Recent technological advances enabled the development of a new broadband Fourier transformmicrowave spectrometer in 2006. Since then, more than 15 broadband spectrometers have becomeoperational worldwide and have also been extended to the millimeter wave and the terahertzfrequency range. In the experiment, the microwave frequency is linearly swept within a short chirpcovering up to 12 GHz so far. This chirped pulse efficiently polarizes the molecular sample at allfrequencies lying within this frequency range. Fourier transformation of the molecular responsefrom the time domain to the frequency domain gives the broadband rotational spectrum. This newinstrument removes one of the major disadvantages of cavity-based Fourier transform microwavespectroscopy, which has been its slowness. As a consequence, rotational spectroscopy is nowconcentrating on even larger and more complex molecules. Also double-resonance experiments arenow facilitated. Furthermore, the broadband technique opens the door towards new directions ofrotational spectroscopy, i.e., towards dynamics studies such as the investigation of isomerizationreactions.
1. Introduction
Currently, the field of high-resolution rotational spectroscopy is being revolutionized,driven by recent major developments in the technology of test and measurement equip-ment: In 2008, Pate and coworkers published a novel broadband rotational spectrometerdesign, which is based on a chirped microwave pulse and which allows for recordingthe rotational spectra of even complex and conformer-rich molecules within a singleacquisition [1]. With this new, so-called chirped-pulse Fourier transform microwave(CP-FTMW) spectrometer, they demonstrated broadband operation over up to 12 GHz,
therefore eliminating one of the main disadvantages of conventional cavity-basedFTMW spectroscopy, which has been its slowness. Depending on the experimental pa-rameters and the particular molecules under study, the CP-FTMW technique is about2–3 orders of magnitude faster than conventional cavity-based FTMW spectroscopy forrecording spectra with comparable signal-to-noise ratios [1]. The high speed of CP-FTMW spectroscopy combined with its sensitivity now allows the field to move onto investigate the structure and dynamics of ever larger and more complex molecules,supported by advanced double-resonance techniques, as discussed in this review article.
Over the last decades, pure rotational spectroscopy as well as rotationally re-solved spectroscopy techniques have been proven to be an ideal tool for the structuredetermination of smaller molecules and molecular complexes as well as for furthermolecular parameters, such as the dipole moment, barriers to internal rotation and nu-clear quadrupole coupling effects, with high precision. Furthermore, pure rotationalspectroscopy does not rely on the presence of a chromophore in the molecules as is ne-cessary for UV-based spectroscopy techniques. The only requirements on the moleculesis that they have to be polar, i.e., have a non-zero electric dipole moment.
In addition to pure rotational spectroscopy in the microwave and millimeter fre-quency range, also laser-based techniques such as the rotational coherence spec-troscopy and rotationally resolved UV spectroscopy are important to study moleculargeometries and related parameters. Rotationally-resolved UV spectroscopy (see forexample the recent studies on the hormone melatonin and the neurotransmitter p-methoxyphenethylamine [2,3]) allows to also determine the structure of electronicallyexcited states, however they rely on the presence of a chromophore. In rotational coher-ence spectroscopy, an IR pulse generates a coherent rotational wave packet by meansof non-adiabatic alignment. After a variable delay, the wave packet is probed by a UVpulse which excites and ionizes the molecule via a resonant electronic state. In theCRASY (Correlated Rotational Alignment Spectroscopy) approach [4], femtosecondpump-probe is used. The collected electron and ion signals are Fourier transformed,which then reveal the rotational Raman spectrum for each species in the sample. Inmass-CRASY experiments, the masses of molecules and molecular fragments can becorrelated with the structure of the initially photoexcited species. In electron-CRASYexperiments, structure-selective electron spectra are obtained. Finally, also dynamics-CRASY experiments can be transformed, where excited state lifetimes can be assignedto particular molecular structures.
The application of rotational spectroscopy to a variety of molecular problems is, forexample, nicely described in the recent book chapters by Caminati and Grabow [5–7]and references therein. The molecular parameters which can be obtained using rota-tional spectroscopy are also highly interesting for studies of large, biologically relevantmolecules. Their investigation in the gas phase is a growing interdisciplinary effort thatseeks to understand the interactions within and between such species at the most fun-damental level. CP-FTMW spectroscopy can make an important contribution to it bydetermining molecular structures, the energy landscape of individual conformers, or thetype of interaction in a molecular cluster, to name a few.
However, using CP-FTMW spectroscopy, it is now not only possible to recordthe rotational spectra of complex, conformationally rich molecules in only a singlemeasurement, and thus having an improved handle for their structure determination.
Broadband Rotational Spectroscopy for Molecular Structure and Dynamics Studies 3
Probably equally important, it also strongly facilitates double-resonance experiments,see for example Refs. [8,9], which become increasingly relevant for the analysis ofspectra of large molecules. In addition, it even opens the door towards new direc-tions of molecular spectroscopy, such as dynamic rotational spectroscopy. Its power toinvestigate the isomerization kinetics of polar molecules has impressively been demon-strated by Dian et al. in a recent study [10]. The molecules are excited above the barrierto isomerization with a narrow-banded infrared laser, and subsequently probed witha broadband chirped microwave pulse. The obtained spectra display completely newfeatures that arise from the nuclear motion associated with intramolecular vibrationalenergy redistribution (IVR) and isomerization, resulting in changes to the overall en-velope of the spectrum. This, in turn, allows for the determination of the time scale ofisomerization. The approach and further prospects for double-resonance experimentsare discussed in more detail in Sect. 4.
Since the first demonstration by Pate et al. in 2006 [1,11], there are now more than15 CP-FTMW spectrometers operational world-wide (about a dozen in North America,and, to the best of our knowledge, three in Europe) [12–21]. More are currently beingassembled. They cover various frequency ranges and offer different broadband opera-tion, depending on the scientific questions and molecular systems they were designedfor. These activities resemble well the very lively atmosphere in the field.
This review article is structured as follows: In Sect. 2 we will introduce the basicidea behind broadband CP-FTMW spectroscopy and discuss some interesting varia-tions of the original setup by Pate et al. [1]. In Sect. 3, selected applications of CP-FTMW spectroscopy to molecular problems will be presented, while Sect. 4 is devotedto double-resonance experiments with particular emphasis on dynamic rotational spec-troscopy.
