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Faraday Discuss. Chem. Soc., 1983, 75, 141-153 The Correspondence Principle and Intramolecular Dynamics BY ERIC J. HELLER Los Alamos National Laboratory, University of California, Los Alamos, New Mexico 87544, U.S.A. Received 10th Jaiiuary, 1983 It is the purpose of this paper to describe some recent developments in the semiclassical approximations to quantum vibrationaI dynamics. In section 1 we describe a new and very simple method for finding uniformized semicIassica1 wavefunctions. The wavefunctions are given expIicitly as contractions over Gaussian functions, with the parameters of the Gaussians chosen according to an arbitrary classical trajectory. The semiclassical functions moreover are highly suitable for use as basis functions in ab initio work. In section 2 we present new resuIts for the quantum dynamics of a highly anharmonic classically chaotic system with an infinite number of quantum bound states.The results show the utility of the spectral criterion we have been advocating as a measure of phase-space flow in molecular systems, and they show some interesting quantum effects. Also, we show that the classical and quantum dynamics of a local-mode C-H stretch agree extremely well as to the fraction of available phase space covered in the course of the subsequent dynamics. In quantum- mechanical systems the optical spectrum gives a direct measure of this fraction. 1. A SIMPLE QUANTIZATION SCHEME FOR WAVEFUNCTIONS We have two previous publications on finding multidimensional, uniformized semiclassical wavefunctions.'*2 The first made use of methods developed by Sorbie and Handy for finding semiclassical eigenvalues.Our idea was to.run the trajectory that semiclassically quantized a dynamical system, and to allow this trajectory to " guide " a Gaussian wavepacket (or, equivalently, a coherent state) as in our previous The wavepacket was taken to be " frozen " about the trajectory, i.e. it did not spread, but followed the trajectory (both in position and momentum). Then, using the idea that we replaced the exact quantum dynamics of v/,(x) by the moving frozen Gaussian (FG), used the classical action plus Maslov corrections for the phase of the FG, and used the semiclassical energy E of Sorbie and Handy in the Fourier transform. This technique worked extremely well (fig. l), but required that the quantizing trajectories be found.This is a tedious procedure at best, and made calculations in three and more dimensions seem forboding. led us to conclude that the success of the Sorbie-Handy method for eigenvalues was surprising in view of the fact that it was not a topologically " proper " quantization in many cases. Instead of holding the iV topologically invariant action integrals to integer-plus-Maslov corrections, the Sorbie and Handy (S.H.) method held only the sum of the actions to the correct value, Discussions with Marcus and Noid142 CORRESPONDENCE PRINCIPLE AND INTRAMOLECULAR KINETICS while making approximations to the individual actions. Yet we found the S.H. method worked quite well. This led us to investigate its success further, and we came upon a general technique for using arbitrary trajectories to find energies and semi- classical wavefunctions of comparable quality.2 It turned out that the S.H.method is one of a class of extrapoZation methods that work away from the true E.B.K. quantizing trajectories, but extrapolate to the E.B.K. values. This realization freed us from having to make the search for the quantized actions in the first place, but did Fig. 1. (left) Semiclassical wavefunctions generated as a superposition of Gaussian wave- packets along a classical trajectory. (right) Numerically converged ab initio wavefunction corresponding to the semiclassical state on the left. require us to find the value of the independent actions for the (arbitrary) trajectories used to quantize the system.We found a new way of getting these true actions by running trajectories nearby the arbitrary trajectory. This arbitrary trajectory necessarily falls somewhere in action space near E.B.K. quantized actions, and a simple linear extrapolation to the corresponding energies and wavefunctions of those states was satisfactory. As the extrapolation distance in action space increases, the accuracy naturally decreases, but several energies and wavefunctions can be obtained from a single trajectory. The method for finding the actions is, quite importantly, independent of the topology of the trajectory. This means that classical resonances of any order present no difficulties. (Chaotic trajectories are not quantizable, how- ever, by this method.) Here we report a similar but greatly simplified procedure to obtain semiclassical energies and uniformized semiclassical wavefunctions.6 The method works even in the quasi-integrable (partly chaotic) domain.To derive it we return to eqn (l), and project both sides of the equation into some state, Ip), which for the moment is arbitrary The amplitude (plyE) will be non-zero only if a correct quantum eigenvalue E is used in eqn (2). We again use FGs to approximate ly,, call this ly;". This gives This equation is none other than that used previously to obtain molecular spectra, using FG dynamic^.^.^ The idea is to examine the FG spectrum and use the energiesE. J. HELLER 143 E obtained as spectral peaks as Fourier-transform energies in eqn (l), with yo and yt replaced by y;", I,$".The resulting YE", obtained as a finite superposition of Gaussians by making the time integration discrete, are equivalent to those obtained by the earlier method of DeLeon and Heller.2 The present approach is greatly simplified, however. The FG spectrum is trivial to obtain: only a single classical trajectory, overlaps of Gaussians and a Fourier transform are required. Then the same trajec- tory and the same Gaussians are used with the E values obtained from the spectrum in eqn (1) to " build up " the wavefunctions. A typical spectrum and four of the wavefunctions obtained are shown in fig. 2. The arrows show the peak energy used 3 1 C B A D -10 - 6 - 2 2 6 10 El Fig. 2. Frozen Gaussian spectrum, with arrows showing four spectral peaks whose energies were used in the Fourier transform to generate the four FG semiclassical wave- functions A-D.in the Fourier transform. All four arise from the same trajectory, but have a different nodal structure. All the larger peaks in the spectrum give a reasonable wavefunction, each of which is given in terms of the same trajectory. In the original paper on the FG appro~imation,~~ it was noted that the spectral peaks fell near the true energies. There are several choices for ways to refine the1 44 CORRESPONDENCE PRINCIPLE AND 1NTRAMOLECULAR KINETICS phase of ly,"", and we see from eqn (1) and (3) that we can multiply yr" by e-l(dEE'), and shift the Fourier transform energy E and dE, without changing the wavefunction t,uEc. Thus the semiclassical energies will vary according to the convention used for the phase.One convention, however, gives energies identical to those of ref, (2) without having to know the actions. The classical frequencies of motion are needed, however. These are usually easy to obtain by Fourier transform of a classical variable. Details may be found in ref. (6). The eigenvalues, and indeed the contracted-Gaussian-sum wavefunctions are of poorer quality than if the true E.B.K. quantizing trajectories were used. However, the important advantages of this method are (1) its extreme ease of implementation and (2) the ability to use the semiclassical, Gaussian-contracted wavefunction as basis functions for solving the time-independent Schrodinger equation. These functions start out very close to true eigcnfunctions, even for very anharmonic potentials.Then a very small set of these can be used to converge on the true eigenfunctions. We have just started to explore the possibilities of this " contracted-classical Gaussian basis set " idea. Returning to the spectrum seen in fig. 2, we note it is best to pick the large peaks in the spectrum as Fourier energies in eqn (1). The physical reason for this i s easily understood, If the initial Gaussian yrc has a large component in a particular eigen- state, that means the action variables of the Gaussian match those of the eigenstate, i.e. the guiding trajectory of the Gaussian looks like the eigenstate itself. In such a case the Gaussian superpositions can readily represent the eigenstates. Tho further away in action space that the eigenstate is from the guiding trajectory, the smaller the intensity of the spectral peak.To get all the eigenstates we need to move the guiding trajectory to several new spots in action space. Finding the eigenvalues by this method is not really the point, however. The basis functions are roughly of the quality shown in fig. 1 ! 2. QUANTUM AND CLASSICAL ENERGY TRANSFER For some time now, we have advocated a spectral intensity criterion 9-12 for measuring the flow of probability through the available quantum mechanical phase space. The basic ideas follow. An absorption or emission spectrum is a measurable. Any spectrum with a spread in energy corresponds to some non-stationary state, i.e. let the spectrum be where p i are the spectral intensities, determined by where pa is the spectral non-stationary state and II,Y,,) are the eigenstates of the system.In an electronic absorption, for example, qa would typically correspond to the ground vibrational state multiplied by the transition m~rnent.~'-~. Thus va is a displaced wave- packet on the upper electronic potential surface. Other qa values may be produced by varying the experimental conditions, or may be produced at will by theorists trying to understand the dynamics of a particular potential surface. In any case, the distri- bution ofpi values contains much information about the dynamics of va. Indeed, the P,* values may be used to calculate the fraction of available phase space covered in the course of the dynamics of q3,.I2 By " available " phase space, we mean all those states or cells in phase space whose total energy E and energy dispersion AE match or are consistent with the mean energy E and spread AE of the state qa.This is the directE. f. HELLER 145 analogue of classical phase-space flow. Because energy is conserved in both classical and quantum mechanics, the " available " phase is restricted by energy conservation. A totally chaotic, or R.R.K.M. molecule, would be expected to cover 100% of its available phase space; a quasiperiodic molecule much less. However, the amount of phase space covered depends not only on the intrinsic dynamics but also on the initial state ya. Some states qa might already be distributed through much of phase space (like the metal filaments in an old-style Aash bulb) while other states pa might be more compact.Clearly, a filamentary pa is, in general, expected to cuver more phase space than the compact one, given the same dynamics. So two factors emerge as important: (1) the intrinsic dynamics and (2) the states qa used to test the dynamics (in the case of theorists) or the spectroscopic states va (avaiIable experimentally). The key to understanding the importance of spectral intensities in elucidating energy transfer lies in the two formulae and where P(alb) = P(bla) is the time-averaged probability of starting in the state qa and being found later in the state q b , i.e. Thus by measuring a spectrum (to high resolution) we can say how much time qa spends in the vicinity of its own birthplace [i.e. P(ala), eqn (6)], or we can say where in phase space it goes [P(alb) for all b].Note that for a = b in eqn (8), the integrand is the often studied autocorrelation function P ( t ) = ](~l,lq,(,)>l*.~~.'~,~~ Contrary to the impression which seems to exist. the fundamental quantity is not the functional form ofP(t), but rather its average area: There is a very simple interpretation for P(a\a). Suppose qa is an eigenstate. Then P(a]a) = 1. Suppose pa is an equal-amplitude sum of No eigenstates. Then Suppose Pb is one of the eigenstates composing pa. Then also P(alb) = I/N,,.146 CORRESPONDENCE PRINCIPLE AND INTRAMOLECULAR KINETICS Suppose qc is in a normalized state constructed out of the No vn, but otherwise arbitrary. Then P(alc) = l/No. (12) Thus qa spends (I/N,)th of its time in the state qa, or (l/N,)th of its time in any state pb or pc, which is made up of one or more of the No states that have intensity in the spectrum of QI,.The spectrum is where w,, = EJh. It is as if pa has No cells to visit in phase space, and it spends equal time in each cell. It does not matter how we divide up the cells, as long as each cell has unit volume and lies within the space of No states. The point of eqn (10)-(13) is that P(ala) 5 (no. of phase space cells visited by ya)-I = 2 (p3' n In general we have learned to deal with non-equal amplit~des,~-'~ but the interpret- ation, eqn (14), remains the same. Eqn (14) is paramount to the realization that " 7.0 - 3.5 0.0 3.5 7.0 U Fig. 3. The anharmonic potential discussed in the text. Contours range from E = 80.0 to E = -25.0 in increments of 5.0, measurable spectra contain information about energy flow in molecules.Note that assignments of the spectra are not necessary: We take a spectrum, normalize the line intensities pi so that and then use eqn (14) to determine the number of phase-space cells visited by y,(t). This number becomes all the more significant if we know how many states N existE. J. HELLER 147 6 4- - - 2 - - s 0- - 2 - - - within a range AE of the mean energy E of the state qa (where AE is the energy dis- persion of a given pa). That is, if the No states seen in the spectrum are only a subset of those states available in the same energy regime, then we can say that pa has visited only a fraction of the available phase-space cells. This fraction is simply F = NolN 6 - 4- 2 - 0- - 2 - - - where PSTo(ala) = 1/N.(17) STO stands for stochastic, because if P(ala) = PSTo(aIa), the state pa visits all N available cells. All we need to determine N is the energy uncertainty AE of qa, and the density of states B(E) of the system, so that N = D(E)AE. (1 8) Note that in a given spectrum a Iot of missing lines (i.e. low or zero spectral intensity in certain eigenstates) implies No > N . Crudely speaking, if we look at a spectrum and see No lines in a range AE, but there are N eigenstates in AE, then F is just the 6 , 0 - 2 :i -4 I 6 1 :1 0 - 6 -4 - 2 0 2 4 6 - 6 - 4 - 2 0 2 4 6 - 4 4 1 - 4 1 1 - 6 -4 - 2 0 2 4 6 -6 - 4 - 2 0 2 4 6 U 11 Fig. 4. Four consecutive wavefunctions near E == 40.0 for the potential of fig. 3.148 CORRESPONDENCE PRINCIPLE AND INTRAMOLECULAR KINETICS ratio given by eqn (16).These arguments lead to the conclusion that a completely chaotic system in quantum mechanics ought to have every line present in a spectrum, as dense a spectrum as the density of states permits. The sparser the spectrum, the fewer phase-space cells sampled by the initial state. energy l-T-T-l 0 20 40 60 80 9 .Q 4 . 5 '00 0.0 - 4 . 5 -9.0 -4 - 2 0 2 4 S - 7 - 6 - 5 - 4 - 3 -2 - 3 0 NFCF Fig. 5. Spectrum of a wavepacket placed in the chaotic region (uo = 0.5, so = -3.55) at E =1 40 (upper left), histogram of spectral intensities (lower left), and classical surface of section for the potential discussed in the text. The inset shows a magnified portion of the spectrum. The tick marks at the bottom show the eigenvalues of the system. We now give the results of some very recent application of the ideas presented so far in section 2.In the first we examined the classical and quantum dynamics of a highly an- harmonic potential, obtained by adding a quartic term to the " Barbanis " type of pot en t ial : Three different studies are involved. V(s,u) = +w:u2 + +wfs2 + Au2s + p(u4 + d). With the choices ci), = 1.1, us = 1 .O, 1 = -3.24 and p = 0.324 we obtain the poten- tial seen in fig. 3. Severe anharmonicities are present. We diagonalized this potential in a basis set consisting of 1750 coherent states.'5v'6 In fig. 4 we plot several wavefunctions obtained near E = 40.0, and in fig. 5 we show the spectrum of a par-E. J. HELLER 149 ticular coherent state !pa (very localized in phase space) (upper left), a histogram of the p i plotted as log (pi) against number of states, and a surface of section (s,ps).Note that the spectrum has most lincs present, as seen from the inset or the histogram. The spectrum and histogram differ radically from the typical separable case (fig. 6, left-hand column) when many missing lines and many zero p i are seen. However, t 15 u 12 14 16 L I 4 1 71 I 20 25 30 0 5 10 15 20 25 30 energy 120 I x energy - 7 - 6 -5 - 4 - 3 - 2 -1 0 -7 -6 - 5 - 4 - 3 - 2 - 1 0 NFCF NFCF Fig. 6. Spectrum and histogram (left) of a wavepacket in a separable harmonic system with energy predominantly in one rnodc, and with energy shared equally in all modes (right) if we start with all modes stretched we get, for two separable degrees of free- dom, fig.6, right-hand column. This latter case superficially resembles the chaotic case, and indeed the fraction F is much larger in a quasiperiodic system if we start it out with all degrees of freedom sharing the energy, This is not the problem of a " filamentary " pa discussed earlicr, but rather the simple consequence of the compli- cated yet quasiperiodic motion that results from starting the system with all degrees of freedom active. In any such quasiperiodic system, most initial conditions will give a very sparse spectrum as in fig. 6, left-hand column. This is not the case for a nearly chaotic system, which gives a spectrum as seen in fig. 5 for any coherent state, no matter where it is initially localized. It is fascinating that at E = 40 there is a small quasiperiodic domain seen in the surface of the section.No such domain exists at E = 10 or E = 60, for example,150 CORRESPONDENCE PRINCIPLE AND INTRAMOLECULAR KINETICS t ' I 'i Fig. 7. Classical trajectories plotted as probability densities in u and s in the quasiperiodic sub-domain near E = 40. See fig, 4, lower right, for the corresponding quantum wave- function. The corresponding classical trajectories in (s,u) space are shown in fig. 7. Compare it with the bottom right wavefunction in fig. 4! The other wavefunctions in fig. 4 look fairly chaotic, but not as chaotic as the chaotic trajectories look, in that the wave- functions do systematically avoid more regions than the trajectories do. This tendency seems to be a quantum effect tied to the rute of approach to chaos in the 0.6- 0 .5 - 0.4 - F 0.3- 0.2 - 0.1- 2.0 2 . 5 3.0 3.5 2.0 4.5 5.0 energy Fig. 8. Fraction of available phase space covered in the evolution of a local-mode C-H stretch initial condition for a collinear model of HCN. Quantum results are shown as various lines, classical as the large dots.E. J, HELLER 151 classical system. If the rate is slow (small Lyopanov exponent) the quantum rnech- anics may “ freeze ” at some time less than the time for complete mixing. This freezing effect is due to the finite energy-level spacing: after a time governed by the inverse of the smallest spacings, no ‘‘ new ” dynamics may occur quantum mechanic- ally. This freezing, discussed in ref. (9), may be classed as a quantum smoothing effect.17 It is consistent with the quasiperiodic state being so well reproduced.Fig. 9. Wavefunctions showing tunnelling involving two very distinct types of wavefunctions, one involving mainly x-vibration (horizontal motion) and one y-vibration (vertical motion). For a small change in any parameter in the Hamiltonian these two states would become, separately, a vertical and a horizontal state. No single trajectory looks like the wave- functions shown here. The overall conclusion is that quantum mechanics is a little sluggish to respond to classical chaos, but the response is definitely there. This sluggishness has been seen before in the work of Hutchinson and Wyatt? The second development concerns fig. 8, which shows the fraction F, determined quantum-mechanically as described above and in ref.(12) and (19), for local-mode C-H stretch initial conditions for a model HCN potential, as a function of energy of152 CORRESPONDENCE PRINCIPLE AND INTRAMOLECULAR KINETICS the stretch. Without detailing the differences between the quantum calculations (denoted by lines), note the very good agreement with P determined from the same initial condition by classical mechanics (dots). Here we see classical and quantum mechanics agreeing very well on the dynamics of a local-mode stretch. The fraction F was obtained just from the spectrum. We emphasize it as available experimentally. Finally, our third development has to do with quantum tunnelling. In the exten- sive wavefunction calculations we have performed recentIy we occasionally noticed a near degeneracy in the eigenvalue spectrum.Sometimes this was associated with a symmetry related tunnelling pair of' states, as discussed by Lawton and Child 2o and by us.21 Sometimes the states were not dynamically related in any way, either by symmetry or by a classical resonance condition, Two such eigenstates are shown in fig. 9. They represent tunnelling between two very different kinds of classical motion labelled crudely as vertica1 (V) and harizontaI (H). A sIight change of a parameter in the Hamiltonian would change this state (and its partner) to separate V and H states. The V and H states both look like classical trajectories and fig. 8 respresents tunnelling between these classical trajectories. In ref. (21b) we conjectured about the possible generic importance of such tunnelling.The tunnelling has two immediate implications. One is that quantum energy flow can be enhanced over the classical, due to the tunnelling. Analysis of the HCN data l9 showed the enhancement of the quantum F seen in fig. 8, between the energies of 3.5 and 5.0, to be due to quantum-dynamical tunnelling. The second implication is that avoided crossings seen in the quantum eigenvaIue as a function of a parameter are due genericalIy to such quantum tunnelling, not to classical resonance conditions,22 We have seen many such avoidances, but none so far has been a clear-cut result of a classical resonance. The work described herein is based on the results of coIlaboration with N. DeLeon R. Sundberg, E.Stechel and M Davis; it was performed under the auspices of the U.S. Department of Energy. M. J. Davis and E. J. Heller, J . C h m . Phys., 1981, 75, 3916. N. DeLeon and E. J. Heller, J. Chew. Phys., in press. K. S. Sorbie and N. C. Handy, Mu/. Phys., 1977, 33, 1319; 1976, 32, 1327. (a) E. J. Heller, J . Chem. Phys., 1975, 62,1544; (b) 1978,68, 2066; ( r ) 1978,68, 3891 ; (a') 1976, 64, 63 ; (d) K. C . KuIander and E. J. HelIer, J. Chem. Phys., 1975, 69, 2439; (e) S. Y . Lee and E. J . Heller, J . Chern. P h y ~ , 1979, 71, 4777; (f) E. J. Heller, J. Chern. Phys., 1981, 75, 2923; (g) E. J. Heller, Arc. Chem Res., 1981, 14, 368; (A) S. Y . Lee and E. J. Heller, J. Chem. Pkys. 1982, 76, 3035; (i) D. J. Tannor and E. 3. Heller, J. Chem. Phys., 1982, 77, 202.' R. Marcus and D. Noid, personal communication. See also W. Eastes and R. A. Marcus, J . Chem. Phys., 1974,61,4301; D. W. Noid and R. A. Marcus, J. Chem. Phys., 1975,62,2119; 1977, 67, 559. ' N. DeLeon and E. J. Heller, to be published. ' E. J. HelIer, J. Chem. Phys., 1981, 75, 2923. The idea of Fourier transforming yr to get vE was used by M. Feit and J. Fleck, J. Cumput. P h y . ~ , 1982, 47, 412, using vt determined numerically on a grid in coordinate space. ' E. J. Heller, J. Chem. Phys., 1980, 72, 1337. lo E. J. HeIIer and M. J. Davis, J . Phys. Chem., 1982, 86, 2118. M, J. Davis, E. B. Stechel, and E. J. Heller, Chem. Phys. Lett., 1980, 76, 21. l2 M. J . Davis and E . J. Heller, to be published. P. Brumer and M. Shapiro, Chem. Phys. Left., 1980, 72, 528. l4 M. Shapiru and P. Brumer, G e m . Phys. Left., 1982, 90, 481 ; E. J. Heller and E. B. Stechet, Chem. Phys. Lett., 1982, 90, 484. l5 M. J. Davis and E. J. Heller, J. Chern. Phys., 1979, 71, 3383. The work described here is detailed in R. Sundberg and E. 3. Heller, to be published.E. J. HELLER 153 l7 M. V. Berry, N. L. Balaz and A, Voros, Ann. Phys, (N, Y.), 1979,122,26; M. V. Berry and M. Tabor, Proc. R. SOC. London, Ser. A, 1976,349, 101, J. S. Hutchinson and R. E. Wyatt, Phys. Rev. A , 1981, 83, 1567. lished. l9 The work describcd in this paragraph is detailed in E. B. Stetchel and E. J. Heller, to be pub- 20 R. T. Lawton and M. S. Child, Mol. Phys., 1979, 37, 1799; 1980, 40, 733. 21 (a) M. J. Davis and E. J. Heller, J. Chem. Phys., 1981, 75, 246; (b) E, J. Heller and M. J . Davis, J. Phys. Chem., 1981, 85, 307; (c) M. J. Davis, N. DeLeon and E. J. Heller, to be published. 22 D. W, Noid, M. L. Koszykowski, M. Tabor and R. A. Marcus, J . Chem. Phys., 1980,72,6169; R. Ramaswamy and R. A. Marcus, J. Chenz. Phys., 1981, 74, 1379; 16, 1385.

