The Journal of
Physical Chemistcy
0 Copyright, 1982, by the American Chemico! Society
VOLUME 86, NUMBER 10
MAY 13, 1982
FEATURE ARTICLE Vibrational Energy Flow within Excited Electronic States of Large Molecules Charles S. Parmenter oepertment of Chemlshy, Indiana Unlvefsity, Bhmlngton, Indiana 47405 (Received: September 8, 198 1; In Flnal Form: January 26, 1982)
The experimentalapproaches to both collision-induced and collision-free vibrational energy flow within S1states of large polyatomics are described along with discussionsof the principal findings. The studies use narrow-band excitation to excite single S1vibrational levels or narrow S1regions and take advantage of the short electronic state lifetimes to control the extent of collisional interactions. Various types of S1-So electronic spectroscopies (high-resolution absorption, steady-state fluorescence spectra, time-resolved fluorescence spectra) monitor excited-state vibrational populations and level interactions. Collision-inducedlevel-to-levelflow can be seen low in the S1manifold. From intermediate regions, experiments monitor the collision-induced flow of vibrational energy into the neighboring dense field of vibrational states. From higher levels, collision-free vibrational redistribution can be followed with remarkably direct probes.
Introduction State-resolved studies of vibrational relaxation in polyatomic molecules came of age with lasers, heralded by Yardley and Moore's work' on CHI. Their sudy was, in fact, among the earliest applications of lasers to largemolecule chemical physics. The subsequent use of infrared lasers to probe state-to-state energy flow in polyatomics has become a well-practiced art,and the results now comprise the bulk of our knowledge about state-resolved vibrational energy flow in polyatomics.2 The infrared studies are concerned with vibrational relaxation within the ground electronic state. Relaxation within excited electronic states can be studied by analogous (1) J. T. Yardley and C. B. Moore,J . Chem. Phys., 45, 1066 (1966). (2) E. Weitz and G. W. F l p , Annu. Reu. Phys. Chem.,25,275 (1974). 0022-3654/82/2086-1735$01 .25/0
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techniques using UV or visible lasers and SI So fluorescence. The excited-state studies prove to be technically less difficult than the infrared work. They can also explore larger molecules than have been studied by infrared techniques, and in many aspects they can see finer detail in relaxation characteristics. Regions of S1manifolds can be studied for which ground-state counterparts are inaccessible. With this ensemble of advantages, it is ironic that so little work has yet been completed on excited states of large polyatomics. This paper will discuss several type of experiments that are building a picture of relaxation in various vibrational energy regions of S1polyatomics, commenting on the types of Questions that can be explored and the emerging answers to these questions. While connections with theory be made, the discussions have a strong and empirical flavor since the experimental characteriza0 1982 American Chemical Society
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The Journal of Physical Chemlstry, Vol. 86, No. 10, 1982
tions are far ahead of detailed theories. The experimental work concerns molecules that are truly vibrationally complex, often with 20 or more vibrational degrees of freedom. I t will become apparent that the extent to which the characteristics of S1relaxation also apply to So behavior remains largely an open question. That question is of great interest, however, since it is important to understand whether the S1characteristics have general application. Polyatomic vibrational manifolds fall naturally into three regions for discussions of vibrational energy transfer. The regions are defined by the questions that one can ask and by the types of vibrational energy flow that can occur. The regions can also be defined by vibrational energies and level densities, but from these prospectives the boundaries are indistinct as well as variable from molecule to molecule. Nevertheless, the vibrational domains are usually identified by their relative energies-low, intermediate, and high-for want of better labels. Low levels are discrete, being far apart relative to their widths. Their individual positions and identities can be characterized experimentally. In this region tuned lasers can excite single levels, and the individual level populations can be monitored by resolved S1 So fluorescence. The single-level excitation allows accurate and sensitive studies of collision-induced level-to-level vibrational energy transfer. This is the domain that has been so well studied in ground electronic state molecules. Intermediate levels are also discrete, but the levels occur at energies so high that large level densities preclude direct experimental characterization of their positions and identities. In all polyatomics, a few levels within this domain have large Franck-Condon factors with Sothermal levels, and these levels can be pumped with narrow-band tuned excitation sources to form a starting point for relaxation studies. Populations of other individual intermediate levels can never be brought high enough by the subsequent vibrational relaxation to monitor selectively. Thus S1 Sofluorescence after excitation of the accessible levels only allows determination of absolute cross sections for vibrational energy transfer into a dense field of nearby levels surrounding the accessible levels. Determinations of energy loss accompanying this collisional transfer is a less successful venture. Given license for loose definition, these studies are analogous to those concerned with collisional stabilization of reactive So molecules with high vibrational energy produced thermally or with multiphoton infrared pumping. High levels have level densities that are large enough to establish a vibrational quasi-~ontinuum.~Levels may actually overlap on account of their natural widths or may merely be dense enough so that many levels fall within coherence widths of normal optical excitation sources (a width purposefully left undesignated here). Favorable optical properties of large polyatomics allow laser excitation to pump narrow vibrational regions in this domain, setting the stage for studies of collision-free intramolecular vibrational redistribution (IVR). This energy flow is entirely within the S1manifold. The studies are based primarily on S1 Sofluorescence spectroscopy which even in CW experiments has the built-in time scale of excited electronic state lifetimes which places collisional cross sections on an absolute basis. This lifetime (usually nanoseconds to micraeconds) allows precise control of collisional interactions so that even extremely fast processes with gas kinetic cross sections can
Parmenter
looo~
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-
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(3) A. Amirav, U. Even, and J. Jortner, Opt. Commun., 32,266 (1980).
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Figure 1. Schematic dlagram of every vibrational level in SIbenzene below 1200 cm-'. Heavy levels show palrs or triads too close to depict separately on the diagam. The level 6' (522 cm-') has been pumped In exdtatbn for relaxatlon measurements. The vibrational populations of six levels reached by colllslonal relaxation can be followed in fluorescence, but in two cases the populatlons of level pairs cannot be separately resolved. The numbers Mlcate the separation (in cm-') of levels from 6'. Some of the benzene normal modes are given at the bottom. The modes vS and vl0 are each doubly degenerate.
be monitored easily. This characteristic is one of the principal advantages offered to the experimentalist when studying energy flow within excited rather than ground electronic states.
Low Levels and Level-to-LevelCollisional Flow of Vibrational Energy Figure 1 is a vibrational schematic enumerating the levels in the first 1200 cm-l of the SI benzene manifold. Such a system, with 30 vibrational degrees of freedom, is typical of those accessible by electronic fluorescence. It is possible to pump one of these levels with a tuned laser and then to use fluorescence spectroscopy to deduce the absolute cross sections for added gas collisions that induce energy flow to each of several other levels within the S1 manifold. A large ensemble of cross sections for specific level-to-level energy flows can be measured by repeating the experiment with initial excitation to other levels. Since the collision always induces energy flow between levels within the S1electronic state, all transfers are in this sense intramolecular vibration-to-vibration processes. Differentiation among transfers occurs by focusing on the collision partner. In some cases the S1flow is accompanied by a simultaneous change of vibrational energy within the collision partner. These processes are called V-V exchanges, even though some transfer to translation and rotation inevitably occurs as well. In other cases it is
The Journal of Physical Chemlstty, Vol. 86, No. 10, 1982 1737
Feature Article
known that no vibrational changes occur in the collision partner, and such processes are labeled as a V-T,R exchanges. Acquisition of a full cross section matrix for flow among the S1levels induced by each of a variety of collision partners is a worthy experimental goal, since it provides the ultimate bench mark for theoreticl discussions of these polyatomic processes. A full matrix is unattainable, however, since many levels are inaccessible for initial pumping on account of selection rules and unfavorable FranckCondon factors in the S1 So absorption spectrum. As a further complication, congestion of structure in fluorescence spectra sometimes obscures the growth of new S1levels populated by collisions. Inspite of these interferences, substantial parts of the energy flow matrix are accessible and enough information has become available to begin building a picture of collisional vibrational energy flow in S1polyatomics. As later discussion will point out, the theoretical description of such detailed information is not well advanced and we must instead turn to experiments to answer the elementary questions about the energy flow in these complex systems: (i) What is the general magnitude of the cross sections for intramolecular flow induced by collision partners ranging from inert gas to vibrationally complex hydrocarbons? (ii) Can selection rules, or perhaps less compelling propensity rules, be perceived within the set of crow sections? (iii) How do the crow sections for a given partner depend on collisional and molecular parameters such as (a) the energy bE that must be switched between vibrational and translational/rotational degrees of freedom, (b) the magnitude of vibrational quantum number changes, (c) the symmetries of the initial and final vibrational states, (d) the types of the vibrational modes undergoing change, and (e) mode mixing by Fermi resonances? (iv) To what extent is a vibrational resonance between the collision partner and the S1molecule recognized by an enhanced cross section in these large polyatomic systems? (v) Consider a ground electronic state parent molecule as the collision partner. In this case vibrational energy flow can occur by the mechanism of electronic energy switching between the vibrationally excited S1molecule and ita thermal ground electronic state collision partner. Is this mechanism competitive with more conventional V-V,T,R energy transfer, and, if so, what are its characteristics? The answers to some to these questions are now emerging from the data in published studies on benzene," a ~ ~ i l i n eand , ~ ?pyra~ine.~JO ~ We use the Indiana work on benzene as illustrative of the technique and the findings. The S1 level schematic of Figure 1 and S1 So fluorescence spectra in Figure 2 set the state for discussing the technique. The S1level vgl = 522 cm-l (in common parlance, this is termed the level 6l)has been singled out as the initial level for the first experiments since it can be pumped easily by tuning a laser to a prominent absorption band. Without added gas and with the benzene pressure low enough to avoid collisional scrambling of S1vibrational energy during the 80-ns S1lifetime, all fluorescence will
60 .-y
I
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(4)S.A. Rice, Adu. Chem. Phys., 57, 237 (1981)(a review that appeared after this discussion was written). (5)C. S. Parmenter and K. Y. Tang, Chem. Phys., 27, 127 (1978). (6) G. H. Atkinson, C. S. Parmenter, and K. Y. Tang, J.Chem. Phys., 71,68 (1979). (7)C . S. Parmenter and K. Y. Tang, ACS Symp. Ser., No. 56, 175 (1977). (8)D.A. Chernoff and S. A. Rice, J. Chem. Phys., 70,2521 (1979). (9)M.Vandersall, D. A. Chernoff, and S. A. Rice, J . Chem. Phys., 74. 4888 (1981). (10)D. B.McDonald and S. A. Rice, J. Chem. Phys., 74,4907 (1981).