2. Chirped-pulse Fourier transform microwave spectroscopyFigure 1 displays a scheme of the setup of our new chirped-pulse Fourier transformmicrowave spectrometer COMPACT (compact-passage acquired coherence technique),which is operational since summer 2011 [17]. It is a combination of the setups pre-sented by Pate et al. [1,21] and the setup proposed by Grabow [7]. The heart of thespectrometer is an arbitrary waveform generator which creates the chirped microwavepulse. We use chirped pulses covering the 2–8 GHz frequency range, i.e., within 1 μsthe microwave frequency is swept linearly from 2 to 8 GHz. The spectrometer is es-pecially designed to operate in this low frequency range since we are particularlyinterested in investigating larger molecules as well as molecular complexes. Due to theirlarge size and comparatively high mass, they exhibit large moments of inertia and thussmall rotational constants resulting in low rotational transition frequencies. The band-width of our spectrometer is currently limited by the specifications of the traveling wavetube amplifier and the horn antennas.
Low-frequency chirped-pulse rotational spectroscopy offers several interestingproperties. In cavity-based FTMW spectroscopy, the actual size of the microwave cav-ity becomes an important aspect for the low frequencies. Microwave reflectors aslarge as 48 inch (about 122 cm) are used to access the low frequency range down to1 GHz [22]. Furthermore, in our experiments the ultimate line width scales linearly
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Fig. 1. Schematic of the Hamburg COMPACT microwave spectrometer covering the 2–8 GHz range. Bothtrigger lines and microwave cables are indicated.
with frequency, since the dephasing time is related to Doppler motion. Thus, in princi-ple, higher resolution can be obtained for the lower frequency range compared to the7–18 GHz range. In addition, many molecular features such as the K manifolds forasymmetric-top molecules become more complicated with increasing value of the ro-tational quantum number J so that having access to low J transitions can become veryvaluable.
The 1 μs long chirped pulse is amplified by a 300 W traveling wave tube amplifier.It is transferred into the vacuum chamber using horn antennas. In our setup, the distancebetween the horn antennas amounts to about 40 cm. The molecules are supersonicallyexpanded into the vacuum chamber using two pulsed valves, where they will interactwith the microwave excitation pulse.
The excitation procedure is in principle analog to FT-NMR spectroscopy wherea coherent superposition of individual nuclear magnetic “substates” is created by ap-plying a short pulse (typically about 1 μs) of RF energy to the sample, followed bya Fourier transformation of the free-induction decay (FID) to obtain the frequency-resolved spectrum [23]. Since in NMR spectroscopy the entire spectrum usually onlyspans a few kHz, the broadband operation became technologically feasible much earlierthan in rotational spectroscopy where the molecular spectra usually span many GHz.
If the difference in energy between two rotational energy levels of the moleculesunder investigation is resonant to a frequency within the chirped microwave pulse, the
Broadband Rotational Spectroscopy for Molecular Structure and Dynamics Studies 5
two respective rotational energy levels will be coupled, i.e., a coherent superpositionis created, which can also be described as a macroscopic polarization. The decay ofthis macroscopic polarization is recorded as a free-induction decay (FID) using a fastdigital oscilloscope, after it has been amplified with a low-noise microwave amplifier.The description of the macroscopic polarization by using a fast frequency sweep hasbeen worked out previously [1,7,24–26]. The important advance of CP-FTMW spec-troscopy compared to previous experiments such as Stark sweeping is that it is nowpossible to perform broadband chirped pulse excitation in a time scale shorter comparedto the transient emission time (T2) which is about 10 μs. This became possible with thenew generation of arbitrary waveform generator (AWG). This allows us to detect themolecular emission in the absence of the polarization pulse.
Pate et al. discuss in Ref. [1] that the signal from chirped pulse excitation has theform
S ∝ ω ·μ2 · Epulse ·ΔN0 ·(π
α
) 12, (1)
with ω being the frequency, μ the transition dipole moment, Epulse the electric fieldstrength of the microwaves, and ΔN0 the population difference at equilibrium, assumedto be unchanged by the pulse. This is true for the weak pulse limit, which can be ap-plied for high bandwidth measurements for all practical amplifier choices. As discussedin more detail in Ref. [1], a key aspect is that the signal S scales as α
12 . This means that,
for a fixed pulse duration, the signals decrease with the square root of the bandwidth.This is contrary to transform limited pulses where the signal decreases linearly with theexcitation bandwidth [24].
Finally, the rotational spectrum is obtained via Fast Fourier transformation of theFID. All frequency sources and the digitizer, i.e., the oscilloscope, are phase-locked toa 10 MHz Rb-disciplined quartz oscillator. On the receiver end, a high-power diode lim-iter and a solid-state single-pole, single-through (SPST) switch are integrated to protectthe sensitive receiver electronics from the high-power excitation pulse (Fig. 1).
The CP-FTMW technique also allows us to exploit the multiplexing effect by firingtwo pulsed valves simultaneously to increase the number of molecules in the interactionregion which further decreases the acquisition time. In the Fourier transform measure-ment, the signal amplitude is linear in the number of emitters, and the noise decreasesas the square root of the number of signal averages. Therefore, the use of N nozzles forsample injection decreases the measurement time required to reach a target signal-to-noise ratio by a factor of N2 and the sample consumption by a factor of N. The use ofup to three valves simultaneously has been demonstrated by the Pate group [1].