ISSN:0301-7249    

DOI:10.1039/DC9837500141

出版商:RSC    

年代:1983

数据来源: RSC

摘要:

GENERAL DISCUSSION Mr. P. V. Coveney (Oxford University) said: What interests me most here is the putative relationship between classical and quantum " chaos ". Sure enough, as the initial part of Dr. Heller's contribution to this Discussion shows, if you tie a wave product to a trajectory, thus preventing it from spreading out, you find striking similarities between the semiclassical and the classical motion. What I find difficult to grasp is how one moves from classical to purely quanta1 chaos; in other words, can one continue to uphold this as a sharply defined concept in quantum mechanics in the light of Feynman's path integral formulation, according to which, in propagating from a point A to a point B, a " particle " always samples, in some sense, every conceivable trajectory? I do not see how one can expect to obtain such sharply defined " chaotic " behaviour in a purely quantum-mechanical system.Classical and quantum mechanics are fundamentally different ways of describing phenomena, but a generally accepted interpretation of the latter's formalism remains elusive. It might therefore be of interest to bring out the difference between the two predicates " chaotic " and " deterministic " for both classical and quantum mechanics. For example, does the so-called quantum chaos have any relevance to the stochastic interpretation of quantum mechanics:2 are the two concepts supposed to be seen on different levels? E. Heller, Furaday Discuss. Chem. Sac., 1983, 75, 141. M. Jammer, The Philosophy of Quantum Mechanics, (Wiley, New York, 1974), chap.9. Prof. R. A. Marcus (California Institute of Technology, Pasadena) said: In response to Mr. Coveney's questions I should first remark that there seems to be no generally agreed upon definition of the term " chaos ",I although it has recently become widely used in the literature. Ford uses it in the sense of exponential separation of neigh- bouring classical orbits (C and K systems).' There is, of course, a hierarchy of randomness in classical systems,2 describing different behaviour of their time evolution or time-average. Correspondingly, in the quantum case one could consider the properties of the time evolution or average and include wavepackets of eigenstates, therefore, in the definition of different degrees of randomness. I have chosen, instead, to use the term " chaotic " loosely to describe an eigenstate whose plot of v or Ityl in space shows a quite disordered pattern, and have set aside for the moment an investigation of the resultant temporal behaviour of a packet of such eigenstates. Some eigenstates will have this disordered pattern whereas others, for e ~ a m p l e , ~ have patterns which are quite ordered.Since only the former are defined here to be " chaotic ", this term has no connection with probability concepts of interpreting quantum mechanics itself. Regarding the question of how one moves from classical to quantum " chaos ", I have done so via a connection between overlapping avoided crossings and overlapping classical reson- ances [cf. several paragraphs following eqn (3.4) of my paper].J. Ford, personal communication. E.g. J. L. Lebowitz and 0. Penrose, Phys. Today, 1973, 26, 23; V. I. Arnold and A. Avez, Ergodic Problems of Classical Mechanics (W. A. Benjamin, New York, 1968); J. Ford, Phys. Today, 1983,36,40. M. D. Feit, J. A. Fleck Jr and A. Steiger, J. Comput. Phys., 1982, 47, 412; D. W. Noid, M. L. Koszykowski and R. A. Marcus, J. Chem. Phys., 1979,71, 2864. We turn now to specific questions.156 GENERAL DISCUSSION Prof. S. A. Rice (University of Chicago) said: There are several points I wish to put to Prof. Marcus. (a) As you know, there is no generally accepted definition of quantum chaos. For example, based on a generalization of the concept of Kolmogorov entropy to quantum-mechanical systems, I believe that a bounded quantum-mechanical system cannot display chaos as defined for a classical-mechanical system.Simply put, the bounded quantum-mechanical system must always be nearly periodic and have zero Kolmogorov entropy, whereas the definition of chaos in classical mechanics requires that the Kolmogorov entropy be non-zero. In your paper you discuss several sub- jective definitions of chaos, and select one. Are you not concerned that the sub- jective criterion chosen forces a similarity in the quantum-mechanical and classical- mechanical pictures by not fully accounting for information contained in the phase of the system wavefunction, and the memory of that phase in the time evolution of the system? Are you not underestimating the influence of interference effects in the global dynamics? There are many methods of forcing quantum mechanics to resemble dassical mechanics, but should we not focus attention on the differences, and how to exploit those differences for the purpose of guiding the time evolution of the system via sophisticated interactions in the preparation stage? (b) M.S. Child has shown how to transform the description of a vibrating system from a normal-mode picture to a local-mode picture, and the importance of the ratio of kinetic to potential energies for the determination of which picture is better. An unrelated analysis of the continuous transformation from the normal-mode representa- tion to the solitary-wave representation covers similar ground but in a Iess relevant fashion for the problem you consider. How does your description of energy transfer through a " blocking group " as a function of local energy relate to other descriptions of the normal-mode to local-mode transformation? Can you use the ratio of kinetic to potential energies, or some other simple diagnostic, to predict when energy transfer will be rapid or slow? M.S. Child and R. T. Lawton, Faraday L)iscuss. Chem. Soc., 1981, 71, 273. J. Dancz and S. A. Rice, J. Chem. Phys., 1977, 67, 1418. Prof. R. A. Marcus (California Institute of Technology, Pasadena) said : In response to Prof. Rice's first question, the description I have used of chaotic states does not force a similarity between the quantum- and classical-mechanical pictures. Indeed, using that description we found classical chaotic states whose quantum counterparts were not chaotic1 It will indeed be very interesting to explore and seek out the differences in time evolution of classical and quantum states (wavepackets or eigen- states in the latter case). I have not as yet studied that time behaviour.Regarding the question on the role of the blocking group in the systems which we studied and the relation to normal- and local-mode descriptions, there is indeed a close relationship. For this reason we proposed the term " group local modes '' by analogy with local bond modes, to describe the behaviour. Responding to the last question on rates, I note that we give an expression in the paper for predicting whether or not there will be an equipartitioning of the energy and an estimate of what the rate of energy transfer might be.We hope to test these and related expressions with numerical computations. Of course, as Prof. Rabinovitch may have implied in his Discussion comment which shortly follows, other interpretations of the existing data should also be explored. The notion of a blocking group was also taken up by several participants at this Discussion. I refer you to the immediately following contributions.GENERAL DISCUSSION I57 E.g. D. W. Noid, M. L. Koszykowski, M. Tabor and R. A. Marcus, J. Chem. Phys., 1980, 72, 6169; cf. also eqn (3.5) and (3.6) of R. A. Marcus, Furuduy Discuss. Chem. Soc., 1983, 75, 108. ' V, Lopez and R. A. Marcus, Chem. Phys. Lett., 1982, 93, 232. Prof. R. N. Zare (Stanford University) asked: Would the -C=C- or --C=C- - CGC- linkage be expected to inhibit intramolecular energy redistribution ? Prof. R.A. Marcus (California Institute of Terhnology, Pasadma) replied: If one regards the high-frequency bridging mode -C=C- as a rigid bond, its mass is 24, compared with thc effective mass of 84 for Si (mass of 28, but the effective mass varies inversely as the cosine of the angle bctween the bonds it joins, when the dominant coupling tcrm connecting the two sides of the block is kinetic rather than potential). Thus a -C=C- group would not be expected to block energy transfer under the conditions reported by Rowland for Si in this Discussion, since Si did not block it. However, both the possibility of blockage and the rate of leak through a block depend not only on the effective mass of thc bridging atom or group but also on whether or not the actions (" quantum nurnbcrs ") of the principal pair of coupled modes lie within the resonance half-width [eqn (7.1 1) and (7.12) of my paper].The values of the parameters in these expressions vary from system to system. They also depend on the energy excess on one side of the blocking group. The effectiveness of a block depends on these features as well, Dr. M. S. Child (Oxford Unizwrsity) said: The vibrational spectra of acetylene and deutcroacetylene provide an answer to Prof. Zarc's question about the acetylenic linkage as a '' p blocker ". The strength of coupling between the terminal C-X bonds (X = H or D), as measured by the fundamental frequency separation, is 78 cm-l in C,H, and 266 cm-l in C,D,, and this difference is attributable to a near resonance between the CD and CEC frequencies (2500 cm-I and 1974 cm-', respect- ively) whereas the C-H frequency at 3500 cm-I is much higher.'P2 The conclusion is that coupling via the CI-C linkage will be more efficient the closer any terminal frequencies are to the frcquency of the C-C mode.Even an infinitely stiff C=C mode would, however, have an effective mass of only 24. We have also made local-mode style calculations on XF, species (X == S , W or U) which bear on the question of how heavy a " heavy atom " should be. These indicate mass determined coupling strengths llL21 z 130 cm-1 in SF, and 24 cm-' in UF,. There are also potential-energy coupling terms of order /All z 20 cm-' in these species .3 M. S. Child and R. T. Lawton, Furuduy Discuss.Chem. Sw., 1981, 71, 273. L. Halonen, M. S. Child and S. Carter, Mu/. Phys., 1982, 47, 1097. L. Halonen and M. S. Child, 1. Chetn. Phys., in press. Prof. C . S. Parmenter (Indiana University) commented: Tn reference to a point raised by Prof. Zare concerning the effectiveness, if any, of a -C-C- linkage in blocking vibrational energy transfer, there exists in the literature an experiment specifically probing that issue.' It concerns redistribution in the S, state of alkyl benzenes where a ring mode of S1 benzene is pumped and a search is made in the ensuing S,-So fluorescence for evidence of level mixing with (or energy flow into) the skeletal modes of the alkyl tail. Comparisons of alkyl benzenes where the tail is attached directly to the ring and where the tail is separated from the ring by a -C=C- linkage show little difference in behaviour.There is facile mixing of the ring modes and the alkyl skeletal modes in each. D. E. Powers, J . B. Hopkins and R. E. Smalley, J . Chem. Phys., 1981, 74, 5971.158 GENERAL DISCUSSION Prof. I?. S. Rowland (Unicersify of Calvortziu) said: Prof. Marcus has described his trajectory calculations with the linear seven atom " molecule " C-C-C-Sn- C-C-C, and I wish to present some experimental details for our related studies of the reactions of fluorine atoms with allylic organometallic compounds. The first experiments were carried out with tetra-allyltin as the substrate molecule,' and have now been extended by Patricia Rogers and myself to Ge, Si and C compounds.The basic initial experimental observation is that we found as a product from the reaction of F with (allyl),Sn a measurable yield of vinyl fluoride with a pressure dependence in the 0.5-5 atm range. This vinyl fluoride yield is intermediate between that observed with propene and but-1-ene in comparable experiments despite the increase in the number of atoms in the resulting radical from 10 for CW,CHFCH--I*, to 13 for CH,CH,- CHFCHZ to 34 for (CH,=CHCH,),SnCH,CHFCH~. From R.R.K.M. theory, the increase in number of vibrational degrees of freedom by 63 from but-1-ene to (allyl),Sn should have slowed the decomposition reaction by a factor of ca. lo" and decreased the yield of CH,=CHF to an undetectable level in our experiments. This did not happen, as is shown by the comparable slopes for the measured yieIds plotted against reciprocal pressure, shown in fig.1 . c4 1.5 I I 8 1.0 rc 0-0 0.5 1 .o 1.5 2.0 103 Torr/p Fig. 1. Variation with total pressure of yield of CH2=-CHl8F from the reaction of thermal ''F with terminal olefins in the gas phase. (a) CH,=CHCH,, (b) (allyl),Ge, (c) (allyI),Sn, ( d ) CH3CHZCHrCH1. The basic mechanistic steps in these reactions are the same for all of these terminal olefins. Thermal fluorine atoms can add to either the C(1) or C(2) positions, and do so with comparable probability [C(l)/C(2) z 1.4 with propene and but-1-ene]. When the addition occurs at C(2), the resulting radical in reaction (1) can either be stabilized by collision, reaction (2), or decompose with the formation of vinyl fluoride as in reaction (3).All of these experiments have been carried out with a large excess of SF, as the bath gas: F + RCH,CH=CH, -+ RCH,CHFCH; RCHZCHFCH; 4- M -+ RCHZCHFCHZ + M RCH,CHFCH; + RCH, + CHF=CH2. (1) (2) (3) The relative time scales for the two reactions can be measured through the competi- tion between reactions (2) and (3), and measurement of the pressure dependence ofGENERAL DISCUSSION 159 the CH,=CHF yield serves to provide a semi-quantitative indication of the magnitude of k3. Quantitative evaluation requires knowledge of the collision frequency and the energy loss per collision for reaction (2), and cannot be done with precision as yet. An observed pressure dependence in the range from 0.5 to 5.0 atm indicates reaction times in the nanosecond range, or k3 z lo9 s-l.Pressure-dependent yields are found with both propene and but-1-ene as substrates for thermal F-atom addition, as shown in fig. 1. The values of k, for propene and but-1-ene are both reasonable for normal R.R.K.M. behaviour, with the slower rate for the CH3CH2CHFCHf radical expected for an additional CH2 group and 9 more degrees of vibrational freedom. With still larger molecules one can expect even slower decomposition rates and negligible yields of CH,=CHF in the pressure range of fig. 1. Nevertheless, comparable experiments with (CH,=CHCH,),Sn, i.e. R = (allyl),Sn, have also exhibited pressure-dependent yields of CH,=CHF (fig. l).' Our preferred explanation for this experimental observation is that the central C-Sn-C bonding in (CH2=CHCH2),Sn seriously impedes the transfer of energy from one allylic side chain to another, and hence restricts the excitation energy released by F-atom addition to the one group in which the reaction occurred for a long enough period of time to allow decomposition by k3 to occur. Clearly, with this hypothesis the decomposition time scale is roughly nanoseconds, and the redistribution of intramolecular energy energy within (C3H,),SnCH2CHFCH; is far from complete at that time.The trajectory calculations of Lopez and Marcus on the linear C-C-C-Sn- C-C-C chain have been published and elaborated upon here. They have found that under appropriate conditions energy transfer across the C-Sn-C bonds can be very slow. The conditions (relatively high excitation energy and anharmonic Morse oscillators) are appropriate for our experimental system, and the analogy is inviting.Lopez and Marcus also tested the importance of the mass of the heavy central atom, and found that energy flowed readily through the C-M-C grouping when the mass of M was reduced to half that of Sn.2 P. Rogers, J. Selco and I have now carried out further analogue experiments using tetra-allylgermanium as the ~ubstrate,~ and Rogers has continued with allylic silicon and carbon compounds. The key con- clusions from these added experiments are that a pressure-dependent yield of CH,= CHF from reaction (3) is still found with Ge as the central atom, but not with Si or C. The latter systems are not completely analogous because the available compounds are mixed methyl/allyl derivatives rather than tetra-allyl, but this difference is not critical if the present understanding is correct.The actual silicon compounds we have used are (CH3),Si(CH2CH=CH2), and (CH3),Si(CH2CH=CH2), together with 4,4- dimethylpent-1-ene, the carbon analogue of the latter silicon compound. For these three compounds the vinyl fluoride yield is (0.05% for each at our lowest operational pressure, and does not indicate any decomposition by k3. Our present experimental technique does not permit measurement of the decomposition yield below ca. 0.5 atm, so we are not able to determine k3 but can only state that it is at least 40 times slower than for propene. Our experiments have been performed using radioactive tracer ''F atoms with the detection of the product, CH2=CH18F, by radio gas chr~matography.~ High- kinetic-energy lSF atoms are formed by the 19F(n, 2n) 18F nuclear reaction during the 14 MeV neutron irradiation of gaseous SF6, and are capable of undergoing " hot " substitution reactions if collisions are made with potentially reactive species prior to thermalization.Even in pure gaseous SF6, however, <2% of these energetic 18F atoms react to form SF,l8F by hot F/F substitution reactions. The SF6 serves also as a moderator gas in removing this excess translational energy from the "F. The limitation to pressures of 0.5 atm or greater arises from the combination of the160 GENERAL DISCUSSION experimental irradiation geometry which limits bulb size to 2 cm diameter together with the need for sufficient mass of gas to bring to thermal energies the energetic nuclear reaction products.With mole fractions of SF6 :> 0.95, only a very small fraction of the remaining lSF atoms undergo translationally energetic '' hot '' reactions with any of the other substrate molecules which may be p r e ~ e n t . ~ These hot reactions disappear with further dilution by SF,, with zero yield when extrapolated to zero mole fraction of the other substrate molecules. Matheson SF6 of both 99.8% and 99.99% purity has given comparable results in these experiments. Gaseous samples were filled by standard vacuum line techniques at 0 "C to avoid condensation problems during irradiation. The target area of the fast neutron generator is cooled to 14 "C, which was the temperature of the samples during neutron irradiation.The germanium compound was synthesized in our lab~ratory,~ while the others were commercially available. After the 15-20 rnin irradiation periods, the samples were analysed on an appro- priate gas-chromatographic column, often the 50 ft dimethylsulpholane column as described previ~usly.