I
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36000
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Figure 2. Changes in the benzene S1 So fluorescence spectrum due to vibratlonal relaxatlon by isopentane collisions after pumping the level 6'. The number of collisions of an SI benzene molecule with isopentane during the 804s electronic lifetime are indicated to the right. A measured collision cross section of about 1.5 times gas kinetic has been used for these numbers. Benzene pressure is about 100 m t w , and little relaxation occurs In the absence of isopentane. Isopentane pressures In torr are from bottom to top 0, 0.5, 1.0, 5.0, 10, and 50. Maxima from the levels 0' and 6' 16' are marked on the 1.2-collision spectrum. Data from Tang.'
occur from SImolecules in the 6l level. The result is a fluorescence spectrum with open discrete structure, as shown at the bottom of Figure 2. Collisional interactions and the collisional flow of vibrational energy can be controlled precisely by added gas pressure even when steady-state rather than pulsed excitation is used to pump the initial level, the 80-ns S1 lifetime being the magic clock that makes it possible. It can be seen in Figure 2 that vibrational energy transfer causes a dramatic transformation of the fluorescence spectrum as foreign gas additions increase collisional interactions. The spectra in Figure 2 represent the extreme case where added gas pressure ultimately becomes high enough to drive S1benzene nearly to vibrational equilibrium fluorescence. Some of the more prominent qualitative changes in those spectra illustrate the method. The depopulation of 6l as a result of collisions can be monitored by following any of the maxima prominent in the bottom collision-free spectrum. Those maxima become minor contributors to the spectrum as vibrational equilibration is approached. Emission from the S1zero-point level is easily detected by a prominent band (marked Oo in Figure 2) falling neatly between two 6l bands, and it is seen ultimately to dominate the spectrum in the advanced stages of equilibration. Emission from a third level, namely, 6I16l is especially interesting. This level lies 287 cm-' above the initial level 6l,and a band from it can be seen to first grow and then recede as energy transfer becomes more extensive. This level is reached by addition of the out-of-plane ring distortion mode v16/ to the initial level, and it is an importaant intermediate to equilibration. Thus, the stepwise nature of vibrational relaxation is readily apparent. A crucial experimental question concerns the extent to which emissions from many levels in such large molecules can be superimposed while preserving at least some dis-
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The Journal of physical Chemistty, Vol. 86, No. 10, 1982
-
1 -
6.3 +
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7
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3. Data for leveCtdevel vlbratbnal relaxation from 6' benzene. The numbers above each colllslon partner show the number of gas kinetic collisions required for the overall relaxation of the level 6' by vlbrational energy Row into Its nelgtborhg field. The vertical bars show the fraction of relaxation used by each channel, with belng the sum of channels A-D. The crosses show calculated fractions using the propensity rules. Figure taken from ref 7.
tinctive structure from individual levels. In the case of benzene after 6l pumping, emission from seven S1levels or level pairs reached by collisional energy flow can be seen unambiguously. Emission intensities from six of those seven can be monitored quantitatively, and these levels constitute the set of levels for which level-to-level cross sections can be deduced. The actual levels are identified in Figure 1. Individual state-to-statecross sections are obtained from changes in fluorescence spectra that occur in the very earliest stages of relaxation where one-collision transitions are dominant. For isopentane, the added gas of Figure 2, this domain occurs at pressures of less than about 0.2 torr. An exceptionally complete set of collision-freelifetimes for S1vibronic levels of benzene is available," so that the study can be accomplished with steady-state techniques, using the lifetimes to place the relative cross sections on an absolute basis. The extraction of cross sections from the fluorescence band intensities is based on a simple model that leads to Stern-Volmer kinetics for a decaying level and analogous kinetics for the growth of a level. The uncertainty in the absolute state-to-state cross sections in benzene data is about 30%. Situations arise where spectral resolution alone, no matter how high, cannot open a window to see uniquely emission from a given level. In such cases, time resolution of fluorescence added to spectral resolution can sometimes provide the means to unlock the obscured level for study.12 The observable state-to-state processes after pumping 6l are shown in Figure 1. They turn out to be few in number. In the midst of many neighboring levels, relaxation can be seen to only six levels. Emission from some of those levels occurs in regions too close for separation so that the language of "relaxation channels" is useful. As Figure 1 shows, four channels can be followed, two representing transfer to single levels (channels A and D)and two containing relaxation to pairs of levels (channels B and C). (11)K. G. Spears and S. A. Rice, J . Chem. Phys., 55, 556 (1971). (12) R. P.H. Rettschnick, H. M. Ten Brink, and J. Langelaar, J. Mol. S t r u t . , 47, 261 (1978);H. M.Ten Brink, J. Langelaar, and R. P. H. Rettachnick, Chem.Phys. Lett., 62,263 (1979);G. de h u w , J. Langelaar, and R. H. P. Rettachnick, J. Mol. Struct., 61, 101 (1980).
Parmenter
Figure 3 summarizes the experimental level-to-level data in a form convenient for comparisons among collision partners. With 10 added gases concerned with four collisional channels, there are 40 crow sections for vibrational energy transfer. These form the picture of energy flow in this region of S1 benzene. The data contain answers to some of the questions posed earlier. Three aspects of the transfers are perhaps most striking: (i) Large cross sections, near gas kinetic, are commonly observed even for V-T,R transfer. (ii) Strong propensity rules exist. (iii) Vibrational resonances between S1benzene levels and polyatomic collision partners are significant contributors to energy transfer. Consider first the appearance of large cross sections. The data in Figure 3 show that helium is the least efficient partner, yet only 11collisions are required for vibrational energy flow from the level 6l into the neighboring field of states. The remarkably large cross sections are perhaps best illustrated by the channel D cross section for He. The data in Figure 3 show that only about 17 hard-sphere collisions are required to add a quantum of v16/ (237 cm-') to the original level 6l. Such high efficiencies for a T V transfer are not seen for energy flow within ground electronic states. In fact, large cross sections appear to be the rule in excited electronic states, appearing in virtually every large polyatomic so far studied, including aniline? pyrazine,1° gl~oxal,'~-'~ and tetrazine.15J6 Ennen and OttingeP have summarized data pointing to a similar situation for diatomics. These data reveal a fundamental difference between collision-induced energy flow in ground and excited electronic states. While a number of reasons for the large cross sections have been suggested, a convincing theoretical account has yet to be provided. The large cross sections for vibrational energy transfer remain a pressing enigma of excited electronic state behavior. The existence of strong propensity rules is a second characteristic of excited electronic state energy flow. Their presence is revealed when one asks why so few levels near 6l seem to be populated in the one-collision regime. Is it because propensity rules h i t the transfer possibilities or is it merely an experimental artifact associated with the problem of identifying emission from certain levels in the midst of fluorescence congestion? The answer comes quickly by looking at the fraction of energy transfer out of 6l that actually occurs in the four channels A-D. This is the column of Figure 3. That fraction is large, lying always between 72% and 92% for the 10 collision partners. In fact, collisions with He and N2 place over 7090 of the flow into just two channels. Quite obviously there are severe restrictions on vibrational energy flow pathways in benzene. The data for aniline,* pyrazine,1° gly~xal,'~-'~ and tetrazinelsJ6 also reveal high selectivity among the possible channels for energy flow. What are the rules that govern the energy flow? Sets of specific propensity rules cast in terms of simple molecular and collisional parameters have been developed. They now have qualitative success in describing the excited-state energy flow in the three aromatic molecules for which data have so far been published. The rules have
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(13)R. A. Beyer and C. W. Lineberger, J. Chem. Phys., 62, 4024 (1975). (14)L.B. Anderson, C. S. Parmenter, and H. M. Poland, Chem. Phys., 1, 404 (1973). (15)J. Langelaar and R. P. H. Rettachnick, Abstract PH242,28th Congress, International Union of Pure and Applied Chemistry, Vancouver, Canada, 1981. (16)G.de Leeuw, Ph.D. Thesis, University of Amsterdam, Amsterdam, Holland, 1981. (17)G. Ennen and C. Ottinger, Chem. Phys., 3, 404 (1974).
Feature Article
their roots in the theoretical treatment most commonly used for excited electronic state intramolecular energy flow in polyatomics, namely, Schwartz-Slawsky-Herzfeld (SSH) theory18J9as modified by Tanczos.20 SSH theory is a quantum-mechanical atom-molecule scattering treatment of V-T transfer developed for diatomics or linear polyatomics. It is a first-order perturbation approach with a highly simplified model of the collisional interaction. The intermolecular potential is assumed to be a spherically symmetric one-parameter exponential approximation to the Lennard-Jones repulsive wall, scaled at large distances to the potential well depth. The principal contributions to the transition probabilities arise from interactions close to the repulsive wall. The linear molecule axis is always oriented in the most favorable direction for transfer. Steric fadors are introduced to approximate the effect of the real orientation distribution. Tancms" adapted this treatment to molecule-molecule collisions involving quasi-spherical polyatomics such as methane and halomethanes. A central aspect of his extensions to polyatomic interactions is to model a polyatomic vibration as being only motion of the surface atoms, giving rise to the name "breathing-sphere" model. This approach forces the complex polyatomic interaction into the model of a collinear collision of diatomics with a vibrational coordinate x expressed x = AQ where A is the average Cartesian displacement of surface atoms for unit change in the normal coordinate Q. A values for specific modes of a number of small polyatomics have been calculated by Tanczos20 and by Stretton.21v22 By this modeling, the symmetries and dynamic characteristics of the polyatomic vibrations are masked. The theory was developed for application to sound dispersion measurements of vibrational energy transfers and has been useful in describing these experiments where the principal relaxation is a V-T,R process from (usually) one of the lowest fundamentals. Collisional efficiencies are often on the order of quite appropriate for a perturbation treatment. The theory has been used in discussions of level-to-leveltransfers as deduced by IR laser experiments on ground electronic state but the model is so simplified that it has had limited success with such detailed data. The theory has served quite a different role in discussions of vibrational energy flow within excited states. Here it has provided a basis for the establishment of propensity rules. The actual rules, however, are so far removed from the theory with respect to calculations on the specific system under study that they must be considered strictly as empirical. The rules describe the relative magnitudes of cross sections among a set for transfer to each level in the field surrounding the initial level. In other words, the propensity rules are designed to account for the flow pattern from a given level. The SSH-Tanczos theory identifies three factors central to setting the relative probabilities for transfer, namely, final level degeneracies g, vibrational matrix elements U , and a dependence Z(AEw) on the amount of energy AEw switched between vibrational and translation/rotation degrees of freedom. For a transition in which mode A (18)R.N. Schwartz, Z. I. Slawsky, and K. F. Herzfeld, J.Chem. Phys., 20, 1591 (1952). (19)R.N.Schwartz and K. F. Herzfeld, J.Chem. Phys., 22,767(1954). (20)F. I. Tanczos, J. Chem. Phys., 25,439 (1956). (21)J. L. Stretton, Trans. Faraday SOC.,61, 1053 (1965). (22)For a review of these methods, see J. L. Stretton in "Transferand Storage of Energy by Molecules",G. M. Burnett and A. M. North, Eds., Wiley-Interscience, New York, 1969,p 58. (23)See, for example, ref 1, 2,and 24-26.