Another possibility to significantly decrease the acquisition time is to record mul-tiple FIDs per valve opening. This is possible since the length of the gas pulse (severalhundred μs) is significantly longer than the chirp (1 μs) and the time to record the free-induction decay (FID, 20–50 μs). In practice, up to 10 FIDs for each sample injectionpulse can be measured in a standardized way. In Ref. [27], Nicholas Walker describesan interesting experiment in which he used a sequence of more than thirty-five chirpedexcitation pulses to extensively map out the concentration of a given molecule withina supersonically-expanding gas sample (Fig. 2). (Note that he does not recommend thereaders to repeat this experiment because the maximum specified power per time unit
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Fig. 2. Multiple FID experiments to map out the molecule concentration in a gas pulse using CP-FTMWspectroscopy. The blue trace in this figure indicates the position and duration of each chirped excitationpulse in a sequence. Each chirp is triggered by the falling edge and deactivated on the rising edge of thepulses shown. The yellow trace shows the intensity of the molecular microwave emission (reproduced withpermission from Ref. [27]).
for the protection switch could be exceeded.) The yellow trace of Fig. 2 shows the in-tensity of the molecular microwave emission. Each chirped excitation pulse is followedby intense microwave emission that decays from the peak intensity over about 20 μs.The timescale expands beyond the period during which the gas pulse interacts with themicrowave excitation pulse. The peak intensity of the molecular microwave emission isgreatest about 590 μs after the nozzle pulse. After this maximum, the peak intensity isseen to decrease gradually between 600 and 1200 μs.
The sum of the discussed developments and improvements (chirped pulse, multiplesources and multiple FIDs per gas pulse) leads to an decrease in acquisition time forthe entire 12 GHz spectrum compared to conventional cavity-based spectrometers byabout a factor of 1000 [1]. With the cavity-based setup, only about 1 MHz of the spec-trum can be interrogated at once (due to the narrow bandwidth of the high-Q microwaveresonator). To measure the next 1 MHz, the resonator has to be mechanically adjusted,which accounts for a large fraction of the actual acquisition time. However, on the otherhand, the microwave resonator does not only amplify the microwave excitation pulsebut also the molecular response signal. To compensate for that, a high-power amplifieris used and more measurement repetitions are performed in CP-FTMW spectroscopy.
Figure 3a shows the 2–8 GHz rotational spectrum of trifluoro iodo methane CF3Iafter one acquisition (1 μs), 10, 100, and 1000 data acquisitions obtained with ourCOMPACT spectrometer. CF3I is a symmetric top which can be described by the quan-tum numbers J , K , I and F = J + I . The individual rotational transitions are hyperfine-split due to nuclear quadrupole coupling of the iodine nuclear spin (I = 5/2) with theoverall angular momentum. The resulting splitting pattern and its intensities are verycharacteristic and can facilitate the spectral assignments. As can be seen, the main fea-tures of the rotational spectrum are already available after one acquisition. After 1000
Broadband Rotational Spectroscopy for Molecular Structure and Dynamics Studies 7
Fig. 3. Rotational spectrum of trifluoro iodo methane CF3I obtained with the Hamburg COMPACT spec-trometer after 1, 10, 100 and 1000 acquisitions using two valves simultaneously with neon as carrier gas(a). The J +1 ← J : 1 ← 0 (around 3 GHz) and the J +1 ← J : 2 ← 1 (around 6 GHz) rotational transi-tions are displayed. Both transitions are split due to nuclear quadrupole coupling arising from the iodinenucleus. Part (b) shows a comparison of the experimental spectrum (J +1 ← J : 2 ← 1 rotational transi-tion) with a simulation indicating the very good agreement for both the frequencies and the intensities ofthe quadrupole hyperfine transitions.
acquisitions (about 20 min) all spectral features are present with a good signal-to-noiseratio. Figure 3b displays a comparison of the experimental and the calculated rotationalspectrum for the J +1 ← J : 2 ← 1 transition of trifluoro iodo methane CF3I. The in-tensities for the various hyperfine transitions can be calculated following text bookprocedures (see, for example, Ref. [28]). Contrary to results from cavity-based FTMWspectroscopy, the experimental intensities of chirped-pulse FTMW spectroscopy, i.e.,when working in the linear-passage regime, are accurate over the entire frequency rangeand agree well with the calculated ones. This is extremely useful for the assignment ofnew species, in determining relative dipole components and in estimating the relativepopulations of different species in the spectrum.
With the current setup, the spectral resolution is mainly limited by Doppler broad-ening to 40–100 kHz depending on the length of the recorded FID and on the carriergas and thus on the velocity of the molecules in the molecular beam, since the molecu-lar expansion is oriented perpendicular to the microwave excitation fields. The spectralresolutions obtained with cavity spectrometers are usually on the order of 3–5 kHzfor the coaxial beam-resonator arrangement COBRA [29,30]. If higher resolution than40–100 kHz is needed, rotational transitions obtained with the CP-FTMW spectrometercan be specifically remeasured with a cavity FTMW instrument. One possible way toincrease the resolution in a CP-FTMW experiment would be to develop a coaxial-likearrangement.
Grabow proposed another new setup which will allow for both the broad-band character of the spectrometer as well as the outstanding resolution of FTMW
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spectroscopy, the wide-IMPACT (in-phase/quadrature-phase-modulation passage-acquired-coherence technique) apparatus [5]. It relies on in-phase/quadrature-phase(I/Q) modulation and can cover 20 GHz in a single acquisition (for example the6.5–26.5 GHz range). Via an antenna/reflector assembly, the energy of the excitationsignal is converged towards the expansion volume of the supersonic jet. The maximumfield amplitude for the polarisation of the molecules is thus available in the regionof high particle density. In the proposed setup, the relative arrangement of molecularjet and high-frequency field is very similar to a semi-confocal microwave cavity, butthe parabolic mirrors are not forming a resonator and thus allow for broadband op-eration. As in the cavity-based spectrometers, the molecules are expanded coaxiallywith respect to the high-frequency incident and reflected radiation beam and thus alsoa Doppler doublet is obtained. Its components exhibit a very narrow spectral widthbeing comparable to the cavity-based FTMW spectrometers, i.e., a full width at halfmaximum (FWHM) of about 3 kHz can be obtained, since the observation time inthis arrangement is similar to the cavity experiment. This spectrometer is currentlyassembled at the Leibniz University of Hannover.
