Faraday Discuss. Chem. SOC., 1983, 75, 7-22 Introductory Lecture Vibrational Redistribution within Excited Electronic States of Polyatomic Molecules BY CHARLES S. PARMENTER Department of Chemistry, Indiana University, Bloomington, Indiana 47405, U.S.A. Received 18th April, 1983 The diversity of intramolecular vibrational redistribution (IVR) studies displayed in this Discussion testifies to the high interest in this fundamental aspect of polyatomic reaction dynamics. Moreover, the fact that the Discussion has attracted so many responses on a problem that has been under active study for at least 30 years demon- strates both the importance and the elusive nature of IVR. IVR is truly a child of theory, first arising within the competing R.R.K.M. and Slater theories of thermal unimolecular dissociation.' R.R.K.M.theory included IVR as a necessary prerequisite to dissociation, whereas IVR was explicitly excluded in the Slater picture. The dichotomy sparked lively discussions and much experi- mental interest, leading to the demonstration in 1960 by Butler and Kistiakowsky of IVR as in experimental reality in molecules with high (reactive) vibrational excitation. While the R.R.K.M.-Slater debates are now quiet, in part because of such demon- strations, theoretical discussions retain their intensity. Fundamental descriptions of quasiperiodic and chaotic behaviour are being sought,' and better descriptions of dense field coupling and 1VR dynamics are being developed. The papers in this Discussion and a recent issue of the Journal of Physical Chemistry devoted almost entirely to the topic of chaos illustrate the point. The early experimental approach to IVR was dominated by the productive efforts of Rabinovitch and coworkers that still continue^.^ Their work provided several methods to populate energy-selected regions high in the vibrational manifold where excitation is sufficient for chemical reaction.Coupled with tests for subsequent IVR that used the chemical clocks of reactivity, their studies revealed the ubiquity and fast time scales (picoseconds) of IVR in these high regions. They also probed the issue of ergodicity, demonstrating how difficult it is to hold IVR to a limited region of vibrational phase space. In contrast, much of the recent experimental progress on IVR has been down and out, so to speak. It is down in the sense that attention has increasingly focused on ground-state systems with lower vibrational energies.It is out in the sense that new technologies have allowed experiments to branch out with a diversity of techniques, many of them spectroscopic. Again, this Discussion reflects well these ingenious adventures, as do several summaries.'*6 Some of the newer experiments, such as high vibrational overtone spectroscopy and photodissociation, probe with relatively precise preparation, IVR in the high reactive regions of the vibrational manif~ld.~ Interest in infrared multiphoton8 VIBRATIONAL REDISTRIBUTION WITHIN POLYATOMIC MOLECULES dissociation has generated a variety of IVR studies both in beams and bulk gases t h d probe IVR at much lower energies.' Vibrational product distributions as seen in infrared fluorescence also search lower regions,6 as do infrared fluorescence experi- ments after pumping the first C-H overtone in variety of polyatomic~.~ Most recently, infrared fluorescence after excitation of C-H fundamentals has brought the IVR probe to the 3000 cm-' region of ground-state rnanifolds.'O As an ensemble, these and other experiments on ground-state systems are com- pelling on several issues. Most importantly, they show that IVR is a general property of ground-state manifolds, found in regions with low state densities (< 100 per cm-l) and occurring all the way up to high regions of the quasi-continuum responsible for chemical reactivity.Exceptions exist, but they are few.6 In spite of these triumphs, the experimental characterization of IVR remains largely incomplete in the sense that no comprehensive study of IVR from various vibrational regions within a molecule has yet been possible.The systematic explora- tion of the molecular parameters that control IVR dynamics has remained largely out of reach. This in turn has contributed to the most pressing deficit in discussions of IVR, namely the absence of a predictive theory or even empirical correlations. The dilemma stems in large part from the experimental difficulty of monitoring ground-electronic-st ate vibrational populations with the required sensi tivi ty . The problem is particularly compounded by the need to impress fast time resolution (nanosecond, picosecond) on these measurements.Substantial experimental advances will certainly be brought to these problems, and perhaps much of the progress will derive from fast non-linear spectroscopies. In the meanwhile, one can retreat (or advance) to IVR in excited electronic states where some of these experi- mental problems are greatly eased. INTRAMOLECULAR VIBRATIONAL RELAXATION WITHIN EXCITED ELECTRONIC STATES Bright ultraviolet laser sources tunable over wide regions with controlled band widths in either pulsed or C.W. operation offer close control over initial vibrational excitation. By selective pumping of S1 t So absorption features, opportunity occurs in many molecules for exploration of IVR characteristics after preparation of zero- order levels varying systematically in mode structure and energy.Resolved S1 -+ So fluorescence spectroscopy provides a monitor of Sl vibrational identities which, when combined with bright pump lasers, generates detection sensitivities that exceed those in the infrared by orders of magnitude. Furthermore, the short S, radiative lifetime (commonly nanoseconds) provides a built-in clock for excited-state processes that is often made even more useful by faster non-radiative electronic-state decays. Thus nanosecond or sub-nanosecond time limits are imposed on detection even without deliberate efforts. The short radiative lifetime has an even more important con- sequence, however, that is now being exploited in several laboratories. As several papers of this Discussion illustrate, sufficient optical