~ The absolute product yields of lSF activity are determined by comparison with an external Teflon monitor irradiated coaxially with the sample. The observed yields of CH2=CH1'F from mixtures of SF6 with propene, but-1-ene, (CH,=CHCH,),Sn and (CH,=CH-CH,),Ge are plotted as a function of the reciprocal of the total pressure in fig. 1. The error bars shown for the latter com- pound are typical for all of the experiments. Experiments with propene and but-1-ene at mole ratios varying from 20 to 1000 for SF6 vis-A-vis hydrocarbon have shown that essentially all 18F atoms except those reacting hot with SF6 undergo thermal reaction when the ratio of SF, to substrate exceeds 100.The vapour pressures of both tin and germanium tetra-ally1 are so low that the mole ratio of SF, to substrate is :,5000. In the typical alkene experiment, a radical scavenger such as H1 is normally added to the sample in small amounts in order to convert stabilized radicals into stable products measurable by radio gas chromatography, i.e. CH,CHFCH, -+ CH3- CHFCH,. With propenc and but-1 -ene these corresponding stable products have been observed and both the decomposition and stabilization products are observed and the ratio directly measured.However, the organometallic substrate is always in extremely low concentration and small amounts of HI would effectively compete as a reactant with thermal l*F and divert almost all of it from reaction with the tetra-ally1 molecules into the formation of H1'F. We have, therefore, not included HI in any of our organornetallic experiments, and have not detected any radioactive products corresponding to the stabilized products. The product CH218FCH-CH2 has been observed in some experiments, consistent with the contribution both from direct displacement of Sn or Ge to form the weak allyl-F bond and from addition to the C(l) position followed by the bond-breakage of the appropriate C-M bond. The formation of vinyl fluoride is exothermic by 21-24 kcal mol from propene, but-1-ene, pent-I-ene and hept-1-ene, and by ca.35 kcal 11101-~ from penta-1,4- diene. to vinyl fluoride is ca. 10 times more rapid from penta-l,4-diene than from pent-1-ene, indicating that even quite large changes in the exothermicity cannot alone account for a factor of 10 change in the decomposition rate constant. Little is known about the precise thermochemistry of these organometallic radicals, but the extra stability of the residual radical from reaction (3) is unlikely to be as large as from thc ally1 radical which accompanies the decomposition following fluorine atom addition to penta- 1,4-diene. Rate constant calculations by R.R.K.M. theory indicate approximately a factor of three reduction in rate per additional CH, group following the reaction of H atoms with terminal The observed rate of decompositionGENERAL DISCUSSION 161 ~ l e f i n s , ~ and we have observed similar reductions in the alkyl series with R=CH3 to II-C~H,.~ The factor of 5 observed in fig.1 between propene and but-1-ene repre- sents only a factor of 3 in decomposition rate because the fraction of all thermal fluorine atom reactions following the addition pathway is less with but-1-ene than with pr0pene.l The primary conclusion from the experiments with tetra-allylgermanium is the demonstration that the reaction with tetra-allyltin is not an aberrant case of non- R.R.K.M. mode-selective behaviour, and suggests that the trapping of excitation energy in a single side chain of an organometallic radical or compound may be a rather general phenomenon.A secondary conclusion is that the prevention of extensive energy transfer through C-M-C bonding is at least as effective in the M-Ge case as for M-Sn. However, the mass effect calculated by Lopez and Marcus is found in our experiments between Ge and Si, assuming that diallyl and monoallyl systems behave analogously to the tetra-ally1 systems. Finally, in comparable experiments with thermalised radioactive 38Cl and (CH2= CHCH,),Ge as the substrate in excess CClF, we have found a pressure-dependent yield of CHz=CH38C1.6 This chlorine reaction appears to be directly analogous to the fluorine reaction, with both contrasting the H-atom addition reactions reported to this meeting by Rabinovitch. We will be proceeding with butenyl substituent experiments as soon as the substrate materials can be obtained.P. Rogers, D. C. Montague, J. P. Frank, S. C. Tyler and F. S. Rowland, Chern. Phys. Lett., 1982, 89, 9. V. Lopez and R. A. Marcus, Chem. Phys. Lett., 1982,93, 232. P. J. Rogers, J. I. Selco and F. S. Rowland, Chern. Phys, Lett., 1983, 97, 313. F. S. Rowland, F. Rust and J. P. Frank, in Fluorine-containing Free Radicals, ed. J. W. Root (American Chemical Society, Washington D.C., 1978), p. 26. M. Kikuchi, J. A. Cramer, R. S. Iyer, 5. P. Frank and F. S. Rowland, J. Phys, Chem., 1982, 86, 2677. P. Rogers and F. S. Rowland, unpublished experiments. E. A. Hardwidge, B. S. Rabinovitch and R. C. Ireton, J. Chem. Phys., 1973, 58, 340, Prof. B. S. Rabinovitch (Uniucwity of Washington) said : We have been stimulated by the experiments on heavy-atom blocking by Rowland et al.described elsewhere and in the previous remark, and by the calculations of Lopez and Marcus to undertake some work in this area.3 We have made a theoretical analysis of the F-atom tetra-ally1 tin chemical activation system of Rowland, described in ref. (I), and conclude that the data are described by an intramolecular vibrational energy relaxation rate, A < 10'' SKI. However, some closely related studies that we have conducted using H-atom chemical activation on tetra-allyltin do not show evidence of blocking action. The data were not of high quality, and consequently we undertook additional experiments on the activation of but-3-enyltrimethyltin) : H + (CH,),SnCH2CH2CH=CH2 (CH,),SnCH2CH2CHCH;. The vibrationally excited radical decomposes to produce propylene. This system is intrinsically more favourable than was our first one and reproducible results of good quality were obtained over the range 10-2000 Torr.Deconvolution of the data4 yields an estimated internal relaxation rate, 2 z 1013 s-', based on the Sn atom as the postulated blocker. The discrepancy between our results and those reported by Rowland and co-workers has several possible sources, including both real and arte- factual ones, and further work is necessary to confirm such an effect. We are presently extending our studies to several related systems, including the case of Pb-atom block- ing.162 GENERAL DISCUSSION P. Rogers, D. C. Montague, J. P. Frank, S. C. Tyler and F. S. Rowland, Chem. Phys.Left., 1982, 89, 9. See S. P. Wrigley and B. S. Rabinovitch, Chem. Phys. Lett., submitted, for a fuller description. See A. B. Trenwith and B. S. Rabinovitch, J. Phys. Chem., 1982, 86, 3447 for details of such calculations. * V. Lopez and R. A. Marcus, Chem. Phys. Lett., 1982,93, 232. Mr. S. Ruhman and Prof. Y. Haas (Hebrew University of Jerusalem) said: In con- nection with Prof. Marcus’ paper on the possibility of localizing initial vibrational ex- citation in one part of the molecule, we would like to present some preliminary results in the study of an acetylenic compound. This is also a partial answer to Prof. Zare’s question regarding the efficiency of a triple bond in blocking energy flow in a molecule. The reaction we studied is the i.r. multiphoton excitation and dissociation of CH,-S-C-C-S-CD,.The i.r. spectrum shows three absorption bands within the C o t laser tuning range that are due to either the CH3 or the CD, groups. In this experiment we study the decomposition of this molecule after COz laser multiphoton excitation, by time-resolved V.U.V. laser ionization mass spectrometry. The prototype of this setup has been described e1sewhere.l Briefly, in this setup a TEA COz laser output is focused into the ionization region of a time-of-flight mass spectrometer. The COz laser pulse is terminated by a plasma shutter activated by a light pulse breakdown derived from a Nd: YAG laser at 532 nm. The 355 nm pulse generated by the same Nd : YAG laser is optically delayed with respect to the green pulse and focused into a cell filled with a rare gas to generate the ionizing V.U.V.radiation. The ionizing pulse is focused at right angles to the COz laser beam and probes the products of the C02 excitation. Preliminary results are shown in fig. 2. The whole mass spectrum is divided into two parts for improved mass resolution. In fig. 2 we can see an overlay of mass spectra at different time delays between the onset of the COz pulse and the plasma shutter cutoff. The mass spectra show that in the absence of the C 0 2 laser pulse no fragmentation takes place. Upon exposure to the infrared radiation, fragmentation becomes fairly extensive. Note that the probability for the creation of a CH,-containing fragment is equal to that of a CD,-containing fragment. This result was found to hold for a large number of C02 laser lines throughout the available tuning range. Fragment ions can be formed in this experiment by two different mechanisms: infrared laser- induced dissociation and then ionization, or dissociative ionization of hot parent molecules.More detailed experiments are now being performed in an attempt to distinguish between these possibilities. The conclusion from the experiments so far is that no internal isotope effect has been found in the fragmentation process of this molecule following infrared multiphoton excitation at bands associated with either the CH, or the CD3 groups. The experiments were conducted in collaboration with Prof. Welge’s group in Bielefeld. D. Feldmann, J. Laukemper and K. H. Welge, J. Chem. Phys., 1983, 79, 278.Prof. R. A. Marcus (California Institute of Technology, Pasadena) (communicated) ; One of the questions which I answered earlier concerned a suitable definition for levels in the hierarchy of chaos. A very recent article by J. Ford provides a nice summary-l J. Ford, in Lung-Time Prediction in Dynamics, ed. C. W. Horton Jr, L. E. Reichl and A. G . Szekehely (John Wiley, New York, 1983), p. 79. Dr. E. Heller (Los Alamos) said: Prof. Brumer correctly observes that there is no significant distinction between the spectra of the “ circle in stadium ” and “ circle in rectangle ” cases. In both cases, the spectral criterion we have proposed is indicatingGENERAL DISCUSSION 163 \ I I I I 15 18 59 62 mle a \ I I I I 1 I 59 6 2 88 103106 121 mle Fig. 2. Time-of-flight mass spectrum obtained by V.U.V.laser ionization of CH3SCCSCD3 after excitation by a high-power C02 laser. Each trace shows a complete mass scan, obtained at the indicated time delay between the onset of the C02 laser pulse and its termination, which is almost coincident with the ionizing laser pulse. The mass peaks are identified as follows: parent, m/e = 121; parent minus CH3(CD3), m/e = 106 (103); parent minus CH3-CD3, m/e = 88; CD,SC, m/e = 62, CH3SC, m/e = 59. The lower traces show the higher masses and the upper traces the lower masses at an enhanced sensitivity. The C02 laser was operated on the R(20) line of the 00'1 -+ 10'0 transition, with a maximum energy of 1 J per pulse. The V.U.V. photon energy is ca. 10.47 eV.164 GENERAL DISCUSSION significant tendencies toward ergodicity (f=PsT0/P=0.5 to 0.7).This is expected in the stadium, which is classically ergodic, but why such a largeffor the rectangle, which is quasiperiodic? The reason is that the prepared states arising from the circle ground state are essentially chaotic in either the rectangle or the stadium. This may seem surprising, since the ground initial state is obviously localized in coordinate space. (Prof. Brumer uses only a small piece of the total ground-state wavefunction, some high-energy components whose squared Franck-Condon factors total only ca. 0.006. This does not cause serious difficulties, however.) However, note the follow- ing facts : (1) The ground state of a circle is completely delocalized in momentum space. (2) For any potentials with hard walls and flat bottoms almost all trajectories cover all of coordinate space evenly.The difference between chaotic and quasiperiodic motion in such potentials shows up in momentum space. (3) Therefore, by being evenly distributed in momentum space, Brumer’s initial state cannot distinguish between quasiperiodic (rectangle) dynamics and chaotic (stadium) dynamics as regards the time-averaged properties related to ergodicity. (4) In the case of the rectangle the large fraction of phase space explored by the wavefunctions reflects the initial conditions, not the dynamics. (5) The spectral criterion is behaving exactly as it should under this circumstance: it tell us about the fraction of phase space explored. This fraction does not reflect on the dynamics unless the initial state is in some sense localized.(6) The extreme delocalization of Brumer’s initial states, can be seen in his fig. 4. (Note the random nodal directions.) (7) By using as initial states the excited states of a rectangle or harmonic oscillator, which have momentum space localization, the spectral criterion will clearly distinguish stadium and rectangle dynamics. (8) However, it might be better to avoid the unphysical (from the point of view of chemistry) properties of such infinite-wall, flat-bottom potentials and consider smooth potentials. This we have done in our paper and references therein. The spectral criterion shows clearly the effects of chaos on the spectrum, P(a/a), etc. Dr. R. Taylor and Prof. P. Brumer (University of Toronto) replied: There is little doubt that the quantum dynamics of localized wavepackets initiated in the stadium and rectangle will show differences similar to those expected in classical mechanics, at least over a specific time scale.Such a situation would arise if the laser pulse is infinitely wide in frequency space so that the ground-state circle wavefunction is “ lifted ” on to the excited surface. This is not, however, the case in our study with a finite frequency width laser which yields a linear combination of ca. 20 “ vibrational ” levels which is distributed over coordinate space. Nevertheless, “ ( 1 ) for the regular and irregular cases do differ, but in a manner not readily discerned via the quantitative measures discussed in our paper. Dr. Heller provides an explanation of why his spectral criterion does not distinguish the two cases studied.In doing so he sheds considerable light on its applicability, noting in particular its restriction to initial states which are “ in some sense localized ”. He also provides a correct description of the importance of the momentum space representation, as we note e1sewhere.l However, focusing on the specific viewpoint advocated in his comment tends to obscure the simplicity of our “ experiment ”, which attempts to discover whether the characteristic differences in the nature of the excited regular and irregular wavefunctions manifest themselves in observable consequences in preparation via pulsed laser excitation. Specifically, we categorize our systems as regular or irregular depending upon whether two obvious integrals ofGENERAL DISCUSSION 165 motion exist or not.In this sense the ground-state wavefunction, albeit distributed over angles in momentum space, is regular. We further note that this ground state is similar to that of the isotropic harmonic oscillator which is a realistic ground state. The results reported thus far make clear that characteristic dynamical differences of the prepared state do appear but that specific experimental techniques which would display this difference are yet to be found. Further studies are, therefore, in progress. Finally, we agree that studies of the type reported in our paper, but using smooth potentials, are highly desirable. They were avoided in this initial study since the stadium provides the least ambiguous example of irregular quantum wavefunctions and adjacent energy-level spacings.2 R.D. Taylor, D. Gruner and P. Brumer, to be published. S. W. McDonald and A. N. Kaufman, Phys. Reu. Lett., 1979,42, 1189. Prof. D. H. Whiffen (University of Newcastle upon Tyne) said: Dr. Taylor and Prof. Brumer in their section (3.2) include the assumption " radiative emission is neglected ". This may be realistic for spontaneous emission, but the case where stimulated emission is significant provides important modifications for the theory of state preparation when strong laser power densities are used. The theory relating to short pulses is well known in the field of n.m.r. and can be handled using density matrices and their time development. Simple discussion usually refers to the Rabi frequency and the pulse length as a fraction of the Rabi period, this fraction usually being expressed as a phase angle. If initially the lower state is occupied and the higher state in exact resonance is unoccupied, then a 2n or 360" pulse leaves this situation unchanged. But adjacent upper states, differing in exact frequency or transition moment, may only experience a n or 180" pulse leading to an emptying of the lower state into the off-resonance upper state.With the nomenclature of eqn ( 5 ) and (6) of the paper, the Rabi frequency, vR, is given by V R = ~ e 1 f o n I 2 h . Inserting E = lo9 V m-l, pel = 1.27 D = 4.24 x cm then vR/JOn = 3.2 x 10l2 Hz = 107 cm-I E 13 meV. The real-time pulse width of 1.665 z with z = 11 000 au is 4.4 x 10-l3 s, which would amount to a 2 .8 ~ pulse if fon = 1 and there is exact frequency resonance. The fon in table 1 of the paper are much smaller, but real experiments are unlikely to have such low Franck-Condon factors for the spectra examined and probably longer pulses. The main point to be made is that this case, especially where a number of different resonances share the same lower state, deserves a full treatment which could be applied when the laser fields are strong and the observed effects no longer linear in intensity. Prof. P. Brumer (University of Toronto) said: I fully agree with Prof. Whiffen's point regarding the importance of including both stimulated and spontaneous emission, particularly in computations directed towards comparison with specific experiments or in specific studies of effects which are non-linear in field intensity.Our theoretical work was not designed to address either of these situations. In addition, in our case both stimulated and spontaneous emission have a negligible effect on the nature of the prepared state. Prof. X. de Hemptinne (University of Leuven) said: In evaluating the quantum166 GENERAL DISCUSSION nature of the states prepared by laser radiation, the laser itself should be considered as a part of the system. The quantum superposition in the target does not depend only on the intensity of the radiation. The entropy flux which is associated with the radiation and which is a consequence of the thermodynamics of the laser itself is an equally determining factor, although it has been overlooked by the theoreticians to date.The laser is a thermodynamic machine which transforms heat into radiation. Heat is supplied to the set of radiators spontaneously, thereby producing entropy. If the system is to reach a steady state, this amount of entropy must flow along with the radiation. This is the origin of the phase fluctuations of the coherent radiation. The relationship between the correlation function of the phase fluctuations and the thermodynamic properties of the light source has been discussed extensively in a recent paper.' The theory shows that the phase does not diffuse or drift exponentially as is usually assumed. This assumption leads to inconsistencies. In contrast, laser light has been shown to be phase (frequency)-modulated.The average square rate of change of the phase angle depends (1) on the rate constants for the exchange of heat and polari- zation between the radiating dipoles and the heat source and (2) on the physical properties of the cavity (transmittance of the mirrors and geometrical dimensions). In the same paper the result of coherent excitation of harmonic oscillators has been discussed extensively, taking into account the role of phase fluctuations. 