Recently, the chirped-pulse technique has also been extended to room-temperaturesamples [20] and to the millimeter-wave region (chirped-pulse millimeter-wave (CP-mmW) spectroscopy) [13], which is particularly important for the existing and upcom-ing instruments in astrochemistry such as the Atacama Large Millimeter/submillimeterArray ALMA. The initial chirp generated by an arbitrary waveform generator isfrequency-up-converted to the 70–102 GHz region. The spectrometer can acquire up to12 GHz of the spectrum in a single shot. However, the performance is currently limitedby the capabilities available for broadband amplifiers, which can attain peak powers ofonly about 10–100 mW compared to the TWT amplifiers delivering for example 300 Wused in CP-FTMW spectroscopy (vide supra). In Sect. 3, we will discuss CPmmWspectroscopy of Rydberg–Rydberg transitions in Ca atoms in more detail, as recentlypublished by the Field group [31].
In 2011, Plusquellic et al. extended the chirped-pulse technique to the terahertzrange, and constructed a novel chirped-pulse terahertz spectrometer for broadband tracegas sensing [32]. It operates in the 530–620 GHz spectral region with a bandwidth of10 GHz, and it is capable of generating and detecting precise arbitrary waveforms atTHz frequencies with ultra-low phase noise by using the newly developed heterodyneterahertz technology. With this approach, they constructed a rapid broadband multi-component gas sensor with low ppb sensitivities and spectral resolution of better than20 kHz in real time. The system is based on solid-state sources to achieve rapid broad-band detection in a portable and relatively inexpensive package [32].
3. Selected applications to molecular problems
In this section, we will discuss a selection of spectroscopic applications in the areaof molecular structure determination which demonstrates the potential of the new CP-FTMW broadband technique. It is ideally suited for large molecules since it is ableto analyze samples that contain a rich mixture of molecular species, including con-formers, simultaneously. It is uniquely suited for investigations of large molecules with
Broadband Rotational Spectroscopy for Molecular Structure and Dynamics Studies 9
rich conformational landscape where we are interested in the molecular conforma-tional structure. By using isotopic substitution and Kraitchman’s equations, explicitatomic positions can be determined. Thus, the precision with which molecular pa-rameters can be determined using rotational spectroscopy now also becomes availablefor larger species, potentially offering new insights into long-standing chemical ques-tions such as molecular recognition. Furthermore, it strongly supports the application ofdouble-resonance experiments which can help to analyze the spectra of more complexmolecules [8] and which will be discussed in more detail in Sect. 4.
In a recent work, Shipman et al. studied the conformational landscape of strawberryaldehyde (ethyl 3-methyl-3-phenylglycidate, C12H14O3) (Fig. 4) [33]. It contains 15heavy atoms and possesses two chiral centers, and thus is one of the largest moleculesinvestigated with high-resolution microwave spectroscopy so far. Due to the two chi-ral centers, the conformational isomers of strawberry aldehyde are either homochiral(cis) or heterochiral (trans). In the homochiral (cis) diastereomer, the terminal alkylchain is able to interact with the phenyl ring via a through-space dispersion interac-tion (long-range). In the heterochiral (trans) diastereomer the molecule is not flexibleenough for this interaction to affect the molecular energy substantially. Within eachconformational family, there are twelve isomers, resulting in 24 possible conformers intotal. Calculations predict that 12 of these 24 conformers are expected to be populatedin the supersonic expansion: six of cis and six of trans.
The spectrometer used was equipped with a heated nozzle to bring liquid and solidsubstances into the gas phase. The rotational spectrum, recorded in the 6.5–18 GHzrange, was obtained with a 1000 : 1 signal-to-noise ratio on the most intense transition(Fig. 4). In total, 8908 transitions with a signal-to-noise ratio greater than 3 : 1 havebeen counted for the spectrum. Shipman et al. could assign 1925 of these transitions tothe rotational spectra of five normal species conformers, 24 13C isotopologues in naturalabundance and thermal decomposition products.
Strawberry aldehyde is sufficiently flexible that intramolecular interactions betweenfunctional groups on the molecule are present. It was shown by Shipman et al. thatthe B3LYP density functional can only adequately describe the conformers of trans-strawberry aldehyde but not the cis conformers, whose energies and interconversionbarriers are strongly influenced by long-range interaction between an alkyl group anda phenyl ring (vide supra) [33]. They could determine an experimental heavy-atomstructure using assignments of each singly-substituted 13C isotopologue of the mostpopulated conformers to derive atom positions. The M05-2X density functional as wellas MP2 methods appropriately treated the intramolecular interaction in the conform-ers of cis, and excellent agreement between calculated and experimental structures wasobserved.
This work does not only impressively demonstrate the power of broadband rota-tional spectroscopy for a detailed investigation of larger molecules, it also points tosome of the difficulties that we will have to overcome in the course of this endeavor.As molecules increase in size, they have a larger number of populated conformers, andsome fraction of these conformers will almost certainly be stabilized by intramolecu-lar interactions that are poorly treated by the theoretical methods currently in use byexperimentalists. Broadband rotational spectroscopy experiments such as on the straw-berry aldehyde by Shipman et al. will be essential to allow experimental results to foster
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Fig. 4. (A) Two dominant conformers of strawberry aldehyde (c-sg− and t-aa), and (B) the rotational spec-trum of strawberry aldehyde from 6.5 to 18.5 GHz as reproduced from Ref. [33] with permission. Thenoise level of the spectrum is about 0.3 μV. The two marked peaks are the c-sg− 909–808 and the t-aa 441–330 transitions at 7980.75 and 8781.62 MHz, respectively.
the appropriate use of existing theoretical methods and the development of new ones, ifnecessary.
Similar aspects are also important for studies of molecular aggregates aiming atgaining more insights on molecular recognition processes in biology and chemistry.During the last decades, gas-phase high-resolution spectroscopy has been demonstratedto be an efficient tool to study molecular complexes in great detail and extract valuableinformation about the characters of the bonds between the two binding partners. Thediversity of interaction forces leads to an increased complexity for understanding andpredicting the outcome of a molecular recognition event. A correct description of the
Broadband Rotational Spectroscopy for Molecular Structure and Dynamics Studies 11
interaction forces between the binding partner in molecular complexes is still one ofthe remaining challenges in theoretical chemistry. The recent themed issue “Weak hy-drogen bonds – strong effects?” of the journal “Physical Chemistry Chemical Physics”demonstrates this in an impressive way [34]. In there, Kisiel et al. published a study onthe structure and properties of the (HCl)2(H2O) cluster and demonstrated impressivelyhow chirped-pulse Fourier transform microwave spectroscopy can foster this kind ofresearch [35].
