Pickett program. In the case of linear closed shellmolecules β is always one but for the C2N radical α=6.7 and β = 1.2 .


0 20 40 60Eu[K]

10,0

10,5

11,0

11,5

log 10

(Nu/g

u)

0 20 40 60Eu[K]

9,5

10,0

10,5

11,0

log 10

(Nu/g

u)

Figure 8.7: Boltzmann plot for C2N. The left plot is calculated for a non-diluted beamand the right plot is calculated for a diluted beam. (Left) A rotational tempertureof 78±60 K and a column density of 1014 cm−2 could be estimated in the case of adiluted beam.

plotted in a Boltzmann plot.

The spacial extend of a molecular gas can influence the value of the integrated lineintensities. This is because the beam size diameter θB of the telescope varies withfrequency, i.e.

θB ∼ 1/ν (8.8)

The IRAM 30m telescope beam width is roughly 2400”/ν[GHz], i.e. 28” for 83 GHz, 15”for 154 GHz, 10” for 224 GHz, and 9” for 248 GHz. The range of possible line intensitiescan be estimated by considering two cases of telescope beam and source diameter ratios.In one case the area of emitting molecules is larger than the beam size so that the beamis completely ’filled’ independent of frequency. On the other hand, when the source issmall the telescope beam can easily be larger than the diameter θs of the emitting area, i.e. the beam is diluted. Assuming that the intrinsic intensity distributions Ts of asource is Gaussian a beam filling factor can be introduced to calculate the measuredintensity TL, i.e.

TL = TS ·(

θ2S

θ2S + θ2

B

)(8.9)

If θs θB this equation reduces to TL = TS · ( θ2

θ2B) and applying Eq. 8.8 gives

TL(ν) ∼ TS ·(

ν

νnorm

)2

. (8.10)

with νnorm > ν. A factor (ν/νlowest)2 added on the right side of Eq. 8.5 modifies the

column densities and thus also the rotational temperature Trot into Trot in the Boltzmannplot, see Fig. boltz, i.e. Trot represent the cases of a diluted beam. The distributionof the C2N radicals around IRC+10216 is not known. However, if it is similar to the


C3N intensity distribution (see [15]) which is shell like with some larger irregularitiesthen the determination of the filling factor for each frequency can only be obtained bymapping the star envelope. This has not been done here. The result of the Boltzmannfit for a diluted beam is the temperatures Trot = 78±60 K and the total C2N columndensity NT = 1014 cm−2. The uncertainties of the temperature fit are very large andpartly due to the fact that the integrated line intensity at 224 GHz is lower than theone at 248 GHz, i.e. it does not exactly follow a boltzmann distribution 20. Calculationswith a non-diluted beam result in a negative temperature. If the three lines at 154, 224and 248 GHz belong to C2N, it has to be shown that the non-detection of the 83 GHztransition is consistent with this assignment. To proof this the noise at the 83 GHz linepositions were integrated according to the beam filling factor 1 or (83/154), see Tab. 8.3.The integrated noise intensities are above the fitted line (dotted) in Fig. 8.7 (left) whichmarks the level of consistent signal intensities. The expected C2N signal at 83 GHz issmaller than the noise intensity and should therefore not be detectable. Hence, the nondetection of the 83 GHz is consistent with a C2N assignment of the other three lines.

8.1.3 Discussion

If C2N is produced via photo-destruction of HC2N the physical conditions and the regionin which they are detected should be similar or at least correlated to each other. In 1991Guelin & Cernicharo [74] detected HCCN towards IRC+10216 using the IRAM 30mtelescope. They found a source diameter ≤ 25” (i.e. little or no beam dilution). Com-parison of the line profile of HC2N with HC3N and HC5N indicate that this moleculeis essentially present in the outer envelope. The rotational temperature of HCCN isTrot = 12 ± 4 K and C3N has a rotational temperature of 20 K [34]. Guelin & Cer-nicharo detected a faint signal which coincides with the 13/2 → 11/2 of C2N but nofeature stronger than 0.02 K at the frequency of the 11/2 → 9/2 transition. Both thenon-detection at 130 GHz by Guelin & Cernicharo as well as the discrepancy of the ro-tational temperatures in the case of a non-diluted beam between HC2N and C2N makeit difficult to assign the newly observed transitions to the C2N molecule. Guelin & Cer-nicharo who assumed a dipole moment of 1.3 Debye for C2N estimated an upper limitof NT (1.3 D) = 5 · 1013 cm−2 for the column density of C2N towards IRC+10216. Theobservation presented in this thesis together with the assumption that C2N has a dipolemoment of 0.425 Debye (Pd & Chandra [145], 2001) suggest that the column density ofC2N is NT (0.425 D)= 1014 cm−2 whereas astrophysical models by Millar & Herbst [132]predict a column density21 of 3.6 · 1012 cm−2, see Table 8.1.

20In this situation the uncertainties of the individual line intensities become particular important forthe result of the fit.

21Note: It should be NT (0.425 D) ≈ 10 · NT (1.3 D).