The Journal of Physical Chemisfty, Vol. 86, No. 70, 7982
1739
changes quantum number from i to j and mode B (perhaps but not necessarily in the collision partner) changes from k to 1, the relative probability P of the transition is P(Aij;Bd
gjglUA2UB2z(MVT)
(1)
While the g factors are straightforward, choices taken in the evaluation of the matrix elements and the Z ( A E m ) factor become the points of departure for building the propensity rules. The results of ground-state SSH calculations for CHI, C2H2,and CH3X system^^^-^^ were first applied to S1 benzene almost without change as a zeroorder starting point, with anticipation that modifications would be required to shape the factors to fit the S1 benzene data. It was surprising to find that the predicted patterns were so close to the observations that further tuning was unwarranted in the absence of more data. In principle, SSH calculations of the coupling matrix elements U contain a sensitivity to the type of mode under consideration. Matrix element calculations for four modes in CH4%show little sensitivity to mode type, with P values lying within a factor of 2 for all four cases. A similar result is found for C2H2.25The change in quantum number, Av, is the dominant influence on these factors. Thus u2 values for benzene are taken to be identical among various modes. The absence of mode discrimination is the most severe approximation contained in the benzene rules. The Z(AEw) factor in SSH theory contains details of the collisional dynamics additional to the AEw gap. Calculations for the three collisional systems CH3Cl-CH3Cl, CH3F-CH3F, and CH4-CH4, s h o ~ e d little ~ ~ pdis~~ tinction among these cases, presenting a rather uniform dependence of Z upon AEVT. As a starting point, a replication of that dependence was taken directly for application to SI benzene flow. As in the case of the u2 factors, the result was close enough to observations so that further adjustment cannot be justified without better data. The actual propensity rules for benzene flow are given to illustrate how remarkably simple they are: (a) Use eq 1 to calculate relative transfer probabilities with the g values taken directly as the degeneracy of the final levels. (b) Set the u2 factors to lo-' for each Au = 1vibrational change without distinction as to the mode type. Thus, a change in which AuA = 2 and Avg = 1 would have the = (c) Z(AEw) is an (V-T,R) energy product UA2UB2 gap factor set to (i) 0.6 for AEw I50 cm-' or (ii) 10-(m~l'oo for AEvT 1 50 cm-l. (d) Multiply either result i or ii by the Boltzmann factor exp(-AEw/kT) for T,R V processes (endoergic). The use of these rules is seen in Figure 3, where the calculated flow patterns (indicated by crosses) are compared with the observations (verticle bars). Predictions are made by calculating the relative transition probability for transfer to each individual level within 600 cm-' and summing those probabilities to get the relative probability for transfer into a full field of levels. Figure 3 shows that the propensity rules are remarkably effective in fitting the data, with serious descrepancies found only for channel C when He or N2 is the collision partner. Thus, the dominant factors controlling the flow in this region of S1 benzene are identified: final level degeneracies, vibrational quantum changes, and the hEvT gap. A brief tour of the flow patterns illustrates how the factors play against one another to make some transitions highly favored and others improbable.
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(24)J. T.Yardley and C. B. Moore, J. Chem. Phys., 49,1111 (1968). (25)R.C. L.Yuan and G. W. Flynn, J. Chem. Phys., 58,649(1973). (26)F. R.Grabner and G. W. Flynn, J. Chem. Phys., 60,398(1974).
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The Journal of Physical Chemistry, Vol. 86, No. 70, 1982
Energy Flow by V-T,R Transfer. V-T,R processes are expected to be dominant for He, N2, CO, and COP,and indeed these gases all induce similar flow patterns. Remarkably, up-pumping by the addition of v16/ = 237 cm-' (channel D)dominates the transfer with each. In contrast, the simplest process, removal of the fundamental v i (522 cm-') pumped in excitation (channel A) has a cross section too small to observe. Clearly, the large value of AEvT blocks the vg channel from competition, but what allows the v1g T V channel to be dominant? The answer lies in a combination of factors, one of which is the fourfold degeneracy of the final level 6'16'. That degeneracy plus the fact that it is a single-quantum transition (6' 6'16') overcomes the modest uphill AEm prohibition and allows it to be so competitive. Channel B is the other important channel for these V-T collision partners. It contains a level vll nearly resonant with the starting level 6'. The fact that this channel competes poorly with transfer to a level 237 cm-' higher emphasizes the fact that AEW prohibitions are not so dominant for levels within k T of the starting level. The prohibition on quantum changes proves to be more important, with Au = 1 in each v6 and vll being required to reach the resonant level. Close Vibrational Resonance in the Collision Partner. As we traverse the top row of Figure 3, the next partner is OCS. It and C02were both included to probe the degree to which a vibrational resonance inthe collision partner is recognized by a vibrationally complex molecule. The OCS bending mode v2 = 520 cm-l is almost exactly resonant with the initially excited benzene fundamental vd = 522 cm-l. Removal of that fundamental (channel A) with C02 as a collision partner (in C02 v2 = 667 cm-') is too inefficient to observe. With OCS, on the other hand, the channel A cross section is about the same as that for the very efficient transfer into channel D. The comparison shows that near-resonant transfers are important in these complex systems. The absolute cross section for the OCS-benzene resonance is about 0.1 gas kinetic and matches closely those for ground electronic state near-resonant V-V transfer in HX and DX system^.^' Perhaps the most intriguing aspect of the OCS resonant transfer is the fact that it is only competitive with the V-T channel D and does not exceed it. It is not that the V-V cross sections are small. It is rather that V-T processes are remarkably efficient in excited electronic states! But why is the V-V resonant transfer so reluctant to exceed the V-T efficiency of channel D? The propensity rules identify the principal prohibition on the V-V transfer. Changes Au = 1in each of two vibrations (v2 in OCS and vd in benzene) drop the transfer probability by a factor of 10 compared with the single v16/ change involved in the T-V transfer. The factor of 4 picked up by the channel D degeneracy is also important in sustaining the channel D efficiency.28 Energy Flow with Intermolecular V-V Transfer. The bottom row of Figure 3 concerns vibrationally complex added gases for which intermolecular V-V transfers should be able to reach distant benzene levels with low V-T transfer probabilities on account of large energy gaps. The V-V transfer is favored by the reduced energy gap, but, on the other hand, it is hindered by the extra vibrational
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(27)S.R.Leone and C. B. Moore, Chem. Phys. Lett., 19,340(1973); A. B.Horwitz and S. R. Leone, h o c . SOC.Photo-Opt. Instrum. Eng., 113,
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114-20 (1977). (28) The role of degeneracies has been specifically checked in S benzene by comparing the 0" 16l transfer with the 6l- 6l16* AU parameters in the propensity rules are identical except the final state degeneraciea, beiig 2 and 4, respectively. The observed cross sections are in the ratio of 2 to 3.4.
Parmenter
change in the collision partner. The rules predict that the trade-off favors the V-V exchange only when the benzene levels are more than 200 cm-' apart. The flow patterns for these gases show the entrance of intermolecular V-V processes by the active role of channel A (6l- Oo). In other respects, the flow patterns are not much different from those of V-T gases. Most remarkably, the flow patterns for these five vibrationally complex partners are essentially the same, notwithstanding the fact that the specific V-V resonances must vary substantially from gas to gas. We can judge the importance of intermolecular V-V exchange vs. V-T,R exchange by using the propensity rules to compute the relative transfer probabilities under two assumptions. We first consider V-T transfer alone. We then consider the most probable V-V transfers, namely, those to levels more than 200 cm-' away from 6l where a Au = 1excitation of the collision partner reduces AEw to less than 50 cm-'. When these calculated V-V and V-T probabilities are compared, it is found that V-V probabilities exceed the V-T probability in only one channel, namely, 6'- Oo. In fact, when all transition probabilities are summed, the addition of V-V processes boosts the total probability of transfer out of 6l by only about 60%. Thus, the rules suggest that V-V transfers are important but not dominant contributors to vibrational energy flow induced by vibrationally complex collision partners. We can now understand or at least rationalize the similarity of flow patterns among the vibrationally complex partners. A large component of the collision cross sections, save for channel A (6l Oo), remains V-T transfer so that the vibrational details of the collision partners are largely masked. This long discourse concerning flow patterns from a single benzene level has been set forth to show that strong propensity rules control the flow. Final level degeneracies, Au changes, and energy gaps AllvTare the dominant factors in transfer probabilities. Other parameters play a secondary role in benzene flow, at least from the level 6l. Certainly most significant among these secondary factors would be a sensitivity to specific benzene modes and a sensitivity of V-T flow patterns to detailed characteristics of the collision partner. Extensive sets of data are now available from Chernoff and Rice8for energy flow in S1 aniline and from McDonald and Ricelo for energy flow in S1 pyrazine. These studies have taken a different approach to the problem. They use a single collision partner, argon, to probe flow from a variety of initial S1levels. Brief reports on benzene6and on anilines show the fEst steps in combining these approaches. The data on benzene, aniline, and pyrazine have common characteristics: (a) V-T cross sections are large relative to those seen in ground electronic states, although pyrazine cross sections are generally not quite as large as those in aniline and benzene. (b) The dominant V-T channels are often endoergic even in the midst of many exoergic channels. (c) Propensity rules based on Au changes and the energy gap Allw can be seen controlling the energy flow patterns. On the other hand, the aniline and pyrazine data show substantial variation from the benzene flow in several details and one main characteristic. The details concern the scaling of the Av prohibitions and the AEVT prohibition. A steeper dependence on AEW and a somewhat relaxed prohibition on Av = 2 changes seems appropriate for aniline and pyrazine. The most prominent departure from benzene flow concerns the dynamic characteristics of the interaction. In
-
Feature Article
aniline and pyrazine, there is clear differentiation between mode types in the efficiencies of energy transfer. Efficient transfer occurs within groups of modes and markedly less efficient transfer occurs to modes outside of those groups. Thus, selectivity with respect to the dynamics of vibrational motion is a primary factor in these molecules as opposed to its secondary nature in 6' benzene. The accumulation of V-T flow patterns for aniline and pyrazine now provides a sufficient data base for a start on the difficult problem of accommodating mode selectivity into the propensity rules. A means is provided in principal by SSH-Tanczos theory, but intuitively that approach seems poorly suited to the dynamics of planar aromatics. In particular it is not easily associated with flow bettween modes within the aromatic under collisional attack. Micklavc and F i ~ c h e rhave ~ ~ developed an alternative treatment for ground-state flow that has had good success for CH3X systems. It has not yet been applied to the aromatic systems. McDonald and Rice30 have laid out a treatment appealing by its intuitive connection with the collision dynamics and its accessibility for calculation in aromatic systems. It uses the SSH approach of scaling the interaction between the molecule and the collision partner according to the projection of vibrational mode amplitudes onto the collision axis. McDonald and Rice, however, set up systematic methods to separate the collision-induced nuclear displacement that correspond to vibrational motion from displacements associated with rotation and translation. With isolation of the vibrational interactions, the principal modes that couple effectively to specific collision trajectories are identified. By then sampling a variety of trajectories, estimates are made of the relative coupling efficiences of mode-to-mode energy flow paths. The use of symmetry correlation procedures makes the entire enterprise tractable. The McDonald-Rice scheme has been used to establish a more refined set of propensity rules for S1benzene flow induced by helium collisions, and it predicts substantial mode sensitivity. While the He-benzene flow pattern of Figure 3 is fitted better by these rules in some channels, the mode-insensitive rules of Parmenter and Tang6 do better in others. The most revealing test of these modesensitive rules occurs with the aniline and pyrazine data where mode sensitivity is more apparent experimentally. When applied to those data, the McDonald-Rice rules have good success considering the complexity of the problem. It is clear that this procedure is a significant advance in describing vibrational energy flow. The discussion has centered on energy flow patterns within S1 aromatics since these are the first systems for which appreciable data have become available. A large ensemble of data is now forthcoming on flow patterns within S1 glyoxal (CHOCHO) and glyoxal-d2l2 This first glimpse of nonaromatic behavior shows some characteristics reminiscent of aromatics, namely, efficient endoergic (upwards) transfers, large V-T cross sections to favored channels, and strong propensity rules that limit the number of channels contributing to energy flow. Those rules, on the other hand, would appear to to require substantial variation from the broad confines of rules that embrace the aromatic flow. Similar study is now underway on s-tetrazine.16J6 The emerging story of energy flow within these SIsystems is awaited with interest, since it portends some highly individual characteristics for vibrational en(29) A. Miklavc and S. Fischer, Chem. Phys.Lett., 44,209 (1976); J . Chem. Phys.,69, 281 (1978). (30) D. B. McDonald and S. A. Rice, J. Chem. Phys.,74,4918 (1981).