Their work is an interesting contribution to improve our present understanding ofthe process of protolytic dissociation at the molecular scale, which is an exciting partof ongoing small-cluster research. Of particular interest is the formation of hydrochlo-ric acid, which seems to take place on dilution of a hydrogen chloride molecule in fourmolecules of water [36,37]. Recently, an observation of this “smallest droplet of acid”,namely (H2O)4HCl, has been reported based on laser infrared spectroscopy in heliumnanodroplets [37]. However, a large number of different small clusters can be formedfrom hydrogen chloride and water molecules, while infrared investigations are limitedto the crucial OH and HCl stretch regions so that unambiguous assignment can be dif-ficult. For example, a reassignment of the above-mentioned IR band to (HCl)2(H2O)2
has recently been proposed based on IR spectroscopy in the 2500–3000 cm−1 rangeand careful measurements of the pickup pressure dependence as well as the transitionmoment angles associated with the HCl stretch vibrations [38].
On the other hand, each cluster will exhibit a unique rotational spectrum provid-ing detailed information on their properties, once their spectra can be assigned. Thesmallest clusters of this system, i.e. H2O-HCl [39,40] and (H2O)2HCl [41] have alreadybeen investigated by cavity FTMW spectroscopy. But, as in the infrared spectral region,further progress was hindered by assignment problems arising from the multiple possi-bilities of the carriers of observed new lines. The problem, however, did not arise froma lack of resolution and line blending which complicate the infrared investigation, butfrom the time consuming access to the spectrum using the cavity FTMW spectrometer.For example, the studies of (H2O)2HCl [41] resulted in many unassigned lines due to thedifficulty of finding more lines of the same species. The much more efficient chirped-pulse rotational spectrometer now offers the opportunity to make further progress onthis topic and to unravel the molecular properties of these small clusters step by step,with the ultimate goal of reaching the ionic cluster regime. Kisiel et al. recorded thechirped-pulse rotational spectrum of the supersonically expanded water + hydrochloricacid mixture in order to assign rotational spectra of further clusters in this system [35].
Figure 5 shows a zoom-in to the 15 360–15 620 MHz region of the chirped-pulserotational spectrum as reproduced from Ref. [35]. The raw spectrum in this region isdominated by the rotational transitions of the H2O-HCl cluster (both the 35Cl and the37Cl isotopologues) to an extent that lines of other species are almost two orders ofmagnitude smaller in intensity (top panel). A closer look (middle panel) reveals a richstructure arising from lines belonging to rotational spectra of the water dimer (H2O)2,the Ar2H35Cl cluster and the (H2O)2H35Cl cluster (Ar has been used as carrier gas).A series of rich hyperfine multiplets could be identified in the residual spectrum (lowerpanel) by subtracting the spectra of all known clusters from the rotational spectrum.This pattern of four rich multiplets is characteristic for one particular rotational transi-tion of a species with two chlorine nuclei, i.e., four different chlorine isotopologues.
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Fig. 5. Identification of a series of rich hyperfine multiplets in the residual spectrum obtained on sub-tracting the spectra of all known clusters from the chirped-pulse rotational spectrum of a supersonicallyexpanded Ar + H2O + HCl mixture. (Reproduced with permission from Ref. [35].)
More insight into the molecular and spectroscopic properties reveals the observa-tion of the lowest rotational transition J = 111 ← 000, which is displayed in Fig. 6 alongwith the deduced cluster structure. The J = 111 ← 000 transition is characterized by thesimplest hyperfine structure possible for this cluster. It reveals clearly that a rotationaltransition of (HCl)2H2O is made up of two overlapping hyperfine splitting patterns, atan intensity ratio of 1 : 3, as indicated by the stick spectra. This feature is characteristicfor a loosely bound water molecule with relatively low barriers to reorientation motions.Also note the very good intensity agreement between the experiment and the respectivesimulation. Due to these motions, the (HCl)2H2O cluster has two energetically equiva-lent minima on the intermolecular potential. The cluster can be interconverted betweenthese minima via a combination of inversion and tunneling motions, while switchingthe hydrogen atoms [35]. However, detailed information about the internal motions arestill to be resolved. A detailed permutation-inversion group-theoretical analysis com-bined with advanced ab initio calculations might be necessary to unravel the underlyinginternal dynamics [42–44].
The two single 37Cl isotopic species and the double 37Cl species have been assignedin the natural abundance sample. By using also isotopically enriched samples, namely18O and HDO species, the rS heavy atom geometry of the cluster was determined(Fig. 6) and the strongest bond in the intermolecular cycle, r(O-HCl) = 3.126(3) Å, isfound to be intermediate in length between the values in H2O-HCl and (H2O)2HCl. The
Broadband Rotational Spectroscopy for Molecular Structure and Dynamics Studies 13
Fig. 6. The hyperfine pattern of the lowest J rotational transition for (H35Cl)2H2O. For a single chlorinenucleus, this would be a simple triplet, while presently it is made more complex by the presence of twoquadrupolar nuclei and overlapped patterns for two vibrational states, W and S (see Ref. [35] for moredetails). The transition marked with an asterisk is unidentified, potentially having hyperfine structure. (Re-produced with permission from Ref. [35].)
rich nuclear quadrupole hyperfine structure due to the presence of two chlorine nucleihas been fitted and provided useful information on the nonlinearity of intermolecularbonds in the cluster. This chirped-pulse rotational spectroscopy study on (HCl)2H2Ocompletes the rotational spectroscopy investigations of clusters containing H2O andHCl up to the level of the trimer. This prepares the ground for a search for the heavierspecies and for more detailed studies of the “smallest droplet of acid”.