Figure 8.8: The IRAM 30m telescope at Pico Veleta, Granada

8.1.4 Conclusions and Prospects

During the measurements at the IRAM 30m telescope (see Fig. 8.8) three lines at fre-quency positions of C2N transitions could be detected and have been assigned to C2N asa possible carrier. This assignment can only be tentative and more data is needed. How-ever, an upper limit of the column densities of C2N towards the envelope of IRC+10216can be given. They are of the same order than those obtained from previous measure-ments by Guelin & Cernicharo [74] and are a factor of ten larger then predicted valuesby Millar & Herbst [132]. An unambiguous detection of C2N may still be possible withdedicated searches using long integration times. In a free line fit procedure the observedline positions reveal deviations > 1σ with reference to the calculated frequencies. Up tonow the predicted line positions in the mm range are mainly based on laboratory mea-surements at 35 GHz by Ohshima et al. [142]. Therefore new laboratory measurementsof C2N are necessary in the frequency region between 100 and 300 GHz.

The measurements reported in Chapter 7 should serve as a guide for future astronomicalobservations of C4N, C6N, and the isotopic species of C3N. The provided spectroscopicconstants allow the astronomically most interesting radio lines of these to be predictedto an uncertainty of 0.30 km sec−1 or better up to 50 GHz. Astronomical detection ofthe carbon-13 species of C3N in the cold molecular cloud TMC-1 is also likely, becausethey have already been detected by Cernicharo et al. [34] in the circumstellar shell ofthe evolved carbon star IRC+10216.


Part IV

Appendix

A Linear CnHLinear CnH radicals are iso-electronic to CnN and therefore of interest for this thesis.The following table is the analogue to Tab. 5.1 and 5.2 for CnN radicals.

Table A.1: Linear CnH (n=1-8) radicals

molecule ground dipole exp. B first orig. contributionstate moment B value detection (see for reference)

[Debye] [MHz]

CnH, n odd

CH X2Π 1.46 425472.8 lab, vis (1920-25) (Herzberg [83])astro, vis (1937) Dunham, Swings [125, 174, 49, 83]

astro, radio (1973) Turner [185]lab, MW (1983) Brazier, Brown [22]

C3H X2Π 3.29 11186.335 lab (1985) Gottlieb, Vrtilek [68]astron (1985) Thaddeus, Hjalmarson [178]

C5H X2Π 4.44 2395.131 lab (1986) Gottlieb, Thaddeus [65]astron (1986) Cernicharo, Kahane [36]

C7H X2Π 5.29 875.484 lab (1996) Travers, McCarthy [182]astron (1997) Guelin et al. [75]

C9H X2Π 413.258 lab (1997) McCarthy [122]C11H X2Π 226.900 lab (1997) McCarthy [122]C13H X2Π 137.710 lab (1998) Gottlieb [64]

CnH, n even

C2H X2Σ 0.769 43674.53 astron (1974) Tucker, Kutner, Thaddeus [183]lab (1981) Sastry, Helminger [163]

C4H X2Σ 4.09 4758.657 astron (1978) Guelin, Green [79]lab (1983) Gottlieb [66]

C6H X2Π 5.05 1391.186 lab (1988) Pearson, Gottlieb [146]astron (1986) Suzuki, Ohishi [172]

C8H X2Π 6.94 587.264 lab (1996) McCarthy [119]astron (1996) Cernicharo [32]

C10H X2Π 301.410 lab (1998) Gottlieb [64]C12H X2Π 174.784 lab (1998) Gottlieb [64]C14H X2Π 110.242 lab (1998) Gottlieb [64]

A general overview is given in Takahashi [176] and Pauzat [144]. Isotopomers of CCH were examinedby McCarthy et al. [120] and Saleck et al. [162]. Isotopic CCCCH was measured by Chen et al. [37].

146 A Linear CnH

B The HQ Matrix Elements

The matrix elements of the electric quadrupole interaction HQ (Eq.6.48) can be writtenin the Hund’s case (a) using 3j- and 6j-Symbols 1

〈ηΛ′SΣJ ′Ω′IF |HQ|ηΛSΣJΩIF 〉 =1

4

(I 2 I−I 0 I

)−1

(−)J+I+F

F J I2 I J ′

×[(2J ′ + 1)(2J + 1)]1/2


(J ′ 2 J−Ω 0 Ω

)+

∑q=±2

δΛ′,Λ∓2(6)1/2eQq2(−)J ′−Ω′

(J ′ 2 J−Ω′ −q Ω

)](B.1)

This equation can be split in two matrices, M(eQq0) and M(eQq2)

M(eQq0) =1

4

(I 2 I−I 0 I

)−1

(−)J+I+F

F J I2 I J ′

×[(2J ′ + 1)(2J + 1)]1/2


(J ′ 2 J−Ω 0 Ω

)](B.2)

M(eQq2) =1

4

(I 2 I−I 0 I

)−1

(−)J+I+F

F J I2 I J ′

[(2J ′ + 1)(2J + 1)]1/2

×[ ∑

q=±2

δΛ′,Λ∓2(6)1/2eQq2(−)J ′−Ω′(

J ′ 2 J−Ω′ −q Ω

)](B.3)

2Π states have Ω or Ω′ values of 3/2 or 1/2 so that Ω’=Ω±1. For the energy the ∆J = 0elements are calculated using the basis functions 2

|2Π±|Ω|, J〉 =|Λ,Σ, J,Ω〉 ± | − Λ,−Σ, J,−Ω〉√

2(B.4)

with ± referring to the e/f parity respectively. To calculate the 3j- and 6j-symbols thefollowing equalities are useful:

4J ≡ [(2J + 3)(2J + 2)(2J + 1)(2J)(2J − 1)]1/2

I ≡ [(2I + 3)(2I + 2)(2I + 1)(2I)(2I − 1)]1/2

1see Brown & Schubert [27], Eq. 22The matrix elements are in a non parity conserving basis.