sensitivity exists to monitor vibrational flow with imposed picosecond fluorescence timing.These experiments are the forerunners of direct explorations of IVR dynamics. Excited-state studies also encounter substantial experimental liabilities. Thermal congestion or inhomogeneous broadening in electronic absorption spectra is far more extensive than encountered with ground-state infrared pumping and is a severe problem for room-temperature experiments. Even with narrow-band sources, the ability to restrict pumping to single zero-order S1 vibronic levels or even narrow regions is severely compromised by sequence- and hot-band structure. Thus room-CHARLES S. PARMENTER 9 temperature studies are restricted to low resolution with respect to single-level preparation or restricted to molecules with special characteristics (such as high symmetry) that endow them with reduced congestion.For this problem, the supersonic nozzle expansion is the great redeemer. The reduction of inhomogeneous broadening by rotational cooling to near 1 K and vibrational cooling to tens of K enormously expands the opportunities. As an example, it has opened remarkably large molecules such as the macro-ring system free-base phthalocyanine l1 or ten-ring aromatics l2 to spectroscopic study of IVR. Supersonic beams will be the dominant technology for excited-state IVR studies. A second limitation inherent in spectroscopic probes of excited-state IVR stems from the restricted span of the Franck-Condon absorption envelope. The severe Franck-Condon attenuation of S1 t So transitions that terminate on higher S1 levels restricts most studies to the first 3000 or 4000 cm-I of the S1 vibrational manifold. In fact the bulk of present S1 IVR data concerns levels below 2000 cm-' excess energy.This is quite a different vibrational world from that historically considered in the context of IVR. In this low region, level densities can be calculated by direct counting, anharmonic normal modes seem to provide acceptable vibrational descriptions and one can discuss the zero-order vibrational identity of the levels initially pumped. Thus the language of IVR in these studies is more detailed than in ground- state probes of higher regions. The interconnections between the low-region IVR results of these studies and the picture that emerges from the high-energy ground-state work will surely become a topic of lively discussion.As recent papers ill~strate,'~*'~ information about IVR within excited electronic states can come from the photophysics of excited-state decay rather than from explicit spectroscopy. IVR is manifested in these decay measurements by the control that redistribution has over the details of radiationless transitions, and inference about IVR characteristics from photophysical measurements follows appropriate modelling. A most interesting suggestion from early discussions of IVR and photo- physics concerned the wide variation in IVR lifetimes, extending in cases to as long as hundreds of nanosecond^.^^ The more recent IVR characterizations from spectro- scopic measurements do not yet confirm these suggestions.Much more work is required before enough is known about IVR from independent sources to secure its role in non-radiative decay. In contrast, we might term the spectroscopic probes of S, IVR as " direct '' studies, and in spirit this is correct although some of these also rely on rather subtle modelling. Three complementary spectroscopies have been used both with supersonic beams and in room-temperature measurements. Homogeneous linewidths as inferred from the rotational contours of S, t So absorption bands may reveal rovibronic interactions within the S, manifold that, given proper initial preparation, are associated with IVR. The prime challenge is (a) to get an accurate measure of this width from complicated spectra and (b) to understand the cause of that width.With respect to the latter, IVR becomes a compelling cause when the linewidths correspond to relaxation times much faster than the known S, electronic state lifetime. Naphthalene is such a case.16 IVR lifetimes on order of lo-', s are inferred from the absorption linewidths in supersonic-beam experiments. A striking example has been provided recently by Riedle et al. for IVR in S, benzene,17 and in fact the work is described in one of the papers of this Discussion.18 Two-photon sub-Doppler spectroscopy has exposed many individual rotational lines in vibronic bands of the benzene S, +- So transition. The spectra show most bluntly a rotationally selective broadening of rotational lines in a band associated with ca. 3400 cm-' of excess vibrational energy.K = 0 structure remains sharp at the present10 VIBRATIONAL REDISTRIBUTION WITHIN POLYATOMIC MOLECULES resolution whereas K > 0 structure is severely broadened. The authors note that linewidths in many bands reaching thse vibrational regions l9 correspond to relaxation times far shorter than the relaxation time of the S, population itself.20 Hence the broadening must be associated with intrastate coupling, namely IVR. These remark- able data show that rovibronic coupling rather than purely vibronic coupling is basic to IVR in this domain. The other spectroscopic approaches to excited-state IVR use S1 -+ So fluorescence spectroscopy in two variants. Collsion-free S, + So fluorescence spectra can reveal IVR within the S1 electronic state by extra structure in fluorescence that usually appears in the form of unresolved congested emission after pumping a single zero- order vibronic state.The natural clock of the s, lifetime puts a long limit on the time scales of IVR that produces such congestion. The more direct approach is to impose timing on these collision-free spectra. Picosecond fluorescence spectroscopy is just beginning to display its role in discovering S, IVR characteristics. There is little doubt that as improved techniques are worked out, these experiments will be among the more important consequences of picosecond technology. Reviews have described the operation of these 1VR spectroscopies.21p22 Our present interest concerns the results that are coming from such