The new possibilities of high-resolution CP-FTMW spectroscopy go hand in handwith the need for more sophisticated molecular beam methods to bring these moleculesinto the gas phase, which are often liquids and even solids at room temperature. By now,a large variety of sources has been developed so far by the molecular beams commu-nity: valves equipped with heated reservoirs, DC discharge nozzles to produce transientspecies such as radicals and/or vibrationally excited species, as well as laser-desorptionand laser-ablation sources. Laser desorption is often supported by a matrix such asgraphite. Only low-power laser light (a few mJ) is used to bring delicate (bio)moleculessuch us amino acids (see for example Refs. [45,46]) and sugars [47] into the gas phase.Those often decompose when being heated. Laser ablation, on the other hand, usuallyincludes the use of a focused high-power (YAG) laser which is producing a plasmaat the surface of the material to be ablated. In this plasma (and in the course of thesubsequent supersonic expansion) for example metal clusters of varying sizes can be
14 M. Schnell
produced. The combination of these modern laser-desorption and -ablation sources withCP-FTMW spectroscopy opens the door to other molecular systems, such as sugarswhich are also conformationally rich or metal cluster systems.
In a very recent study, Stephens et al. investigated the molecular geometry of theOC-AgI complex in the gas phase, employing a combination of chirped-pulse rotationalspectroscopy and laser ablation as well as ab initio calculations [48]. They find that thecomplex is linear. Isotopic substitutions at the silver, carbon and oxygen atoms allowedall bond lengths to be established by r0, rs and r (m)
m methods of structure determination.The molecular structure and spectroscopic parameters determined from the experimen-tal data were presented with the results of calculations at the CCSD(T) level. It is foundthat both the lengths of the CO and the AgI bond in the complex are significantlyshorter than in the free CO and AgI molecules. An analysis of the nuclear quadrupolehyperfine structure of the 127Ag nucleus (χaa(I ) = −769.84(22) MHz) based on theTownes–Dailey model [28] implies an ionic character of 0.66 for the metal halide bondin the complex. This corresponds to a reduction of the ionic character compared to thefree AgI of about 10% and can explain the shorter bond lengths. Thus, the combina-tion of CP-FTMW spectroscopy with a laser-ablation source demonstrated in the workby Stephens et al. promises new access to the chemical and physical properties of, forexample, metal clusters and their aggregates with other species.
The recent extension of the chirped-pulse technique to the millimeter-wave fre-quency range [13] found an interesting application in the spectroscopy of Rydberg–Rydberg transitions [31], which are still not much explored. The Field group generateda pulsed beam of Ca atoms, which are excited to their 4s36s 1S0 Rydberg state. A chirpedpulse covering the 70–100 GHz frequency range polarizes all Rydberg–Rydberg tran-sitions, i.e., it creates coherences, for which the resonance frequency occurs within thefrequency range of the chirp. These independent coherences undergo free-induction de-cays (FIDs), as explained above for the CP-FTMW spectroscopy technique (Sect. 2).Here, the resulting oscillating electric field is heterodyne detected by mixing witha local oscillator, and down-converted to the microwave range for data processing andFourier transformation.
With this technique, Prozument et al. were able to record the CPmmW spectrumof the 36p–36s Rydberg–Rydberg transition in Ca atoms [31]. The line width amountsto 420 kHz, which is mainly due to Doppler dephasing. Other contributions can befrom (superradiant) population decay, the transit time of Ca atoms and dipole-dipoledephasing. The observed line is split into three Zeeman components due to the Earth’smagnetic field and the stray magnetization of the vacuum chamber, which have beenpartially compensated for by Helmholtz coils.
Because of the kilodebye transition dipole moments of Rydberg–Rydberg transi-tions, a Rydberg CPmmW experiment operates in a qualitatively different regime froma rotational CP-FTMW experiment, where a typical transition dipole moment is about1 D. Thus, a low power chirped pulse in the millimeter wave frequency range can com-pletely polarize the transitions and create an FID that is of comparable strength tothe chirped pulse. As a consequence, interference between the FID and the chirpedpulse has been detected [31]. The interference beats can report important informationabout the system, such as number density, transition dipole moment or excitation fieldstrength and the dephasing rates of the driven two-level systems, thus complementing
Broadband Rotational Spectroscopy for Molecular Structure and Dynamics Studies 15
the spectral information obtainable from the FID, which is worked out in more detail inRef. [31]. Furthermore, using CPmmW spectroscopy, the Field group found evidencefor superradiant decay which occurs in a polarized Rydberg gas where the particlesinteract via long-range dipole–dipole interactions [49–51].
4. Double-resonance techniques
The chirped-pulse rotational spectroscopy technique offers unique double-resonancecapabilities due to the drastically reduced time effort for wide frequency coverage in themicrowave domain. Using the cavity-based setup, two-dimensional double-resonancespectroscopy required unrealistically long measurement times if broad coverage in bothdomains was desired. This is now becoming feasible for many frequency regions inthe second domain. As indicated in the introduction, this allows for a paradigm shiftin microwave spectroscopy: Being well established for determining the geometricaland electronic structure of molecular systems, including various effects of nonrigid-ity, rotational spectroscopy focused on problems that did not require a time-dependenttreatment. Mostly systems in the ground state or only moderately vibrationally excitedstates are accessible in conventional microwave spectroscopy instruments. In combi-nation with laser excitation, however, also dynamical effects can be investigated withmicrowave spectroscopy, which offers unrivaled resolving power and high sensitivity.
In principle, the chirped-pulse technique can be combined with double-resonanceexcitation from almost any frequency region of the electromagnetic spectrum. The gen-eration of the microwave chirped pulse with powerful arbitrary-waveform generatorsallows the generation of microwave excitation sequences at almost any complexityso that, for example, a microwave-microwave double-resonance experiment (2D CP-FTMW spectroscopy) can be performed using an arbitrary waveform generator as theonly source [9]. Such experiments can be very useful in facilitating or even enabling theassignment and the analysis of the spectra of larger molecules, as will also be discussedbelow.