148 B The HQ Matrix Elements

X = −R(F ) ≡ J(J + 1) + I(I + 1)− F (F + 1)

K(F ) ≡ 3R(F )[R(F )+1]−4J(J+1)I(I+1)I(2I−1)(2J+3)(2J+2)(2J)(2J−1)

s ≡ F + J + I

The following formula are taken or derived from Edmonds [51].(I 2 I−I 0 I

)=

2[3I2 − I(I + 1)]

I

(B.5)(J 2 J−Ω 0 Ω

)= (−1)J−Ω 2[3Ω2 − J(J + 1)]

4J

(B.6)F J I2 I J

= (−1)s 2[3X (X − 1)− 4J(J + 1)I(I + 1)]

4J I

(B.7)(J 2 JΩ −2 Ω− 1

)= (−1)2J+2

(J J 2Ω Ω− 1 −2

)(B.8)(

J J 2Ω Ω− 1 −2

)=

√3(J + Ω− 1)(J − Ω + 2)

(2J + 3)(2J − 1)

(J J 1Ω Ω− 2 −1

)(B.9)

(J J 1Ω Ω− 2 −1

)= −

√(J + Ω− 2)(J − Ω + 3)

(2J)(2J + 1)

(J J 0Ω Ω− 3 0

)(B.10)

For Eq. B.9 3 and Eq. B.10 ([51], Eq. 3.7.13) was used.

The diagonal matrix elements M(eQq0) can be calculated directly using Eq. B.5 - B.7with J = J ′ and Ω = 1/2 for the lower left matrix element of Tab. B.1 and Ω = 3/2 forthe upper right matrix element.

In Eq. B.3 the index q of the sum separates the upper right and lower left matrix elementof M(eQq2). HQ is hermitian and it is thus sufficient to calculate only one addend.(

J ′ 2 J−Ω′ −q Ω

)≡ Ai (B.11)

is non zero if (−Ω′ + (−q) + Ω) = 0, but because |q| = 2 and Ω′,Ωε±1/2,±3/2 thisis only possible for (Ω′ = −3/2, q = +2,Ω = 1/2)1 or (Ω′ = 3/2, q = −2,Ω = −1/2)2.Because of the δΛ′,Λ∓2 only A1 applies and M(eQq2) can be derived by setting Ω′ = −3/2and Ω = 1/2 using Eq. B.8 with (−Ω′(= −3/2)=Ω = 3/2 and Ω(= 3/2)=Ω− 1 = 1/2).Eq. B.8 can be solved by Eq. B.9 and B.10. In the case Ω = 3/2 it is(

J J 0Ω Ω− 3 0

)(Ω=3/2)!

=

(J J 0Ω −Ω 0

)= (−1)J−Ω(2J + 1)−1/2 (B.12)

The result is summarized in Tab. B.1.

3With j1 = j2 ≡ J , j3 = 2, m1 = Ω, m2 = Ω− 1, m3 = −2 to terms vanish because j3 + m3 = 0

149

Table B.1: Matrix with electr. hf interaction

|2Π±3/2JIF 〉 |2Π±1/2JIF 〉

〈2Π±3/2JIF |...... eQq0

2 K(F )[274 − J(J + 1)] ± eQq2

4 K(F )[(J2 − 14)(J + 1

2)(J + 32)]1/2

〈2Π±1/2JIF |...... (Hermitian) eQq0

2 K(F )[34 − J(J + 1)]

with K(F ) = 3R(F )[R(F )+1]−4J(J+1)I(I+1)I(2I−1)(2J+3)(2J+2)(2J)(2J−1)

R(F ) = F (F + 1)− J(J + 1)− I(I + 1)

Matrix elements in non-parity conserving basis derived by Tom C. Killian and Guido Fuchsfrom Brown & Schubert, [27]

150 B The HQ Matrix Elements

C Molecular Constants of C13CCN andCC13CN

In Chapter 7.1.2 the measurements and analysis of the 13C-C3N isotopomers have beendescribed. Tab. 7.4 shows the results of the global fits including the mm-data fromMcCarthy et al. [121] and the newly measured MW-data. The fit of the data has beendone in 3 steps. First the mm-data were fitted with Herb Pickett’s spfit/spcat program.With the B and D constants contraint to the values of the mm-data fit a new fit withonly MW-data was done. A final fit including all available mm- and MW data was doneto derive the ’recommended values’ of the C3N isotopomers. Tab. 7.3 shows the resultof the intermediat steps of the fit for 13CCCN. The tables for the intermediate resultsfor C13CCN and CC13CN are given here.