The Journal of Physical Chemistry, Vol. 86, No. IO, 1982 1741
ergy flow among various classes of molecules. A final note concerns switching of electronic energy between vibrationally excited Sl and thermal So benzene molecules as a mechanism to accomplish vibrational reluxation within the S1state. The process has been studied by selective excitation of the S1C6D6zero-point level in the presence of C6H6as an added gas.31 Efficient E-E transfer is seen by the appearance of resolved fluorescence from c,&, and strong vibrational effects are present. The transfer populates predominantly the C6H6zero-point level (AE= -203 cm-') and not vld which is nearly resonant (AE = +3? cm-') with the initial c6D6level. Among the p a sible routes, the dominant path for this transfer is the Av = 0 process C&(S1:O0)
+ CeH6(So:Oo)
-*
C~D~(SO:OO) + C&(S1:O0)
which has a cross section about the gas kinetic value.
Intermediate Levels As one climbs the S1 vibrational ladder to regions where there are tens of levels per cm-', it is still possible to bias excitation strongly into a single level. The selection is by the virtuous behavior of Franckqondon factors connecting the thermal Solevels with higher-lying S1 vibrational levels. In aromatic molecules, these factors are large typically for only a few vibrational modes. Thus, rising out of an absorption background crowded with many Av = 0 (sequence) transitions and weak Av # 0 transitions are prominent maxima reaching, if pumped, overtones and combinations of those few modes with large Av # 0 Franck-Condon factors. These maxima allow us to pump a bright level in the midst of dark neighbors. Fermi resonances often complicate the picture, in the simplest case resulting in mixed vibrational character of the bright level. Alternatively, a group of levels within a narrow energy band will be excited. Inspite of these complications, the ability to excite one or a narrow group of levels within a dense region of states opens the opportunity to observe the collisional energy flow characteristics in a particularly interesting region of large polyatomics. The vibrational complexity, however, obscures the view of mode-bmode flow and forces a more restricted inquiry. The experiments can follow the flow only into the neighboring vibrational field without resolution of individual levels. While the level of detail in these experiments is modest, the issues that they probe are not. They respond to central questions concerning activation to chemical reactivity by thermal excitation or by infrared multiphoton pumping: (a) What are the cross sections for flow into a dense neighboring vibrational field with various collisional partners? (b) What can be learned about the average energy loss during collisional destruction of the initial level? Most information about collisional activationdeactivation in dense vibrational fields comes from studies of thermal unimolecular reactions or related probes such as those of molecules activated by chemical reaction or by photochemical processes. The advances on this problem are summarized by Tardy and R a b i n ~ v i t c hand ~ ~by Quack and T r ~ e . ~ ~ Absolute cross sections for collisional vibrational energy flow from initially populated SIregions are determined (almost) unambiguously in fluorescence studies without (31) C. S. Parmenter, B. Setzer, and K. Y. Tang, J . Chem. Phys.,66, 1317 (1977). (32) D. C. Tardy and B. S. Rabinovitch, Chem. Reu., 77, 369 (1977). (33) M. Quack and J. Troe, React. Kinet., 2, 175 (1977).
1742
The Journal of phvsical Chemistry, Vol. 86, No. 10, 1982
Parmenter
TABLE I : Data Concerning Collisional Deactivation of Selected S, Benzene Levels bv Vibrational Relaxation
t
I
I
I
39,000
I
I
38.000
37,000
He HZ
1
I 36,000
I
I 35,000
I
I
I
34,000
cm-1 Figure 4. Segment of the emlssion spectrum from coillslon-free S, benzene after exc#atkn wlth the 253.7-nm (39412 cm-' (vac)) Hg Ilne. Thk segment shows the struchrre extending to about 3000 cm-' bebw the exdtatkn posltkn. The crosses mark stmy lhes fromthe excitation source appearing in various spectrometer orders. The spectrum Is adapted from ref 38 and was obtained by Dr. A. H. White at Indiana University.
0.24 0.33 0.38 0.69 0.73 0.78 0.85 0.96 0.96 1.1 1.2 1.3 1.8 1.9 2.5
0.10 0.13 0.15 0.28 0.29 0.31 0.34 0.38 0.38 0.44 0.48 0.52 0.72 0.76 [1.00]
0.091
[1.0] 0.03 2.9 0.08 DZ 2.7 0.08 CH,=CH, 13 0.37 Ax 1.3 0.04 0.16 2.2 0.06 NZ Xe 1.3 0.04 SF, 0.33 14 0.40 0.40 8.7 0.25 LOz 1.2 0.03 CJ-42 26 0.74 CHF, 7.5 0.21 (C,H,),O 33 0.94 26 0.74 HZ 0 i-C$H,, 1.0 35 [1.0] a Data from ref 40 for the level 6 2 1' excited by 253.7nm excitation. Data from ref 5 for the level 6l. The efficiency of collisional destruction by added gas M defined as PM = U M / U & where u& is the gas kinetic cross section for M-benzene collisions. Efficiency normalized to that of the most efficient collision partner. e The efficiency of i-C!sH,2 is accidentally unity. Thus, these are at the same time absolute and normalized efficiencies. The relative efficiency in thermalizing the S vibrational population after pumping levels at E V i b = 1970 cm-I.
appreciable sensitivity to kinetic models. One monitors emission in a narrow spectral range that is dominated by fluorescence from the level pumped in excitation. In either time-resolved or steady-state experiments with known collision-free lifetimes, it is then a straightforward matter to deduce absolute cross sections for collisional destruction of that level. It is then necessary to determine the various contributions of its parts: collisional deactivation of the entire electronic state, rotational relaxation, and vibrational study is that of Logan, Buduls, Knight, and Ross,4O and energy flow. It is often easy to sort out or mask the conmany of the data described here are from that source. tributions of the first two so that a secure measure of Figure 4 shows why emission after excitation of the vibrational energy flow emerges. 1970-cm-' S1levels offers such an attractive probe. It has The second issue, that of average energy removal perrich, discrete structure that can be isolated with narrowcollision, AE, is less easily extracted from fluorescence band detection to monitor the excited-level population. experiments. Moreover, such AE values are sensitive to The intense (off scale) transitions near 38200 cm-' are modeling, probably more so than in the sophisticated uses particularly useful because they lie in a region that is of chemical activation and photoisomerhation studies that essentially free of emission from new levels reached by have been so successful for ground electronic state^.^-^^ collisional transfer. This liability is illustrated in the benzene experiments Good Stern-Volmer plots of that band intensity are discussed below. obtained in steady-state experiments for the initial stages The fluorescence method has so far been little used in of vibrational relaxation caused by any of a large variety this region of the S1manifold. It has produced glimpses of gases. From those plots, absolute cross sections for level of relaxation in several aromatics, but only for benzene is destruction emerge in the standard way, using the collithere a reasonably large corpus of data. We use these data sion-free lifetimes of Spears and Rice." There then reto illustrate the potential of the method. mains only the problem of assessing the contributions of The benzene work is relatively old and owe8 ita existence rotational relaxation and of electronic state destruction to to the coincidence of the 253.7-nm Hg line with an S1 the cross sections. This task proves to be relatively easy Soabsorption maximum that biases much of the S1p o p and secure. ulation to two levels, namely, the vibrational angular Table I shows the cross sections CTM derived by Logan momentum components of the level 62 They lie at et al.@for collision-induced energy flow from levels near cvib = 1970 cm-l, where the level density is on the order 1970 cm-' into the surrounding S1 vibrational field. For of a few tens of states per cm-'. facile comparison, they have been cast in terms of effiDetails concerning the collisional flow of vibrational ciencies P, defined as the rates of observed to hard-sphere energy from these levels began to emerge in the 1960s from cross sections. Analogous efficiencies for collision-induced independent studies by the groups of S t ~ c k b u r g e r , ~ ~ flow from the level vg/ = 522 cm-' are also included in the R o s s , ~ and ~ , ~ Parmenter.41 The most comprehensive table. The data reveal a number of significant characteristics both for destruction of the initial levels and for actual equilibration of the vibrational populations. (34)B. S. Rabinovitch and R. W. Diesen, J. Chem. Phys., 30, 729 (1959). Destruction of the Initial Levels Near 1970 cm-l. Two (35)J. Troe and W. Wieters, J. Chem. Phys., 71, 3931 (1979);H. points emerge: (a) The cross sections are extremely large Hippler, J. Troe, H. J. Wendelkan, Chem. Phys. Lett., 84,257 (1981). for all gases, with that for isopentane (the most efficient) (36)G.H.Atkinson, C. S. Parmenter, and M. W. Schuyler, J.Phys. Chem., 75, 1564,1572 (1971). being 2.5 times hard sphere. These cross sections are in (37)G.Fiacher and S. Jacobson, Mol. Phys., 38, 299 (1979). fact quite competitive with those observed for rotational (38)M. Stockburger, Z.Phys. Chem., 35, 179 (1962); H. F. Kemper relaxation within the S1state of benzene.42 (b) The range and M. Stockburger, J . Chem. Phys., 53, 268 (1970). +-
11.36737
(39)L.Logan, I. Buduls, and I. G.Ross, in 'Molecular Luminescence", E. C. Lim, Ed., W. A. Benjamin, New York, 1988,p 53. (40)L.M. Lagan, I. Buduls, A. E. W. Knight, and I. G. Ross, J.Chem. Phys., 72, 5667 (1980).
(41)G.B. Kistiakowakyand C. S. Parmenter, J. Chem. Phys., 42,2942 (1965);C.S.Parmenter and A. H. White, J. Chem. Phys., 50,1631(1969).