The most exciting perspective for CP-FTMW spectroscopy, however, might be itsapplication to dynamics studies. Since the dynamic behavior manifests itself in theoverall spectral envelope (vide infra), the ability to record the broadband spectrum withreliable intensities in a time-efficient manner will be crucial. For such experiments,the excitation laser wavelength is also scanned to unravel intramolecular processes,rather than kept at a fixed double-resonance frequency. For every IR laser frequency,the rotational spectrum is recorded; i.e., the broadband capabilities of the CP-FTMWspectroscopy are essential. This so-called dynamic rotational spectroscopy is a specialform of double-resonance experiments which, for example, allows for the investigationof conformational isomerization kinetics on a picosecond time scale [10]. Despite their,on the first glance, striking simplicity, isomerizations are still not very well understood.Low-barrier isomerization reactions have been the subject of much experimental [52–55] and theoretical investigation (see Refs. [56–58] and references therein) and arebelieved to be a general class of reactions that are poorly predicted by statistical reactionrate theory. Due to this, theoretical predictions of the respective time scales using thewidespread RRKM approach often differ significantly from experimental values. How-ever, experimental data which could support the development of improved theoretical
16 M. Schnell
methods is still quite limited. As demonstrated by Pate et al., dynamic rotational spec-troscopy can give valuable insights into the kinetics describing conformational isomer-ization of a specific molecular system [10]. These experiments on isolated molecules ina molecular-beam environment directly probe the intrinsic intramolecular reaction dy-namics and complement recent 2D ultrafast infrared spectroscopy techniques that havebeen used to measure C–C single-bond isomerization kinetics in room-temperature so-lution [59]. The combination of techniques applicable to isolated molecules in the gasphase and dilute solutions will make it possible to understand the interplay of purelyintramolecular dynamics and intermolecular interactions in thermal conformationalisomerization reactions in solution [60–62]. The theoretical groundwork of dynamicrotational spectroscopy is discussed in detail in Refs. [63,64].
In their work, Dian et al. use the example of cyclopropane carboxaldehyde (CPCA)which exhibits two different conformers, a syn and an anti structure, which show differ-ent pure rotational spectra. The respective rotational transitions are separated by about3 GHz. The barrier to conformational isomerization amounts to about 1600 cm−1 basedon gas-phase microwave [65] and infrared studies of CPCA. The energy difference be-tween the two conformers is with about 10–30 cm−1 only quite small.
In the experiment, Dian et al. combine the CP-FTMW spectroscopy technique withIR laser excitation. The narrow-band IR laser is coupled into the vacuum chamberand into a multi pass cell to allow for efficient excitation. The molecules are excitedabove the barrier to excitation in a conformer-specific manner due to the narrow band-width of the IR laser. However, the IR photon does not directly excite the reactioncoordinate of the conformational isomerization but, as in this example, a C–H stretchvibration. The vibrational energy will quickly be redistributed (intramolecular vibra-tional energy redistribution, IVR). Finally, also vibrations will be excited which belongto the second conformer. Thus, isomerization occurred. This will be probed usinga chirped microwave pulse. For each IR laser frequency, the rotational spectrum willbe monitored. Conformational isomerization, e.g., reveals itself in the composition ofhighly excited quantum states which can be probed in detail by rotational spectroscopy.This becomes possible because the Hamiltonian remains bound, i.e., the isomerizingmolecular system still exhibits stationary wavefunctions with corresponding discreteenergy levels. However, upon isomerization the structurally delocalized nuclear wave-function features characteristics of the involved conformations. The obtained rotationalspectrum is qualitatively different from the pure rotational spectra of the two conform-ers: The rotational spectra of highly vibrationally excited molecules show additionaltransitions since rotational transitions in the manifold of vibrationally excited statesare excited. Interconversion between distinct species of different shape – character-ized by rotational frequencies related to their different moments of inertia – occursand constitutes an oscillation between the characteristic rotations that appears as co-alescence of the spectral features, a well-known phenomenon in NMR spectroscopy.From the overall envelope of the dynamic rotational spectrum, the time scale of theunderlying isomerization reaction can be obtained with picosecond resolution. The an-alysis requires a time-dependent treatment which is similar to the one developed fordynamic NMR spectroscopy, and is based on a two-level Bloch model allowing forisomerization of the two conformers, i.e., modified for chemical exchange. It is de-scribed in more detail in Ref. [63,64] and in the supplementary information of Ref. [10].
Broadband Rotational Spectroscopy for Molecular Structure and Dynamics Studies 17
Fig. 7. Dynamic rotational spectroscopy, as simulated by Keske et al. [64] (a) and as demonstrated by Dianet al. [10] using the example of cyclopropane carboxaldehyde (CPCA) (b). The time scale of isomerizationcan be extracted from the overall envelope of the obtained spectrum (as reproduced from Ref. [64] withpermission). The dynamic rotational spectrum shows qualitatively new features compared to the pure rota-tional spectra arising from the nuclear motion associated with IVR and the isomerization. (As reproducedfrom Ref. [10] with permission.)
The isomerization rate, corresponding to the conformational lifetime, which followsfrom the overall contour, serves as an upper limit, since intramolecular vibrational en-ergy redistribution (IVR) processes within a conformational species also contributes tospectral broadening.
If the isomerization reaction is very slow, the molecules still have enough time toperform at least one full period of rotation before they undergo isomerization. As a con-sequence, the transitions of the dynamic rotational spectrum are located close to theoriginal rotational transitions of the two conformers. This is displayed in Fig. 7a whichshows a simulation by Keske et al. reproduced from Ref. [64]. If the isomerization isfaster, the spectrum starts to coalesce. Finally, if the time scale of isomerization is toofast, it will coalesce to a narrow frequency range that is intermediate between the twoextremes. The timescale of the experiments is thus limited by the distances of the rota-tional transitions of the two conformers from each other. Ultimately, it is limited by therotational period of the individual molecule.
Figure 7b shows the dynamic rotational spectrum obtained by Dian et al. for cyclo-propane carboxaldehyde (CPCA). The two transitions of the pure rotational spectra ofthe two conformers of CPCA located in the respective spectral range (the 202–101 purerotational transitions) are also indicated in the very rich dynamic rotational spectrumwhich arise from transitions between rotational levels of vibrationally excited states,belonging to both conformers.