experiments. There now exists a sufficient corpus of S, IVR data to reveal some general aspects of 1VR within excited states.These and related issues are discussed in the sections to follow. LOW IVR THRESHOLDS The ability to excite a wide variety of known initial S, vibrational distributions in a given molecule is among the principal virtues of excited-state IVR studies. Such excitation allows a systematic study of IVR as functions of excess vibrational energy and initial vibrational identity. The first questions asked in such explorations have been extremely simple. As one climbs the S, vibrational manifold, at what point does one first observe indications of IVR? Answers are now available for many molecules, and there is uniform agreement. The IVR thresholds are always low, in fact amazingly low in the historic context of ground state IVR studies.The thresholds in a variety of aromatics and heteroaromatics occur within the first few thousand cm-I of excess vibrational energy where vibrational level densities range from a few states (or less) per cm-I to hundreds of states per cm-’. Before commenting on these findings it is useful to discuss the meaning of “ IVR thresholds ” as derived from these fluorescence experiments. The collision-free fluorescence experiment is understood within the context of the level-mixing model shown in fig. 1. Consider a field of zero-order (e.g., harmonic) levels, not necessarily overlapping by their widths, that are mixed with average coupling matrix elements VLl FZ Vsl. The Is) level has large oscillator strength (on account of a favourable Franck-Condon factor) to a thermally populated level in the ground electronic state whereas the { \ I ) } levels do not.In the absence of coupling, the Is) level would give rise to a bright and discrete feature in the S, t So absorption spectrum even though that level is surrounded by a thick field of S, levels. In real life, the coupling disperses the Is) character in a quasi-Lorentzian distribution over the field, so that the absorption now has the structure of the dispersion. If the level structure is sufficiently sparse, the dispersed multi-line structure can be directly observed, but this has been a rare situation for cases other than few-level Fermi resonances.* More commonly, the coupling width is so small relative to the experimental resolution (often limited by * An impressive recent example is the observation of absorption structure as a result of mixing between an SI rovibronic 1s) state and rovibronic states { 11)) in the triplet manifold of pyra~ine.~’CHARLES S .PARMENTER 11 thermal inhomogeneous broadening) that the Is} state dispersion is not readily detected. In these cases the absorption spectrum may still appear " sharp " under conditions of only moderate resolution. The fluorescence spectrum, however, is extremely sensitive to such mixing. It can reveal mixing that is quite undetectable in absorption. If, for example, the excitation resolution was sufficient to pump only one of the absorption components (a single mixed molecular eigenstate), the ensuing collision-free fluorescence spectrum will be rich in structure since it is, in effect, a superposition of zeroth-order (e.g.harmonic) I s> Fig. 1. Schematic diagram of the mixing of zero-order vibrational levels (or rovibrational levels) within a single electronic state. The average coupling matrix elements Vsl and Vzz are expected to be equal. Within the S1 state, the state 1s) has a large Franck-Condon factor so that it is optically accessible from the So zero-point level. The bath levels { Il)} are " dark " on account of small Franck-Condon factors. single vibronic level fluorescence spectra, one from each zero-order vibrational identity contained in the mixed state. In the more common situation, the excitation bandwidth spans much or all of the coupling width, and the ensuing fluorescence is a superposition of so many SVL spectra that the fluorescence congestion becomes a quasi-continuum. By this means, " sharp " absorption can yield unstructured collision-free fluorescence. The threshold measurements generally rely on the appearance of unstructured emission as the indicator of VIR when an excitation laser is tuned to successively higher S1 regions.Fluorescence congestion is a sensitive marker, and the appearance of congestion beyond that expected from thermal inhomogeneous broadening is a sure indication of the extensive level mixing that is a necessary prerequisite of IVR. Drawing further conclusions about IVR from such collision-free spectra can be a bit tricky. The IVR dynamics are particularly difficult to elucidate since, as many have pointed out, the dynamics of IVR are sensitive to the state p r e p a r a t i ~ n .~ ~ - ~ ~ In the limit of single molecular eigenstate pumping no time evolution occurs, but the state mixing will produce congested fluorescence. At the opposite extreme, coherent pumping of the entire eigenstate package will result in evolution from pure Is} at the time of excitation to the full mixed-state vibrational identity at later times. The collision-free fluorescence will reflect this evolution with an abundance of unstructured emission if the evolution time-scale is much shorter than the S, fluorescence lifetime.12 VIBRATIONAL REDISTRIBUTION WITHIN POLYATOMIC MOLECULES In contrast structured fluorescence from Is) will occur if the evolution is slow compared with the S, lifetime.Structured emission may also occur if the excitation bandwidth limits pumping to only a small subset of levels over which the Is) character is distri- buted, and this structure will occur even if the vibrational time evolution is much faster than the S1 fluorescence lifetime. Alternatively, structure can persist in the presence of extensive mixing and fast IVR if the set {IZ)} is small. From these choices it is clear that relative contributions of Is) and unstructured (IZ}} emission to collision-free fluorescence cannot by themselves be particularly informative about the time-dependence of the S1 vibrational identity of IVR dynamics. Congested fluorescence only reveals the necessary state mixing of IVR. It is in this sense and only this sense that we talk about IVR thresholds as derived from collision- free fluorescence.Table 1. Upper limit of IVR thresholds within S1 electronic states as determined from collision-free S1 -+ So fluorescence molecule threshold vibrational p v l b vibrational a source /cm-l degrees of per cm-' temperature freedom /K p-difluorobenzene g-fluorotoluene coumarone 1 -azaindolizine indole ethyl benzene naphthalene azulene (S,) t-butyl benzene anthracene stilbene tetracene pentacene ovalene p-O-CH3 P-NHZ-V)-C~H~ v-CEFEC-C~H~~ 1760 1590 720 1110 1440 760 930 2570 670 530 1380 1200 730 1900 500 1060 1280 30 39 39 39 39 42 48 48 48 66 66 72 72 84 87 102 132 10 300 10 300 <1 300 -1 300 3 300 cold cold 400 cold <1 300 cold cold cold cold cold cold cold cold ref. (29) b C C C d ref.