'X. de Hemptinne, J . Chem. Phys., 1983, 79, 727. Prof. M. Quack and Mr. E. Sutcliffe (ETH, Zurich) said: In relation to the paper by Dr. Taylor and Prof. Brumer we mention two approaches to the statistical mechanics of molecules: The first (used by Taylor and Brumer) starts from a Hamiltonian description (Hamilton's classical equations of motion, the Schrodinger equation or other, equivalent mechanical equations of motions) and then addresses questions such as chaos, mixing, ergodicity etc.This approach is also implicit in the work of Marcus (p. 103) and of Heller (p. 141). The second approach starts from, say, the quantum-mechanical equations of motion and then addresses the question of deriving simpler, statistical-mechanical equations of motion using coarse-graining procedures and hypotheses to be tested by experiment or by calculation. This is the route taken, for instance, by us in the treatment of multiphoton excitation and dissociation of polyatomic molecules.lg2 One goal is of a fundamental nature: what are the conditions for getting relaxation from the underlying oscillatory behaviour of the quantum-mechanical equations ? The second goal is practical: When can we use the much simpler statistical-mechanical equations instead of the quantum-mechanical equations, which often cannot be solved to a reasonable accuracy? Within this framework we would like to present here recent results on the multi- photon excitation and dissociation of ozone.Complete quantum-dynamical calcula- tions have been made in the quasiresonant approximation, taking into account the detailed spectroscopic properties of the ozone molecule known from high-resolution investigations. Details of the results will be presented el~ewhere.~ Here we show only that for this realistic calculation one obtains relaxation behaviour very similar to the limiting case C of multiphoton excitation, if one has a thermal initial state at 300 K (fig.3). The populations shown are coarse-grained level populations (sum of the populations of many states). On the other hand, if one has an initial state at 0 K one obtains highly oscillatory solutions as shown in fig. 4. This important role of the initial state has been discussed in detail elsewhere.lV2 In summary, we think that in a discussion of the statistical mechanics of mole-GENERAL DISCUSSION 167 1 .o h * 0.5 4 0.0 I I 1 1 I 1 I 0 5 10 15 20 25 tlPS Fig. 3. Time-dependent populations of second (upper curve) and third (lower curve) level in the multiphoton excitation of ozone. The initial condition is a thermal ensemble at 300 K, the intensity ca. 40 GW cm-2 and v” = 1045 cm-I (assumed to be monochromatic of constant intensity).cules one should focus also upon the derivation of practically useful equations. One should furthermore take into account that “ statistical behaviour ” (defined by the applicability of a statistical-mechanical equation of motion) may in general depend upon the nature of the state prepared before considering the time evolution (here 0 K, ‘ * O I 0 5 10 15 20 25 t i p s Fig. 4. Time-dependent level populations in the multiphoton excitation of ozone as in fig. 3 but with a 0 K initial state (i.e. only the vibrational, rotational ground state is populated initially). Note that “ level ” populations in the sense discussed here are sums of populations of many vibrational, rotational states which differ in energy by much less than one laser quantum (1045 cm-’). In the calculations a sufficient number of vibrational rotational states has been taken into account for the lower levels in order to achieve convergence. Only excitation up to the third level is included here, whereas in other calculations dissocia- tion, requiring nine photons, has been ~onsidered.~168 GENERAL DISCUSSION specific state or 300 K, thermal state), upon the quantity observed or measured (here coarse-grained level populations, corresponding to the probability of finding a molecule with n photons absorbed & AE, where AE is small compared to the energy of one photon) and upon the nature of the molecular system (here the ozone molecule).Recalling the critical remarks made by Prof. Rice and Marcus concerning the difficulties of defining " quantum chaos '' (or other, related concepts) I (M.Q.) should like to add here a comment, which I have made already several times before and which I repeat here as my ceterum censeo: The origin of the difficulties in the definition of quantum chaos comes from the fact that one starts from some well defined concepts in classical mechanics and tries to translate these into quantum mechanics (all sorts of criteria and translations have in fact been suggested).However, quantum mechanics is not a limit of classical mechanics, but the opposite is true. Therefore one should first work out a proper definition of quantum chaos. This can then be translated to classical mechanics simply by properly going to the classical limit of quantum mechanics.Although this procedure has not, to my knowledge, been used so far, it is clearly superior to the current attempts in the field taking the opposite route; much confusion might disappear if a more systematic, although possibly difficult approach to the problem of classical and quantum chaos were used, as suggested here. ' M. Quack, J. Chem. Phys., 1978, 69, 1282. M. Quack, Adv. Chem. Phys., 1982, 50, 395. M. Quack and E. Sutcliffe, to be published. A latin version is available from the author (M. Q.). Prof. J. P. Simons (University of Nottingham) (communicated) : In their forced- oscillation model of unimolecular decomposition, Drs Holmer and Child drew attention to the consequences of resonances in the activated molecules and their influence on lifetimes and product state distributions.Similar correlations have been proposed recently by Segev and Shapiro for the photodissociation H,O + hv --f H20(B 'A,) -+ H + OH(A 'C+). On the basis of quantum-scattering calculations they predict a correlation between long-lived resonances in the photoexcited molecular continuum and dissociation channels populating low rotational levels in the molecular fragment. Direct dis- sociation channels, in contrast, tend to populate high rotational levels. Measurements of product rotational alignment (via determination of fluorescence polarisation) provide a sensitive indication of the photoexcited molecular lifetime since delays in dissociation can lead to loss of alignment and strong fluorescence depolarisation. In agreement with the predicted behaviour, we find that the rotational alignment of OH(A 2C+) fragments, generated through photodissociation of H20 at 130.4 nm in the ' A , +- f ' A , continuum, is near the maximum possible level in high rotational levels (N' z 14) but almost disappears when N' decreases to values N ' z 2.2 E.Segev and M. Shapiro, J. Chem. Phys., 1982, 77, 5604. J. P. Simons, Faraday Discuss. Chem. SOC., 1983, 75, 276; J. P. Simons and A .J. Smith, Chem. Phys. LPtt., 1983, 97, 1. Mr. P. V. Coveney (Oxford Uniuersity) said: How does the approximation represented by eqn (41) of Dr. Child's paper relate both to F(t) of the linearized potential, eqn (39) and (40), and to the exact Hamiltonian, eqn (34)? I was confused by the citing of a " mean probability " P = 0.09, on p.138 of the paper, which compares well with a statistical value of P = 0.13, when, in fact, there isGENERAL DISCU'SSION 169 a spread in computed probabilities from 0.006 to 0.6. T could not grasp what significance such a mean probability has. was reduced by a factor of ten. Since p is related directly to other parameters of the model, I wondered if it might help to know how these were varied, so that one could achieve a physical under- standing of the reasons for the transition from statistical to selective decomposition. In the last paragraph, the coupling parameter Dr. M. S. Child (Oxford Univerxity) said: I should like to comment on the possible observable consequences of chaos. Prof. Marcus has mentioned the magnitude of the rate constant for unimolecular decomposition as one observable, and spectroscopic studies on stable species as a field for other observations.He has also emphasised the importance of the nature of the prepared state in the latter case. 1 should like to draw attention to the unimolecular fragment state distribution as another relevant observable. Here there seems to me no a priori objection to a single quantum state behaving chaotically and the statistical comments at the end of the paper were addressed to this question. With reference to the first point raised by Mr. Coveney, eqn (41) is a linear approx- imation to eqn (40), when u(t) is given by eqn (37). Secondly, with respect to the statistical and mean probabilities and the probability spread, a fully statistical situa- tion would be one in which all resonances had the same lifetime [related to the probability by cqn (47) and (48)], with this mean lifetime having the statistical value.Our results show a mean probability close to the statistical estimate, but the wide range invalidates a fully statistical picture. Finally, the practical effect of reducing the parameter ,!l is to reduce the mean-energy-transfer parameter E without disturbing the forms of the channel potentials. Prof. P. Brumer (University of Toronto) said : The substance of these comments on Dr. Child's paper was developed in concert with Dr. K. G. Kay. I wish to comment on the appearance of certain narrow resonances in the calculation of decomposition dynamics by Holmer and Child.' Rai and Kay2 have observed similar features in accurate R-matrix calculations of harmonic-plus-Morse oscillator systems and we believe that these resonances have interesting implications.The purpose of the work was to determine whether systems which exhibit statistical intramolecular vibrational energy transfer and dissociation dynamics when classical mechanics is applied also do so when quantum mechanics is obeyed. To this end, we performed preliminary classical calculations to verify that most of the internal phase space of our systems is indeed statistically equilibrated after a few vibrational periods. We also verified for our systems that no significant proportion of trajectories is classically trapped in bound regions when the energy exceeds the dissociation threshold. We examined the time evolution of these systems initially prepared in quasi-bound, zero-order, mixed states.In most cases we found good agreement between the quantum and classical predictions for the dynamics of intramolecular energy transfer and unimolecular decay. In these cases, the quantum behaviour was statistical. Exceptions to this good agreement, however, occurred for initial states with large projections onto Feshbach resonances similar to those labelled e andf by Holmer and Child. In such cases the quantum and classical dynamics showed significant differ- ences and the quantum behaviour was non-statistical. The special resonances responsible for such non-statistical behaviour have the following properties: (a) they are unusually narrow, in some cases yielding uni- molecular lifetimes of lo5 vibrational periods, (b) they have dominant projections onto170 GENERAL DISCUSSION only one or two quasi-bound zero-order states (these states have low harmonic and high Morse-oscillator energy) and (c) they tend to have energies that lie just below channel thresholds.These properties are most dramatic at low energies where only one vibrational channel is open but do persist in a weakcr form at higher energies. Kay emphasizes that the non-statistical behaviour associated with these resonances is a purely quantum phenomenon and that this behaviour survives even when inter- ference effects arc quenched by averaging over states. Kay found that similar non-random dynamics occurred in a bound Morse-plus-Morse system for initial states analogus to those giving non- random behaviour in the recent calculations.He explained the appearance of a ‘‘ zone of reduced ergodicity ” in the bound system by noting that the mechanism producing classical stochasticity in that region relies on the overlap of nonlinear resonances that are too narrow to have a significant effect on the quantum behaviour. This analysis led to predictions that similar non-ergodic zones would appear in many molecular systems and that these zones would affect dissociation kinetics. Recent calculations support these predictions. The narrow resonances appearing in the Holmer-Child work are also consistent with these predictions. In previous work B. K. Holmer and M. S. Child, Faraday Discuss. Chern. Soc., 1983, 75, 131. S. N. Rai and K.G. Kay, in preparation. K. G. Kay, J. Chem. Phys., 1980,72, 5955. Dr. R. D. Taylor and Prof, P. Brurner (University of Toronto) said: Dr. Heller has noted the presence of a regular wavefunction at relatively high energies in a coupled oscillator system and has related it to a regular sub-domain evident on the Poincar6 surface of section. In this regard we call attention to our observation that the classi- cally mixing stadium systems discussed in our paper also display quantum wave- functions which are quite regular in character. Such wavefunctions are interspersed, with an as yet undetermined probability, amongst eigenstates with highly irregular nodal patterns. Fig. 5(a) shows an example of such a comparatively regular wave- function which occurs at K, = 52.254 702 (Erl = h2Kn2/2m; h2/2m = 1) and which can be compared with its nearest neighbour of similar parity at K,, = 52.381 607 shown in fig. 5(b) seen to be highly irregular.The former displays relatively low probability in the region of the hemispherical caps of the stadium, that is, the region responsible for mixing behaviour. An analysis of the wavefunction shown in fig, 5(a) in terms of an adiabatic model reveals that this eigenstate is composed of ca. 54% of a single regular eigenst at e. M. Shapiro, R. D. Taylor and P. Brurner, to be published. Prof. A. H. Zcwail (California Institute of Technology, Pasadena) said : We return again to the definition of chaos. (1) What do we really mean by ergodic behaviour in an isolated molecule? and do chaotic, ergodic and stochastic all mean the same thing: are they related to what we call dephasing? In my opinion, a clear description is needed. (2) What is the experimental criteria for the onset of this chaotic behaviour? I noticed in, for example, Dr. Heller’s paper (fig. 8) that there exist some quantum “ oscillations ’’ when the fraction of available phase space is plotted as a function of energy. Does this mean some onset for a unique behaviour? Also, does the classical calculation in this ‘‘ oscillations region ” predict the trend found by the quantum calculation? This brings me to the question: how good is the correlation between quantum and classical behaviour in isolated molecules ?GENERAL DISCUSSION 171 1.0 Y O - 1 .o 1.0 Y O - 1 -0 2.0 1.0 0 1.0 2.0 Fig. 5. Stadium wavefunctions at K, given in text. Stadium area is n; axes are labelled in units of [n/(rr + 4)]*. Only non-negative contours at 0, 0.5, 1.0 and 1.5 are shown. Prof. R. A. Marcus (California Insfitute of Technology, Pasadena) said : Technically, the words stochastic and ergodic have different meanings, while chaotic is less well defined; however, in Joseph Ford’s use, for example, the latter’s meaning is different from that of the former two. There are further terms in the literature indicating still other degrees of randomness; a few references are given earlier in the discussion comments. Chaotic behaviour in the sense I have used it has several experimental consequences: the spectrum of an isolated chaotic molecule is expected to be irregular (the molecule has “ overlapping Fermi resonances ”); the reaction decay constant for such a quasi-bound “ eigenstate ” of the molecule is expected to be a monotonic function of the energy; probing of the various vibrational modes for their energy content is expected to yield an approximate microcanonical distribution; and there are probably consequences for the time-evolution of a wavepacket of such chaotic eigenstates, which I have not explored. Finally, a molecule may, in principle, be chaotic with respect to some modes and not others.