Table C.1: Molecular Constants of C13CCN (in MHz).Data reduction was done with the Pickett-program.


valuesB 4920.7107(8) 4920.712(2) 4920.7095(2)D ×10−3 0.78(4) 0.749(2) 0.7453(4)γ −18.62(2) −18.9(2) −18.574(5)γD ×10−3 2.4(8) 0.2(2) ...bF (13C) 188.6(2) 210.(30) 188.6(2)c(13C) 52.4(2) −40.(200) 52.9(1)bF (14N) −1.244(7) −8.(200) −1.234(6)c(14N) 2.86(4) −40.(100) 2.82(3)eQq0 −4.(1) −30.(200) −4.331(9)w-rmse 1.35 0.54 1.16a Uncertainties (in parentheses) are (1σ) in the last significant digit.b 13 lines were used, see Tab.7.7.The uncertainties of the lines is estimated to be 2 kHz.


d Total fit with all measured 41 lines.e w-rms is normalized with uncertainties of measured lines.

152 C Molecular Constants of C13CCN and CC13CN

Table C.2: Molecular Constants of CC13CN (in MHz).Data reduction was done with the Pickett-program.


values

B 4929.0640(5) 4929.0639(2) 4929.0640(2)D ×10−3 −0.76(2) 0.7496(2) −0.7497(3)γ −18.643(7) −18.60(2) −18.648(3)γD ×10−3 −0.2(2) −0.02(1) ...bF (13C) 23.54(3) 21.(6) 23.55(2)c(13C) 2.19(4) 40.(100) 2.17(3)bF (14N) −1.184(8) −1.193e −1.182(8)c(14N) 2.87(2) 2.837e 2.88(2)eQq0 −4.32(1) −4.321e −4.323(8)w-rmsf 0.79 1.00 0.77a Uncertainties (in parentheses) are (1σ) in the last significant digit.b 32 lines were used, see Tab.7.8.The uncertainties of the lines is estimated to be 5 kHz.


d Total fit with all measured 44 lines.e fixed value.f w-rms is normalized with uncertainties of measured lines.

D Tables: Interstellar C3N ,C5N, andC3N Isotopomers

C3N was first detected in gas phase with a radio telescope by Guelin and Thaddeus[78, 79] in 1977 towards IRC+10216. Further C3N sources are IRAS 15194-5115, IRC+10216, TMC-1, TMC-2, HCL 2, CRL 618, CRL 2688, and it has also been observedin direction of Cas A. Table D.2 summerizes the astronomical measured transitions ofC3N.

During a line survey towards IRC+10216 Cernicharo et al. [34] detected three 13Cmono-substituted C3N isotopomers. In the case of 13CCCN the assignement of two ofthe astronomical observed lines is not in agreement with the data derived in this thesis,see Table D.1.

In 1998 Guelin et al. [77] detected C5N in the dark cloud TMC-1. Up to now TMC-1and IRC+10216 are the only sources in which C5N has been detected, see Table D.3.

Table D.1: Transitions of isotopic C3N in IRC+10216, Cernicharo et al. [34]. Thetransitions with a question mark do not agree with the laboratory data of this workand a correct assignment is not possible.

isotope transition frequency∫Tmbdν

(N,J,F1,F)”→(N,J,F1,F)’ [MHz] [K km/s]13CCCN (15,,,)→(14,,,)a ? (143 104.0) ? 0.71

(15,31/2,15,)→(14,31/2,14,) 143 124.0 0.92(16,,,)→(15,,,)a ? (152 640.0) ? 0.62

(16,33/2,17,)→(15,31/2,17,) 152 659.7 1.26C13CCN (14,29/2,14,)→(13,27/2,14,) 137 763.2 1.17

(14,27/2,[13],)→(13,25/2,[12],) 137 778.3 0.55(15,31/2,[16],)→(14,31/2,[15],) 147 602.2 0.45(15,29/2,14,)→(14,27/2,14,) 147 617.6 0.38

CC13CN (14,29/2,15,)→(13,27/2,14,) 137 996.2 1.30(14,27/2,[14],)→(13,25/2,[13],) 138 014.7 1.17

154 D Tables: Interstellar C3N ,C5N, and C3N Isotopomers

Table D.2: Astronomical detections of C3N

source transition frequency T∗A∫

TAdν reference(Tmb) (

∫Tmbdν)

(N,J,F)”→(N,J,F)’ [MHz] [K] [K km s−1]

CSE1

IRAS 15194-5115 (11,23/2,)→(10,21/2,) 108 834.27 (0.4) [140]IRC +10216 (17,33/2,)→(16,31/2,) 168 213.1 (10.90) [34]