The J o m l of phvsicel Chemlstty, Vol. 86,No. IO, 1982 1743
Featwe Article
of cross sections is restricted. From the least efficient (He) to the most efficient gas, the cross sections vary by only a factor of about 10. If we delete the three least efficient and H2,the range reduces to only collision partners He, D2, 3.6. A theoretical correlation of these cross sections is available. The large cross sections and compressed range both suggest that the interactions causing energy flow occur predominantly on the attractive part of the intermolecular potential. A theoretical account of the general problem of collisional transfer from an initial state A* into a field of states B A*+M*B+M has been constructed around this assumption.43 The second-order rate constant kMis the kinetic parameter that we seek. The treatment assumes that the rate of destruction of A* is given by -d(A*)/dt = kd(A*-M) where kd is a rate constant for B formation from a collision pair A*-M (not a bound complex). One approach assumes equilibrium for [A*-MI against its precursors A* and M so that the transient-pair concentration can be calculated from molecular partition functions. With an assumption of small variation in kd among pairs with different M gases, the calculation then leads to the expectation that
c eXp{€A*M/kn
k~
(2)
where C is a constant and cA*M is the intermolecular well depth for the pair A*-M. The well depth in this treatment is analogous to the heat of reaction for complex formation, and thus the correlation is related to the collision-pair "stability". An alternative approach usea statistical mechanical fluid theory with pair distribution functions to give the concentration of transient pairs. Equation 2 is then derived with any of a variety of intermolecular potentials (square well, Sutherland, Lennard-Jones)and simple assumptions concerning the dependence of kd on the intermolecular distance. The latter treatment, being free of detailed equilibrium assumptions, is intuitively the more satisfying, and its derivation has the advantage of displaying the dominant influence of the attractive forces for inducing state change. Both treatments ignore all specific details of the molecular interactions so that eq 2 should have general applicability to processes of many types where an initial state decays into a large field of states. To use eq 2, one must know the well depths eA.w This problem can be circumvented when comparing a series of M gases effecting the same state transformation. In this case, the geometric mean approximation gives where the depths are for the indicated pairs. Since ( E A * A * ) ~ /and ~ temperature are constants among a series of M gases acting on A*, eq 2 becomes kM
= [tAIAI/(kP)]'/', With the standard conversion
where ~~~
c' eXp(B(EMM/k)'/2)
~~
~
(42) R. A. Coveleskie and C.
S.Parmenter, J. Chem. Phys., 69, 1044
(1978). (43) H.M.Lin, M.Seaver, K. Y. Tang, A. E. W. Knight, and C. S. Parmenter,J . Chem. Phys., 70,5442 (1979).
( E,,
k )I/*
Figure 5. Plot of In u,,, against ( ~ y M / k ) ~for ' * vibrational relaxation of S1 benzene levels near 1970 cm- Into the neighboring Reld of levels. The M gases and data are from Table I. The figure is reprinted with permlsskn from ref 43. Copydght 1979 American Institute of physics.
into cross sections uM for a series of M gases inducing the change, one obtains the final expression In UM 0: f i ( ~ M M / k ) ' / ~ (3) The correlation of eq 3 has been used for collision-induced radiationless transitions, predissociations, vibrational relaxation high in ground-state manifolds of ground-state diatomics, polyatomics, and ions, and for rotational relaxation. Ita application to the destruction of the 1970-cm-' S1 benzene levels involves correlation of the data in Table I. The results are shown in Figure 5. The correlations of this and other processes are sufficiently good so that semiquantitative predictions of relative cross sections for these processes can be made. Energy Loss and Vibrational Equilibration. The buildup of the lowest vibrational levels in S1benzene by collisional relaxation from the initial 1970-cm-' levels can be followed by monitoring three emission bands that are clear of other overlapping These bands are from the SIzero-point level, from an out-of-plane ring mode u16/ = 237 cm-' and from its overtone 2 ~ ' . In these experiments, the stepwise nature of vibrational equilibration is unmistakable. (a) Far higher pressures of added gases are needed for equilibration than for initial level destruction. (b) Inversion of populations among the three lower levels occurs at intermediate stages with some (c) The ordering of the relative efficiencies of gases for full equilibration differs from that for initial level destruction (column Drel,Table I). (d) The range of efficiencies for equilibration expands about fourfold from that observed for initial level destruction. The data of Logan et al.& in Table I show that the equilibration efficiencies span a range of 37. Thus, it is apparent that equilibration, that is to say, loss of nearly 2000 cm" of vibrational energy, involves factors quite distinct from those governing initial level destruction. These data now bear on the question of average step size during the process of equilibration, that is to say, the average energy loss A E per effective collision. Stochastic models of the stepwise equilibration can be built, but the data are so sparse relative to the complexity of the process that fits with many models can be obtained. Hence, little is learned. Logan et aLM have taken the reasonable approach to ( AE)of noting the added gas pressures required to achieve half thermal equilibration in the benzene experiments. Combined with knowledge of the excited-state lifetime and
1744
The Journal of Physlcal Chemistry, Vol. 86, No. IO, 1982
Parmenter
a function of 3.0 [
0 0 0
0
1J
0
0
0
0.2.
0.1
B1 0
m-.
0
lo 1
I
level energy in S1 benzene. The comparisons are shown in Figure 6. The efficiencies of the V-T collision partner CO fall off almost monotonically as transfer occurs from lower levels, dropping by about a factor of 7 as one descends to the zero-point level from Edb = 2000 cm-'. In contrast, the drop is only about a factor of 3 for the vibrationally complex partner, and furthermore the efficiencies for several lower levels are comparable with those of high levels. Thus, the picture of vibrational equilibration shows profound differentiation between V-T and V-V collision partners. V-T partners are quite comparable with vibrationally complex gases for relaxation from high levels but quickly become ineffective as the widely separated thermal levels are encountered. On the other hand, partners with many vibrational degrees of freedom sustain their efficiencies for low-level destruction, presumably on account of near-V-V resonances. It is probable that this variation of level destruction efficiencies, as illustrated in Figure 6, is the dominant factor in explaining why various gases have such different abilities to bring about vibrational equilibration. It is clear from the benzene data, obtained primarily with the humble 253.7-11. Hg line, that fluorescence is an effective method for revealing the characteristics of collisional energy flow in regions with moderate level densities. The great question concerns the extent to which such data can be extrapolated to the higher regions encountered with reactive molecules. The answer will only come when modern techniques are used to explore such intermediate regions of many S1systems.
I
1:
co I
I
2000
1000
(cm-') Figure 6. EfAciency P for destructkm of vibrational levels in S, benzene by vibratlonel relaxation into the nearby Reld of S, levels as a functbn of the level energy. Isopentane and CO are used as coliisbn partners. Data from ref 45.
the hard-sphere collision frequency, these pressures then albeit with a weak collision mechanism yield an (a), assuming uniform steps. The results give very small energy loses: a few cm-' per hard-sphere collision for monatomic gas@ of diatomics and between 20 and 70 cm-l for polyatomics. If the calculation is repeated with real rather than hard-sphere crow sections, the numbers grow for monatomia and decrease a little for polyatomics. The spirit of the result, however, remains the same. Small ( M )values, between 3 cm-' (Kr) and 44 cm-l (cyclohexane) are obtained. These ( M )ranges are almost 2 orders of magnitude below those observed in studies of relaxation high in ground-state manifolds?2~s~u Considerations introduced below make it certain that the benzene values are underestimated, perhaps seriously. Nevertheless, it appears that a qualitative difference exists between this work and relaxation high in ground-state manifolds. Average energy loss in the latter appears to increase with total energy, and this trend is consistent with the low ( AE) values for benzene. Without more data for dense regions of S1 states, however, little can be said concerning the true origins of the dichotomy. We can identify two fadors in the benzene experiments that would lead to the calculation of larger ( AE) values. Perhaps most obvious is the omission of up-transfer from the calculation. When one deals with low levels, an uptransfer is the dominant transition, occurring in benzene on account of a low-frequency out-of-plane mode that is easily V-T coupled in collision. As one climbs high enough in the SImanifold, such effects of single levels may be overwhelmed by the sea of lower probability transitions. It is unlikely, however, that this has ocurred in the region t d b = 2000 cm-' of the benzene studies. The second factor is probably unique to lower vibrational regions (as in the benzene experiments). It concerns the dependence of cross sections for level destruction on the level energy. Unpublished studies of Tang45are extremely revealing on this point. He has measured the absolute cross sections for a stiff diatomic (CO; probably V-T,R transfer only) and for a vibrationally complex hydrocarbon (isopentane with V-V and V-T,R transfer) as (44)J. Troe, J. Phys. Chem., 83, 114 (1979).
High Levels and Collision-Free Intramolecular Vibrational Redistribution (IVR) It has been just over 20 years since publication of the first experimental demonstration of collision-free energy flow high in the manifold of a large polyatomic.48 That work was motivated by the fundamental role that IVR played in the RiceRamsperger-Kassel-Marcus(RRKM) theory of unimolecular dissociation of polyatomics with high vibrational excitation. The continued interest in the problem of thermal dissociations and more recently in dissociation by multiphoton infrared excitation has generated many ingenious experimental approaches to the problem of IW in ground electronic state molecules.4' The phenomenon has proved to be difficult to study, primarily on account of the problem of monitoring the vibrational populations high in ground electronic states. As a result, the experimental characterization of IVR is no better than fragmentary. While IVR is known to occur in certain energy regions of a number of molecules, and while time scales have been identified in some of these systems, many of the fundamental questions remain without satisfying experimental answers: (a) As one climbs the vibrational ladder in a given molecule, at what energy does IVR first occur? What role does density of states have in this threshold? (b) What is the kinetic characterization of IVR as a function of vibrational energy? (c) How ergodic is IVR, that is to say, to what extent do all vibrational levels in a given region participate in the redistribution? (d) How do IVR characteristics depend on the symmetries and types of modes intially excited? In a more general sense, how do molecular parameters such (45)K. Y.Tang, Ph.D. Thesis, Indiana University, Bloomington, IN, 1975. (46) J. N. Butler and G. B. Kistiakowsky, J. Am. Chem. SOC.,82,759 (1960). (47)For a review, see J. D. McDonald, Annu. Rev. Phys. Chem., 30, 29 (1979).