ISSN:0301-7249    

DOI:10.1039/DC9837500155

出版商:RSC    

年代:1983

数据来源: RSC

摘要:

Faraduy Discuss. Chem. Soc., 1983, 75, 173-182 Intramolecular Dephasing Picosecond Evolution of Wavepacket States in a Molecule with Intermediate-case Level Structure BY DUANE D. SMITH, STUART A. RICE AND WALTER STRUVE * Department of Chemistry and the James Franck Institute, The University of Chicago, Chicago, Illinois 60637, U.S.A. Received 21st December, 1982 We present preliminary picosecond optical decay measurements of pyrazine seeded in He supersonic expansions. Pyrazine is a molecule which, in the vicinity of the first excited singlet, is classified as having " intermediate-case " level structure. From the effects of (i) a static homogeneous magnetic field, (ii) variation of the bandwidth of transform-limited excita- tion pulses and (iii) the rotational-state dependence of the spontaneous emission decay, we conclude that the fast-component decay contains very little triplet character.It follows that the fast decay represents evolution of a primarily singlet state into mixed singlet and triplet states. The quasi-stationary state that is prepared by photon absorption, and the molecular decay, are very sensitive to the coherence width of the laser pulse, which effect is characteristic of phase and not population relaxation in the molecule. We also find that the density of rota- tional states plays an important role in determining the evolution of the initially excited wave- packet state into a compound state. 1 . INTRODUCTION Despite the fact that under almost all circumstances it is necessary to use quantum mechanics to describe intramolecular dynamics, our primitive understanding of said dynamics is dominated by classical mechanical concepts.Consider relaxation of some initial state in an isolated molecule. Neglecting radiation damping, that relax- ation can only be part of the temporal evolution generated by dephasing of the initial- state wavepacket. In principle, for a truly isolated system, that initial-state wave- packet must recur if the spectrum of the system is discrete. In the absence of the coupling of the molecule to the radiation field, and below the dissociation threshold, the spectrum of states must be discrete. Of course, in the real world the coupling of the molecule to the radiation field Ieads to a finite lifetime for emission of radiation by an excited state, so that even vibrational levels of the ground electronic state, except for the zero-point level, have intrinsic widths of the order of a few kilohertz or so.Moreover, there are other perturbations which cannot be eliminated under the most stringent available experimental conditions, so it is the case for almost all initial-state wavepackets that the average time required for recurrence is unachievably long relative to the time-scale of phase-interrupting perturbations to the system. Never- theless, it remains the case that phase memory is a very important aspect of the tem- poral-evoluation of prepared states of an isolated molecule, and we are poorly served if we focus attention only on the amplitudes of the motion, forgetting the information * Permanent address: Department of Chemistry, Towa State University, Ames, Iowa 50010, U.S.A.174 INTRAMOLECULAR DEPHASING contained in the phases.The language of relaxation kinetics and the use of computer simulations of energy flow in classical models of molecules do, in fact, underestimate the importance of phase evolution for our understanding of intramolecular dynamics, while at the same time being valuable tools which provide useful, even if incomplete, insights into the processes involved. This paper reports the first results from a set of studies designed to probe the relationships between dephasing of prepared wavepacket states and molecular para- meters, and couplings that lead to depopulation in the absence of collisions. We provide evidence that the initial stage of decay of fluorescence in a molecule with intermediate-case level structure,' specifically pyrazine, is coherent, as predicted by the theory of Freed and Nitzan2 and implied by the model of Frad et aL3 2.BACKGROUND The spontaneous emission from an excited state of a polyatomic molecule with intermediate-case level structure, such as pyrazine, does not decay expotentially, as does an isolated non-stationary state embedded in a smooth continuum of other states. The observed non-exponential temporal decay is interpreted as arising from rapid evolution of the initially formed singlet wavepacket to generate mixed singlet- triplet levels, followed by slow depopulation via radiation from the singlet com- ponents of the mixed levels. The initial rapid evolution is a coherent process, so the mixed states generated have well defined phase relations and can generate a beat spectrum, whereas the depopulation by photon emission from the mixed levels is an incoherent process.The slow-decay component of the emission from cold isolated molecules of lB3" pyrazine has been studied 4-7 and, as predicted, shown to be derived from mixed singlet- triplet levels. However, the few available studies ' w 9 of the fast-component decay have been carried out under static-gas (" bulb ") conditions, and have not revealed the energy, symmetry and density-of-states effects necessary to understand the pre- dicted coherent nature of the decay, nor have prcvious experiments addressed the role of the optical pulse shape on the evolution of the molecular wavepacket.At the present time we know of no direct experimental evidence supporting the prediction that thc fast initial decay of the emission from pyrazine or any other intermediate-case molecule is due to coherent (deterministic) evolution of a singlet wavepacket into a compound state. 3. THEORY Fig. 1 displays the zero-order level structure appropriate to the description of pyrazine. The manifold {IZ)} corresponds to triplet states which have a mean spacing larger than their mean width. For pyrazine the states are split roughly by 0.01 cm-l, or 30 MHz. The level Is) is in the singlet manifold; it corresponds to the particular rovibronic state which has non-vanishing transition dipole moment to the ground state, hence is prepared by absorption of the photon for pulses whose coherent spectral width spans all states containing Is}.The sum of the radiative and non-radiative rates of the s and I states are ys = 75 + 7:' and y f = 7: + ypr, respectively. The two zero-order manifolds of states are coupled by the matrix elements Wsf, The central concept in the analysis of the behaviour of intermediate-case level structure molecules is that, for optical excitation (as opposed to, say, particle impact excitation), those states with transition dipole moments to the ground state are " projected out " of the states which diagonalize the total molecular hamiltonian. These molecular eigen-D. D. SMITH, S . A. RICE AND W. STRUVE 175 states are represented by the quasi-stationary states which are a superposition of the zero-order manifold states.(We use the term quasi-stationary here to mean that the evolution due to the coupling with the radiation field is slow on the time-scale of the initial decay of the wavepacket.) Equivalently, if the exact molecular levels were I j ) , I as er Y, Fig. 1. Schema for level structure used in the theoretical interpretation of intermediate-case molecular decays. the optically prepared molecular wavepacket is a superposition of the Ij), where only the amplitude of the state s survives : Y (t = 0) = Is) = c a j l j ) . (1) A complete quantitative theory of intermediate case decays, including finite duration transform-limited pulses, the modulation depth of the quantum beats, distributions of level splittings, level widths, coupling strengths and so on, has yet to be assembled.Most of the theoretical components exist but there is no " unified " formalism to calculate molecular photoresponse for arbitrary optical excitation. Owing to the brevity of this report and the incompleteness of the available theory we will only touch on the qualitative behaviour predicted by models, such as those dis- cussed by Freed and Nitzan,2 which assume delta function excitation pulses, constant spacing of the 1 levels, constant s-l coupling and oscillator strength only in the tran- sition to the s level with N levels involved; the results have also been shown to be valid for random coupling and spacing of the levels. Under these conditions the population of the level s, P,(t), qualitatively goes as Ps(t) ocexp[-(y, + r)t] (short times) Ps(t) oc - exp(- y j t ) (long times).1 N Here describes the rate of evolution of Is) into the exact molecular levels Ij), and h / ~ ~ is the time elapsed between absorption and emission of a photon. The basic physics implies that as more levels I are coupled, or as the s-1 coupling increases, the amplitude of the state s decays more rapidly to form the quasi-stationary states Ij). In other176 INTRAMOLECULAR DEPfIAS?NG words, the singlet wavepacket will be more rapidly resolved into its component molecular eigenstates. Since only Is} carries oscillator strength, the evolution into compound states will mean smalIer coupling with the radiation continuum and a " fast component " of the decay. Note that this interpretation implies that the fast com- ponent does not exclusively represent population decay, but a phase relaxation in the basis states [ j } , where the initially formed molecuIar wavepacket evolves into a coherent superposition of I j ) levels (nocoherence between the excited I j ) leveIs and the ground state) which results in a dilution of oscillator strength.The pre-exponen- tial factor of eqn (3) represents the dihtion of oscillator strength for the case of evoIving into N mixed states. To probe the evolution into molecuIar eigenstates one must design an experiment where either the density and/or coupling of the I levels can be altered. The experi- ment should be performed on internalIy cold molecules in a collisionless environment to minimize intra- and inter-molecular perturbations as well as spectral congestion.The subtle features of the evoIution of the prepared state, ips0 facto, require time- domain experiments with well characterized excitation pulses. For intermediate case moIecules, such as the archetypal azabenzenes, this means time-scales of the order of hundreds of picoseconds with transform-limited U.V. pulses (every photon in the same state) in the 10-100 ps regime. Moreover, the experiment will be conducted in the weak-field limit to avoid non-linear coherent effects (in our experments, the Rabi frequency is <1 kHz). 4. EXPERIMENTAL A block diagram of the experimental apparatus is shown in fig. 2. Pyrazine was excited by a mode-locked Coherent Inc. CR-15 Ar+ laser pumping a CR-599 dye laser (DCM dye) which was frequency-doubled using a 2 mm thick Lii03 crystal from Cleveland Crystals.Using custom-designed low-finesse 0.25 and I .O mrn etalons (provided by Coherent Inc.) the dye laser produces transform-limited pulses with a duration that can be varied between 30 and 100 ps, i.e. 0.5 and 0.17 cm-'. The U.V. pulses are 2-'j2 narrower in time and 211* broader in frequency. To verify that the pulses were transform-limited (AvAf = 0.441), their temporal and spectral profiles were measured using, respectively, an autocorrelator and a Burleigh Re110 parallel-plate scanning Fabry-Perot etaIon. Optical emission from pyrazine was collected by large f-number (f 2 5) optics to reduce the time-blur function associated with the coIlection lenses. Field stops in an image plane of the collection optics discriminated against scattered light which was not blocked by the absorptive and three-cavity dielectric filters used (Ditric Optics Co).Light was detected with either an Amperex XP2020 photomultiplier (system response 350 ps) or Hammamatsu R1294U channel-plate photomultiplier (system response < 130 ps). The channel-plate detector is a low-gain device when compared with available photo- multipliers (lo5 as against lo'), so it is not the detector of choice when working with poor quantum yields and the low number density (ca. 1015 ~ r n - ~ ) in supersonic expansions. The lowamplitude ( (8 mV> pulses from the channel-plate detector were amplified by cascading the preamplifier and amplifier of a Hewlett Packard 8447F amplifier (1.5 GHz effective bandwidth). For the XP2020, a lower gain and slower (1 GHz bandwidth) Electron Navi- gation Industries 600L ampIifier was adequate.The amplified signals were then sent to an Ortec 583 constant-fraction discriminator which produced start pulses for an Ortec 457 time- to-amplitude converter. Stop pulses for the time-to-ampIitude converter were derived from the mode-locking electronics of the Ar + laser by a LeCroy Research Systems model 161 high- speed discriminator which sampled the mode-locked r.f. output. The output of the time-to- amplitude converter was digitized and stored in a multichannel analyser (Hewlett Packard 5421A, 5415A and 5431B). Data from the multichannel analyser were preprocessed by a DigitaI Equipment Corporation 1 1/03 computer and fitted by convolute-and-compare routines on a Digital Equipment Corporation 11/34 computer.D.D. SMITH, S. A. RICE AND W. STRUVE MULTI CHANNEL ANALYZER 177 TIM E-TO-AM P L I T U 0 E CONVERTER t MOOELOCK ER G=l t I DISCRII;INATOR I FREQUENCY DIVIDER - I AUTOCORRELATOR / BEAMSPLIT POLARIZE 9 I 1 - POCKELS CELL I VARIABLE DELAY I , t '1 I I (VARIABL; DELAY 1 & *I DISC R 1 M 1 N ATOR TLiI03 AMPLIFIER FILTER TER R R Fig. 2. Block diagram of the picosecond laser and supersonic expansion apparatus. As the fast channel-plate photomultipliers are new to picosecond spectroscopy, the per- formance of our sample channel plate was tested. Measuring the well characterized decay of highly purified Rose Bengal in a variety of solvents, it was determined that there was a tail in the channel-plate response function that distorts decays >200 ps.The tail starts ca. 300 ps after the peak of the apparent laser pulse, continues for ca. 1 ns, and is 5 % of the height of the laser pulse. The tail is ostensibly due to electrons backscattered from the first channel plate to the photocathode that are subsequently amplified (the manufacturer informs us that newer models do not have a tail in the response function). Observing the restriction to useI78 INTRAMOLECULAR DEPHASING times t300 ps, the channel plate and conventional photomultiplier studies of the decays of pyrazine and Ruse Bengal agree within experimental error. As a matter of daily routine, the 100 ps single exponential decay of Rose Bengal in water was measured to check reproduci- bility and monitor overall system performance.The experimental chamber was evacuated through a specialIy designed 60” chevron baffle by three non-fractionating Edwards 9B3 ejector pumps backed by a roughing pump (Kinney KTC0021) - Roots blower (Kinney KMBD-400) combination. The system throughput is >45 Torr dm3 s-’.* The He stagnation pressures used ranged from 10 atm t to < I atm, depending on the desired beam temperature at the point of excitation, which was typically 5-10 mm downstream from the nozzle. Chamber pressures were of the order of 1 mTorr as measured by a Granville Phillips model 275 Pirani-convection gauge. We have used two nozzles, one a 100 pm diameter pinhole and the other a 50 x 500 pm slit made by electric discharge machining a 50 pm x 3 mm diameter stainless-steel disc with a tungsten whisker.A free-jet expansion from a slit lo nozzle has a slower decay of temperature with distance along the expansion axis and within the Mach “ ribbon ”, while maintaining a low- collision environment for the seeded molecule. The slit nozzle was used to provide long path-lengths for absorption, when needed, zs well as the higher temperatures employed in the study of the influence of initial rotational state on the fast-component fluorescence decay, The magnetic field was produced by a pair of 15 cm diameter coils and aligned to be parallel to the free-expansion axis and perpendicular to the excitation and collection optical axes. The magnetic field was homogeneous to ca. 1 % within the volume of the free expan- sion that was optically probed, as measured by a Bell model 620 gaussmeter. Despite extensive magnetic shielding around the photomultiplier, the response function was slightly altered by the magnetic field, so each decay was fitted with an instrument response function taken with the same magnetic field as was used to record the decay.The gas-handling system was constructed of stainless steel where all surfaces in contact with the seed gas were Teflon-coated. 99.99% pure helium gas was passed through a Matheson 6814-P4FF 0.02 pm filter and then sent to a 2.0 pm Nupro SS-2FR-2 filter loaded with pyrazine. The seeded helium went to the nozzle, which was gently heated to discourage crystallization of pyrazine on the orifice. Pyrazine (1,4-diazabenzene) was purchased from Aldrich Chemical Co.and purified by sublimation. To characterize the frse-jet expansions and to determine the excitation wavelength within the rotational contour of the transition, the backing pressure was set at 10 atm and the photo- excitation spectrum of pyrazine was measured by scanning the laser intracavity etalons. The photoexcitation spectrum 10 mm from the pinhole nozzle established pyrazine’s rotational temperature to be ca. 1 K. The photoexcitation spectrum was recorded simultaneously with a laser monitor etalon scan, This allowed the monitor etalon scans to be calibrated, thus to determine which rotational state was being optically pumped, measure the laser bandwidth and check for laser mode hopping. The long-term stability of the Iaser/rnonitor etalon system was f O .l cm-’. 5. RESULTS To probe the dynamics of the prepared wavepacket we have measured the fast- component decay as a function of (a) the initial-state rotational quantum number, (b) the coherence width of the laser pulse and (c) the strength of a static homogeneous magnetic field. We must, at the outset, make some comments on the data fitting we have used. In many of the measurements made the excitation pulse width was of the same order of magnitude as the instrument response function and molecular decay. Thus separation of the true molecular decay from the apparent decay must be carefully evaluated. We are in the process of deveIoping a method to execute this separation which does not involve Fourier or Laplace deconvolution since, as is well known, * 1 Torr = 101 3251760 Pa.t 1 atrn = 101 325 Pa.D. D. SMITH, S . A, RICE AND W. STRUVE 179 those methods work poorly with real data. Notwithstanding the pulse shape effects, one does not expect, a priori, the decay to be a simple exponential, as there should be a superposition of decay laws, some of which represent the weakly coupled inter- mediate case, others of which represent strong-coupling intermediate-case decays. In principle these couplings can be characterized from the quantum beats, and we will use such information in the reconstruction of the fast decay. In cases where the laser pulse width is much shorter than the decay, one can get a crude idea of the molecular decay rates by fitting the initial portion of the decay, convoluting with only the instru- ment response function.When this is allowable, the error we quote for the measure- ments includes the approximation of delta-function excitation. When the approxi- mation is not permissible, only qualitative results are quoted. The influence of the rotational density of states on intramolecular phase evolution can be derived from the J quantum-number dependence of the fast decay. As pointed out by McDonald et al.,4 because K is not a good quantum number and each J state is 2J + 1 degenerate, one expects the final density of states in eqn (4) (thus the fast decay) to xcale as 3(2J + l)/a where the factor 3 counts the triplet sublevels and o is the proper rotation symmetry number (4 in [‘H,]pyrazine). Recent high-resolution experiments by Kommandeur and co-workers i1 have demonstrated this to be an accurate assessment of the number of coupled states. We have measured the rotational-state dependence of the fast decay for the 1 5 J”, R branch only 10 Fig.3. The fast-component decay rate for the vibrationless level of the first excited singlet state in pyrazine as a function of rotational quantum number. J” is the final rotational-state quantum number. The error bars are jointly due to time resolution and the approximation of describing the decay as exponential (see text for details). vibrationless level of the first singlet with 21 ps U.V. pulses. Within the limitations described above one can see a trend in the decay rates by fitting the initial part of the decay to an exponential. The results, as a function of rotational quantum number, are shown in fig.3. A sample of the raw data is shown in fig. 4. The data illustrate an increase in decay ‘‘ rate ” with rotational quantum number, starting at ca. 145 ps for the R(1) member and decreasing to (90 ps for the R(5) member. Data were180 INTRAMOLECULAR DEPHASING taken up to R(10), but the decay became too rapid (<60 ps) to measure by time- resolved photon counting (multiple-colour pump-probe experiments are being set up). Despite the complexities in fitting the data it is clear that the pyrazine fast- component decay is a strong function of the rotational density of states, and so con- sistent with coherent evolution of the prepared wavepacket. 0.5 1.0 1.5 2.0 t/ns Fig. 4. Raw data (dots), fit (solid line through dots) and instrument response function for the fast-component decay of the pyrazine (0,O) R(2) member using the Hammamatsu channel- plate photomultiplier and ribbon beam (slit nozzle). Note that one can distinguish the 120 ps decay from the instrument response function. The contribution of the slow-component decay has been subtracted.Pulse f.w.h.m. = 21 ps. If the fast-component decay is a singlet state evolving into singlet plus triplet states, it should be nearly immune to magnetic field strength. Conversely, radiative and non-radiative processes associated with mixed singlet and triplet states (the slow- component decay) should be affected by a magnetic field. Fig. 5 shows the observed decays for the R(2) member of the (0,O) transition with 21 ps excitation pulses in the presence and absence of a magnetic field, normalized to allow simple comparison of the relative quantum yields.The fast-component quantum yield is mildly affected by the magnetic field, whereas the slow-component quantum yield is dramatically affected. Fitting the initial portion of the decay (within the limitations discussed above) the fast-component decay rate is unaltered by the field. Further, our data indicate that the magnetic-field dependence saturates near 100 G, in agreement with studies of pyrazine carried out on the nanosecond timescale.12 The crucial aspect of our observations is that the magnetic field has little effect on the fast-component decay relative to the effect on the slow-component decay, demonstrating the difference in triplet contents of the two components.Another direct method of probing of the intramolecular dynamics is to prepare molecular wavepackets of different energy width by using differcnt transform-limited puIses. If one shortens the excitation pulse (increases the energy spread) more levels will be pumped and one expects the fast component to decay more rapidly [the sum over I states in eqn (1) is larger], the amplitude of the slow component to decrease (dilution of oscillator strength) and the quantum beats to exhibit a denser FourierD. D. SMITH, S. A. RICE A N D W. STRUVE 181 0 0.5 1 .o 1.5 2 .o t/ns Fig. 5. Magnetic-field dependence of the pyrazine fast-component decay [ 'B3,t1A 1,(0,0) member]. Pulse f.w.h.m. = 21 ps. The data shown were taken with the XP2020 photo- multiplier at the full laser repetition rate of 72 MHz, so that the slow-component decay appears as a large baseline.The dark-count contribution to the baseline would not be visible on this scale. I . a 0.5 f.0 1.5 2.0 tlns Fig. 6. Effect of altering the coherence width of the excitation pulse on the decay law. The data were taken with the XP2020 photomultiplier and were taken at the full laser repetition rate (a pulse every 13 ris) so the slow-component decay appears as a baseline. The pulse widths shown are the f.w.h.m. of the ultraviolet picosecond pulses. The amplitudes of the fast-component decays were normalized to allow facile comparison of the relative quantum yields of the slow and fast components. The wiggles to longer time are due to quantum beats.182 INTRAMOLECULAR DEPHASING spectrum.Such measurements have been carried out with 21 and 70 ps transform- limited pulses (see fig. 6). For the data shown in fig. 6, R(2) of the vibrationless first singlet was excited with 21 ps U.V. pulses. Changipg nothing else and adding another etalon to the laser cavity, 70 ps U.V. pulses were produced and a new decay was measured. At all times the monitor etalon was checked fur laser mode hopping. The striking result we find is that the fast and slow decays are altered. As expected, the fast decay becomes so badly non-exponential with 70 as against 21 ps pulses that simple procedures such as fitting the initial portion of the decay are no longer useful. The relative amplitudes of the slow and fast components have also changed with alter- ation of the coherence width of the pump pulse.Quantitative analysis of our data (as in the case of the J dependence) requires a method for synthesizing the fast decay including the pulse-shape l3 effects. The point to be made here is that u n h s the fast decay were coherent and represented the evoIution of the prepared state into a com- pound state (phase, not population relaxation) the fast-component decay would be independent of the laser coherence width. 6. CONCLUSIONS Picosecond spectroscopy allied with the well known properties of supersonic expansions allow direct probing of the evolution of an optically prepared wavepacket state into quasi-stationary molecular eigenstates. From our preliminary studies of the intermediate-case molecule pyrazine, we conclude that the fast-component decay indeed represents phase, not population, relaxation, and is the evolution of a highly non-stationary singlet state into a compound state (singlet + triplet).Due to the complexity of the fast-component decay law, a proper procedure to quantitatively synthesize the decay from knowledge of the quantum beats and excitation pulse must be developed. Such work is under way. This work has been supported by the National Science Foundation and the Air Force Office of Scientific Research. We are grateful to Prof. G. Fleming for the loan of the microchannel-plate photomultiplier, Dr. A. Lorincz for assistance in the con- struction of the apparatus and to Jeanne Siemion and Ron Rosman for technical help. A. Nitzan, J. Jortner and P. M, Rentzepis, Proc, R. Soc, Lodun, Ser. A, 1972,327,357. A. Frad, F. Lahmani, A. Tramer and C . Tric, J. Chem. Php., 1974,60, 4419; F. Lahmani, A. Tramer and C. Tric, J. Chern. Phys., 1974, 60,4431. V. J. van der Meer, H. Th. Jonkman, G. M. ter Horst and J. Kommandeur, J. Chem. Plrys., 1982,76,2099. S. Okajima, H. Saigusa and E. C. Lim, J. Chern. Phys., 1982, 76, 2096; H. Saigusa and E. C. Lim, Chew. Phys. &if., 1982, 88,455. P. M. Felker, Win. R. Lambert and A. H. Zewail, Chem. Phys. Left., 1982, 89, 309. B. J. Van der Meer, H. Th. Jonkman, G. Ter Horst and J. Kommandeur, J. G e m . Phys., 1981, 74, 3616. D. €3. McDonaId, G. R. Fleming and S. A. Rice, Chem. Phys., 1981, 60, 335. I. Yamazaki, T. Murao and K. Yoshihara, Chern. Phys. Lett., 1982, 87, 384. B. J. van der Meer, H, Th. Jonkman, J. Kommandeur, W. Leo Meerts and W. A. Majewski, Chem. Phys. Lett., 1.982, 92, 565. ’ K. F. Freed and A. Nitzan, f. Chern. Phys., 1980,73,4765. lo M. SuIkes, C. Jouvet and S. A. Rice, Chem. Phys. Lett., 1982, 87, 515. l2 David Pratt, University of Pittsburgh, personal communication. l3 See for exampk, G. W. Robinson and C . A. Langhoff, Chem. Phys., 1974,5, 1 or F. A. Novak, J. M. Friedman and R. M. Hochstrasser, in Laser and Coherence Spectroscopy, ed. J. I. Stein- feld (Plenum Press, New York, 1978).