(17,35/2,)→(16,33/2,) 168 194.4 (10.08) [34](16,31/2,)→(15,29/2,) 158 321.1 (24.00) [34](16,33/2,)→(15,31/2,) 158 302.3 (22.47) [34](15,29/2,)→(14,27/2,) 148 427.8 (27.97) [34](15,31/2,)→(14,29/2,) 148 409.1 (26.37) [34](14,27/2,)→(13,25/2,) 138 534.6 (27.89) [34](14,29/2,)→(13,27/2,) 138 515.7 (26.27) [34](11,21/2,)→(10,19/2,) 108 853.0 2.14 [79], [15](11,23/2,)→(10,21/2,) 108 834.3 2.14 [79], [15](10,19/2,)→( 9,17/2,) 98 939.9 0.18 [78](10,21/2,)→( 9,19/2,) 98 958.6 0.13 [78](9,17/2,)→(8,15/2,) 89 045.7 0.13 [78](9,19/2,)→(8,17/2,) 89 064.4 0.14 [78](5,9/2,)→(4,7/2,) 49 485.2 0.226 5.58 [101](5,11/2,)→(4,9/2,) 49 466.5 0.270 6.82 [101](4,7/2,)→(3,5/2,) 39 590.2 0.172 4.01 [101](4,9/2,)→(3,7/2,) 39 571.3 0.205 5.04 [101](3,5/2,)→(2,3/2,) 29 695.1 0.043 1.13 [101](3,7/2,)→(2,5/2,) 29 676.1 0.058 1.69 [101]

MC2

TMC-1 (3,5/2,7/2 )→(2,3/2,5/2) 29 695.13 0.15 [56], [76](3,5/2,5/2 )→(2,3/2,3/2) 29 695.13 0.15 [56], [76](3,5/2,3/2 )→(2,3/2,1/2) 29 694.99 0.04 [56]?, [76](3,7/2,9/2 )→(2,5/2,7/2) 29 676.28 0.12 [56], [76](3,7/2,7/2 )→(2,5/2,5/2) 29 676.14 0.11 [56], [76](3,7/2,5/2 )→(2,5/2,3/2) 29 676.14 0.11 [56], [76](2,3/2,5/2 )→(1,1/2,3/2) 19 800.121 0.055 [76](2,3/2,3/2 )→(1,1/2,1/2) 19 799.951 0.022 [76](2,5/2,7/2 )→(1,3/2,5/2) 19 781.094 0.094 [76](2,5/2,3/2 )→(1,3/2,1/2) 19 780.826 0.05 [76](2,5/2,5/2 )→(1,3/2,3/2) 19 780.800 0.058 [76](1,3/2,5/2 )→(0,1/2,3/2) 9 885.89 0.02 [76]

(continued on next page)

1circumstellar envelopes2molecular cloud

155

(continued from previous page)source transition frequency T∗A

∫TAdν reference

(Tmb) (∫

Tmbdν)(N,J,F)”→(N,J,F)’ [MHz] [K] [K km s−1]

TMC-2 (3,7/2,7/2 )→(2,5/2,5/2) 29 676.14 0.06 [56](3,7/2,9/2 )→(2,5/2,7/2) 29 676.28 0.07 [56]

HCL 2 (2,5/2,7/2 )→(1,3/2,5/2) 19 781.094 - [33]

PPN3

CRL 618 (,21/2,)→(,19/2,) (0.1) [28](,19/2,)→(,17/2,) (0.13) [28]

CRL 2688 (9,17/2,)→(8,15/2,) 89 045.7 0.2 [139](9,19/2,)→(8,17/2,) 89 064.4 0.2 [139]

othermolecules in (1,3/2,)→(0,1/2,) 9 885 ? 0.01 [10]direction Cas A

Table D.3: Transitions of C5N in IRC+10216 and TMC-1, see [77]

source transition frequency∫Tmbdν

(N,J)”→(N,J)’ [MHz] [mK km/s]TMC-1 (9,19/2)→(8,17/2) 25 249.938 7.3

(9,17/2)→(8,15/2) 25 260.649 6.4IRC+10216 (32,65/2)→(31,63/2) 89 785.6 95

(32,63/2)→(31,61/2) 89 797.0 105

3proto planetary nebulae

156 D Tables: Interstellar C3N ,C5N, and C3N Isotopomers

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List of Figures

2.1 Spectra of C2 at 516 nm obtained by using two different types of molecularsources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2 C60 mass spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3 Pressure-temperature diagram of graphite . . . . . . . . . . . . . . . . . 132.4 The Cologne Laser Ablation Source . . . . . . . . . . . . . . . . . . . . . 142.5 Jet produced by excimer laser ablation technique. . . . . . . . . . . . . . 152.6 QMS experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.7 Mass spectrum of Nd:YAG laser ablated graphite rod . . . . . . . . . . . 202.8 Excimer laser ablation on different kinds of material. . . . . . . . . . . . 232.9 The effect of an Nd:YAG laser beam on different kinds of material. . . . 242.10 Discharge slit nozzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.11 Jets produced by a discharge slit nozzle. . . . . . . . . . . . . . . . . . . 262.12 Experimental setup for mass spectrometry on a molecular beam . . . . . 272.13 Energy distribution of a He+ produced in the ion source of the plasma

monitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.14 Mass spectra of a molecular beam . . . . . . . . . . . . . . . . . . . . . 29

3.1 The Cologne carbon cluster experiment . . . . . . . . . . . . . . . . . . . 343.2 Sensitivity of IR detectors . . . . . . . . . . . . . . . . . . . . . . . . . . 353.3 Frequency calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.4 Rovibrational transition of C3 at 2067 cm−1 . . . . . . . . . . . . . . . . 38