(28) ref. (33) ref. (28) ref. (39) ref. (48) e g C f .f f ' 300 K are room-temperature bulk experiments. " Cold " refers to measurements from super- K. W. Holtzclaw, A. E. W. J. B. Hopkins, D. E. Powers and D. E. Powers, J. B. Hopkins and R. E. Smalley, A. Amirav, U. Even and J. Jortner, J. Chem. Phys., 1981,75,3370; D. E. Powers, J. B. Hopkins and sonic beams. b C. s. Parmenter and B. M. Stone, unpublished results. Knight, C . S. Parmenter and B. M. Stone, to be published. R. E. Smalley, J. Chem. Phys., 1981, 74, 6986. J. Chem. Phys., 1980,72,5721. Opt. Comrnun., 1980,32, 266; Chem. Phys. Lett., 1980,69, 14. R. E. Smalley, J. Chem. Phys., 1981, 74, 5971. Table 1 summarizes many of the IVR thresholds that have been observed by the criteria of fluorescence congestion in collision-free experiments.These thresholds are in fact conservative limits, because other sources of congestion (such as thermal inhomogeneous broadening) tend to obscure the first IVR onsets. The quoted thresholds merely cite the lowest energies where it can be determined with certainty that the congestion exceeds that possible from non-IVR sources. True IVR onsets will generally be lower. The remarkable aspect of these data concerns the ubiquity of low thresholds amongCHARLES S. PARMENTER 13 these aromatic and heterocyclic systems. Low thresholds appear in every molecule, and IVR at low energies is clearly the rule. IVR turns on at first chance as one climbs the S1 vibrational ladder. The low energies are further emphasized by the threshold vibrational level densities estimated for a few cases in table 1.IVR occurs in truly sparse regions of the vibrational manifold, where densities are built primarily on the lowest ring frequencies. Stewart and McDonald lo have concluded that a rovibronic level density of 5-30 per cm-' characterizes the IVR thresholds in ground-state systems. S, thresholds are too indistinct to set such figures, but the data in table 1, based on vibronic level densities, could well be in accord. Zewail 27 in this Discussion has offered an intriguing correlation of thresholds with low-frequency modes of large polyatomics. FROZEN MODES AND PROMOTING MODES A singular aspect of collision-free fluorescence concerns the persistence of IVR congestion from all levels that have been probed above the threshold.The experi- ments have yet to reveal " frozen modes " above the threshold, i.e. zero-order modes for which level mixing is so restricted that the IVR indicators are absent. Whereas frozen modes have so far failed to appear, it must be noted that the searches are forced to sample only a few types of modes in any molecule. The vibrational excitation depends on choosing those S, levels that have unusually large Franck-Condon factors with the So zero-point level. Thus the IVR probes see mainly the progression forming modes (often appearing in combination levels) as excitation climbs the S, ladder. Smalley's group have reported a particularly interesting series of probes designed to look for frozen modes or barriers to IVR in S, substituted benzenes.2s As reported in table 1, early thresholds (530 and 930 cm-') are observed in cold-beam fluorescence as excitation pumps a benzene-ring mode coupled to an alkyl side chain that provides level density.If that chain is isolated from the ring by a -C=C- linkage or a -0- linkage, the early thresholds persist and inhibitions to the IVR coupling fail to appear. An even more pervasive coupling was discovered in S, p-alkylanilines, where pumping of an -NH2 inversion mode overtone (730 cm-') displayed IVR coupling through the ring to ap-alkyl side chain. These studies emphasize the message of table 1 : IVR couplings are indeed ubiquitous in low-S, regions of ring systems. Refinements of these probes, especially with time-resolved experiments, will surely reveal evidence of the variable coupling strengths and fields that must exist in these systems.In fact, collision-free experiments presently give indications of sub- stantial sensitivity of IVR to excitation of a low-frequency out-of-plane ring mode ( ~ 3 0 ) in S, p-diflu~robenzene.'~ The sensitivity is seen as a marked boost in fluores- cence congestion as excitation pumps combination bands carrying increasing quanta of ~ 3 0 . As described below, time-resolved studies confirm the special activity of v~~ in IVR. Further suggestions of this activity appear also in the high-resolution S, f- So absorption of p-difluor~benzene.