2 state: Vibrational statedependence of the product fine-structure distribution
David J. Leahy,a) David L. Osborn,b) Douglas R. Cyr,c) and Daniel M. Neumarkd)Department of Chemistry, University of California, Berkeley, California 94720,and Chemical Sciences Division, Lawrence Berkeley Laboratory, Berkeley, California 94720
~Received 14 April 1995; accepted 9 May 1995!
The predissociation of the O2B3Su
2 state~y50–11! is investigated using fast beam photofragmenttranslational spectroscopy. The energy resolution of the experiment, 7–10 meV, is sufficient to yieldthe correlatedfine structure distributionP( j 1 , j 2) for the two O~3Pj ! fragments. These spin–orbitbranching ratios depend markedly on the vibrational quantum number, providing detailed insightinto a relatively unexplored facet of molecular dissociation dynamics. No less than four repulsivestates are expected to mediate the predissociation of theB 3Su
Since the origins of molecular spectroscopy, tSchumann–RungeB 3Su
2(y8)←X 3Sg2(y9) bands of mo-
lecular oxygen have received a great deal of well-deserattention.1–20 The long progression of rotationally resolvevibrational bands provides a textbook example of the etronic excitation of a homonuclear diatomic molecule. Moover, the photochemistry and photophysics of theB 3Su
2
state of oxygen have important practical ramifications forchemistry of the earth’s atmosphere. The Schumann–Rubands are the dominant absorbers of solar ultraviolet lighthe wavelength range from 180 to 205 nm. The penetradepth of this photochemically important radiation into tearth’s atmosphere depends sensitively on the details oB 3Su
2(y8)←X 3Sg2(y9) spectrum, particularly on the natu
ral linewidths.In 1936, Flory reported that the irradiation of O2 with a
mercury lamp at 184.5 nm led to the photochemical prodtion of ozone, and was the first to suggest that theB 3Su
2
state was predissociated by the repulsive3Pu state to form apair of O~3Pj ! atoms.
21 Some controversy ensued over thissue for decades. However, since the work of Wilkinson aMulliken,5 it has been known that theB 3Su
2 state predisso-ciates with near unity quantum efficiency. The resulting oxgen atoms are responsible for the formation of ozone inupper atmosphere via three-body collisions. The reversecess, O~3Pj ! atom recombination, forms highly excited O2molecules,22–25which may radiate~this process is presumeto make up much of the terrestrial atmosphere nightglo!,
a!Current address: Worlds, 510 Third St., Suite 530, San Francisco,94107.
b!NDSEG Predoctoral Fellow.c!Current address: Combustion Research Facility, Sandia National Labories, Livermore, CA 94550.
d!Camille and Henry Dreyfus Teacher–Scholar.
J. Chem. Phys. 103 (7), 15 August 1995 0021-9606/95/103(7)
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electronically activate other species in collisions, or possibeven react with O2 to form ozone.26,27Oxygen atom recom-bination is a formidably complicated process because itvolves the collision of two open shell atoms. While somprogress has been made, definitive experimental informais sparse, and it remains to be proven which moleculartential states are the most important.28
In this paper, we investigate the predissociation of thelowest vibrational levels of the O2 B
3Su2 state by measuring
the photofragment energy distribution resulting from thphotodissociation of a fast~5 keV! beam of O2. Vibrationallyexcited O2 in its groundX 3Sg
2 state is generated by photodetachment of a fast beam of O2
2 anions. The O2 is excited tovarious predissociating levels of theB 3Su
2 state, and theresulting O atoms are detected using a coincidence detecscheme which yields high kinetic energy resolution for thphotofragments~7–10 meV!. Our experiment shares somfeatures in common with previous studies of O2 photodisso-ciation by van der Zande29 and Cosby,30 in which excited O2was generated by charge transfer neutralization of O2
1 .The resolution of our instrument is sufficiently high t
reveal thecorrelatedspin–orbit distributionsP( j 1 , j 2) of thepair of product O~3Pj ! atoms. This sort of measurement ilargely unprecedented and provides a new perspectivediatomic photodissociation dynamics, as well as the reveprocess, collisions of open shell atoms. Because the prodare a pair of atoms with only electronic degrees of freedothe process of diatomic molecule dissociation appears sosic that one might expect an uncomplicated model to provpredictive power of the product state distributions. Howevthe results presented in this paper show that this is notcase, and that the simple molecular dissociation systO2B
3Su2(y8)→O(3Pj 1
), O(3Pj 2) is sufficiently complex to
defy any straightforward explanation.Figure 1 shows the potential energy curves for the2
states most relevant to our experiment. The open shell~1pg!2
structure of ground state O2, together with the relatively highmultiplicity of the ground state photodissociation [email protected]., a pair of O~3Pj ! atoms#, results in a great richness olow-lying O2 electronic states. With this in mind, it comes ano surprise that theB 3Su
2 state, which correlates asymptotcally to the O~1D!,O~3Pj ! limit, is crossed by a large numbeof repulsive states that correlate to the ground state produIn Fig. 1, only the four dissociative states believed to cotribute significantly to predissociation of theB 3Su
2 state areshown; in fact, there are no less thantenrepulsive curves thatcross this state on the way to the O(3Pj 1
),O(3Pj 2) limit. In
addition, several bound states correlate to this atomic limThe product state distributionsPy( j 1 , j 2) obtained from
our experiment are complementary to the extensive and ctinuing body of research into the predissociation-inducbroadening of theB 3Su
2(y8)←X 3Sg2(y9) absorption spec-
trum. Following Wilkinson and Mulliken’s original observation, it has long been observed that the natural linewidthsthe Schumann–Runge bands have a strongy8dependence.5,6,8 The lines are especially sharp fory850,reach a maximum in width fory854, and show some oscil-lations in width to highery8. Murrell and Taylor31 showedthat the application of the Franck–Condon principle leadsthe idea that a single curve crossing between the repuls3Pu state and the outer limb of theB state can account forthe y8 dependence of the predissociation rate. SchaeferMiller32 later proposed that three repulsive states, namthe 1Pu ,
3Pu , and5Pu states, all play important roles in th
predissociation of theB 3Su2 state. They deduced that th
primary predissociation mechanism is spin–orbit couplibetween theB state and those repulsive states which aconnected by the first-order spin–orbit selection rulDV50, DL52DS50, 61 ~also,g←/→u andS1↔S2!.33
Their electronic structure calculations showed that the3Pu
crossed theinner limb of theB state, while the1Pu state and5Pu state were predicted to cross the outer limb. JulienneKrauss34 supported these conclusions at a higher leveltheory; Julienne35 went on to point out that there is alsostrong spin-orbit interaction with the 23Su
1 state, which
FIG. 1. Diagram of relevant potentials surfaces of O2 and O22 .