4.1 Block diagram of the FTMW low band system, 5 - 25 GHz . . . . . . . . 434.2 The Production of CnN radicals . . . . . . . . . . . . . . . . . . . . . . . 464.3 Nozzle for the production of molecules and radicals . . . . . . . . . . . . 474.4 Test nozzle to optimize the geometry of the discharge nozzle . . . . . . . 484.5 The radical nozzle during a discharge . . . . . . . . . . . . . . . . . . . . 504.6 The supersonic jet expansion . . . . . . . . . . . . . . . . . . . . . . . . . 504.7 The long nozzles during a discharge . . . . . . . . . . . . . . . . . . . . . 514.8 Continuum free-jet expansion . . . . . . . . . . . . . . . . . . . . . . . . 534.9 Mach number and Temperature along the centerline axis of a free expansion 564.10 Model of flow development . . . . . . . . . . . . . . . . . . . . . . . . . 574.11 Theoretical intensities of the C4N rotational transitions . . . . . . . . . . 624.12 Cavity mode Lorentzian line shape . . . . . . . . . . . . . . . . . . . . . 65

174 List of Figures

4.13 Measured Qeff and calculated Qth for the Fabry-Perot cavity . . . . . . . 664.14 Time and Frequency Domains . . . . . . . . . . . . . . . . . . . . . . . . 68

5.1 Schematic diagram of electron configuration of CN and CCN . . . . . . . 715.2 Calculated geometries of C2N . . . . . . . . . . . . . . . . . . . . . . . . 745.3 Theoretical geometries of C4N . . . . . . . . . . . . . . . . . . . . . . . . 75

6.1 Hypothetical energy level diagram of a 2Π radical . . . . . . . . . . . . . 786.2 Vector diagram of Hund’s coupling cases a) and b) . . . . . . . . . . . . 846.3 Unpaired electron distribution for a 2Π state in Hund’s case (b). . . . . . 90

7.1 Measured CCC15N transition with Zeeman splitting . . . . . . . . . . . . 987.2 Energy level diagram of CCC15N . . . . . . . . . . . . . . . . . . . . . . 1027.3 Measured 13CCCN transitions. . . . . . . . . . . . . . . . . . . . . . . . . 1037.4 Hund case bβs and bβJ with 2 nuclear spins . . . . . . . . . . . . . . . . 1047.5 13CCCN energy level scheme . . . . . . . . . . . . . . . . . . . . . . . . . 1057.6 Resonance structure of CCCN . . . . . . . . . . . . . . . . . . . . . . . . 1077.7 bF and c-values of different isoelectronic carbon chains . . . . . . . . . . 1097.8 C4N stick spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1127.9 Measured C4N transition . . . . . . . . . . . . . . . . . . . . . . . . . . . 1147.10 Measured transition of C6N . . . . . . . . . . . . . . . . . . . . . . . . . 1147.11 Hund’s case a with one nuclear spin . . . . . . . . . . . . . . . . . . . . . 1157.12 Relative abundances of the CnN radicals per gas pulse in the supersonic

molecular beam as a function of chain length. . . . . . . . . . . . . . . . 1177.13 Molecular constants 〈1/r3〉, 〈sin2 θ/r3〉, and 〈ψ2(0)〉 . . . . . . . . . . . . 1187.14 Schematic C4N energy level. . . . . . . . . . . . . . . . . . . . . . . . . . 119

8.1 The molecular clouds in the plane of the Milky Way . . . . . . . . . . . . 1288.2 13CCCN detection in IRC+10216 . . . . . . . . . . . . . . . . . . . . . . 1298.3 Major pathways to cyanopolyyne formation in IRC+10216 . . . . . . . . 1308.4 Column densities of CnN, CnH, and HCnN in IRC+10216 . . . . . . . . . 1338.5 Possible C2N transition towards IRC+10216 at 248 GHz . . . . . . . . . 1348.6 Possible C2N transitions towards IRC+10216 at 154 and 224 GHz . . . . 1358.7 Boltzmann plot for C2N . . . . . . . . . . . . . . . . . . . . . . . . . . . 1398.8 The IRAM 30m telescope at Pico Veleta, Granada . . . . . . . . . . . . . 141

List of Tables

1.1 Known Interstellar and Circumstellar Molecules (Dec 2002) . . . . . . . . 5

2.1 Particle numbers of C3, C9 and C13 using excimer laser ablation . . . . . 162.2 Technical data of applied ablation lasers . . . . . . . . . . . . . . . . . . 192.3 Relative C-cluster concentration of different production techniques . . . . 21

4.1 Free jet flow properties for Ne . . . . . . . . . . . . . . . . . . . . . . . . 59

5.1 CnN, n odd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 765.2 CnN, n even . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

6.1 Selection of important interactions and their constants . . . . . . . . . . 806.2 Angular momenta and their projections . . . . . . . . . . . . . . . . . . . 846.3 Theoretical Λ-type doubling for 2Π state . . . . . . . . . . . . . . . . . . 876.4 Matrix with Spin-Orbit, Rotation and Λ-doubling . . . . . . . . . . . . . 946.5 Matrix with electr. hf interaction . . . . . . . . . . . . . . . . . . . . . . 956.6 Matrix with magnetic hyperfine interaction . . . . . . . . . . . . . . . . . 966.7 Transformed matrix with magnetic hyperfine interaction . . . . . . . . . 96