~~ One observes that the apparent sharpness of a combination band 5',31, (&b = 2069 cm-l) is markedly degraded by the addition of a vi0 component to give the band 51,3;30,1 (&b = 2189 cm-').While quantitative estimates of the linewidths are yet to be reported, it is known that any additional linewidth must come from intrastate IVR couplings since the S, electronic state lifetimes are themselves about the same for each S , level.31 We find further comments about this elusive aspect of IVR in several papers of this Discussion. The experimental work of Chuang et al.32u describes an intriguing14 VIBRATIONAL REDISTRIBUTION WITHIN POLYATOMIC MOLECULES exploration of variable IVR couplings in t-butylhydroperoxide (Bu'OOH) as energy is pumped into the 6th 0-H overtone (ground electronic state) and -0-0- bond dissociation provides a molecular clock. Marcus 32b considers theoretically the possibility of damping coupling among a system of oscillators -C-C-C-M- C-C-C- by a massive central atom M.ERGODIC MIXING The IVR mixing model presented earlier allows us to view congested fluorescence as a superposition of SVL fluorescence spectra. As such, the fluorescence provides opportunity for experimental comment on whether IVR coupling is ergodic. Two probes have been completed, both using the same approach. Smalley and co- workers 33 have modelled by computer simulation the congestion appearing in the cold-beam fluorescence spectrum of naphthalene pumped to S, &vib = 3068 cm-', where the level density ranges from 400 to 2000 per cm-' depending upon the sym- metries allowed for inclusion in the calculation. They observe that the lesser density is adequate to simulate the observed congestion, but that a subset of these states would be insufficient.By this test, IVR appears ergodic, at least within a limited symmetry class. It is not possible to learn about the further participation of other field states. Dolson 34 has completed analogous simulations for fluorescence from S, p- difluorobenzene with dlb = 2189 cm-l, where the ungerade level density is ca. 40 per cm-l (an ungerade S1 level is initially pumped via a sequence band). These results are markedly different. The density falls far short of being sufficient to provide the required congestion. Ergodicity becomes a moot issue, for it is apparent that an additional source of level density is being used in IVR by S, p-difluorobenzene. That density is, by all odds, provided by rotational levels through Coriolis vibration- rotation coupling.ROTATIONAL LEVEL CONTRIBUTIONS TO IVR There is extensive documentation of vi bration-rotation coupling among dense fields of levels in a closely related problem, namely that of S1-T radiationless transi- tions between electronic states. The intersystem crossing (ISC) is modelled with the same phenomenology as the IVR problem of fig. 1, with the exception that Is) and ( ] I ) ) now are zero-order levels of different spin states. Early indications of rotational- level participation in the { \ I ) ) state density came from studies of ISC dynamics in intermediate-case molecules such as methylglyo~a1,3~9~~ biacetyl 35 and ~yrimidine.~~ In each molecule, analysis of kinetic data showed that the density of levels in the coupled field far exceeded that available from vibrational levels alone.There is no clear source of additional level density other than rotational levels brought in by Coriolis rotation-vibration coupling. Separate studies of quantum beats due to S,-T coupling in methylgly~xal,~~ pyrazine 39y40 and other molecules further emphasize the importance of rovibronic states in the intrastate coupling. An antilevel-crossing study of S,-T-level mixing in glyoxal 41 shows coupling with rovibronic mixing. Additionally, an increasing body of data illustrates the rotational dependence of decay dynamics in S, states where intermediate case S,-T coupling has important control over the S, r e l a ~ a t i o n . ~ ~ * ~ ~ * ~ ~ ~ ~ ~ Another demonstration is provided by super- sonic-beam spectra of the s, +- So pyrazine where the individual molecular eigenstates of fig.1 are explicitly resolved (in pyrazine Is) is a pure spin singlet and (IZ)} are triplet rovibronic levels). These rovibronic couplings are entirely consistent with the pyrazine quantum beats found earlier by Zewail's g r o ~ p . ~ ~ * ~ OCHARLES S. PARMENTER 15 With such a body of evidence concerning the importance of rotation-vibration mixing in electronic-state combination, it would be quite remarkable if such mixing did not contribute also to the IVR characteristics in both ground and electronic states. Several lines of evidence now show S, rotational-vibronic mixing in IVR coupling. The beautiful sub-Doppler experiments of Riedle et al.discussed earlier are per- haps the most explicit.18 The selective disappearance (broadening) of K > 0 rotational structure in absorption bands reaching to higher S1 demonstrates extensive participa- tion of rotation-vibration coupling within the S, state. An equally compelling, but indirect, indication of rotation-vibration coupling in IVR is provided by the threshold data in table 1. As described above, the threshold vibrational level densities in room-temperature studies are too low to support the extent of congestion observed in the fluorescence, and by default it is difficult to find the required level density from a source other than rotation-vibration coupling. including one of this In symmetric and near-symmetric tops, for example, the rotation-vibration coupling precludes K from being a good rotational quantum number.Thus while overall angular momentum and hence J must be conserved among the coupled levels, the AK = 0 requirement is relaxed. Since each rovibronic level is (2J+ 1) degenerate, the accessible level density is increased by order J. In an alternativeview, if the AK = 0 rule amongst coupled levels is relaxed, then an initial rovibronic level can mix with nearly resonant rovibronic levels built on vibronic levels that span a large energy range around the initially pumped level. Consider, for example, the near-prolate top p-difluorobenzene with S, rotational constants ( A - B) = 0.13 cm-'. An initial rovibronic level with, say, J = 50, will be nearly resonant with rovibronic members of vibronic levels whose energies are some- where within the K stack energy for K = 50.The boost in density by such coupling has been discussed in several From E(rot) z J(J + l ) B + ( A - B)K2 the K stack energy for a given J is ( A - B)J2. This energy is 325 cm-l for p-difluoro- benzene with J = 50. Thus some rovibronic level with J = 50 from every vibronic floor within a span 325 cm-l will be accessible for near-resonant coupling (in the absence of AK and symmetry restrictions). Thus in the approximation that the vibronic level density is constant over this span, the rotation-vibration coupling boosts the effective density by the factor ( A - B)J2. In either treatment, mixing scales a s f ( J ) . If selective excitation or cooling can limit the initial J to low values, a