J. Chem. Phys., Vol. 103
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crosses theB 3Su2 state at a somewhat larger internucle
distanceR.The calculations in Refs. 34 and 35 were of sufficie
accuracy to provide qualitative numbers for the crossipointsRx and slopesMx of the repulsive curves, as well avalues forAx , the strengths of the spin–orbit couplingsHowever, their Franck–Condon calculation of the predissciation widths based on their curve-crossing parametagreed only qualitatively with the best spectroscopic liewidths available at the time.6,8 The agreement did not im-prove under the scrutiny of higher resolution spectra,12,13,16
and two separate research groups have taken semiempiapproaches to adjust the characteristics of the curve crossto improve the agreement between experiment atheory.11,15,19,20These efforts have culminated in refined vaues for theRx , Mx , andAx parameters that are consistenwith experiment. These new curve-crossing parameters arclose enough agreement with the purelyab initio values thatit is safe to conclude that the theoretical framework for tmechanism proposed by Schaefer and Miller and expanby Julienne and Krauss is essentially correct. The resultsthe semiempirical models thus provide relatively reliabpartial cross sections for dissociation onto the5Pu ,
3Pu ,1Pu , and 23Su
1 states as a function ofy8.While these earlier studies have focused on the mec
nism of the initial curve crossings, our experiment shelight on a second, equally fundamental problem, namehow these repulsive states project onto the atomic oxygspin–orbit states (j 1 , j 2). The uncorrelated fine structurebranching ratios have been measured for predissociationtheB 3Su
2 state to O~3P!1O~3P! and, at higher energy, di-rect dissociation to O~1D!1O~3P!.36–38 In a recentpublication,39 we reported the first measurements of corrlated spin–orbit populationsP( j 1 , j 2) arising from the pre-dissociation of a selected vibration–rotation level of the O2
B 3Su2 state, the~y57,N54! level. In this paper, we extend
our earlier work to the~y50–11, N54! levels of the O2B 3Su
2 state. The correlated fine structure distributions sha marked dependence on the vibrational quantum numbethe B 3Su
2 state, showing that the detailed predissociatimechanism depends strongly ony.
Our results will be presented in terms of two simplimiting cases for evolution of the molecule to the atomasymptotes. One limit, the ‘‘relativistic adiabatic’’ modepredicts the product states on the assumption the atoms reinfinitely slowly with respect to the electronic motion. Thsecond model approaches the problem from the oppositerection: It predicts atomic state distributions in the ‘‘suddelimit,’’ where the molecular states are projected onto tatomic states without account for the evolution of the eletronic wave function during the dissociation. The validity othese two limits will be discussed in the context of O2 dis-sociation. We also present a more phenomenological analthat provides further insights into how the repulsive stat1Pu ,
3Pu ,5Pu , and 2
3Su1 project onto the asymptotic limits
( j 1 , j 2). The varying degrees of success of these simple mels show that the observed branching ratiosP( j 1 , j 2) are theend result of a richly dynamical process.
, No. 7, 15 August 1995
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2497Leahy et al.: Predissociation of the O2 B3Su
2 state
II. EXPERIMENT
A. Experimental method
The principle of the experiment is as follows. We formfast, mass-selected beam of O2
2 , photodetach the ions toform fast neutral O2, excite a predissociative transition in O2with a second laser pulse, and measure the recoil of thesulting pair of O atoms. The experimental method was psented in some depth in Ref. 40, and a relatively brief dscription will be presented here. A schematic of thexperimental apparatus is shown in Fig. 2.
The experiment utilizes a pulsed ion source togethwith two pulsed laser systems, operating at a repetition rof 60 Hz. In the source region, a beam of internally cold O2
2
anions is formed by crossing a pulsed supersonic expanof neat O2 with a continuous 1 keV electron beam. The reltively slow secondary electrons from electron impact ioniztion form negative ions via dissociative attachment; dissoction of van der Waals dimers or larger clusters is presumathe mechanism for O2
2 formation. These ions are skimmedcollinearly accelerated to 5 keV, and collimated with an ezel lens. The resulting fast beam of ions is re-referencedground potential by means of an ‘‘ion elevator;’’41,42 thisfeature enables the pulsed valve source and the detectorsimultaneously referenced to ground. Just after exitingion elevator, the beam is chopped by a transverse bemodulator,43 forming a packet of ions which separate intime-of-flight region according to mass. The O2
2 anions arephotodetached by a loosely focused pulsed laser beam~1 mmdiameter spot size! at 480 nm from an excimer-pumped dylaser. Figure 1 shows there is a significant decrease in elibrium bond length on the transition from anion to neutraAs a result, the O2 neutrals are formed in a strongly invertevibrational state distribution44,45while remaining rotationallycold. In addition, somea 1Dg oxygen is formed by photode-tachment, but our experiment is insensitive to these mecules.
The resulting 5 keV beam of vibrationally excited O2neutrals is intercepted by a second pulsed laser beam, wexcites specific O2 B
3Su2(y8,N8)←X 3Sg
2(y9,N9) transi-tions. This laser pulse is formed by frequency doubling toutput of a second excimer-pumped dye laser system iBBO crystal. The wavelengths used in this work range fro206.04 nm for theB 3Su
2(y859)←X 3Sg2(y954) transi-
tion up to 239.17 nm for they850←y955 transition. Thetransitions were chosen according to the Franck–Condfactors tabulated in Ref. 8. The linewidth of the frequendoubled light is typically 0.4 cm21. The electronically ex-cited molecules go on to predissociate into a pair of phofragments. The lifetimes of the excited molecules depestrongly ony8, but they all fall in the range from 1.2 to 50 p
FIG. 2. Schematic of the experimental apparatus. The C-WSA~coincidencewedge-and-strip anode! detector is discussed in the text.
J. Chem. Phys., Vol. 103,
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~the natural linewidths range from 0.1 to 4 cm21!.16,18,20
These lifetimes are sufficiently short that the predissociatis essentially instantaneous when compared to the 5.8msflight time of the fragments through the 1 m drift region.~This was extended to 2 m for they852 data set; see below.!
The photofragment detection scheme is based onmethod developed by DeBruijn and Los46 and involves theobservation of both fragments in coincidence. While the vmajority of the neutrals are not dissociated and impinge obeam block, each pair of photofragments recoils out of tbeam onto the active area of a time- and position-sensitdetector located 1 m downstream from the dissociation las~as depicted by the dotted lines in Fig. 2!. By scanning thewavelength of the photodissociation laser, we can recorddissociative spectroscopy of the neutrals. The primary moof operation of the machine, however, is to study the tranlational energy release following the photodissociationfree radicals. Our detector can record in coincidence the tiand position of the arrival of each of the two photofragmenbelonging to a single parent radical.40 By collecting severalthousand coincident events, we can accumulate the eneand angle-resolved spectrum of the photofragments for agiven photodissociation wavelength.
For each observed coincidence event, the photofragmdetector records the impact positions of both fragments wan accuracy of about 100mm ~see the following subsectionfor a description of the position-sensitive data analysis!. Si-multaneously, we use a time-to-amplitude converter to recthe time interval between the arrival of the two fragmentsan accuracy of 500 ps. Together, these measurements ythe center-of-mass translational energy release and the reangle of each photodissociation event. For fragmentsequal mass~as in the case of O2!, these relationships aregiven by
Ec.m.51
2Ebeam
Rxy2 1~vbeamDt !
2
L2~1!
and
u5arctanS Rxy
vbeamDtD , ~2!
whereEbeamandvbeamare the laboratory energy and velocitof the O2 beam, respectively;Rxy is the observed recoil dis-tance perpendicular to the beam axis~as measured by theposition-sensitive detector!; Dt is the time interval betweenthe arrivals of the two photofragments at the detector; andLis length of the drift region.
The kinetic energy resolution for data collected with am photofragment flight length was 9–12 meV for recoil eergies ranging from 1.0 to 1.75 eV. Photodissociation of olevel ~y852! was reinvestigated with a 2 mdrift region; thisexperiment produced our best resolution to date, with peof 6.8 meV FWHM at a recoil energy of 1.15 eV~DEc.m./Ec.m.50.6%!. The resolution is determined by thprecision to whichRxy andDt are determined; the contribution from the kinetic energy spread in the radical beamnegligible, as DEbeam/Ebeam,0.1%. As pointed outpreviously,39,46 the high resolution of this experiment result
No. 7, 15 August 1995
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2498 Leahy et al.: Predissociation of the O2 B3Su
2 state
from the detection of the photofragments in coincidence,that broadening effects due to the spatial and temporal spof the radical beam largely cancel out.