7.1 Measured Rotational Transitions of CCC15N in the X2Σ+ State . . . . . 997.2 Molecular Constants of CCC15N . . . . . . . . . . . . . . . . . . . . . . . 1007.3 Molecular Constants of 13CCCN . . . . . . . . . . . . . . . . . . . . . . . 1067.4 Spectroscopic constants of the 13C isotopic CCCN species. . . . . . . . . 1067.5 bF (13C) and c(13C) values . . . . . . . . . . . . . . . . . . . . . . . . . . 1087.6 Measured Rotational Transitions of 13CCCN in the X2Σ+ State. . . . . . 1107.7 Measured Rotational Transitions of C13CCN in the X2Σ+ State. . . . . . 1107.8 Measured Rotational Transitions of CC13CN in the X2Σ+ State. . . . . . 1117.9 Spectroscopic Constants of C4N and C6N in the X2Π State. . . . . . . . 1167.10 Hyperfine and Molecular Constants of Carbon Chain Radicals . . . . . . 1207.11 Measured Rotational Transitions C4N in the X2Π1/2 State. . . . . . . . . 1217.12 Measured Rotational Transitions C6N, HUNDA-fit . . . . . . . . . . . . . 122

8.1 Molecular column densities in IRC+10216 . . . . . . . . . . . . . . . . . 1328.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1368.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

176 List of Tables

A.1 Linear CnH (n=1-8) radicals . . . . . . . . . . . . . . . . . . . . . . . . . 145

B.1 Matrix with electr. hf interaction . . . . . . . . . . . . . . . . . . . . . . 149

C.1 Molecular Constants of C13CCN . . . . . . . . . . . . . . . . . . . . . . . 151C.2 Molecular Constants of CC13CN . . . . . . . . . . . . . . . . . . . . . . . 152

D.1 Transitions of isotopic C3N in IRC+10216 . . . . . . . . . . . . . . . . . 153D.2 Astronomical detections of C3N . . . . . . . . . . . . . . . . . . . . . . . 154D.3 Transitions of C5N in IRC+10216 and TMC-1 . . . . . . . . . . . . . . . 155

Acknowledgments

There are many people who have made my graduate career at the Universitat zu Kolnand the Harvard-Smithsonian Institution a successful and rewarding time for me.

Surely the first to mention here is Prof. Gisbert Winnewisser. It has been a pleasure tohave him as a thesis advisor. He was always interested in the progress of my work and hecared about my questions and problems. His connection to Prof. Patrick Thaddeus gaveme the possibility for an important and memorable time as a researcher at the HarvardSmithsonian Institution. And back at home I felt that his door was always open for me.Thanks for that!

Prof. Patrick Thaddeus gave me the opportunity to work in his research group, and Ilearned a lot from him since he is a brilliant scientist. As my research advisor at theHarvard Smithsonian Institution, he really took excellent care of me which I appreciatedso much and for which I want to thank him a lot. Especially his charismatic Tuesday-Wednesday meetings were always very motivating and inspiring for me.

I thank Dr. Thomas Giesen for being my lab advisor. Even before the beginning ofmy Diplom thesis he provided me with the day to day help, advised me and got me onthe road towards molecular spectroscopy. I felt really at home in his work group andnever felt any lack of support. His patience in answering clever and sometimes not atall clever questions is remarkable. I wish him all the best for his future career as a firstgrade scientist.

Dr. Michael C. McCarthy did a really great job as my lab advisor in Harvard. Notonly is he an excellent scientist but he also is capable of making the work in his groupvery pleasant. I just loved following the daily lunch conversations with Carl which werealways interesting, informative, and delightful. Also his first day crash course in thelovely FTMW spectrometer will always keep in my mind.

Carl Gottlieb was one of my big oracles - whenever I had a question he had an answer. Itwas very nice to work together with him and I still see him in front of me writing formulason the white board and make me think that we were working on really important things.Complementary to that his wife Elaine Gottlieb gave me support in Fortran to get somenumbers out of Carl’s theories. Both of them gave me a warm welcome and good traveladvises, Acadia is great!

I also profited a lot by the experience of Sam Palmer whose knowledge about the ex-periments and especially the radio techniques is just incredible and who is a person whoalways seemed to be in a relaxed mood. His interest in teaching and the rest of theoutside world brought up a lot of interesting discussions.

178 Acknowledgments

I also want to thank the rest of the Thaddeus group for creating such a good atmospherein which to work. First of all I want to mention Maria E. Sanz who is an excellentmerengue dancer and who’s Spanish is just to lovely to listen to. She helped me a lot ingetting started with the experiment.

Need a good tip for a restaurant or pub in Cambridge or Boston? Call John Dudeck.But don’t make the mistake and bet a beer for who wins the next Tour de France! Hesupported me with his self-made HC3N precursors and consequently was indispensablefor the success of this project.

Jane Kucera is one of the most diligent first year students I know and it was a pleasureto work with her. I hope that her future career will continue in that successful manner.

Tom Dame was helpful in many ways, e.g. working on data to optimize the dischargenozzle dimensions and supporting me with figures and maps of the Milky Way.