ISSN:0301-7249    

DOI:10.1039/DC9837500173

出版商:RSC    

年代:1983

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1983, 75, 183-195 Energy Conversion in Van der Waals Complexes of s-Tetrazine and Argon BY Jo J. F. RAMAEKERS, HANS K. VAN DIJK, JAN LANGELAAR AND RUDOLPH P. H. RETTSCHNICK Laboratory for Physical Chemistry, Univcrsity of Amsterdam, Nieuwe Achtergracht 127, 101 8 WS Amsterdam, The Netherlands Received 17th January, 1983 The van der Waals complex T.Ar has been prepared by expanding argon seeded with s- tetrazine through a nozzle. The complex dissociates when excited to single vibronic levels of the S1( lB3J state of tetrazine. Information about both the vibrational state distribution of the dissociation fragment T and vibrational relaxation which takes place in the complex has been obtained from spectrally resolved and time-resolved fluorescence. The relative yields of relaxation and dissociation processes depend upon the excess vibrational energy ew absorbed by the van der Waals modes.The magnitude of E, was varied using different sequence transitions of the van der Waals modes, by tuning the laser successively to different wavelengths within the contour of a particular absorption band. The observed effects can be interpreted qualitatively in terms of the momentum-gap law. The dissociation of the6a' state of T-Ar proceeds via two consecutive steps. Lower and upper limits to the dissociation energy 06 (of the 6 2 state) are 276 and 448 cm- l. Energy transfer from the 16a mode as well as from the 16b mode to the van der Waals bond gives rise to dissociation of the complex. The dissociation rates are of the order of lo9 s- and they are dependent on e,.1. INTRODUCTION Van der Waals complexes are suitable prototype systems for studies of photo- dissociation and vibrational redistribution in polyatomic molecules. Generally, the dissociation energy DA of a van der Waals bond is smaller than a quantum of a molecular vibration, and therefore excitation of a single vibronic level of a molecule which is part of a weakly bound complex will eventually cause rupture of the van der Waals bond. The rate of the vibrational energy transfer process within the complex, giving rise to dissociation of the complex, competes with other deactivation processes of the electronically excited complex. Experiments in which the supersonic expansion technique is combined with sophisticated spectroscopic techniques have given interest- ing resu1ts.l The results of such studies have initiated extensive theoretical work.2 Spectroscopic studies of vibrational predissociation and vibrational relaxation of vibronically excited complexes of s-tetrazine and argon have been reported in ref.(3) and (4). The spectra showed three different kinds of emission bands: (i) resonance emission from the originally excited level of the complex, (ii) emission bands originat- ing from vibronic levels of the complex populated by intramolecular vibrational energy flow within the complex, which might be collision-induced, and (iii) emission from dissociation products. The torsional mode 16a appeared to be particularly important in the vibrational predissociation process.The observed emission spectra184 ENERGY CONVERSION IN VAN DER WAALS COMPLEXES and the decay times of selectively detected emission bands give rise to the conclusion that one quantum of mode 16a is transferred to the van der Waals bond, thus causing dissociation of the complex. No modes other than 16a were found to be directly involved in the dissociation process. In the present study we will show that the energy of one quantum of the 16a mode is not enough to cause dissociation of the complex. This implies that energy transfer of one 16a quantum can only give rise to rupture of the van der Waals bond if the initial state already contains a sufficient amount of vibrational energy in the van der Waals modes. The dissociation process is schematically represented by arrow a in fig.1 and the vibrational redistribution RT-Ar+ Fig. 1. Schematic diagram of the T-Ar intermolecular potential for two different vibronic states of s-tetrazine. Vi- brational predissociation and vibrational relaxation of T-Ar are indicated by arrows a and b, respectively. The levels of the van der Waals stretching mode are also shown. process is represented by arrow b. The redistribution process might be induced by collisions. In this paper we will examine the effect of collisions and the influence of excess vibrational energy stored in the van der Waals modes on the processes displayed in fig. 1. Detailed information about fluorescence and absorption spectra of tetrazine vapour and tetrazine-argon van der Waals complexes is available in the literat~re.~.~ A schematic representation of some normal modes of tetrazine, according to ref.(7), is given in fig. 2. Only modes with relatively low frequencies have been represented; the frequencies in the ground state and the excited electronic state are given in table 1. Levy and collaborators have reported high-resolution spectroscopic studies of s- tetrazine (T) and the van der Waals complexes T-X and Tax2 (X = He, Ar or H2)J. J. F. RAMAEKERS, H. K. VAN DIJK, J. LANGELAAR AND R. P. H. RETTSCHNICK 185 The structure of the spectra is consistent with a geometry in which X is situated on the out-of-plane C, axis of tetrazine. For the complexes Tax2 the spectral shifts (with respect to the corresponding transitions of T) are twice as large as for T.X. This indicates that the X species are occupying equivalent positions.Throughout this I + + + - Fig. 2. Schematic representation of some normal modes of s-tetrazine. Table 1. Frequencies and symmetry species of some of the normal modes of s-tetrazine in the So('A,) and Sl(1B3u) electronic states frequencylcm - vibration species SO S1 1 4 5 6a 6b 16a 166 17b 1009 801 994 736 640 336 254 904 755 565 666 703 362 255 403 68 1 paper we will denote vibronic levels and transitions in the complex T.Ar with a line on top of the assignment (e.g. =denotes a transition in T*Ar). 2. EXPERIMENTAL The complexes T-Ar and T-At-, were produced in a supersonic expansion of argon seeded with ca. 0.03 % of s-tetrazine. The carrier gas was conducted through a steel bottle contain- ing s-tetrazine at a temperature of (18 & 1) "C.A free jet was formed by expansion of the gas through a 0.050 rnm pinhole into a chamber pumped by a Roots pump (350 m3 h-l) backed by a mechanical forepump (25 m3 h-l). The stagnation pressure of the gas was varied between 1 and 1.6 bar. The continuous jet was crossed by a focused laser beam at a distance z downstream of the nozzle. The diameter of the laser beam was ca. 0.03 mm in the186 ENERGY CONVERSION IN VAN DER WAALS COMPLEXES central part of the jet. In our experiments z was changed between 0.03 and 1.5 mm by moving the nozzle with respect to the laser beam which was fixed in space. The dimensions of the observed area were taken as small as possible (i.e. 60.1 mm x 1 .O mm depending on z ) in order to avoid detection of fluorescence emission from molecules outside the jet.Optical excitation of the van der Waals molecules was achieved with a dye laser syn- chronously pumped by an argon-ion laser. The bandwidth of the exciting light was 0.1 or 0.2 of 1.0 cm-'. Time-resolved measurements of the fluorescence were carried out with picosecond pulses (z: z 7 or 80 ps) from the mode-locked laser system. The fluorescence emission was dispersed with a 1.5 m Jobin-Yvon monochromator THR 1500 (0.24 nm mm-') equipped with two exit slits in order to allow either spectrally resolved or time-resolved measurements. In most of the experiments the spectral bandwidth of the detection system was 10 cm-', sometimes it was 15 cm-'. Before and after each experiment a calibration of the wavelengths and the linewidth of the dye laser was performed with an accuracy of f 1 pm (i.e.ca. 0.03 cm- '). Fluorescence spectra were measured using a cooled magnetically defocused EM1 9558 QA photomultiplier. For the time-resolved measurements a Philips XP 2020 photomultiplier or a Varian cross-field VPM 154 M instrument was used. The photomultiplier is attached either to a photon counting system or to a single-photon counting system. The time resolution of the detection system is better than 100 ps. Peak positions of emission bands could be obtained with an estimated accuracy between f1.5 and f 2 cm-' depending on the intensity of the emission band. The estimated error in the peak positions of the excitation bands is < f 1 cm- ' except for very weak bands.Before each series of experiments s-tetrazine was distilled into a steel bottle which forms part of the gas supply line to the nozzle. s-Tetrazine was synthesized according to the method of Spencer et aL7 After the last step of the preparation s-tetrazine is sublimated several times by means of a freeze and thaw cycle in order to get rid of volatile impurities. The end product is stored in the dark under vacuum at -20 "C. 3. RESULTS AND DISCUSSION 3.1. SPECTROSCOPIC OBSERVATIONS Fig. 3 shows the @-band of the fluorescence excitation spectrum of T-Ar. This spectrum also exhibits the molecular 0; band which appears as an extremely weak feature 23 cm-l to the blue of the @band. Three stronger bands appear at +34, +38 and +43 cm-l from the band. These bands must be ascribed to the complex because their relative intensities with respect to t h e q band are independent of the experimental conditions.The band at +43 cm-l, which exhibits the same spectral structure as the @band, is ascribed to the >$transition, i.e. the transition v" = 0-t 0' = 1 of the (totally symmetric) van der Waals mode 0. The bands at +34 and +38 cm-l are probably due to transitions in which the (non-totally symmetric) bending modes p,, and /Iz are involved. In the emission spectrum of TSAr, observed after excitation, again three weak bands are present. They appear at positions -33, -37 and -41.5 cm-l from the @j band. The relative intensities of both the %absorption band and the $emission band, with respect to the intensity of the parent bandBFare ca. 0.02.The low Franck- Condon factors indicate that electronic excitation of the complex causes a very small change of the equilibrium distance T-Ar, while the lower part of the intermolecular potential is only slightly changed. It is not clear why the spectra should exhibit PTand /ITtransitions of the non- totally symmetric bending modes. Perhaps the corresponding bands must be ascribed to transitions /Izand fl;: The zero-point-level fluorescence spectrum of T*Ar is red-shifted 23 & 1.5 cm-l with respect to the Oo fluorescence spectrum of the free tetrazine molecule. Apparently,J. J. F. RAMAEKERS, H. K. VAN DIJK, J. LANGELAAR AND R. P. H. RETTSCHNICK 187 the intermolecular potential well is 23 cm'l deeper in the excited electronic state than in the ground state. The vibrational structure of both spectra is identical.The main emission bands are 16b2, 16a& 6ay, 8aP and several 6a progressions of these bands. wavenumbericm - Fig. 3. Part of the fluorescence excitation spectrum of T*Ar near the Ktransition. Laser linewidth 1 cm- '. Fluorescence was detected at 17 369 cm- ' @q transition), bandwidth 10 cm- l, po = 1.5 bar, z = 0.03 mm. The amplification factor has been changed from 1 to 20 beyond 10 cm- ' from the origin. The spectral shifts of the bands are -23 & 1.5 cm-l except for the 16bg band which is shifted (-18 & 1.5) cm-l with respect to the 16b: band in the spectrum of the free tetrazine molecule. Table 2 shows the frequencies of some bands in the fluorescence Table 2. Spectral shifts of fluorescence excitation bands of TmAr.The minus sign indicates a shift to the red with respect to the corresponding band in the excitation spectrum of un- complexed t e t r azine . excitation observed frequency, estimated band V,ac/Cm-' shift/cm- accuracy/cm- 18 105 - 23 f l 00 16ai 18 629 -8 +1 6ai 18 809 -22 *I 6bt 18 888 - 24 f l 0 166: 18 261 -17 h 1 . 5 - - - excitation spectrum of TSAr, including the weak hot band 16bf. The frequencies (vvac) are referring to the peak positions of the excitation bands. In these experiments the emission was always detected in a resonance band, for instance, the excitation bands OT and W w e r e measured by detecting the 6 x a n d 6xemission bands, respec- tively. The spectral shifts of the excitation bands (with respect to the corresponding bands in the spectrum of the uncomplexed molecule) are not identical.This indicates that the depth of the intermolecular potential is slightly affected by the vibrational motion of the nuclei of the tetrazine molecule. This effect seems to be more pro- nounced in the excited electronic state than in the ground state.188 ENERGY CONVERSION IN VAN DER WAALS COMPLEXES The fluorescence excitation bands all display the same spectral structure (cf. fig. 3). This structure has not yet been analysed. The band contour is a superposition of rotational structure and sequence band structure of activated van der Waals modes. The contribution of such sequence transitions u"+d with Av = 0 to the band contour is indicated by the following experiment. When the laser frequency is tuned successively to different positions within the excitation band, the spectral positions of the resonance emission bands shift in the same way.As an example, table 3 gives the Table 3. Change of spectral position vem of emission bands resulting from a change of the excitation frequency v,,,. Frequencies ( v , , ~ ) and shifts are given in cm- '. Vexc 18 808.8 18 812.3 18 816.4 6a: 17 336.5 4-3.6 17 340.1 f3.9 17 344.0 6ai16a: 18 138.1 f2.6 18 140.7 + 3.2 28 143.9 16a: 1796.10 +1.0 I7 962.0 +1.3 17 963.3 5: 17 787.2 f2.5 17 789.7 +1.1 17 790.8 ~ positions of the main emission bands of the complex (centre of the band) for three different frequencies (excitation bandwidth 0.1 cm-') within the 6 3 excitation band. The shifts observed for the intense resonance emission band @-equal those of the excitation frequency.Within the experimental error this is also the case for the much weaker resonance emission band 6ai16a,0. On the other hand, the shifts observed for the emission bands 16ai and q, which originate from a relaxed level of the complex, are smaller, but they both show an increasing blue shift. This behaviour is also exhibited by the weaker relaxed emission bands of the T.Ar complex (not presented in table 3). The observations are plausible when the formation of the van der Waals complexes in the supersonic jet is considered. These species are formed by three- body collisions; the third particle is required for the stabilization of the complex. In a supersonic expansion equilibration of translational and rotational degrees of freedom is more efficient than the equilibration between vibrational and translational degrees of freedom.For this reason it is concluded that in the electronic ground state of the complex several levels of the van der Waals modes are populated. Fig. 4 displays a schematic representation of a Morse-type intermolecular potential as a function of the distance between the argon atom and the molecular plane of lBfU s-tetrazine for some molecular vibronic states. For each of these curves the vib- rational levels of the van der Waals stretching mode are shown. When the laser frequency is tuned into the blue wing of the excitation band, Ievels u' > 0 of the van der Waals vibration are excited via sequence transitions u"+d with Au = 0.This is due to the fact that the frequency of the van der Waals vibration in the excited elec- tronic state is higher than in the ground state; the shapes of the potential curves are probably very similar in both electronic states. Resonance emission bands should exhibit the same spectral shift as the excitation frequency. The observation that emission bands originating from relaxed levels of the complex show a smaller shift than the excitation frequency can be considered as an indication that the vibrational energy transfer within the complex is collision-induced, so that energy relaxation takes place.J. J. F. RAMAEKERS, H. K. VAN DIJK, J. LANGELAAR AND R. P. H. RETTSCHNICK 189 A lower limit to the intermolecular well depth can be deduced from the observation of the m e x c i t a t i o n band.This weak band could be observed at distances from the nozzle up to 1.5 mm, which implies that the complex T-Ar in its vibrational state 16b, exists at least 1 p s after it was formed. Since vibrational predissociation times of T.Ar appear to be shorter than 1 ns (section 3.2), the appearance of them-excitation band at distances relatively far downstream of the nozzle indicates that the magnitude f E 6 a' 16a' 16b' P I tj O0 RT-Ar Fig. 4. Schematic diagram of the T-Ar intermolecular potential for six vibronic states of s- tetrazine. The level schemes of the van der Waals stretching mode (vo = 43 cm-') are shown. 