While the fast-beam coincidence detection schemeits advantages, it also gives rise to the serious constraintwe may record only one coincidence event per laser sTogether with our 25% coincidence detection efficiency~i.e.,;50% for each fragment!, our maximum coincidence detection rate is around 10% of the experimental repetition rate60 Hz. In the oxygen experiments presented in this papertypically recorded 2–4 coincident events per second, alloing the collection of a typical 50 000 event data set in a fhours’ time.
B. Position-sensitive data analysis
We have recently devoted considerable effort towaoptimizing the accuracy of the time- and position-sensitdetector. For this reason, our data analysis scheme wildescribed in some detail. The fragment impact positionsobserved by using of a pair of wedge-and-strip anodescollect the charge from the detector’s microchanplates.40,47A schematic of the wedge-and-strip anode pattis shown in Fig. 3; the actual pattern is considerably denThis pattern consists of two separate wedge-and-strip an~one upper and one lower, which we will label 1 andrespectively!, comprised of three conductors each~‘‘wedge,’’‘‘strip,’’ and ‘‘zigzag’’ !. These anodes divide the;107 elec-trons from the microchannel plates between the three cductors in a spatially specific manner. The wedge condutapers in the horizontal direction while the strip conducchanges in width along the vertical direction, so the telectrodes determine the horizontal and vertical position,spectively, of the centroid of the electron cloud. The folloing equations relate these charge fractions to the impactsitions:
x15a1xFwedge1b1x , ~3a!
FIG. 3. Schematic of the wedge-and-strip anode. The five-period pashown is to illustrate the structure of the anodes; the actual anode haperiods per half. The terminal for the wedge, strip, and zig–zag conducon both halves of the anode are indicated in the figure. The solid lbetween the conductors represents the insulating gaps.
J. Chem. Phys., Vol. 103
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ashatot.
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dsebereatelrner.des,
n-torroe--po-
y15a1yFstrip1b1y1c1yFstrip2 , ~3b!
x25a2xFwedge1b2x , ~3c!
y25a2yFstrip1b2y1c2yFstrip2 . ~3d!
The Cartesian coordinatesx andy are the horizontal andvertical positions, respectively, of the fragment impacts relative to the origin, which we define to lie at the center of theradical beam. The multiplicative constantsak and additiveconstantsbk define the nearly linear relationship between theanode charge fractionsF and the Cartesian coordinates. Inaddition, we have included a small quadratic term in theycoordinate equations to model an inherent nonlinearity in thdetector’s charge division. Equations~3a!–~3d! are differentand somewhat simpler than those that appear in Ref. 40; four charge amplification scheme, the cross-talk correctionhave proven to be of negligible importance. The crux of thdata analysis is the determination of the values of the parametersak , bk , andck . While rough guesses forak andbk canbe made based on the anode geometry, in a quantitatianalysis the ten constants appearing in Eqs.~3a!–~3d! mustbe determined from experimental data directly. We accomplish this by treating the constants as parameters in a nonliear least squares fit to the oxygen data, with the merit funtion
x25(i
~Rcalc2Robs,i !2
s recoil2 1
Rcentroid,i2
scentroid2 , ~4!
where
Robs,i5@~x1i 2x2
i !21~y1i 2y2
i !21~vbeamDt i !2#1/2 ~5!
and
Rcentroid,i5$@~x1i 1x2
i !/2#21@~y1i 1y2
i !/2#2%1/2. ~6!
The indexi stands for the independent coincident eventsRcalc is the calculated recoil distance given by inverting Eq~1! and using the known oxygen bond strength~5.117 eV,Ref. 48!, the photon energy, the parent oxygen beam velocitvbeam, and the length of the fragment drift region.Rcalc isfirst determined using the kinetic energy release corresponing to the~j 152, j 251! final state; this was the most prob-able state from predissociation of they857 level.39 In subse-quent iterations, the mean kinetic energy release for eadata set is used.Robs is the length of the observed threedimensional recoil vector between the two fragments, whicdepends on the adjustable parametersak , bk , andck . Simi-larly, Rcentroid is the parameter-dependent distance from thcenter of the radical beam to the parent radical impact~asinferred from the fragment impacts, using conservation omomentum!. The constantssrecoil and scentroid characterizethe standard deviations in the recoil measurements~150mm;the detector’s effective diameter is 40 mm! and centroid po-sitions ~namely, the radical beam width, which is 1.6 mm!.
The nonlinear least squares fit utilizes a LevenbergMarquardt algorithm.49 The fit is provided with data sets of afew tens of thousands coincident events in the form of thraw charge fractions of Eqs.~3a!–~3d!. Following an initialestimate, the adjustable parametersak , bk , andck are opti-mized by the algorithm to minimizex2. This results in a set
ern32
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2499Leahy et al.: Predissociation of the O2 B3Su
2 state
of parameters that yield the high resolution kinetic enerrelease spectra presented in this work. In addition, the ogen data fits provide an excellent absolute calibration forposition sensitive detector, which is an essential first stepour photodissociation studies of other polyatomic frradicals.40,50,51
III. RESULTS
Our experimental results can be grouped into three cegories: wavelength scans, kinetic energy release~KER!spectra, and photofragment angular distributions. The walength scans allowed us to identify specific rovibrationtransitions for subsequent dynamical study by our photofrment coincidence detection scheme. The KER spectrathe photofragment angular distributions are both derivfrom the coincidence data sets recorded at the selected etation wavelengths. The angular distributions were foundexhibit saturation effects and will not be discussed here.
A sample of our scans of photofragment yield vs wavlength are shown in Fig. 4. The spectra are rotationallysolved and were easily assigned. It is clear from Fig. 4 tthe natural linewidths depend strongly ony8, with y850 and4 representing the narrow and broad extremes, respectivin agreement with earlier results.5,6,8 An analysis of the in-tensity distributions yielded a rotational temperature of 55for the neutral O2 molecules. Since neutrals produced bphotodetachment will have a slightly broader rotational dtribution than the parent anions, the anion rotational tempeture should be somewhat colder than this.
FIG. 4. Total photofragment yield wavelength scans for several bands ofSchumann–RungeB 3Su
2←X 3Sg2 system.
J. Chem. Phys., Vol. 103,
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These spectra show all of the essential features of tSchumann–Runge bands. These bands are very stronglygraded to the red by the large increase inRe from 1.21 Å intheX 3Sg
2 state to 1.60 Å in theB 3Su2 state. As a result, the
R branch runs directly to the red and is strongly overlappewith the P branch for many bands. TheR and P branchtransitions are nominally labeled asR(N9) and P(N9), asshown in Fig. 4 for they 852←y 955 band. However, alllines for whichN9 andN8>1 consist of at least three over-lapping transitions withDJ5DN originating from theF1,F2, andF3 fine structure components of theN9 rotationallevel. A few weak ‘‘case~a!’’ transitions for whichDJÞDN@such as theRQ32~1! transition# may be seen near the originof the well-resolvedy 850 and 2 spectra.
Photodissociation kinetic energy release spectra weobtained by tuning the dissociation laser to theR~3! transi-tions for ally 8. This transition was chosen since it was typically the most intense for a vibrational band. The results ashown in Fig. 5 fory850–11, with the results fory852 ex-panded in Fig. 6. A small number of kinetic energy releasspectra were obtained for other rotational transitions bwere found to be virtually identical to the results in Fig. 5~for the samey8!. At sufficiently highN8, one expects effectsdue to rotation–electronic coupling to appear in the predisociation dynamics,20 but the cold rotational temperature inour beam precludes us from examining these levels.