Dr. Rolf Berger provided the quadrupole mass spectrometer and was invaluable ingetting it started. Thanks to Dr. Ute Berndt, Petra Neubauer-Guenther, and MichaelCaris which were great lab-mates. Especially Petra helped me whenever she could interms of getting the lab supply organized or by advising ’our’ molecular physics students.I hope that for both of the doctores-to-be, Michael and Petra, the work in Lab 320 willbe interesting and that they will have a rich scientific harvest.

I also want to thank Frank Schloder, Dr. Frank Schmulling, and Michael Olbrich fortheir computer support. Especially Frank Schloder was very helpful with his patienceconcerning my Linux, LATEX and dada problems.

Friedrich Wyrowski helped me when ever I struggled with astrophysical problems. Thanks!

Sandra Brunken, Patrick Putz, Jorg Stodolka, Guido Sonnabend, and Daniel Wirtz aregreat comrades and I think we had a lot of fun working together in the I. Institut.

The machine shop did a great job and never ran out of solutions. Thanks!

No doubt, Thomas Giesen and Katja Roth did a great job in correcting this thesis.Thanks!

My family has always given me their total support. I would like to thank my parents,Agnes and Werner Fuchs, my brother Tobias and sister Sabine, as well as Christel andJosef Feldt who have always provided me with every opportunity. My aunt Elisabethand uncle Wilhelm guided me through all steps of my education - thanks.

Special thanks go to my wife Uli. Both of us studied at the same time, same place andnearly on the same topic: The pitfalls of physics and molecules. There is no other personto whom I owe such high esteem than her who during many years of scientific battlenever stopped hoping that it all will have an happy end.

This work was supported by the Deutsche Forschungsgemeinschaft and the SmithsonianInstitution.

Ich versichere, daß ich die von mir vorgelegte Dissertation selbststandig angefertigt, diebenutzten Quellen und Hilfsmittel vollstandig angegeben und die Stellen der Arbeit - ein-schließlich Tabellen, Karten und Abbildungen -, die anderen Werken im Wortlaut oderdem Sinn nach entnommen sind, in jedem Einzelfall als Entlehnung kenntlich gemachthabe; daß dieser Dissertation noch keiner anderen Fakultat oder Universiat zur Prufungvorgelegen hat; daß sie abgesehen von unten angegebenen Teilpublikationen noch nichtveroffentlicht worden ist, sowie daß ich eine solche Veroffentlichung vor Abschluß desPromotionsverfahrens nicht vornehmen werde.

Die Bestimmung der Promotionsordnung sind mir bekannt. Die von mir vorgelegte Dis-sertation ist von Herrn Prof. Dr. G. Winnewisser betreut worden.

(Guido W. Fuchs)

Parts of this thesis are published in:

1. M.C. McCarthy, G.W. Fuchs, J. Kucera, G. Winnewisser, and P. Thaddeus, Ro-tational Spectra of C4N, C6N, and the Isotopic Species of C3N, Journalof Chemical Physics, 118, 3549 - 3557 (2003)

Publication List:

1. T.F. Giesen, U. Berndt, K.M.T. Yamada, G. Fuchs, R. Schieder, G. Winnewisser,R.A. Provencal, F.N. Keutsch, A. Van Orden, and R.J. Saykally, Detection of theLinear Carbon Cluster C10: Rotationally Resolved Diode-Laser Spec-troscopy, ChemPhysChem 2, 242-247 (2001)

2. P. Neubauer-Guenther, T. F. Giesen, U. Berndt, G. Fuchs, and G. WinnewisserThe Cologne Carbon Cluster Experiment: Ro-Vibrational spectroscopyon C8 and other small carbon clusters Spectro.Chem.Acta Part A, 59/3,431 - 441 (2003)

Curriculum Vitae

Personal Name: Fuchs, Guido Wilhelmrepresentation: Date of birth: 14th December, 1971, Polch

GermanyMarital status: married

Education: 1978 - 1982 Grundschule Kehrig1982 - 1988 Realschule Mayen1988 - 1991 Kurfurst-Balduin-Gymnasium

Munstermaifeld

Community 03/1992 - 04/1993 Arbeiter-Samariter-Bund (ASB)service: LV Koln

Studies: 10/91 - now Universitat zu Koln:Subject: Physics

10/94 Vordiplom01/1999 Diplom:

”Charakterisierung einerKohlenstoff-Cluster-Quelle”

Studies in 02/1996 - 11/1996 University of Cape Townforeign countries: theor. physics

Termination: B.Sc. (Honours)03/2001 - 9/2001 Harvard-Smithsonian Institution,

Center for Astrophysics(FTMW research on reactivemolecules)

Activities: 03/1995 - 04/1995 ”Miniforschung” at theUniversitat zu Koln (I.PI) sectionfor receiver technology

03/1996 - 11/1996 tutor for ”first year students”at the University of Cape Town

05/1998 - 02/1999 student assistant at the I.PI02/1999 - 02/2001 scientific assistant at the I.IP12/1999 - 06/2000 lecturer at the IFBM Cologne

(Institut fur Biologie und Medizin)9/2001 - now scientific co-worker at the I. IP

Koln, 15th May 2003

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