0; is assumed to be ca. 300 ern-'. of the 16b quantum is too small to break the van der Waals bond. Therefore a lower limit to the dissociation energy D: in the electronic ground state is 254 cm-I for the vibrational level Ebl.If it is assumed that D: is independent of the molecular vibrations in the electronic ground state, a lower limit of 254 + 23 = 277 cm-I for DA in the vibrationless An upper limit to DL follows from the observation that excitation of t h e w level always gives rise to dissociation of the complex. In these experiments the dissociation fragment tetrazine is formed in the 16a' vibronic state (not in the 0' state). This result is independent of the position of the excitation frequency within the a band. Therefore the upper limit to DA is 703-255 = 448 cm-l for t h e w s t a t e of the complex. This value is probably too high since the dissociation fragment of tetrazine appears state follows from table 2.190 ENERGY CONVERSION IN VAN DER WAALS COMPLEXES to be rotationally excited (see fig.5). For this reason, the calculated value of 448 cm-' must be reduced with the rotational energy gained by the tetrazine molecule. How- ever, note that such a calculation is not reliable when the energy of the initial state is not known with certainty. We attribute the appearance of rotational energy in the 577 579 +l/nm 581 Fig. 5. Part of the fluorescence spectrum after excitation into the z, absorption band of T-Ar. The emission between 577 and 578 nm originates from the rotationally excited 16a' level of the tetrazine fragment. The strong bands at 576.6 and 580.3 nm are due to the transitions 6 3 (resonance emission) and 16ai6ay (relaxed emission), respectively.Detection bandwidth 10 cm-', po = 1.3 bar, z = 0.05 mm, liberated tetrazine molecule, at least in part, to the population of levels v, > 0 by optical excitation of the van der Wads stretching vibration in the 6ai state. More experiments have to be done in order to elucidate this point. The observed difference between the frequencies of the van der Waals stretching mode in the ground and excited electronic state is ca. 1.5 crn-l. This value is in agree- ment with the observed difference of 23 cm-' between the potential well depths if we assume Morse potentials with the same steepness parameter for both electronic states and a value of Do between, say, 275 and 450 crn-l. 3.2. VIBRATIONAL RELAXATION AND DISSOCIATION In ref. (4) we have reported the preliminary results of time-resolved experiments dealing with the decay of selectively detected emission bands in the dispersed fluores- cence, observed after excitation of the =level of TnAr.The main bands in this spectrum originate from the prepared level from the relaxed levels 16a2, 16a'16b' and 9, and from the 16d level of the tetrazine molecule, which is formed by dissoci- ation of the complex. The decay times of these levels were obtained from the slope of a semilogarithmic plot of the fluorescence intensity against time. An indication of the processes which take place after excitation of theGI level was obtained from a comparison of these decay times with those observed after directJ. J . F. RAMAEKERS, H. K. VAN DIJK, J.LANGELAAR AND R. P. H. RETTSCHNICK 191 excitation of the corresponding states of tetrazine in a supersonic jet. These latter decay times are almost identical to those measured in the static gas phase at room temperature. It turned out that the decay times of the relaxed levels 16Zand 16a116b1 of T-Ar are significantly shorter than those measured for tetrazine. On the other hand, the decay times of the levels 6al- a n d F o f T-Ar and 16al of the liberated tetra- zine appeared to be identical with those measured directly for tetrazine in the gas phase or in a supersonic jet. From these observations it was concluded that the vibrational predissociation of the 6a' state proceeds via two consecutive processes : first, a vibrational relaxation process 67-+E2 or @+16a116bi, which has no s i p nificant effect on the lifetime of the optically prepared state 6a1, and secondly, the actual dissociation process, which is fast enough to cause a significant reduction of the lifetime of the 16a2 and 16a116b1 states of the complex.Since no emission from tetrazine in the vibrationless state Oo was observed, it was concluded that one quantum of the torsional vibration 16a is transferred from tetrazine to the van der Waals bond giving rise to the ejection of the argon atom. This conclusion is supported by the results obtained after excitation of the 16a2 level of T-Ar. The main emission bands originate from the prepared level 16a2 and from the 16al level of the dissociation fragment. Once again, the lifetime of t h e m level appeared to be reduced with respect to the lifetime of the 16a2 level of uncomplexed tetrazine.According to this interpretation of the preliminary data presented in ref. (4) an important dissociation channel of vibronically excited TSAr is based on the transfer of one quantum of mode 16a to the van der Waals vibrations, probably the stretching mode. Note that the 16a quantum (255 cm-l) is smaller than the lower limit to the dissociation energy DA, which is 277 cm-' for the r s t a t e and (according to table 2) 278 - 15 = 263 cm-l for the 16a2 state. Therefore it must be concluded that after the vibrational relaxation process 6&+ 16z which might be collision-induced, has taken place, the excess vibrational energy stored in the van der Waals modes exceeds the energy difference D; - 255 crn-'.The observation that optical excitation of- can give rise to the dissociation process~2-+16a1 + Ar implies that in these experi- ments a sufficient amount of energy is absorbed by the van der Waals modes (as a result of sequence transitions v"+v' with Av = 0) to compensate for the energy deficiency 0; - 255 cm-l. In the present paper we will pay attention to: (i) the role played by collisions between the van der Waals complexes and the atoms of the expanding carrier gas and (ii) to the effect of optical excitation of van der Waals vibrations on the yields of relax- ation and dissociation processes. The results of improved time-resolved measure- ments will be considered. In order to obtain information about the influence of collisions we have varied the distance z between the illuminated part of the jet and the nozzle.The collision frequency and the collision energy decrease strongly with increasing z. The energy absorbed by van der Waals vibrations has been varied by using different excitation frequencies vex, within a particular absorption band. When vex, is shifted to the blue the complex ends up in higher levels of the van der Waals modes in the excited elec- tronic state (cf. section 3.1). In our experiments collision-induced vibrational relaxation of uncomplexed tetrazine is negligible (i.e. the intensity of relaxed emission bands is (0.5% of the intensity of resonance emission). This means that the distribution of vibronic states of tetrazine formed in the dissociation reaction is not disturbed by collisions in the jet.However, under the same experimental conditions collisional effects may not be192 ENERGY CONVERSION IN VAN DER WAALS COMPLEXES negligible for van der Waals complexes, even for large values of z. This is because the hard-sphere cross-section of the complexes is greater than that of uncornplexed tetrazine, and especially because the density of vibrational states of the complex is considerably higher than that of the free molecule, owing to the contribution of the van der Waals vibrational manifolds. For these reasons it is inevitable that Vibrational relaxation of the complexes is influenced by collisions in the jet- If the density of the background levels, owing to the contribution of stretching and bending modes, is sufficiently high, vibrational energy flow will occur in an isolated complex, but generally the efficiency of this process will be enhanced by collisions.Fig. 6 shows a part of the fluorescence spectrum obtained after excitation of the 3 0 0 I I 550 560 l/nm Fig. 6. Part of the fluorescence spectrum obtained after excitation of the 6a'level of T-Ar, vcxc = 18 808.8 cm-', laser bandwidth 0.2 cm-', detection bandwidth 15 cm-l, po = 1.25 bar, z = 0.3 mm. Assignments: 0, resonance emission from the 62 level of T-Ar; 1, %bz 2,16a:l%h:j 3, 16a: (tetrazine molecule); 4, 16az 5 , 17b:; 6, c o r 6bi; 7 , x 6aA band at 18 808.8 cm-I (frequencies are given as v,,,, wavelengths are presented as ;lair). When the excitation is achieved at 18 808.8 cm-l the complex ends up in the lowest vibrational level (or in the lower levels) of the intermolecular potential well (cf.section 3.1). It depends on the width of the rotational contours of adjacent sequence bands of the van der Wads modes whether the excitation process gives rise to the population of single levels of the van der Waals vibrations or not. The most striking changes of the relative peak heights in the spectrum when z is increased are (i) an increasing contribution of resonance emission from the excited level 6 F a n d (ii) a decreasing contribution by the emission from the relaxed combination level 'i6$16h1i leading finally to the disappearance of band 2 in the spectrum for z > 0.8 mm. On the other hand, the relative contributions of the emission bands 3 (originating from the molecular dissociation fragment) and 4 (originating from level 16z) to the total fluorescence intensity (which decreases because of the lower particle density further downstream of the nozzle) do not change significantly when z is increased.When the The spectrum displayed in fig* 6 was obtained for z = 0.03 mm.J. J. F. RAMAEKERS, H. K. VAN DIJK, J . LANGELAAR AND R. P. H. RETTSCHNICK 193 excitation is achieved in the blue wing of the =absorption band (vex, > 18 812 cm-l) the changes in the relative intensities of the emission bands exhibit a similar dependence on z, but these changes are considerably smaller. In the latter case the complex is prepared in higher vibrational states of the van der Waals modes than in the former case. These observations indicate that the efficiency of the vibrational energy flow in the complex is slightly enhanced by collisions when the density of background levels is high, whereas the energy flow is completely collision-induced when the level density is low (cf.fig. 4) as demonstrated by the example 6a’-d6%q-67. Intermolecular energy transfer during a collision compensates for the energy separation between initially prepared and final levels. The z-dependence of the relative intensities can be understood qualitatively as being a consequence of decreasing collision frequencies and decreasing collision energies when z is increased. More experimental data are required to get quantitative information about collisional effects. The relative inten- sities of the emission bands depend on both z and vex,.The data given in table 4 demonstrate the influence of the excitation frequency (bandwidth 0.1 cm-l) on the efficiency of vibrational energy flow within the complex. For increasing values of vex, the intensity of resonance emission from the excited level 6Fdecreases whereas the intensity originating from relaxed levels of the complex increases. These observ- ations are in agreement with the arguments given above, since an increase of vex, gives rise to the preparation of complexes in higher levels of the van der Waals vibrations (due to the excitation of higher members of the van der Waals sequence bands), which implies that the density of the van der Waals manifold in the final vibronic state is higher. As a consequence, the intramolecular energy flow to the final state is more efE.cient whether this process is collision-induced or not. Table 4.Relative intensities of fluorescence bands after 6 3 excitation of T-Ar. Relative intensities are normalized to 100 for the sum of the intensities. Excitation frequency (vYBc) Excitation bandwidth 0.1 cm-’, z = 0.03 mm, po = 1.2 bar. in cm-l. vex, 17b: 16b: 16a: 18 808.8 38.8 (1) 3.9 5.0 14.3 0 38.4 18 812.3 29.5 5.0 4.7 9.7 17.4 8.0 25.7 18 816.4 14.6 5.2 6.3 13.8 23.6 14.4 22.1 From the data given in table 4 it follows that the dissociation process yielding tetrazine in the 16al state becomes less efficient for increasing vexc. This is in agree- ment with the momentum-gap law,’ as well as the energy-gap law,2 which predict that vibrational predissociation (VP) is less efficient when the fragments are produced with more translational energy.A plausible explanation for the increasing yield of T(16b’) seems to be the increasing efficiency of the relaxation process 6if-+16a116b’, which will be followed by a VP process 16a’16b’+16b1 + Ar in which again one quantum of the 16a mode is transferred to the van der Waals bond, or by a VP process 16a116bi+16a’ + Ar. Table 4 shows that the dissociation channel yielding T(16bl) is closed for the lowest value of vexc although energy is transferred towards 16a’1.6b’, This indicates that only the dissociation process 16a11651+16a1 + Ar takes place when the 16a’16bi level is prepared with hardly any excess energy in the van der Waals modes. Apparently, the energy of the 16b quantum is sufficient to break the van der Waals bond.If this dissociation process is not assisted by excess194 ENERGY CONVERSION IN VAN DER WAALS COMPLEXES energy of the van der Waals modes in the 16a'16bT state, the energy -____ of the 16b quantum is to be considered as an upper limit to D;, i.e. 403 cm-' for the 16a'16b1 state. Energy transfer from the 16a mode to the complex bond can give rise to rupture of this bond only when the van der Waals modes have absorbed sufficient energy. which have been reported recently, using an improved method which allows the determination of rise and decay times of fluorescence signals on a sub-nanosecond timescale with higher accuracy than before. Details of this work will be published el~ewhere.~ The lifetimes of the S1 vibronic levels of tetrazine are determined primarily by photodissociation of the molecule, which gives rise to the formation of HCN and N2.The quantum yield of the molecular photodissociation process is approximately unity.1° The photodissoci- ation rate appears not to be influenced by the formation of complexes T-Ar since the lifetimes of most of the vibronic levels of T and T-Ar are identical. Therefore it seems reasonable to consider the observed difference between the lifetimes of T( 1 6a2) and T.Ar(16aZ) as due to an additional decay channel (i.e. dissociation of the complex into T and Ar) which competes with the photodecomposition of the molecule. The rate constant for vibrational predissociation, kvp, follows from the difference between the decay times. Very recently we have observed that the decay time of the 16a2level depends on the amount of excess energy E~ stored in the van der Waals vibrational manifold.The magnitude of cW can only be estimated. A quantitative interpretation of the relation between E~ and vex, is not yet possible since the structure of the excitation bands is not yet analysed in sufficient detail. Furthermore, E~ might be reduced by collision-induced deactivation of the van der Waals vibrations. We have continued the time-resolved experiments For E~ = 0 (direct optical excitation of the 16a2 level) we have found kVp = 0.54 x lo9 s-l and for estimated values of E~ z 175 cm-' and cW z 250 cm-I we obtained rate constants kvp = 2.3 x lo9 s-' and k,, = 0.95 x lo9 s-', respectively excitation). The dissociation channel r6T-+16a1 + Ar is closed for E~ = 0, since the energy of one quantum of the 16a mode is less than 0 6 .Only the dissociation channel 16a2-+ Oo + Ar is energetically open. The latter channel is less efficient than the former one, according to the momentum-gap law (or the energy-gap law). Dissociation of T-Ar into T(16al) + Ar will be possible for E~ z 175 cm-' since 175 + 255 = 430 cm-' probably exceeds D;. When cw is increased to ca. 250 cm-' the dissociation rate is reduced, which is again in agreement with the momentum-gap law. At present, detailed studies are carried out which are dealing with the dependence of the relative yields of relaxation and dissociation products upon the position of vexc within the absorption bands 16a$and 6%; of T-Ar. These studies are performed in combination with time-resolved measurements of selectively detected emission bands. From these experiments it follows that it is again the 16a mode which is involved in the VP process following optical excitation of the-6Jz level. Similar studies concerned with the complex T.Ar2 are in progress. The data ob- tained after excitation of the =level of T-Ar, show that vibrational relaxation of this complex is more efficient than for T-Ar under the same experimental conditions (Po and z ) and withcorresponding positions of vexc within the absorption bands. The experiments with T-Ar, demonstrate that also in this case the 16a mode is involved in the principal dissociation channel. These investigations were supported by the Netherlands Foundation for Chemical Research (SON) and were made possible by financial support from the Netherlands Organization for Pure Research (ZWO).J. J. F. RAMAEKERS, H. K. VAN DIJK, J. LANGELAAR AND R. P. H. RETTSCHNICK 195 D. H. Levy, Adu. Chem. Phys., 1981,47, 323. J. A. Beswick and J. Jortner, Adv. Chem. Phys., 1981,47, 363. J. E. Kenny, D. V. Brumbaugh and D. H. Levy, J. Chem. Phys., 1979,71,4757. J. J. F. Ramaekers, J. Langelaar and R. P. H. Rettschnick, in Picosecond Phenomena 111, ed. K. B. Eisenthal, R. M. Hochstrasser, W. Kaiser and A. Laubereau (Springer-Verlag, Berlin, ' K. K. Innes, L. A. Franks, A. J. Merer, G. K. Vemulapalli, T. Cassen and J. Lowry, J. Mol. Spectrosc., 1977, 66, 465; D. V. Brumbaugh and K. K. Innes, Chem. Phys., 1981, 59, 413; K. K. Innes, J. Chem. Phys., 1982,76, 2100. R. E. Smalley, L. Wharton, D. H. Levy and D. W. Chandler, J . Chem. Phys., 1978,68,2487. 1982), pp. 264-268. ' G. H. Spencer Jr, P. C . Cross and K. B. Wiberg, J . Chem. Phys., 1961, 35, 1939. * G. E. Ewing, J. Chem. Phys., 1979,71, 3143; G. E. Ewing, J. Chem. Phys., 1980,72, 2096. J. J. F. Ramaekers, L. B. Krijnen, H. J. Lips, J. Langelaar and R. P. H. Rettschnick, to be published. lo J. H. Meijling, R. P. van der Werf and D. A. Wiersma, Chem. Phys. Lett., 1974, 28, 364.