The photofragment kinetic energyEc.m. is related to thedesired quantity, namely, the internal energy of the photproductsEint , by
Ec.m.5Eint,01hn2D02Eint . ~7!
Eint,0 andD0 ~5.117 eV! are the initial internal energy and thebond dissociation energy of the parent, respectively.Eint,0 isdetermined by our choice of predissociation resonancwhich selects specific rovibrational levels from the distribution of X 3Sg
2 molecules in the fast beam. The fact that weexcite a few overlapping rotational levels~as discussed inSec. IV! adds 2 meV of energy uncertainty toEint,0. BecauseEint,0, D0, and the photon energyhn are known quantities,the internal energyEint is obtained directly from the observedkinetic energy release.
The internal energy of the products in this case is limiteto the oxygen atom O~3Pj ! spin orbit levels:j51 andj50 lie20 and 28 meV above the ground statej52, respectively.52
Formation of a pair of O~3Pj ! atoms results in six energeti-cally distinct (j 1 , j 2) channels, with the ground state prod-ucts ~j 152, j 252! appearing at highest kinetic energy. Thekinetic energy resolution of the spectra shown in Fig. 5 ihigh enough for the structure associated with the correlatspin–orbit states (j 1 , j 2) to be manifest. These states are labeled in the spectrum in Fig. 6. It is immediately clear thathe fine-structure branching ratios depend strongly on thvibrational level prepared in theB 3Su
2 state. The clearestexample of this dependence appears in the ground state chnel ~2,2!, which is relatively well resolved from its nearestneighbor~2,1! by a 20 meV energy gap. The~2,2! peak isintense in they 850 and 1 spectra, appears more weakly fointermediatey 8, and recurs strongly in they 858 and 9 spec-tra. For all of the spectra, the most intense feature appears
he
No. 7, 15 August 1995
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2500 Leahy et al.: Predissociation of the O2 B3Su
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the middle of the spin–orbit distribution, correspondingthe partially overlapped~2,1! and ~2,0! channels. A cursoryanalysis of the data also reveals that the most energetic oopen channels, the~0,0! channel, is completely absent in aof the observed kinetic energy releases.
FIG. 5. Photofragment kinetic energy release for the predissociation oy850 to 11 levels of the O2 B
3Su2 state. The circles represent the data, a
the solid lines are the fits of the data to the correlated spin–orbit populaPy( j 1 , j 2).
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IV. ANALYSIS
A. Correlated spin–orbit distributions
Following the method described in our recencommunication,39 we extracted quantitative branching ratiosPy( j 1 , j 2) from each of the spectra shown in Fig. 5 by fittingthe data with Gaussian line shapes separated by O~3 Pj !energies. In this fit, the intensity of each Gaussian was ajusted, as well as a common linewidth for all peaks. Thabsolute recoil energy scale was easily determined direcfrom the spectra, because the energy resolution of the dataFig. 5 is sufficiently high that the pattern of energy spacingin the (j 1 , j 2) products is evident; the~2,2! peaks are particu-larly prominent. The actual fitting procedure involved optimizing the nonlinear parameters~peakwidth and absolute en-ergy! ‘‘by hand,’’ with a linear least-squares fit of theintensities of each peak being performed at each iteration.all cases, the fits converged rapidly to give an unambiguoassignment of the spectral features to the correlated spiorbit channels (j 1 , j 2).
The results of the fits are given in Table I and are alsshown in Fig. 5 as solid lines. The uncertainties in thbranching ratios in the table are 1s as derived from the least-squares fitting procedure. Because the features proved tovery well fit by the Gaussian line shapes, the branching ratifor even strongly overlapped product states such as~2,1! and~2,0! are fairly well determined. The data represented iTable I are the major result of this work, and the discussioin Sec. V is devoted to the information content in these vbrational state-dependent spin–orbit branching ratios.
B. Rotational level populations
In Sec. V, we will explore the relationship between theshort-range predissociation mechanism and the observspin–orbit distributionsPy( j 1 , j 2). To do so, it is importantto characterize the levels of theB 3Su
2 state that we areaccessing in our experiment. As discussed in Sec. III, thR~3! transition that we are nominally exciting for eachBstate vibrational levely8 actually consists of at least threeoverlapping transitions, namely, theR1~4!, R2~3!, andR3~2!transitions which originate from the threeFi fine-structurecomponents of theN953 level with J954, 3, and 2, respec-tively. Moreover, fory8>4, the individual linewidths are suf-
thedns
FIG. 6. Expanded view of photofragment kinetic energy release for thy852 level of the O2 B
3Su2 state.
, No. 7, 15 August 1995
2501Leahy et al.: Predissociation of the O2 B3Su
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TABLE I. Correlated spin–orbit distributionsPy( j 1 , j 2) as a function ofB 3Su2 state vibrational levely8. No
products were observed in the~0,0! state. Uncertainties are given inside parentheses.
ficiently broad so that theP~1! andRQ32~1! lines overlap theR~3! transition. Finally, for the most diffuse bands suchy854, theR~3! line overlaps additional transitions, especialthe R1~3! andR2~2! transitions originating from theN952rotational level.
These issues are important because the short rangedissociation mechanism depends on the rotational fine stture through theV dependence of the coupling between thB 3Su
2 and the four repulsive states.20,34,35 The F2 levelsconsist purely of the3S1~V51! component, whileF1 andF3are complementary mixes of theV50 and 1 components.53
Only theV51 components of theB 3Su2 state couple to the
1Pu and 23Su
1 states. As a result, theF2 fine-structure stateshave approximately twice the dissociation rate onto thetwo curves as do theF1 andF3 components belonging to thesamey, N level. On the other hand, the5Pu state couples tothe threeFi components with almost equal strength, whilfor low rotational levels, the3Pu state couples somewhamore strongly to theV50 component of theB 3Su
2 state,thereby slightly disfavoring dissociation from theF2 compo-nent. The overall effect is that the predissociation ratestheF1, F2, andF3 fine structure components of a rotationlevel N8 are all different. This is seen most dramaticallythe experiments by Cosbyet al.,18 and is also evident in thework by Yanget al.16 and Yoshinoet al.17 It is therefore veryuseful to know the fine-structure composition of each of tpredissociating levels accessed in our experiment; thispends on which transitions are overlapped for each nomR~3! line.
We have simulated the excitation spectrum, taking inaccount the detailed spin–rotation structure and its effectthe rotational line strengths.53 Using our spectrum simula-tion, we calculated the populations of overlapping spinrotation levelsPu(J,Fi) prepared in our experiment for eacvibrational level. The simulation takes into account the exlinestrengths, line positions and linewidths of all possibtransitions, in addition to the bandwidth of the excitatiolight. The result is a set of normalized fine-structure poputions for each ensemble of transitions associated withB 3Su
2 state vibrational levely
ny~Fi !5(J
Py~J,Fi ! Y(J,i
Py~J,Fi !. ~8!
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The results may be summarized as follows: Roughl80% of theB 3Su
2 state molecules are formed inN854 foreach vibrational level, with the rest going intoN850 @viaP1~1!# andN852 @via RQ32~1!#. Note thatN8<4 for all ofthese contributions. TheN854 fine-structure populations areroughly proportional to theM 8 degeneracy of the originalrotational quantum numbersJ9. These degeneracies favorpopulation ofF1, with theM 9 degeneracies going as 9:7:5for F1, F2, andF3. For y854–11, theF1 population wasfurther enhanced because of the overlappedP1~1! transition,which accounted for 10%–15% of the total excitation. Onthe whole, though, the fine-structure populations of the excited rotational ensembles are largely statistical.