The Journal of Physical Chemlstry, Vol. 86, No. 10, 1982 1745
Feature Article
as state densities and state mixing by anharmonic coupling and other means control IVR? (e) What role do rotational levels play in IVR? If one turns to the exploration of IVR within excited electronic states, the experimental situation improves. Within the last few years, remarkably direct probes of ME in S1states have been developed from various types of Sl-So electronic spectroscopy. It is quite possible that these techniques will yield a more detailed experimental picture of IVR than has so far emerged from the experimentation with ground electronic state systems in spite of that long history. The primary purpose of this section is to show how clearly IVR can be seen in the S1 states of aromatic molecules. Before the techniques are described, however, it is useful to point out the most surprising finding that has emerged from the early studies. IVR in ground electronic states has been generally considered a phenomenon particularly important at high vibrational energies, e.g., 20 000-30 OOO cm-', the domain of thermal dissociations and isomerizations where state densities exceed lo6 per cm-'. With interest in the problem of mode-selective infrared multiphoton dissociations, attention has shifted to lower domains, and particularly to the threshold question. As the photon pumping climbs the vibrational ladder, where does IVR first smear out the vibrational identity? An answer has come quite clearly from studies of IVR in S1 states, at least for aromatic molecules. In these systems the IVR threshold occurs at remarkably low vibrational energies. The grand champions, so to speak, are presently the alkylbenzenes@ in which the extensive vibrational state mixing associated with IVR has been found as low as 530 cm-' above the zero-point level. Evidence for IVR characteristics in four- or five-ring systems is found within 1000 and 1500 cm-' of the zero-point level: and some single-ring aromatics without side chains have been shown to display IVR as low as fvib = 2000 cm-1.49950 We are still looking for the exception where IVR characteristics are clearly absent at such low energies. Thus, the adjective "high" in the title of this section is in a sense misleading since vibrational regions under consideration generally lie below the C-H stretching fundamentals of aromatic systems. Vibrational level densities are as sparse as 100 per cm-', sometimes even a bit lower. Within such low regions, one must be careful about the meaning of IVR. This issue has been addressed recently,6l and further comments are made later. Three types of S1-So spectroscopy have been used to study Si IVR: (i) High-resolution S1 So absorption spectroscopy reveals S1level widths that far exceed those due to the S1 electronic lifetime. Fast IVR is the most reasonable explanation of such widths. (ii) Collision-free steady-state S1 So fluorescence spectra are without resolvable structure even when narrow-band excitation biases much of the initial S1 population to a single zero-order level. The absence of structure is consistent with the extensive mixing among vibrational levels that is associated with IVR. (iii) Picosecond single vibronic level (SVL)fluorescence spectroscopy shows a time evolution in fluorescence
-
-
(48)J. B.Hopkins, D. E. Powers, and R. E. Smalley, J.Chem. Phys., 73, 683 (1980);72, 2905, 5039 (1980);J. B. Hopkins, D. E. Powers, S. Mukamel, and R. E. Smalley, ibid., 72, 5049 (1980). (49)R. A. Coveleskie, D. A. Dolson, and C. S. Parmenter, J. Chem. Phys., 72, 5774 (1980). (50)D. A. Dolson, C. S. Parmenter, and B. M. Stone, Chem. Phys. Lett., 81, 360 (1981). (51) K. F. Freed and A. Nitzan, J. Chem. Phys., 73, 4765 (1980).
Y
-
Flgure 7. Rotational contours of vlbrational bands in the room-temperature SI Soabsorption spectrum of pdifluorobenzene. Top left and right bands are the 0,O and the 30; bands, respectively, the latter termlnatlng In vm' = 122 cm-'. Bottom left and right are the 3; 5; (vi = 2069 cm-') and the 3; $30: bands v ~ '= 2189 cm-'1, respectively. The figure is printed with the permission of T. M. Dunn.
+vi
(vi+ v l +
spectra that is most satisfactorilyattributed to IVR. When levels above the IVR threshold are pumped, the fluorescence has prominent structure from the pumped level at short times (tens of picoseconds) which disappears into broad fluorescence congestion at longer times. Each is discussed in turn. View of IVR by Sl-So Absorption Spectroscopy. An example is provided by p-difluorobenzene (pDFB), whose S1 photophysics,5wS1 So absorption spectroscopy," and S1 So collision-free SVL f l u o r e s ~ e n c have e ~ ~ been well explored. Sharp rotational band heads occur in the contours of many S1 So absorption bands. From these band heads, remarkably large S1 rovibronic level widths are detected in room-temperature high-resolution spectra.% Examples are shown in the four absorption bands of Figure 7 . Those reaching SI levels with Cvib = 0 and tdb = 122 cm-l have sharp rotational band heads and are characteristic of all bands terminating in S1levels with Cvib = 2189 cm-'. As can be seen in Figure 7 , the contour of the band reaching the 2189-cm-' level shows substantial broadening of the rotational band heads. Such broadening perists in every band reaching higher S1levels and becomes so severe that all traces of the rotational heads are lost in bands reaching S1 levels above about 2800 cm-'. The loss of sharp rotational structure shows that the terminating SIrovibronic levels are themselves broadened. With a technique similar to that used in S1benzene,57 Dunn% has estimated level widths from the absorption spectra. Individual rovibronic level widths correspond to lifetimes on the order of a few tens of picoseconds in S1 vibrational regions where broadening is first detected, and
-
-
-
(52)C.Guttman and S. A. Rice, J. Chem. Phys., 61, 661 (1974). (53)L. J. Volk and E. K. C. Lee, J. Chem. Phys., 67, 236 (1977). (54)A compilation of references is contained in ref 49. (55)R. A. Coveleskie and C. S. Parmenter, J.Mol. Spectrosc., 86,86 (1981). (56)T. M. D u n , University of Michigan, private communication. (57)3.H. Callomon, J. E. Parkin, and R. Lopez-Delgado, Chem. Phys. Lett., 13, 125 (1972).
1746
The Journal of Physical Chemistry, Vol. 86, No. 10, 1982
picosecond lifetimes (or shorter) for S1levels above about 3000 cm-'. The significance of these lifetimes becomes apparent after comparison with the collision-freefluorescence lifetimes.s2 The zero-point-level value is about 12 ns, and the fluorescence lifetimes decrease rather smoothly to about 5 ns for levels near 3300 cm-'. Note particularly the units of the fluorescence lifetimes. They are nanoseconds! The fluorescence lifetimes of higher S1 levels are 3 orders of magnitude longer than lifetimes derived from rovibronic level widths. The lifetimes also take no notice of the level broadening that occurs as one ascends through E,$-, ii: 2200 cm-l on the S1 ladder. These comparisons show that the large level widths are in no way associated with processes that destroy the S1 electronic state. The level broadening must derive from interactions within the S1 electronic state itself. Extensive vibrational level mixing within the S1 state appears as the only feasible way to understand the level broadening. That mixing is necessarily associated with redistribution, and, without attempting to identify the sources of the mixing, the level widths are taken as a view of IVR in SI pDFB. The level widths reveal a straightforward pattern of IVR in SI pDFB. The onset occurs early on the SIladder, and the interactions increase rapidly above the threshold to give IVR times in the picosecond or subpicosecond range. IVR occurs from every S1 vibrational level above the threshold that can be seen in the S1 So absorption spectrum. These experiments require sharp rotational structure and clear vibrational bands that rise above the congestion of all large-molecule, room-temperature absorption spectra. Many molecules do not have such a conjunction of virtues, but spectroscopy in cold supersonic nozzle beams solves the problem. With rotational temperatures reduced to about 1 K and with hot bands (nearly) eliminated, the structured S1 So absorption can be followed into the interesting SI regions of very large polyatomics. It is certain that IVR studies will be among the important uses of cold-beam spectroscopy in the coming years. The certainty is proved by an early naphthalene study by Smalley et a1.68 Beam conditions so reduce the congestion that level widths can be estimated in bands reaching excited-state levels lying above 4000 cm-'. All levels above 3000 cm-I have widths exceeding those attributable to electronic state decay, indicating an IVR time of about 10 ps in the onset region. Subsequent work using the fluorescence technique described below has built a comprehensive picture of IVR in S1n a ~ h t h a l e n e . ~ ~ The term IVR is used in discussions of level mixing probes. Strictly speaking, differentiation should be made between static level mixing and the dynamic process of redistribution. Whether level mixing actually leads to a true time-dependent evolution of S1 vibrational identity depends on aspects of the mixing and on the initial peparation of the S1 levels. More is said about this point later. View of IVR by Collision-Free Single Vibronic Level Fluorescence Spectroscopy. SVL fluorescence spectroscopy has been used to probe S1vibrational level properties in many polyatomics. Its success is based on the fact that
-
-
(58)S.M. Beck, D. L. Monte, M. G. Liverman, and R. E. Smalley, J . Chem. Phys., 70,1062 (1979);S.M.Beck, D. E. Powers, J. B. Hopkins, and R. E. Smalley, ibid., 73, 2019 (1980). (59)S. M. Beck, J. B. Hopkins, D. E. Powers, and R. E. Smalley, J . Chem. Phys., 74,43 (1981).
Parmenter
1869
*
,
0
26000
20000
30000
c rn-' Flgure 8. Collision-free fluorescence from lazainddizine wtth tuned excitation that biases the S1 population to the S1 vibrational region indicated by the labels to the right. Azaindoilzine pressures were in the range 6-40 mtorr. A frequencydoubied dye laser (Chromatix CMX-4) with a bandwidth of about 4 cm-' was used for excitation. Spectra from K. W. Hottzclaw, Indiana University.
SVL excitation usually produces (under collision-free conditions) fluorescence with relatively simple and easily analyzed structure.@ Simple fluorescence spectra are lost, however, after excitation pumps higher levels. The discrete spectrum characteristic of low-level SVL fluorescence is replaced by congested emission with little comprehensible structure. In many cases, this congestion derives trivially from thermal vibrational congestion in the absorption spectrum (sequence and hot bands) which is transferred directly to the SI state by the absorption act. No excitation source, however narrow or carefully tuned, can bias S1 populations heavily to a single level when pumping a region of many overlapping absorption bands. Instead, a superposition of SVL emission spectra from the multitude of unrelated S1 levels pumped in excitation gives a fluorescence spectrum too crowded for resolvable structure. These spectra generate new interest, however, when a further cause of fluorescence congestion is considered. It was early recognized by Blondeau and StockburgeP that IVR might be contributing to congestion. In an experiment where a substantial fraction of the S1 population is initially excited to a single vibronic level, congested emission would occur if IVR scrambled the S1vibrational identity during the fluorescence lifetime. A search has been made for contributions of IVR to the congested room-temperature fluorescence of a number of aromatics. The approach has been to choose molecules with one or a few modes having long and bright FranckCondon envelopes so that prominent absorption maxima reach the upper S1 levels. Excitation would bias enough of the initial S1 population into a single level so that discrete structure from that level would be normally ob(60) C. S. Parmenter and M. W. Schuyler, Transitions Non Radiat. Mol., Reun. SOC.Chim. Phys., 20th, 1969,92 (1970). ( 6 1 ) J. M. Blondeau and M. Stockburger, Ber. Bunsenges. Phys. Chem., 75, 450 (1971).