The described application of CP-FTMW spectroscopy to isomerization kinetics hasrevealed rich dynamical behavior for a simple, two-geometry reversible reaction. The
18 M. Schnell
unimolecular isomerization rates of the isolated molecule are 16 times slower than thosepredicted by RRKM theory. Dian et al. also observe strongly conformer-specific reac-tion yields. This observation suggests that special doorway resonances that are sparse atthis level of excitation facilitate the isomerization reaction. For the future, one can envi-sion that the laser excitation schemes for dynamic spectroscopy probed by CP-FTMWmulti-resonance techniques are expanded to higher energy regions from the IR overVis to the UV, then accessing conformational dynamics at complex ergodicity and evenabove the barrier to bond-breaking structural isomerization.
As mentioned above, CP-FTMW spectroscopy also nicely supports double-resonance experiments which facilitate the assignment and analysis of complex spectraas demonstrated by Neill et al. [8]. Large, conformationally rich molecules exhibita spectral complexity which can make it difficult or even impossible to determinemolecular geometries using a single electronic, vibrational or rotational spectrum.Double-resonance techniques provide a way to extend spectroscopic analysis to morecomplex molecular systems, which is successfully used by several groups (see forexample recent work by the Gerhards group on the structural analysis of a cyclictetrapeptide and its monohydrate by combined IR/UV spectroscopy [66], or by theZwier group on the evolution of amide stacking in larger γ -peptides, where they inves-tigated triamide H-bonded cycles [67]).
But the existing methods of UV/IR double resonance are reaching their limits ofmolecular size. To date, a Watson–Crick configured G–C base pair has yet to be iden-tified, and significant ambiguities in the assignments of the IR spectra of the differentconformers of di- and tripeptides already exist [8]. Beyond this, there are also signifi-cant ambiguities in the interpretation of the dipole moments of such species measuredby electric deflection methods.
A promising solution to these problems and to the challenges that lie ahead isa combination of the novel chirped-pulse FTMW spectroscopy technique with excita-tion by a low-resolution UV laser, i.e., coupling rotational spectroscopy to electronicspectroscopy to provide selective double-resonance spectroscopy of single molecularconformations or complexes. Here, the new broadband technique significantly supportssuch experiments due to its high measurement speed and sensitivity. In contrast to thedynamic rotational spectroscopy described above, however, the CP-FTMW techniqueis not essential for such experiments, but can accelerate and facilitate them. Rotationalspectroscopy in general offers unsurpassed spectral resolution that makes it possibleto determine the structures of large molecules. But all rotational spectra fall into thesame frequency range, making analysis of complex mixtures difficult. For electronicspectroscopy, the fluorescence lifetime limits the spectral resolution and, therefore, themolecular size range for the technique. However, the exquisite structural sensitivity ofelectronic spectroscopy provides molecule-specific frequency discrimination that ro-tational spectroscopy lacks (for example, conformer-specific electronic origin bands).A combination of the two techniques will allow for rapid spectral analysis. This pow-erful combination and its prospects are nicely described in a recent perspective articleby Neill et al. [8] using the example of p-methoxyphenethylamine (pMPEA), for whichnine energetically low-lying rotational conformers have been predicted theoreticallyand at least seven conformers have been found in a low-resolution fluorescence excita-tion study [3].
Broadband Rotational Spectroscopy for Molecular Structure and Dynamics Studies 19
5. Conclusions and outlook
The novel broadband rotational spectroscopy techniques are rejuvenating the field ofhigh-resolution spectroscopy. During the last three years, at least 15 new broadbandspectrometers operating in the microwave frequency range and two operating in the mil-limeter wave and the terahertz range have become operational. By now, a variety ofmolecular systems have been studied with this new technique in the gas phase, rangingfrom more complex molecular clusters, such as the trimolecular complex (HCl)2H2O, tostrawberry aldehyde which contains 15 heavy atoms and two chiral centers and whichis one of the largest molecules studied with microwave spectroscopy so far.
The avenue to investigate the spectra of larger and more complex molecules iscomplicated by the complexity of the obtained spectra due to an increasing numberof conformers, the presence of natural isotopologues in the beam (which are mea-surable in natural abundance due to the high sensitivity of the instruments), internalrotations and potential nuclear quadrupole coupling. Efficient data analysis programssuch as Jb95 [68] and pgopher [69], which for example offer graphical user inter-faces, are becoming more and more important to analyse the spectra. In this reviewarticle, we also point out the increasing importance of double-resonance experimentsfor facilitating the assignment and the analysis of such rotational spectra. Microwave-microwave double-resonance experiments can nicely rule out connected transitions.With the state-of-the-art arbitrary waveform generators, such experiments can in princi-ple be performed with a single microwave source. Also the combination of CP-FTMWspectroscopy with low-resolution UV spectroscopy, as demonstrated by Pratt et al. [8]is an important application and discussed in Sect. 4.
One very intriguing and promising direction of broadband rotational spectroscopyis its application to study the kinetics of isomerization reactions by using the broadbandmicrowave pulse as a probe. This allows to, for example, perform conformer-selectivemeasurements as demonstrated by Dian et al. [10] .
Double-resonance experiments with other frequency ranges such as the visible andthe ultraviolet range can be envisioned and are on the way. Excitation with a UV laserwill lead to electronically excited states. For them, different de-excitation processesare discussed such as intersystem crossing and internal conversion. Such processes areassumed to have played a key role in the development of life on the early earth. Itwas found that many biomolecules exhibit a surprisingly large stability against UV ra-diation. The processes such as intersystem crossing and internal conversion are fastand happen on nanosecond to femtosecond time scales and have been the object ofmany experimental and theoretical investigations. However, their detailed mechanisms,particularly combined with structural changes, are not well understood to date. Bycombining UV excitation with fast CP-FTMW probing, such pathways might becomevisible, thus offering an interesting alternative route to study molecular dynamics pro-cesses.
Acknowledgement
The author is grateful to Jens-Uwe Grabow, Nicholas Walker and Brooks H. Patefor fruitful scientific discussions on chirped-pulse Fourier transform microwave spec-
20 M. Schnell
troscopy. She also acknowledges various discussions with her present group members,V. Alvin Shubert, David Schmitz and Thomas Betz.
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