V. DISCUSSION
The correlated branching ratiosPy( j 1 , j 2) listed in TableI are the first observations of their kind for a light atomsystem. They contain information on both the detailed predissociation mechanism and the long-range dissociation dnamics. To model the branching ratiosPy( j 1 , j 2), we beginby breaking the problem down into two distinct regimesshort-range and long-range. In the short-range regime, thinitial decay from theB state is controlled by the Franck–Condon overlap and spin–orbit coupling strength betweethe vibrational levels and the continuum scattering statesthe four repulsive potentials shown in Fig. 1. This introducea strong vibrational state dependence in the initial predissciation step. In Sec. V A, we review the quantitative description of the coupling of the prepared states with the repulsivstates based on the findings of Chuenget al.15,19 and ofLewis et al.20 For our purposes, the primary result of SecV A will be the y-dependent branching ratios onto the fourrepulsive states.
The second half of the problem concerns how these repulsive states evolve in the long-range regime, ultimatelprojecting onto the asymptotic spin-orbit limits. The experi-mental results presented in this paper provide an interestinnew perspective on this problem. In Sec. V B, we considethe interaction of these states as they evolve towards thatomic limit. Of primary importance is the role of nuclearkinetic energy in the evolution of the atoms along the disso
No. 7, 15 August 1995
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2502 Leahy et al.: Predissociation of the O2 B3Su
2 state
ciative potentials. As a limiting case, we will first examinadiabatic behavior, i.e., what products may be expectedinfinitely slow nuclear recoil. We will also examine the dissociation in the sudden approximation. Finally, we turn tomore phenomenological approach by finding the best fitthe projections of the repulsive states onto the asymptolimits. We discuss what can be learned from the levelagreement between our simple predissociation modelsthe observed branching ratiosPy( j 1 , j 2).
A. Short-range dynamics
The basic nature of the predissociation mechanism woutlined in Sec. I. The high-resolution absorption dataParkinson and co-workers14,15,17have provided our best win-dow onto the nature of the short-range dissociation mecnism. These spectroscopic data hold a great deal of detainformation about the curve crossings, as reflected throuthe vibrational and rotational dependences of the linewidand line shifts. These data have been collectively incorrated into semi-empirical models by Cheunget al.15,19 andLewis et al.11,20 The semiempirical approach takes the beavailableab initio calculations28,35 of the curve crossing pa-rametersRx , Mx , andAx and refines these values to improvagreement between modeled Franck–Condon predissociawidths and the experimental values. The perturbations toterm values of the observed vibrational progressions~in-duced by the spin–orbit couplings! are also taken into ac-count. The most recent and most sophisticated effort to dis the recent work of Lewiset al.20 They analyzed the de-tailed lineshapes by calculating the individual contributioof each of the~typically! unresolved spin–rotation components. By determining the fine-structure dependence ofnatural linewidth one can learn more about which repulsstates dominate the predissociation.
In addition to an improved spectrum simulation ancurve-crossing parameters, the results of the semiempirfits provide a breakdown of each observed natural linewidinto a set of partial widthsGk(y,N,Fi) that describe the de-cay rates into the available repulsive states.54 Following Ref.20, we will label the four repulsive states 23Su
1, 1Pu ,3Pu ,
and 5Pu with k51–4, respectively. Because the fitting procedure is not highly sensitive to some of the adjustablerameters, there may still be room for improvement in tmodel’s results, particularly with respect to the 23Su
1 and3Pu widths. However, the overall level of agreement betwethe spectrum simulation of Lewiset al.20 and the experimen-tal data is of sufficiently high quality to ensure that the pmary mechanism of the predissociation has been wellscribed. If we neglect theN dependence of the partial widthGk(y,N,Fi) over the range from 0<N<4 ~the range ofNvalues contributing to each vibrational levely!, the normal-ized predissociation rates along each repulsive curvek aregiven by
Py~k!5
(Finy~Fi !Gk~y,N54,Fi !
(k,Fi
ny~Fi !Gk~y,N54,Fi !. ~9!
Here,Gk(y,N54,Fi) is obtained from Lewiset al.20,54
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B. Long-range dynamics
Given that the predissociation mechanism has beefairly well elucidated from the absorption data, we now consider how the atoms, as they recoil along these four repulsivpotentials, will project onto the six asymptotic fine-structurestates. Two limiting descriptions of the evolution of the electronic state of the oxygen atoms, namely, the relativistiadiabatic and diabatic limits, will be discussed here. In thadiabatic limit it is assumed that after the initial curve crossing, the nuclei evolve on relativistic adiabatic potentials, defined below, all the way to the asymptotic limit.33 This modelof the dissociation is attractive because it is especiallstraightforward to predict product branching ratios. The relativistic adiabatic model was qualitatively successful in describing the O~3Pj ! spin–orbit state distribution obtained byHuang and Gordon36 following theB 3Su
2 continuum disso-ciation of O2 at 157 nm. We present the predictions of thisadiabatic model in Sec. V B1, and compare them to the ob-served spin–orbit distributionsP( j 1 , j 2).
The diabatic~or ‘‘sudden’’! limit, on the other hand, isthe projection of the repulsive states in the short-range, mlecular regime onto the asymptotic, atomic limits withoutaccounting for any electronic evolution during the course othe recoil. Thus, the initial Hund’s case~a! basis functionsuSLV& for the four repulsive states are simply projected ontothe atomic basisu3Pj 1
,3Pj 2& with care taken to conserve the
g/u and1/2 symmetries as well as the total angular mo-mentumJ, its projectionV, and the total electron spinS. Inmany cases, the coefficients of the transformation from thmolecular Hund’s case~a! basis to the atomic basis may becalculated without any detailed knowledge of the electronistructure; we will take advantage of this fact to make a qualtative analysis of product branching ratios in the diabatilimit in Sec. V B2.
1. Relativistic adiabatic limit
Following the outline given in Ref. 33, we consider thetotal Hamiltonian for a diatomic molecule
H5$Hel1Hso%1TN. ~10!
Here,Hel is the electronic part of Hamiltonian, consisting ofthe electrostatic potential~including e–e, e–N, andN–N!and electronic kinetic energy operators.Hso represents thespin–orbit interaction~other relativistic terms are neglected!,and TN is the nuclear kinetic energy operator. The usuaBorn–Oppenheimer potentialsEi
BO(R) are derived from thesolutions to the electronic Hamiltonian
HelF iBO5Ei
BO~R!F iBO, ~11!
where
^F iBOuHeluF j
BO&50 for all iÞ j . ~12!