The Journal of Physical Chemistry, Vol. 86, No. 10, 1982 1747
Feature Article
1
{
A ABSORPTION
PERCENT BACKGROUND IN E EMISSION
A E
0
aE-------------------------------------------A I
0
,
I
I
1000
2000
v IBRATION AL
,
I
3000
ENERGY (cm-')
Flgure 9. The symbol E gives the percent of emission appearing as background after pumping an absorption maxima leading to the indicated S, vibrational energy. The symbol A indicates the percentage of absorption in the pumping band-pass that results from background under the prominent absorption maxima. The absorption background is buUt from many unrelated transitions of low intenslty. The uncertainty in E and In A is about 10 percentage points. Data from D. A. Dolson6'
servable. If IVR was occurring however, that structure would be lost. The results with 1-azaindolizinein Figure 8 are typical. Each fluorescence spectrum is generated by narrow-band excitation tuned to an absorption maximum that is sufficiently prominent above the background to produce structured fluorescence in the absence of IVR. Normal single vibronic level fluorescence structure is seen from the lowest levels. The fluorescence structure after higher level excitation becomes increasingly submerged in congestion. Ultimately no structure can be resolved, even though the absorption characteristics indicate that structure should be present. Much of the fluorescence congestion is attributed to IVR. In a few cases, quantitative studies define the extent to which rVR has obliterated structure in emission from these higher S1regions. An example involving pDFB is shown in Figure 9. Absorbance measurements give the fraction of excited molecules pumped to a particular S1 level vs. the fraction placed in unrelated S1 levels because of excitation in the underlying absorption background. That fraction represents approximately the fraction of emission that should appear as background if IVR is absent. These fractions are shown in Figure 9 by the symbol A for a variety of S1 vibrational regions. The fraction of emission that actually appears as background is indicated by the symbol E. The comparisons in Figure 9 show a systematic trend. The fractions A and E are within experimental error of each other for levels below about 2000 cm-'. Above that region, far more background appears in fluorescence than would be expected on the basis of absorption. The disappearance of fluorescence structure is characteristic of IVR. We take studies such as those in Figures 8 and 9 as evidence of the onset and persistence of IVR as one climbs the S1 vibrational ladder. Such room-temperature fluorescence studies have now been undertaken in a number of molecules including the single-ring aromatics p-fluorotoluenem and p-difluorobenzene49and the double-ring systems indole,63 t h i ~ n a p h t h e n e~, ~o ~u m a r o n e l-a~aindolizine,~~ ,~~ azulene (S2),65and isoquinoline.@ While the studies are not uniformally complete, the same behavior is observed. The data strongly suggest that IVR is a phenomenon general (62)D. A. Dolson, Ph.D. Thesis, Indiana University, Blwmington, IN, 1981. (63)B. M.Stone, Indiana University, unpublished results. (64)K. W.Holtzclaw, Indiana University, unpublished results. (65)A. E. W.Knight, unpublished results. (66)G. Fischer and A. E. W . Knight, Chem. Phys., 17, 327 (1976).
Is> Flgure 10. Schematic diagram of vibrational level mixing within a single electronic state. Coupling between Is) and 11) and among Ii) Is indicated by the matrix elements V , and V,,.
to all of these molecules and that all have thresholds below 2000 cm-'. While this view of IVR is convincing, it is severely clouded in detail by the thermal absorption congestion (labeled elsewhere as thermal inhomogeneous broadening (TlB)67368) attendant to all room-temperature experiments. It is in this respect that cold-beam experiments display their greatest advantage. Cold beams so reduce thermal congestion that collision-free single vibronic level fluorescence can be obtained from large molecules entirely inaccessible at room temperature because of absorption congestion. A number of reports now confirm the advantages. Among the more remarkable accomplishments has been the generation of high-quality SVL fluorescence spectra from the macroring system, free-base phthalocyanine (Levy and co-workers@),a molecule with essentially no resolvable vibrational structure in its room-temperature absorption spectrum.7o Indications of IVR in the fluorescence spectra first appear as a threshold near 700 cm-'. Amirav, Even, and Jortner have used SVL fluorescence in cold beams to probe IVR in the 10-ring system ovalene3 and the 4-ring molecule tetracene,68 both of which are inaccessible to room-temperature experiments. These systems display IVR with thresholds at 1280 and 1900 cm-l, respectively. A specific discussion of low thresholds has been given by these a u t h ~ r s . ~ The most comprehensive cold-beam studies are those of Smalley and co-workers, who used the technique of SVL fluorescence to probe IVR in alkylbenzenes4*and related molecule^.^^-'^ The concept of the experiments is simple and ingenious, being based on a molecular system that allows excitation of ring modes to set the stage for subsequent IVR into the side chain. The ring modes initially pumped are in every case too low (500-900 cm-l) to produce fluorescence congestion from ring mode interactions alone. The resolved fluorescence spectra from alkylbenzenes reveal IVR after pumping ring modes with 'Vib = 530,932, or 965 cm-l. IVR could be observed from the lower level only when the side-chain length reached butyl, but IVR in ethyl- or propylbenzenes is readily apparent (67)A. Amirav, U. Even, and J. Jortner, Chem. Phys. Lett., 69,14 (1980). (68)A. Amirav, U. Even, and J. Jortner, Chem. Phys. Lett., 71, 12 (1980). (69)P.S.H. Fitch, L. Wharton, and D. H. Levy, J . Chem. Phys., 70, 2018 (1979). (70)P.S.H. Fitch, C. A. Haynam, and D. H. Levy, J. Chem. Phys., 73,1064 (1980). See especially Figure 8. (71)D. E. Powers, J. B. Hopkins, and R. E. Smalley, J. Chem. Phys., 74,5971 (1981). (72)J. B. Hopkins, D. E. Powers, and R. E. Smalley, J . Chem. Phys., 74,6986 (1981). (73)D. E . Powers, J. B. Hopkins, and R. E. Smalley, J. Chem. Phys., 72,5721 (1980).
1748
The Journal of Physical Chemistry, Vol. 86,No. 10, 7982
after pumping the higher levels. We note again the ubiquitous nature of IVR in these S1 systems. It is difficult to localize vibrational energy even at these modest S1vibrational energies. IVR persisted even when the alkyl chain further isolated from the ring by an alkyne linkage (phenylalkyne~~l) or by an oxygen linkage (phen~xyalkanes'~).Smalley et al. explored also p-alkylaniline~'~ in which the laser pumped the NH2-inversion overtone, presumably even more remote from the sidechain vibrtional field on the opposite side of the benzene ring. Again, IVR is observed. View of IVR by Time-Resolved (Picosecond) S1 So Fluorescence Spectra. For convenience, a time-dependent language for IVR has been used in the preceding sections when in fact the expeiments do not measure time dependence directly. Those experiments probe instead the existence of level mixing which, while a prerequisite, is not by itself indicative of true time evolution. A more precise description of IVR is taken from the theory of radiationless transitions between electronic states.51 Its simplest elements are given in Figure 10. The levels Is) and (11))of that figure are the zero-order S1 levels. The level 1s) is distinguished from its neighbors (11)j by its large Franck-Condon factor to a thermal level in the So state. Thus Is) is prominent in absorption whereas the small Franck-Condon factors to all levels in the set (11)) cause them to be relatively "dark" in absorption. By this means, the optical oscillator strength is dominated by a single zero-order level Is) in the midst of a dense field of neighbors (11)). The occurrence of such bright SI levels high in large-molecule manifolds is not particularly rare, and IVR experiments seek out such cases. The levels Is) and (11)) are coupled among themselves with various anharmonic and/or vibronic coupling strengths. In principle, the coupling of 11) levels among each other is no different from the Is)+) coupling. For the purpose of an optical experiment, however, the Is)+) coupling is of prime interest since its presence causes the Is) oscillator strength to be distributed over the set (11)). These couplings generate a new set of levels the true molecular eigenstates, in which the vibrational identity of any given state is now a complicated mixture of Is) and (ll)]. Our specific interest is the resulting distribution of Is) character in it being approximately Lorentzian as shown by the heavy shading in Figure 10. Now consider a high-resolution absorption spectrum. If the levels are sufficiently separated relative to the experimental resolution, the absorption, which occurs entirely on account of the Is) character, will appear as a series of lines having the intensity distribution of the shading in Figure 10. An extreme example is a two-level Fermi resonance in which only one zero-order state carries the oscillator strength. The mixing yields two absorption bands whereas one is expected in the absence of the interaction. In situations of interest for IVR, the level density is generally too high for separate level resolution. Instead, the absorption acquires width, the width being that of the Is) distribution in the set This is the line width cited earlier in the pDFB and naphthalene absorption experiments. Those widths clearly reveal such level mixing. That mixing, however, may or may not be associated with actual time evolution of the S1vibrational identity (see below). Fluorescence of such a system is most easily understood by the example of the two-level Fermi resonance where one of the mixed levels can be pumped to the exclusion of the other. In this case, the SVL fluorescence spectrum is a superposition of emission from both zero-order states of
-
(u)),
(u)),
(u))
(u)).
Parmenter
the Fermi resonance since each level is itself a mixture. Thus, excitation of a seemingly clean single vibronic level produces fluorescence with contributions from more than one zero-order vibrational identity. No time-dependent phenomena are involved. Numerous examples are found in the SVL fluorescence l i t e r a t ~ r e . ~ ~ ~ ~ ~ ' ~ , ' ~ By analogy, if resolution allowed excitation of only one level in the set (b)), a richly structured fluorescence spectrum would be observed that is effectively a weighted superposition of SVL fluorescence spectra from each zero-order Is) and 11) that constitute the single eigenstate Thus, in principle, true single-level excitation can produce seemingly multilevel fluorescence that may be congested to the point of occluding resolvable structure. Again, no time evolution occurs between the absorption and fluorescence acts. The congestion is entirely the result of static level mixing (a super Fermi resonance or perhaps one might say a Fermi hemorrhage). It is questionable whether such single-level excitation could be achieved in a large molecule, even in cold beams. More typically narrow-band excitation will pump many u)'s whose combined absorptions are so closely packed as to preserve the appearance of "sharp" absorption to a single level. The congested fluorescence spectrum, however, reveals the mixing. Time evolution of the S1vibrational identity occurs when the levels are sufficiently dense to place many within the coherence width of the excitation source. At short times after such excitation, the SI vibrational identity is that of a single level, namely, Is). At longer times, a complex vibrational identity will evolve with components from the 11) field dominating the vibrational description. This is the simplest picture of time-dependent IVR in these S1experiments. When the excitation coherence width spans a substantial fraction of the Is) distribution in and when the energy separation of levels in is small relative to the coupling energies, the actual time scale of IVR will be related to the width ysof the 1s) distribution in Explicitly, ysis given as
u).
(u)(
(u))
(u)),
(u)).
Ys = 2 ~ V s I 2 P l where Val is the average Is)+) coupling matrix element and p1 is the (11))level density. That width, in turn, is the line width measured in high-resolution SI Soabsorption spectra. By the simple time-energy uncertainty relationship, those widths give IVR lifetimes that are appropriate for suitable excitation conditions. This picture corresponds to the statistical case of radiationless transition theory. More complicated cases might apply.51 An understanding of when such conditions are achieved depends on a knowledge of molecular parameters (effective state densities, coupling matrix elements) that are difficult to obtain. Thus, inference of IVR lifetimes from time-independent views of level mixing is rather model dependent within the theory, albeit the simple statistical case described above is a useful frame for rough estimates. The time-dependent behavior is best understood by direct inquiry with an experiment such as time-resolved fluorescence. Fluorescence at times much shorter than the IVR lifetime should be markedly different from that after IVR. At short times, the fluorescence structure should be easily resolved, being from only level only, namely, the Is) that carried the excitation oscillator strength. This
-
(74) A. E.W.Knight, C. S. Parmenter, and M. W. Schuyler, J . Am. Chem. Soc., 97,2005 (1975). (75) A. E.W.Knight, C.M. Lawburgh, and C. S. Parmenter, J. Chem. Phys., 63,4336 (1975).