marked inhibition on IVR coupling should be apparent when contrast is made with high-J excitation. Thus a general test for rota- tional participation in LVR is derived from the J dependence of IVR.Fig. 2 shows two comparisons using collision-free fluorescence from S, p-difluoro- benzene. Temperature has been used to bias initial J values, using the extremes of room-temperature fluorescence, where J z 30-50 excitation is common, and super- sonic cold-beam fluorescence, where the rotational temperature is (presumably) a few K. After pumping a lower level (&vib = 2069 cm-'; P v i b z 30 per cm-l), the reduc- tion in unstructured background emission in the cold-beam spectrum is dramatic and substantially exceeds the change that occurs from merely reducing thermal inhomo- geneous broadening. There is little doubt about the contributions of rotations to IVR after this initial excitation.The second pair of spectra contrast fluorescence after exciting a higher level In this case the difference in fluorescence is small and possibly nil. Thus there is sufficient vibronic coupling at this level density = 2888 cm-l; P v i b z 300 per cm-').16 VIBRATIONAL REDISTRIBUTION WITHIN POLYATOMIC MOLECULES F to sustain nearly complete fluorescence congestion even at low-Jexcitation. Whether rotations provide an additional coupled level density cannot be discerned from these spectra alone. For this case it would be necessary to see the appropriate absorption band at sub-Doppler resolution as per the benzene example,lS or alternatively, to monitor the IVR dynamics directly.IVR DYNAMICS The interplay between experiment and theory shows a nice inversion symmetry in working out the related processes of IVR and electronic radiationless transition. Radiationless transitions in isolated molecules were first exposed by experiment, and subsequently many lively discussions concerning the theoretical interpretation of these transitions occurred before the theory was in place. The theory then provided new expectations for the dynamics of radiationless transitions that were soon confirmed by experiments. These experiments are, in fact, still continuing today with increasing The history of IVR is in many aspectsjust the opposite. Theory in the form of the R.R.K.M. discussions of unimolecular reactions emphasized the central importance of IVR to reaction dynamics before any explicit experimental evidence was available. The theory inspired an abundance of ingneious experimental approaches to the problem, with the work of Rabinovitch's group being particularly important in early (and continuing) experimental demonstrations of IVR.Radiationless-transition theory later provided a detailed quantum-mechanical description of IVR with specific predictions that IVR dynamics should display the full spectrum of characteristics sublety. 17 9 23,40.42.45 - 47CHARLES S. PARMENTER 17 found in radiationless transitions. Experiments that probed these IVR dynamics in any detail have come forward only in the past few years. To date, these experiments are only from studies of IVR within excited electronic states.Whereas experimental work on radiationless transitions gave early suggestions that excited-state IVR might operate with sub-microsecond time-scales in low vibra- tional regions of a number of large polyatomics,15 no IVRs have proved so leisurely in subsequent experiments. The time-scales seem to be rather those of nanoseconds and picoseconds. The fast IVR times have proved difficult to handle, and the first direct probes of IVR dynamics have only now begun to emerge. Those first results show that IVR is quite obedient to radiationless-transition theory, as expected. Zewail’s group have observed S, LVR dynamics at &vib% 1400 cm-’ in a cold anthracene beam.27*39 In this threshold region the collision-free spectrum (without time resolution) shows sharp structure attributable to Is) emission and a congested background of { Il}} emission.With picosecond pulsed excitation the time dependence of a structured component shows quantum beats of about nanosecond frequency. These dynamics are much different than the decay of the electronic state itself, and hence the behaviour must be that of IVR. In this aspect the IVR is consistent with the sparse-intermediate case of radiationless transitions with coupling of the Is) state to a small-field {IZ)) and coherent excitation of a small number of these mixed states. Stilbene has provided another example of IVR dynamics.48 In experiments with time resolution of 100-300 ps, IVR can be observed at the S, trans-cis isomerization threshold of ca.1200 cm-’. A third example of direct observation is reported in this Discussion 49 by Hoch- strasser’s group. In this case, time resolution of several picoseconds has been imposed on spectrally dispersed fluorescence. In S , p-difluorobenzene they have been able to observe the time evolution of structured 1s) emission as well as background (Il)) emission. The room-temperature experiments reveal IVR with a time-scale of < 10 ps operating at &,ib % 1616 ern-', where the vibrational-state density is less than ten levels per cm-l.- Very likely this IVR is operating on rotation-vibration mixing, as is observed so commonly in the low-threshold regions. This fast IVR should be contrasted with a much slower time evolution (500 ns) for an S, p-difluorobenzene level at &vib FZ 2190 cm-’ reported by Halberstat and Tramer,” and other indications of slower IVR from levels with &,ib > 2000 cm-l in this molecule.Perhaps the fast IVR at &kib% 1616 cm-’ is associated with pumping of an initial level 3,303, which contains high excitation in via, a probable IVR promoting mode. These time-resolved experiments are the first direct view of IVR dynamics, and they foreshadow much work to come, particularly as picosecond methods become more generally accessible. It is certain that a much fuller understanding of IVR will be an important product of picosecond technology. In the meantime, an alternative approach to picosecond fluorescence spectroscopy has been developed at Indiana University. It is easily operated with conventional fluorescence technology