The functionsEiBO(R) will cross freely unless all of the
quantum numbersL, S, andV are shared between two statesIn this basis, at shortR, the diagonal spin–orbit interaction istreated in a phenomenological fashion by approximating it t
, No. 7, 15 August 1995
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2503Leahy et al.: Predissociation of the O2 B3Su
2 state
TABLE II. Adiabatic correlations between the ground state atomic limit O(3Pj 1), O(3Pj 2
) and O2 molecularstates. The states are energy ordered, with the bottom of the table corresponding to the most stable sta
Atomiclimit( j 1 , j 2) V n~V!a
Ungeradestates Geradestates
VMolecularcorrelations V
Molecularcorrelations
~0,0! 02
%101 0g
1 2 5Sg1
~1,0!1 1 4 1u 2 3Su1 1g 2 5Sg
1
~0,1! 02
%20u
2 2 3Su1 0g
2 5Dg
01
2 2 2g 2 5Sg1
~1,1! 1 4 1u5Pu 1g
5Dg
02
%30u
2 5Pu
01 0g1 ,0g
1 5Dg ,21Sg
1
2 4 2u5Pu 2g
5Dg
~2,0!1 1 4 1u5Pu 1g
5Sg1
~0,2! 02
%201 0u
1 5Pu 0g1 5Sg
1
3 4 3u5Pu 3g
5Dg
~2,1!1 2 8 2u ,2u3Pu ,
5Su2 2g ,2g
5Pg ,5Sg
1
~1,2! 1 12 1u ,1u ,1u3Pu ,
1Pu ,5Su
2 1g ,1g ,1g1Pg ,
5Pg ,5Pg
02
%60u
2 ,0u2 3Pu ,
5Su2 0g
2 ,0g2 3Pg ,
5Pg
01 0u1 3Pu 0g
1 5Pg
4 2 4g5Dg
3 4 3u A8 3Du 3g5Pg
~2,2! 2 6 2u A8 3Du 2g ,2g a 5Dg ,3Pg
1 8 1u ,1u A8 3Du ,A3Su
1 1g ,1g X 3Sg2 ,3Pg
02
01 %50u
2 ,0u2 c 1Su
2 ,A 3Su1
0g1 ,0g
1 ,0g1 X 3Sg
2 ,b 1Sg1 ,3Pg
an~V! is the total number of molecular states withJz5V that correlate to the indicated asymptotic limit. Notethat states withVÞ0 are doubly degenerate.
ew
eof–e
islyis
thhean
th
ole-n
ut
icc-
ved
8
de
er
ro-ot,-
beR independent. Thus curvesEiBO(R) differing only in V
are shifted relative to one another by anR-averaged,V-specific spin–orbit energy.
An alternative ‘‘relativistic’’ basis is produced when winclude the relativistic part of the Hamiltonian, with a neset of curvesEi
rel(R)
$Hel1Hso%F irel5Ei
rel~R!F irel . ~13!
For these states, onlyV is a good quantum number, and thcurvesEi
rel(R) will always avoid crossing at intersectionscommonV. While avoided crossings between the BornOppenheimer potentialsEi
BO(R) arise infrequently, the samcannot be said for the relativistic potentialsEi
rel(R).In light-atom molecules, the spin–orbit coupling
weak, and typical short-range curve crossings carry onsmall probability for relativistic adiabatic behavior. Suchthe case for the intersection between theB state and the fourrepulsive curves. At longer range, on the other hand,Born–Oppenheimer potentials may be nearly parallel at tintersection, and the probability for adiabatic following atavoided crossing is higher. In the limit of the recoiling atommoving infinitely slowly through an intersection~adiabaticlimit !, the weakest of spin–orbit interactions betweencrossing Born–Oppenheimer curves with commonV willgive rise to a perfectly avoided crossing. In the frameworkthe adiabatic basis, the central question is how the nuckinetic energy operatorTN will couple the adiabatic potentials. While the extent of this coupling at long range is u
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known, it is quite useful to examine the fully relativisticadiabatic limit, and find what predictions can be made abothe dissociation products.
The most attractive feature of the relativistic adiabatmodel is that a one-to-one mapping of the molecular eletronic states to asymptotic (j 1 , j 2) states can easily beconstructed.36 Because adiabatic curves with the sameVnever cross, the energy ordering of these states is preserfrom short range to the atomic limit. In Table II we display~with the aid ofab initio electronic structure calculations28!the short-range energy ordering for theungeradestates of O2that correlate to the ground state O~3Pj !1O~3Pj ! limit. Thecontents of Table II are essentially identical to those of Fig.in the paper of Huang and Gordon.36 Establishing the samesort of ordering for the atomic limits is also a straightforwartask with a few minor complications. The 81 states in thground state limit can each be classified asgeradeor unger-ade; furthermore, theV50 states have1/2 parity. Theseclassifications are carried out using the Wigner–Witmrules, which are summarized by Herzberg.55 Sinceg/u sym-metry should be conserved throughout the dissociation pcess, regardless of whether dissociation is adiabatic or nno ~j 150, j 250! products should be formed from predissociation of theB 3Su
2 state because this final state hasg sym-metry; this is borne out by our experimental results.
The adiabatic treatment of theB 3Su2 state predissocia-
tion is further simplified because we assumeV conservationto hold at all internuclear distancesR. The only mechanisms
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2504 Leahy et al.: Predissociation of the O2 B3Su
2 state
that mixV ~beyondS uncoupling! are weak for lowJ, andbecome rapidly weaker as the molecule dissociates.20 TheB 3Su
2 state has onlyV501 and 1 components, so onlthose states in Table II withV501 and 1 ~and with usymmetry! will participate. In this way, of the original 81atomic states, symmetry constraints dictate that only 18 nbe considered here. Thus for example, the accessibleV com-ponents of the3Pu state all correlate adiabatically to th~j 152, j 251! limit.
With the aid of the semiempirical partial predissociatiwidthsPy(k) @Eq. ~9!# and the correlation diagram of TabII, we can predict the correlated spin–orbit distributioPyad( j 1 , j 2) in the adiabatic limit
Pyad~ j 1 , j 2!5(
kPy~k!Cad~ j 1 , j 2 ;k!. ~14!
As mentioned earlier,k labels the four repulsive state2 3Su
1, 1Pu ,3Pu , and
5Pu . With the exception of the5Pu
state~k54!, the correlation coefficientsCad( j 1 , j 2 ;k) are ei-ther one or zero depending on whether or not the repulcurvek correlates adiabatically to the limit (j 1 , j 2) ~Table II!.TheV51 component of the5Pu state~with S50! correlatesadiabatically to both the~2,0! limit and the~1,1! limit, whileits V501 component correlates to the~2,0! limit. To accountfor this, we assume the doubly degenerateV51 componentto be divided evenly between the two limits, and that tV51 andV501 components of each vibrational level apresent in a 2:1 ratio. This yieldsCad~1,1;4!51/3 andCad~2,0;4!52/3. TheCad( j 1 , j 2 ;k) coefficients are listed inTable III.
The results given by Eq.~14! are shown along with theexperimental data in Fig. 7. Agreement betweenPy
ad( j 1 , j 2)and experiment is poor. The most spectacular failure ofadiabatic model concerns the ground state~2,2! limit. All ofthe ~2,2! ungeradeatomic limits correlate exclusively to ththree strongly bound O2 ungeradestates. As such, the~2,2!limit is not adiabatically correlated toany of the repulsivestates involved in the predissociation of theB 3Su
2 state.However, despite being forbidden in the adiabatic limground state products are formed in abundance followingpredissociation of the lowest vibrational levels of theB 3Su
2
state, peaking at 33% fory851. At this recoil energy~;1eV!, the motion of the atoms is apparently fast enoughtransitions to occur at avoided crossings between relativadiabatic curves. Because the adiabatic model representslow recoil limit, the applicability of the model can onldegrade fory8.1. The conclusion to be drawn from Fig. 7that the nuclear kinetic energy is in general too highdissociation to proceed adiabatically.
TABLE III. Adiabatic correlation coefficientsCad( j 1 , j 2 ;k) based on thecorrelations of Table II.