The Journal of Physical Chemistty, Vol. 86, No. 10, 1982 1749
Feature Article
-
collision free m-
ns
4 -
8 ns
d $1n /!v I
J ktorr
JI
30000
II
I
d I
'
37000
I
'
I
"
'
37200
'
I
37400
-
, 35000
c m-
'
8300 ps
L*, 40000
So fluorescence spectra after exciting a level with 1990 cm-' in p-fluorotoluene (pFT). Bottom spectrum: CollIsmfree Rwxescence from 0.3 torr of pfT. The average time between excitatkn and fluorescence is 8300 ps, the natural fluorescence Metime from this S1 region. Upper spectra: Fluorescence from 0.3-1.5 torr of pFT with oxygen added (pressure shown to left) to reduce average fluorescence times into the plcosecond range. Times are shown to the rlght. The feature marked R is Raman scatterlng from 02. The excitation position is marked by an asterisk. Fluorescence resolution is about 50 cm-'.
il
n
I
Flgure 12. S,
\
O2
GZ
'
I
37600
c m-' Flgure 11. Fluorescence spectra showlng the time evolutlon of vIkatknal relaxatkn within the S, manifold of benzene. Top spectrum: Benzene vapor at 0.1 torr is pumped to its S, vibrational level u,,' (522 cm-') by absorption from a CW source. Fluorescence occurs before collisions at this pressure so that the emission is characteristic of that from the single vlbronlc level u,,'. Lower spectra: The experiment is repeated with a 40-torr lsopentane heat bath added to cause nearly complete vibrational equMbratlon wlthln the normal 804s decay lifetime of the S1 state. The evolution of this vlbratbnal equlybratkn Is folkwed by observing the emlsskm spectrum from molecules that, on average, have survived 4, 8, 14, 24, 54, or 80 ns after their excitation. The figure Is adapted with permlsslon from ref 45. Copyright 1975 K. Y. Tang.
structure is lost at longer times, being replaced by the unstructured emission characteristic of the complicated vibrational identity produced by IVR. The challenge to this approach is experimental. Picosecond time resolution is required for many of these systems. The need to have tuned picosecond excitation combined with picosecond resolution of fluorescence spectra places stiff demands on the current technology. Such experiments on gas-phase systems with this time resolution have not been reported.76 We have taken another approach to the timing problem. By adding an electronic state quencher to the cell containing the fluorescing gas, we see only those S1molecules that happened to emit before a quenching collision. The gas collision interval selects the fluorescence observation time. When one uses, e.g., 14 ktorr of a gas with a quenching cross section approaching hard sphere, the ob(76)Timing with wveral hundred picosecond time resolution has been reported for pDFB. N. Halberstadt and A. Tramer, J.Chem. Phys., 73, 6343 (1980).
servation time for fluorescence is limited to roughly the first 10 ps of the excited-state lifetime-even in steadystate experiments. A demonstration of the feasibility of such chemical timing for following the vibrational identities of SImolecules was first provided by Tand5 in the spectra shown in Figure 11. Using modest pressures of O2as the electronic state quencher, he was able to follow vibrational relaxation from a level with 'Gb = 522 cm-' in S1benzene. In this case, the vibrational relaxation is collision induced by the presence of 40 torr of isopentane which is sufficient to cause (almost) complete vibrational thermalization within the normal 80-11s electronic state lifetime. Figure 11(bottom) shows a segment of the fluorescence after such collisional equilibration. It is rich in structure from a Boltzmann distribution of S1emitting levels. As O2additions reduce the observation times, that structure undergoes pronounced changes and becomes more sparse. When O2is sufficient to limit the observation time to about 4 ns or less, no further changes occur and the spectrum shows emission only from the level initially pumped since collisional relaxation cannot build up observable populations of other S1 levels at these short times. The 4-11s spectrum is identical with that from collision-free S1 benzene (no 02,no isopentane, no vibrational relaxation, emission from the 522 cm-' level only). Chihara and Baba7' have used the same technique to quench the dual fluorescence from pyrene vapor, using pressures up to lo3torr of O2or NO. No effects of collision-induced vibrational relaxation from the high O2or NO pressures are detected. IVR has been probed by this technique in p-difluorob e n ~ e n e and ~ ~ ,in~ p-fluorotoluene ~ ( P F T ) , using ~ ~ ~ O2 ~ (77)K.Chihara and H. Baba, Bull. Chem. SOC.Jpn., 48,3095 (1975); Chem. Phys., 25, 299 (1977).
1750
The Journal of Physical Chemistry, Vol. 86, No. 10, 1982
pressures up to 30 ktorr which extend the timing to just below 10 ps. The pFT results demonstrate the method. Figure 1 2 shows a series of pFT fluorescence spectra after using a frequency-doubled CW argon ion laser to pump an S1region about 1990 cm-' above the zero-point level. The bottom spectrum is without special timing, the average time of observation being set at about 8300 ps by the collision-free fluorescence lifetime. This spectrum contains no resolvable structure even though a prominent absorption maximum was pumped to bias 30-407' of the S1molecules to a single zero-order state. The absence of structure in this fluorescence is indicative of IVR since excitation of lower levels produces spectra rich in vibrational structure. When added O2 pressures are sufficient to limit observation times to about 60 ps or less, prominent fluorescence structure appears, which is sustained in both position and relative intensity among its members at shorter times. The principal change as one descends to short times is increasing prominence of the structure relative to the congested background. When read from short to long observation times, the spectra are entirely consistent with IVR. Structure is initially present due to emission from the Is) state carrying the S1-So oscillator strength and disappears as IVR depletes the Is) population at longer times. The crucial test of this picture concerns the character of the structure. Is it consistent with that expected from Is)? The question is easily answered since the vibrational identity of Is) is known and its SVL fluorescence spectrum can be predicted by extrapolation of vibrational activity seen in SVL fluorescence from lower levels. It is shown elsewherem that the answer is affirmative. Similar time-dependent spectroscopy of p-difluorobenzene (pDFB) is described in a preliminary rep0rt.4~In that case the time evolution of the spectra reveal IVR from a level with t,+b = 2190 cm-'. Extensive work has been completed with the pDFB experiments to investigate possible artifacts associated with the chemical timings technique. No substantial interferences have been found. IVR kinetics can be extracted from such time-resolved spectra, and the kinetics in pDFB from 'vib = 2190 cm-' have been so determined. They correspond well with the nonexponential decay of the intermediate case of radiationless transition theory. The initial time scale of decay is about 30 ps. Work is not yet complete on the pFT kinetics. The initial measurements suggest an IVR time on the order of 10 ps. Concluding Remark Concerning IVR. Little has been said here about the level density in the S1 regions where signs of IVR first appear or of the fraction of the final states (11)1 involved in these redistributions. The simplest theoretical estimate3s5' would place the threshold at the lowest region where the mean vibrational coupling matrix elements substantially exceed the mean level spacing, V,, = V,, >> p-'. Such an estimate is conservative, however, since it is based on the statistical case of IVR. That estimate is more accurately an upper limit to the onset, since IVR appearing as the intermediate case should appear in lower regions. Whether S1molecules actually recognize these criteria has not yet been established in published reports, but such comparisons of experiment with theory will emerge as the data become more complete. On the other hand, level densities have been considered quantitatively for IVR in naphthalene and p-difluorobenzene and they have been used to ponder the question of ergodicity. Are all of the available levels used in IVR? The approach has been similar for each. One tries to determine by computer simulation whether the congested
Parmenter
emission resulting from IVR contains contributions from the full set of available levels. Since the emission is without structure, the simulations can only determine the minimum number of emitting levels required to generate structureless emission. Subsequent comparison of this number with the density of states and the level widths associated with IVR can then allow comment on ergodicity. The comparisons for IVR in n a ~ h t h a l e n e(tvib ~ ~ = 3068 cm-l, cold beam) and for p-difluorobenzene@(tvib = 2189 cm-', room temperature) give quite different pictures. The naphthalene level density ranges from about 400 to about 2000 per cm-I depending upon the severity of symmetry restrictions. Simulated spectra using either extreme as the accessible levels each replicate the experimentally observed congestion. The p-difluorobenzene simulations are for a region where the accessible level density is about 40 per cm-'. Simulated spectra with this density do not begin to approach the congestion actually found in emission. Superposition of emission from the order of lo3 levels is required. Such a large number would require contributions from all levels lying within about 25 cm-' of the pumped state, quite inconsistent with the characteristics of the absorption spectrum. The simulated pDFB spectra show that IVR uses a level density quite beyond that provided by ordinary level calculations. It is difficult to fiid the required density from a source other than the rotational manifold. Rotational levels can contribute to level density through Coriolis vibration-rotation coupling which relaxes the AK = 0 prohibition otherwise associated with level mixing. Release from K as a constraining quantum number increases the available state density by a factor of about J, where J is the quantum number of Is) reached by optical excitation.50 This effect can easily increase level densities in pDFB room-temperature experiments by a factor of lo2over the ordinary density calculations that assume AK = 0. The participation of rotational levels in IVR implies that the onset of IVR should be temperature dependent on account of rotational populations within the prepared levels. This effect may account for the fact that indications of IVR in cold-beam (1K) naphthalene (48modes) do not occur until one reached t ~ i=b. 2500 cm-' whereas, at 300 K, IVR appears already at 2000 cm-' in the single-ring system p-difluorobenzene (30 modes). Note Added in Proof. Zewail and co-workers have used time-resolved fluorescence spectra with a system response time of about 150 ps to observe quantum beats in S1 anthracene fluorescence after excitation with 15-ps pulses. The beats are clearly associated with IVR by way of coherent pumping of a small set of mixed levels within the large S1level density near tvib 1380 cm-l. (W. R. Lambert, P. M. Felker, and A. H. Zewail, J. Chem. Phys., 7 5 , 5958 (1981); A. H. Zewail, W. R. Lambert, P. M. Felker, J. Perry, and W. Warren, J. Phys. Chem., 86,1184 (1982)J Zewail and co-workers have extended this technique to the study of IVR in stilbene (Chem. Phys. Lett., in press). Acknowledgment. Financial support by the National Science Foundation (Grant CHE 79-18077) is appreciated. I am grateful to my former colleagues Drs. G . H. Atkinson, R. A. Coveleskie, D. A. Dolson, A. E. W. Knight, and K. Y. Tang and present colleagues K. W. Holtzclaw, S. Munchak, and B. M. Stone, who have provided experimental expertise, data, and discussions. Drs. K. Y. Tang and D. A. Dolson have been most generous by allowing the mining of unpublished results from their Ph.D. theses. Professor T. M. Dunn has provided Figure 7 and valuable private discussions. Comments from Professor J. Troe concerning the intermediate region have been helpful.
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