using either C.W.or pulsed laser excitation. While the method is indirect, it appears to give a view of fluorescence spectra with time resolution reaching to times shorter than 10 ps. Whereas nothing yet reveals that the method gives time-resolved spectra that differ from direct picosecond spectra, an explicit comparison has yet to be made. The comparisons await complete direct picosecond spectra. The indirect method uses molecular or chemical timing imposed by gas collisions in a fluorescence cell. A gas with the property of quenching the S, electronic state with a large cross-section is added to the fluorescence cell. In the presence of this gas, emission occurs only from molecules that have not suffered a deactivating18 VIBRATIONAL REDISTRIBUTION WITHIN POLYATOMIC MOLECULES collision between the absorption act and spontaneous emission.Thus by adjusting the collision interval with added gas pressure, the fluorescence window can be con- trolled from the full s, lifetime (often nanoseconds) to < 10 ps. Molecular oxygen, with an S, quenching cross-section of about half gas-kinetic, has been the most convenient timing gas, but others (NO, CS,) also appear effective. Examples of the time-resolved spectra have been provided with benzene,22 p-difluoro- benzene 2 2 v 5 1 and p-fluor~toluene.~~*~~~~~ Typically when high added gas pressures establish short timing windows, IVR is revealed by a boost in Is) emission intensity relative to unstructured {IZ)) emission. In cases where IVR is so extensive that no discrete structure occurs in untimed emission, (for example the &vib = 2888 cm-I p-difluorobenzene emission of fig.2) the time-resolved emission reveals structure consistent with that expected from initially pumped ls).22944 Since short timing requires high added gas pressures (typically ca. 30 kTorr or 4 MPa of O2 for 10 ps), this transformation is pressure line narrowing as opposed the more conventional broadening. Other examples where Is) structure appears even in untimed spectra are shown in fig. 3. PUMP 3'5' ~ ~ I I I I I I I ~ I 30 000 38 000 Elcm - PUMP 3' 5'30' I [ l " l l " ~ l F 5000 Y- L l l l l l l l l l l 30 000 38 000 E/cm-' Fig. 3. Time-resolved S1-So fluorescence from p-difluorobenzene excited to S, levels &,ib x 2070 cm-' (3'5l) or &,ib % 2190 Cm-l (3l5'30') The average emission time after excitation is shown to the left, with 5000 ps being the collision-free S, lifetime.Shorter times are achieved by quenching with added O2 at pressures ranging from ca. 2.6 kTorr (90 ps) to 30 kTorr (7 ps). Reabsorption due to increased p-difluorobenzene pressures has removed the higher-energy fluorescence structure from the timed 3l5' spectra. The spectra have been provided by K. W. Holtzclaw.CHARLES S. PARMENTER 19 It is interesting to contemplate the extent to which chemical timing introduces collisional vibrational redistribution or other collisional perturbations into the observed spectra. If the quenching cross-section was much larger than that for other collisional processes, the method would appear safe.Molecules would disappear from experimental view well short of other state-changing perturbations. It is known, however, that cross-sections for vibrational relaxation into fields of S, levels are generally as large or larger than hard-sphere even for small gases such as CO, N2 or Ar.47 Thus collisional redistribution would seem a serious complication in chemical timing. The observed pressure narrowing of unstructured emission immediately reveals that collisional redistribution is not dominant. In addition, examination of spectra such as those of fig. 3 at, say 10 cm-I fluorescence resolution, shows abundant detail in [ s) emission that remains remarkably insensitive to added O2 pressures exceeding 30 kTorr, where the congested background is severely Thus the collisional redistribution fails to appear in these specific searches.Why is collisional redistribution absent ? A rationale is found in measurements of collisional vibrational relaxation within S, states of molecules decaying under intermediate case radiationless transition^.^^ The vibrational relaxation cross- sections (for, say, the partner N2) are consistently orders-of-magnitude less than that in statistical-case S, states. We understand this reduction on the basis of mixed electronic states in the intermediate-case molecules. Those states typically have dominant triplet components 25 (whereas statistical-case states do not). Hence there is small probability of vibrational-state change to produce other vibrational levels in fluorescing singZets (there is correspondingly high probability of producing another vibrational state in the " dark " triplet manifold).In the O2 problem, the electronic quenching interaction necessarily involves mixed electronic states. Although the intermediate or even final states may not be well understood, the important aspect is the development of restricted S, character in the molecule under attack with ensuing immunity to collisional vibrational redistribution. It has been commented 54 that even a spectrologist can recognize the opportunity to follow Is) decay by IVR in such spectra as those of fig. 3. It is apparent that a qualitative difference separates the two cases. Emission from the level 3,5' (cVib = 2069 cm-l) in p-difluorobenzene shows a marked change in the ratio of structured to unstructured intensity in the early stages of timing (5000-500 ps) without further evolution as the window becomes shorter.The opposite behaviour exists for emission from the higher level 3'5,301 where the spectrum is largely insensitive to timing until the window becomes shorter than ca. 500 ps. Clearly the IVR times are widely separated for the two cases. Further, since the structure persists at 5000 ps even when the time evolution is much faster, the IVR must be non-exponential. Such decay is not surprising since both levels are in the threshold region. Both sets of spectra have been analysed 55 within kinetic models based on radiation- less transition (i) In neither case does Is) decay, as seen in the time-dependent ratios of structured and unstructured fluorescence intensities, fit the statistical limit.