Diametrically opposed to the relativistic adiabatic approximation is the sudden or diabatic limit. In this approximation, it is assumed that the nuclei progress through curcrossings so quickly that the electronic wavefunction has nopportunity to change its configuration and avoid the crosing. Rather than consider what happens at each avoidcrossing, we consider the limit where the Born–Oppenheimer statesuLSV& @i.e., the solutions to Eq.~11!#on which predissociation occurs at short range are projectsuddenly onto the atomic limit, conservingL andS in addi-tion to V.
While the sudden limit sounds straightforward, it issomewhat awkward to apply, because the BornOppenheimer potentials do not correlate in a simple waythe atomic limits (j 1 , j 2). Instead, a given Born–Oppenheimer stateuLSV& will form a superposition ofatomic states as dictated by angular momentum coupling ain many cases by the electronic structure. This problem hbeen addressed in considerable detail by Singeret al.56 Thematrix elements for the transformation from the moleculabasis to the atomic limit presented in Ref. 56 are reproduchere. We then derive the correlated spin–orbit cross sectioexpected in this limit.
FIG. 7. Predicted correlated fine structure distributions as functionB 3Su
2 vibrational quantum number using adiabatic model@Eq. ~14!# com-pared to experimental results. The model is represented as circles, andexperimental data points are squares.
, No. 7, 15 August 1995
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2505Leahy et al.: Predissociation of the O2 B3Su
2 state
We wish to find the projection of the molecular basuLSV& into the atomic basisu j 1 , j 2&. The matrix elementgiven in Eq.~II.13a! of Ref. 56 as it appears for our applcation ~3Pj atoms:l 15 l 25s15s251! is
^ j l j 1 j 2uLSV&J5~21! l2V2J@~2S11!~2 j 111!
3~2 j 211!#1/2^ l0u j2V,JV&
3 (Ll1l2
@12d j 1 j 2~21!L#1/2
21/2~2L11!1/2
3^LLu1l1 ,1l2&^ jVuLL,SS&
3H 1 1 j 11 1 j 2L S j
J ^l1 ,l2uL&. ~15!
In this equation, j represents the vector sum of thatomic total angular momentaj 1 and j 2, l is the orbital an-gular momentum of the recoiling oxygen atoms,l1 and l2are the projections of the electronic orbital angular momtum of the atoms,l 1 and l 2, and L is the total electronicorbital angular momentum. Theungeradesymmetry of themolecular state manifests itself in two different ways in tatomic limit. When j 1Þ j 2 , exactly half of the asymptoticstates areungerade, and the 21/2 divisor in the sum accountfor this. Whenj 15 j 2 , the nuclear permutation eigenvaluegiven by ~21!L; the factor of@1 2 d j 1 j 2
( 2 1)L#1/2 limitsthe summand toungeradestates~L5odd! and cancels theaforementioned 21/2 divisor. The electronic overlap term^l1,l2uL& hold theR dependence of the transformation, coverging to some limiting value asR→`. For the three2S11Pu states under consideration~S50, 1, and 2!, the onlysuch terms are the symmetric^0,1u1& and ^1,0u1& terms, andthe diabatic coupling to the atomic limits can be calculadirectly. On the other hand, electronic structure calculatiare required to determine the^0,0u0& and ^1,21u0& terms forthe diabatic coupling of the 23Su
1 state to the atomic limit.However, we will take^0,0u0&5^1,21u0& to calculate ap-proximate couplings for the 23Su
1 state.The diabatic transformation cross sections to the asy
totic limit u j 1 , j 2& are found by summing coherently over thunobserved momentaj and l
Cd~ j 1 , j 2 ;kV!5U(j ,l
^ j l j 1 j 2uLSV&J54U2. ~16!
This gives the expected diabatic branching ratio for a sindissociation pathway. However, the predissociation of O2 canbe thought of as a four-slit experiment, where a givenVcomponent of aB state rotational level will connect to eac( j 1 , j 2) product state via up to four available pathwaynamely, the5Pu ,
3Pu ,1Pu , and 23Su
1 repulsive states. Therelative phases of these pathways must be taken into accto calculate the total amplitudes of the product scatterstates. These phases, which depend on the initial vibratilevel y, are unknown, precluding a completely quantitatianalysis of the diabatic limit. As a crude approximation,will sum the diabatic contributions as they appear in Eq.~16!incoherently
J. Chem. Phys., Vol. 103
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Pyd~ j 1 , j 2!' (
k,V50,61Py~k!Cd~ j 1 , j 2 ;kV!. ~17!
In the case of rovibrational levels that decay primarilyvia one surface~e.g., y51 and 4!, Eq. ~17! will be corre-spondingly less approximate~within the overall sudden ap-proximation!. The resulting diabatic branching ratiosPyd( j 1 , j 2) are shown along with the experimental data in Fig
8. Unlike the adiabatic limit, the diabatic model predicts asignificant yield in the ground state~2,2! channel. In fact, thediabatic model does a good job of reproducing they8 depen-dence observed experimentally for this channel, particularat high y8, where the the photofragment kinetic energyshould yield more diabatic behavior. On the whole, thoughthe agreement between model and experiment is once agless than satisfactory. Even fory851 andy854, which disso-ciate with over 75% efficiency into the1Pu and 5Pu con-tinua, respectively, the diabatic model appears to have littpredictive power, with significant discrepancies in the~2,0!and ~1,0! channels.
The conclusions to be drawn from Fig. 8 are not so cleaas those from Fig. 7. It may well be that the dissociation ilargely diabatic, and that the discrepancies between modand experiment in Fig. 8 arise from our neglect of interfer
FIG. 8. Predicted correlated fine structure distributions as function oB 3Su
2 vibrational quantum number using adiabatic model@Eq. ~17!# com-pared to experimental results. The model is represented as circles, andexperimental data points are squares.
, No. 7, 15 August 1995
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2506 Leahy et al.: Predissociation of the O2 B3Su
2 state
ence effects. On the other hand, the dissociation maybetween the adiabatic and diabatic limits. It is possible tone can understand the dissociation dynamics of O2 withinthe confines of a reasonably simple combination of adiabaand diabatic processes. Durup57 has analyzed the predissociation of O2
1 to form O1~4S!1O~3Pj !, and constructed a‘‘mixed diabatic basis’’ which was quite useful in modelinthe observedj distribution of the O~3P! atom. In this basis,some of the dissociative states are found to be largely abatic, while others are predominantly diabatic. The assumtion of pure adiabatic behavior for the former and pure dabatic behavior for the latter yields reasonable, althoughperfect, agreement with the experimental fine-structure dtributions. Whether such a basis can be constructed for pdissociation of the O2B
3Su2 state remains to be seen.
3. Least-squares fit branching ratios
The results in the previous section show that neitheradiabatic nor diabatic limits describe our data very well.this section, we apply a more phenomenological approachour data in which we find the set of coefficients analogousthose in Table III that provide the best fit to the data. Wassume that each of the four repulsive states maps ontoproduct states (j 1 , j 2) independently ofy or V for the pre-dissociating state. We then require 20 coefficients describthe branching of each repulsive statek into the five productstates (j 1 , j 2). These branching ratios are expressed aselements of the arraya( j 1 , j 2 ;k), subject to the normaliza-tion conditions
(ka~ j 1 , j 2 ;k!51. ~18!
The linear coefficientsa( j 1 , j 2 ;k) are fit to the observedPy( j 1 , j 2) for all 12 vibrational levels simultaneously, comprising a system of 60 equations of the form
Py~ j 1 , j 2!5(k
Py~k!a~ j 1 , j 2 ;k!. ~19!
The form of Eq.~19! is identical to Eq.~14! with the excep-tion that the correlation coefficients are now treated asjustable parameters.