(ii) Both decays are entirely consistent with inter- mediate case IVR, implying nonexponential decays and recursion of Is) character. (iii) The initial Is) decay times or dephasing times are, as anticipated, widely separated. That from the lower level is ca. 1000 ps. That from the higher level is ca. 50 ps. Both IVR times are short relative to the collision-free S, lifetime. The persistence of Is) structure at the full S1 lifetime demonstrates the intermediate case recursions or non-exponential decay. Details aside, these spectra provide additional evidence that radiationless transition Several findings emerge.20 VIBRATIONAL REDISTRIBUTION WITHIN POLYATOMIC MOLECULES theory is an appropriate description of IVR.With details admitted, however, some interesting points arise. The variation in initial dephasing times (50 vs 1000 ps) is remarkable when it is placed in context of initial-level energies and vibrational densities. The levels are separated by only ca. 120 cm-l and the densities (30 vs 40 per cm-l) are almost the same. Thus attention must be placed on the initially excited mode. The two levels Is) differ only by the presence of a quantum of vi0 in the higher level. The acceleration of IVR dephasing from this higher level reinforces the proposition 29 that vi0 is an IVR promoting mode. A second detail concerns the size of the rovibronic-coupling matrix element (VsI w VIl of fig. 1). Analysis of the data from the higher level by the intermediate case model gives V,, z value far below the anharmonic matrix elements of 1-10 cm-l commonly found in analyses of Fermi resonances. One suspects that cm-I is far more representative of typical interactions among members of the field rather than those few special interactions so large that they can be observed by strong level perturbations in spectra.It must be recalled that the room-temperature- cold-beam comparisons of fig. 2 suggest that the derived V,, w cm-l is largely dominated by rovibronic couplings. Many of those couplings must be of high order so as to relax effectively the AK restrictions on rotation-vibrational level mixings. The chemical-timing IVR studies in p-difluorobenzene provide an additional demonstration of rotational participation in IVR.The demonstrations occur in a study of the effect of initial level preparation on the IVR dynamics from the 3'5'30' level at 2189 cm-l. The vibrational level density is pvib z 40 per crn-l, so that the levels are >0.02 cm-I apart on average. Since this distance exceeds the intrinsic level width, it should be possible to limit coherent pumping to a single (mixed) level. In this limit, no time evolution should occur (although the fluorescence may well show congestion since the levels are mixed). Such an experiment is in progress 56 using a single mode of a C.W. argon-ion laser. While a full analysis is not yet available, the timed spectra show distinct evolution of structure, not markedly different from the experiments in fig. 3 that used the same laser on all longitudinal modes.The single- mode time evolution makes it clear that IVR operates on a density of states far larger than that provided by vibrational levels alone, i.e. on the rovibronic density as dis- cussed above. The single-mode experiments emphasize a point described in several papers of this Discussion 57*58 and elsewhere.26 Although it is yet to be demonstrated, the IVR dynamics must be sensitive to the initial conditions of level preparation. For the S1 experiments, such sensitivity centres on the coherence bandwidth of the exciting laser and the size of the coherence relative to the intrinsic IVR coupling width in the molecule. If the laser coherence width is substantially less than the IVR width, the dynamics may reveal more about the laser than the intrinsic IVR character.This is a difficult experimental issue in IVR dynamics that will require substantial future attention. cm-l, IVR: EXCITED VS GROUND ELECTRONIC STATES A pressing question concerns the correspondence between IVR characteristics as seen in the ground and upper electronic states. There will be of course differences due to vibrational frequency changes. Differences may also occur in specific cases where geometries change or where vibronic coupling becomes dominant in the upper electronic state. In addition, fast non-radiative processes in upper electronic states may broaden levels to overlap in regions where discrete molecular eigenstates wouldCHARLES S. PARMENTER 21 otherwise exist. All of these effects will produce differences in detail, but none introduce true uniqueness that is general to any aspect of S1 IVR behaviour. Several resourceful studies now specifically illustrate the similarities between IVR within different electronic states.Both concern thresholds. Smalley and co- workers 59 have been able to probe IVR state mixing in the ground electronic state of the alkylbenzenes for which S, thresholds are established. The result is “ n o difference”. Low thresholds persist also in the So states, and the data in the two electronic states look remarkably alike. Stewart and McDonald lo have looked for the IVR state mixing in the ground electronic state of 23 molecules of widely varying types by pumping a C-H fundamental and searching for subsequent infrared fluorescence from states other than that initially pumped.Since these are collision- free cold-beam experiments, such fluorescence is certain revelation of IVR mixing. Again, low thresholds are the rule in these systems just as in the excited-state studies. These data are so extensive that they will probably become the benchmark for IVR thresholds. This work is supported by the National Science Foundation (U.S.A.). I am grateful to the present and former members of my research group and to colleagues elsewhere for enlightening discussions and instruction. D. W. Noid, M. L. Koszykowski and R. A. Marcus, Annu. Rev. Phys. Chem., 1981,32, 267. J. N. Butler and G. B. Kistakowsky, J. Am. Chem. Suc., 1960,82, 759. J . Phys. Chem., 1982,86, issue 12. I. Oref and B. S. Rabinovitch, Acc.Chem. 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