The results of the least-squares fit are given in Tableand shown in Fig. 9. In the fit, it was necessary to imposnon-negativity constraint for many of the coefficiena( j 1 , j 2 ;k); these coefficients appear as zeroes in the taThe level of agreement of this phenomenological treatmwith the experimental data represents a significant improment over both the adiabatic and diabatic limits. This is n
TABLE IV. Best linear fit coefficientsa( j 1 , j 2 ;k) of the partial predissocia-tion widths of Lewis et al. to the observed product state distributionPy( j 1 , j 2).
too surprising, given the large number of parameters usedthe fit. However, the reducedx2 of the fit was 37, indicatingthat this model ofy-independent branching ratios is not consistent with the data given the precision of the measuments. Figure 8 shows that the fit does quite well for t~2,2! channel, somewhat less well for the~1,1! and ~1,0!channels, and gives the poorest results for the~2,1! and~2,0!channels where it fails to reproduce the oscillatory structuwith y seen in the experiment. Such structure may reflquantum interference between competing decay paths, leing to a vibrational dependence in the branching coefficiea( j 1 , j 2 ;k). Alternatively, they dependence of the dissociation mechanism may occur simply because the kinetic eneis increasing with increasingy, thereby affecting the cou-pling at long-range between the molecular and atomic sta
Nonetheless, the coefficients in Table IV reflect the paway specific branching ratios in, at the very least,y-averaged sense. It is instructive to compare these coecients with those in Table III, because there are some patteshared between the adiabatic correlation coefficieCad( j 1 , j 2 ;k) of Table III and thea( j 1 , j 2 ;k) of Table IV. InTable III, no states correlate with the~2,2! products, whilethe 3Pu and
1Pu states correlate with the~2,1! channel. InTable IV, only the3Pu and
1Pu states lead to~2,2! products.
FIG. 9. Predicted correlated fine structure distributions as functionB 3Su
2 vibrational quantum number using adiabatic model@Eq. ~19!# com-pared to experimental results. The model is represented as circles, anexperimental data points are squares.
, No. 7, 15 August 1995
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2507Leahy et al.: Predissociation of the O2 B3Su
2 state
This is the result that would be expected in the case whadiabatic limit is relaxed slightly, in which case moleculewould begin to transfer into neighboring limits by makinsingle curve hops. Such a result is consistent with the expment. Figure 7 shows that the observed~2,2! branching ratiois about 0.3 times the adiabatic prediction for the~2,1! chan-nel for all y; this scaling suggests that the~2,2! channel isdue to nonadiabatic transitions from states that adiabaticcorrelate to the neighboring~2,1! channel. Also, in the adia-batic model, the 23Su
1 state is the only one that correlatesthe ~1,0! product, while in the linear fit, the largest contribution to the~1,0! product also comes from this state. Thus tdegree of nonadiabaticity may not sufficient to completescramble the adiabatic correlations, so that the impressiothe adiabatic correlation may still be found in the data. Othe other hand, a comparison of Tables III and IV implithat multiple hopping between adiabatic curves is requiredexplain the observed branching ratios for the other thchannels.
Overall, it appears that an exact dynamical calculatioprobably including quantum interference effects, on hiquality potential energy curves is required to match the eperimental results. Given that single transitions between retivistic adiabatic potentials can partly explain the dissoction dynamics, it may be preferable to use the relativisadiabatic states as a basis for this calculation. To our knoedge, a multichannel calculation of this type has not beperformed yet, and we hope that our results stimulate thretical activity in this area.
4. Comparison to earlier results
The correlated fine-structure distributions in Table I hanot been measured previously. However, Matsumi and Kwasaki~hereafter referred to as MK! have used multiphotonionization to measure theuncorrelated spin–orbit distribu-tion P( j ) following the predissociation of theB 3Su
2 statey854 level with 193 nm light.37 They observed atoms inj52, 1, and 0 in the ratio of 0.47~5!:0.31~4!:0.22~4!, respec-tively. Casting our results fory854 into uncorrelated ratios,we obtain the ratio 0.451~15!:0.323~14!:0.227~11!, in excel-lent agreement with MK.
In the same paper, MK presented results for the 157photodissociation of theB 3Su
2 state to the excited O~1D!,O~3Pj ! limit. At this wavelength, one is accessing the repusive wall of theB 3Su
2 state~see Fig. 1!, so direct dissocia-tion rather than predissociation is occurring. MK report tP( j ) distribution at 157 nm to be 0.74:0.21:0.04. In anothexperiment at 157 nm, Huang and Gordon~HG! reported asubstantially differentP( j ) distribution, 0.93:0.06:0.01,36 us-ing laser-induced fluorescence to measure O atom poptions. HG suggested that the MK result was in error becaof amplified spontaneous emission affecting Kawasaki’s dtection scheme.36,58 However, the close agreement betweour results and those of MK for they854 level shows thattheir detection scheme at 193 nm is reliable. This suggealbeit indirectly, that MK’s results at 157 nm are also correThis conclusion is significant because the nascent O~3Pj !atom spin–orbit distribution from the atmospheric dissoc
J. Chem. Phys., Vol. 103,
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lly
eyofnstoe
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tion of O2 depends strongly on photodissociation dynamicsin the 157 nm range.
The discrepancy between the two sets of data at 157 nis also important from the perspective of adiabaticity in thedissociation process. Adiabatically, theB 3Su
2 state corre-lates to the O~3P2!1O~1D! limit. Thus HG concluded thatthe dissociation is largely adiabatic, whereas MK’s resultsindicate considerably larger nonadiabatic effects. Our resulthave clearly demonstrated the importance of nonadiabateffects in predissociation of theB 3Su
2 state to formO~3Pj !1O~3Pj !. Given that the densities of states at longrange for the two atomic limits are similar, and that the translational energy of the O atoms is;1 eV in both our experi-ment and those at 157 nm, one might certainly expect nonadiabatic effects to be important at 157 nm as well, in contrasto the results of HG. It is certainly true that we are observingthe products from predissociation on multiple repulsive potentials at short range, whereas dissociation is direct at 15nm. Nonetheless, the agreement of our results with thoseMK at lower energy suggests that the notion of adiabaticdissociation at 157 nm should be re-examined.
VI. CONCLUSIONS
High resolution translational energy release spectra othe O~3Pj ! atoms resulting from O2 B
3Su2 predissociation
have been recorded for 0<y<11. The spectra yield a rela-tively unexplored~both experimentally and theoretically! ob-servable, namely, the correlated fine structure state distributions Py( j 1 , j 2). These show a strong dependence on thevibrational quantum numbery of the predissociating level.The details of the predissociation mechanism are presenteto provide a basis for the analysis of spin–orbit distributionsTwo limiting descriptions of the evolution of the nuclei frommolecule to atoms are discussed. The predictions of the reltivistic adiabatic limit and the sudden limit both fail to re-produce they dependence of the observed spin–orbit distri-butions. We have also performed a phenomenological leassquares fit in which the branching ratios of each repulsivestates to the various product states are determined. Thyields more insight into the long-range~R'5–7 Å! dynam-ics of the dissociation and suggests that while the dissociation lies in a complex intermediate regime, a residual impression of adiabatic behavior persists in the data. It appears tha full quantum dynamical calculation on accurate potentiaenergy curves will be necessary to reproduce our experimetal results.
ACKNOWLEDGMENTS
The authors acknowledge the contributions of David H.Mordaunt to the data collection effort. This research is supported by the Director, Office of Energy Research, Office oBasic Energy Sciences, Chemical Sciences Division, of thU.S. Department of Energy under Contract No. DE-AC03-76SF00098.
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