ISSN:0301-7249    

DOI:10.1039/DC9837500183

出版商:RSC    

年代:1983

数据来源: RSC

摘要:

Faraday Discuss. Chem. Soc., 1983, 75, 197-210 Time-dependent Processes in Polyatomic Molecules During and After Intense Infrared Irradiation BY KATHARINA VON PUTTKAMER," HANS-ROLF DUBAL * AND MARTIN QUACK * Institut fur Physikalische Chemie der Universitat Gottingen, Tammannstr. 6, D-3400 Gottingen, West Germany and Institut fur Physikalische Chemie der Universitat Bonn, Wegelerstr. 12, D-5300 Bonn, West Germany Received 23rd December, 1982 The time-dependent processes occurring in polyatomic molecules during and after intense infrared irradiation, for example in infrared photochemistry, are discussed in terms of under- lying structures in the absorption spectra. Origins of homogeneous and inhomogeneous spectral structures are identified in high-resolution spectra of small molecules (CF3H and CF3CCH).Temperature-dependent bandshapes of large polyatomic molecules, (CF3)3CH and (CF,),C-C=CH are evaluated in terms of the most relevant parameters of the vib- rational structures, using a new method. The bandshape parameters can be interpreted in terms of intramolecular vibrational processes on the picosecond and subpicosecond time- scales. Characteristic differences in the dynamic coupling behaviour of the acetylenic CH stretching and the saturated CH stretching vibrations are identified in the fundamental and the overtone spectra. 1. INTRODUCTION The time-dependent intramolecular dynamics of polyatomic molecules during and after irradiation with coherent, intense infrared laser light is of central importance for the understanding of i.r. multiphoton excitation and i.r.photochemistry.'S2 There exist related questions in coherent laser spectro~copy,~*~ electronically excited state dynamics 5*6 and concerning the role of vibrational redistribution in the theory of unimolecular reactions including ion decay and the theory of mass ~pectra.~-l~ There exists also, of course, a close relationship to high-resolution molecular spec- troscopy. Indeed, the theory of i.r. multiphoton excitation can be formulated efficiently and rigorously on the basis of high-resolution spectroscopic structures or " spectroscopic states " of polyatomic molecule^.^^ In the basis of molecular spectroscopic states the time-dependent Schrodinger equation [eqn (l)] takes the form of eqn (2) for the amplitude vector b(t) (where co is the frequency of the light): ih@ = Z v (1) (2) ii(t) = [W + v cos(cot)lii(t). The spectroscopic information needed concerns the elements of the diagonal matrix W, i s .the molecular energy states Ek = hWkV and the coupling matrix V to be derived * Present address of all authors: Laboratoriwn fur Physikalische Chemie der ETH, ETH-Zentrum, CH-8092, Zurich, Switzerland.198 TIME-DEPENDENT PROCESSES IN POLYATOMIC MOLECULES from the transition moment matrix M in the electric dipole approximation (electric field amplitude Ei with z-polarized light) : vk.i = - M k j l E i l / h * (3) These quantities are, in principle, available from high-resolution spectroscopy, dis- regarding the difficulty of obtaining the phase information for the Vkj. The dynamics of molecules under irradiation can thus be specified as a function of the structure of the spectrum in a general sense, namely in terms of the solution of eqn (2), or generally by the U-matrix satisfying the same equation: b(t) = U(t)b(O) Q(t) = u+Q(o)U (6) P(t) = UP(0)Uf.(7) The last two equations concern the time evolution for the representative matrix (operator) Q of any observable and for the statistical matrix P. Three time ranges should be distinguished : (i) Molecules before irradiation are often characterized by a thermal ensemble (diagonal density matrix). (ii) During irradiation one has a time evolution according to eqn (7). Strictly speaking, the molecular state is not defined separately from the electromagnetic field, but we can consider the state immediately after irradiation at various times t in order to avoid this problem.(iii) During a longer period after irradiation one has time-dependent phenomena, possibly relax- ation, governed by eqn (4) with the diagonal part W of the Hamiltonian only. This time evolution depends upon the structure of W and the initial state created after irradiation. In considering the time evolution, one may stress either the second or third period. Furthermore, one may either consider the time evolution of the wave- function or of some observable (for instance the expectation value of the dipole moment in an optical coherent experiment). The main question in i.r. multiphoton excitation would be the deposition of energy by irradiation. In this last case the spectroscopic information about W and V is sufficient, whereas in the former cases one needs some knowledge about the wavefunction of the spectroscopic states.Further, simpler equations for the time evolution can be derived under certain conditions if only coarse-grained information is required, for instance concerning the population vector p of molecular energy “ levels,” which contain many close-lying states: 2~15 p = Kp. (8) The rate-coefficient matrix in this statistical equation depends upon the structure of W and V (also including a non-trivial dependence upon E,, or upon the radiation intensity I K IE01’). In such an approach the individual line positions and strengths are not by themselves important and would, in fact, be too numerous to be considered in a large polyatomic molecule.Indeed, one needs to know only the coarse shape, the intensity of rovibrational absorption and certain properties of the fine distribution of line densities and tran- sition moments within this absorption, including selection rules determining the “ homogeneous ” or “ inhomogeneous ” nature of the structure (see below). This spectroscopic information is required as a function of molecular excitation. Further- more, a systematic understanding in terms of molecular structure would be desirable.K. VON PUTTKAMER, H-R. DUBAL AND M. QUACK 199 It turns out that there is a lack of such knowledge, particularly for large poly- atomic molecules. Our investigations of the infrared spectra of a number of model systems aim at filling this gap. We report here some results of systematic studies of the CH-chromophore l6 in the series of molecules CF3H, CF3CCH, (CF3)3CH and (CF3)3C-C-CH. The spectrum of the isolated parallel CH-stretching band in these symmetric tops having a heavy frame should be characterized by a sharp Q-branch, which is well separated from the P- and R-branches.Vibrational coarse and fine structure is thus immediately visible in the Q-branch region, which together with the high isotopic purity was one reason for selecting these molecules. Furthermore one has two pairs of saturated and unsaturated compounds, each with a “ small” and a “large” molecule. Characteristic differences in the dynamic behaviour will appear because of the different local environment of the CH-chromophore and because of the different sizes of the frame (in terms of the background density of states).Certain similarities between resolvable fine structures in the small molecules and expected, but unresolved fine structures in the large molecules help the interpretation of the latter. The systematic understanding of the rovibrational spectra of large molecules is a non- trivial problem, and we shall discuss a number of helpful concepts and novel methods for the evaluation of such spectra in terms of quantities relevant to time-dependent intramolecular processes and i.r. multiphoton excitation. The presentation of our results will be conceptual and exemplary rather than exhaustive. 2. HOMOGENEOUS AND INHOMOGENEOUS ROVIBRATIONAL ABSORPTION STRUCTURES As will be seen below, vibrational band structures in vapour spectra of polyatomic molecules are broad owing to the superposition of many vibrational bands with slightly different band centres.(The discussion of rotation is straightforward and is omitted for brevity.) One must distinguish two origins of vibrational crowding : (i) Homogeneous structure arises from the fact that one lower molecular energy state can be coupled with substantial line strength to several close lying upper states. (ii) Inhomogeneous structure arises from the fact that several thermally populated states give rise to vibrational absorption at slightly different frequencies. In terms of the theory of i.r. multiphoton excitation a dense, homogeneous structure corresponds to a linear intensity dependence of the optical pumping rates [case B of ref.(15)], a dense inhomogeneous structure to a non-linear intensity dependence of effective rates [case C of ref. (15)], whereas a combination of a wide homogeneous structure with a dense inhomogeneous structure gives rise to an intensity-dependent transition between non-linear and linear d e p e n d e n ~ e . ’ ~ ~ ~ ~ The two kinds of structure also give rise to different decay behaviour after coherent pumping. In the discussion of the origin of these structures we shall use the following not- ation for vibrational transitions: S(n,m) B(k,l) C(j,j) .. A capital letter (or digit) indicates a vibrational zero-order mode such as CH-stretch- ing (S), CH-bending (B), chain bending (C) in the acetylenes and other framevibrations. The number in the left-hand side of the parentheses gives the number of quanta in the upper state of the transition, the other one the number of quanta in the lower state of the transition.In a strictly separable, harmonic approximation there is only one allowed transition involving the CH- States will be denoted by S(n) B(m) etc.200 TIME-DEPENDENT PROCESSES IN POLYATOMIC MOLECULES vibration from each initial vibrational state, occurring at exactly the same frequency for all n, j and m: S(n + 1,n) B(m,m) C(j,j) * a . In reality one has additional absorption frequencies fur several different reasons. (i) Homogeneous structure arises by resonance interaction of the state S(n) B(m) C(k) with the close-lying states S(n - 1) B(1) C ( j ) [for example Fermi resonances be- tween S(n - 1) B(m + 2) and S(n) B(m) et~.].This structure also occurs in spectra at 0 K, although the mechanism operates at all T. Fig. 1 illustrates the high density p(E) E/cm - Fig. 1. Density of vibrational states p for CFJCCH {lowest curve) (CF3XCH (middle curve), and (CF,),C-CrCH (upper curve) evaluated in the harmonic approximation by direct count.'* For (CF,),CH the frequencies used were mostly from the recent work of Burger and P a ~ e l k e , ~ ~ including the value of 66 cm-' for the torsion, measured by Burger (personal communication). The changes as compared to our previous calculations with estimated frequencies are rninor.l6 (1 cm-I = 11.962 J mol-'). of vibrational overtone and combination states, which could give an extremely dense vibrational spectrum for large molecules if a substantial fraction of the states could interact resonantly.Whether this occurs or not depends also upon the couplings. If only the transition S(1,O) carries oscillator strength, simple models for the coupling with background states result in a Lorentzian envelope for the absorption. As is well known from the theory of electronic relaxation the width r (f.w.h.m.) corresponds to an initial decay time T~ after Iocal coherent, pulsed excitation:19 To = hl2nT. (9) The high density of vibrational states aIso results in a rather high degree of thermal vibrational excitation. In fig. 2 we illustrate for (CF,),C-CrCH the thermalK. VON PUTTKAMER, H-R. DUBAL AND M. QUACK 20 1 vibrational energy distributions for the temperature range investigated in our experi- ments: P(E)dE = p(E)exp( -E/kT)dE p(E)exp( -E/kT)dE .(10) K )-l Average thermal vibrational energies at the three temperatures are ca. 1200 cm-' (220 K), 2300 cm-' (300 K) and 6600 cm-l (540 K) with correspondingly high den- sities of states at these energies (see fig. 1). This high vibrational excitation allows for additional mechanisms (ii) and (iii) providing crowded vibrational band structures. 1 .O 0.8 0.6 0.A 0.2 0.0 u 5 000 1000 Elcm-' Fig. 2. Thermal vibrational energy distributions for (CF3),C-C~CH at three temperatures as indicated. (ii) Homogeneous structure can arise from sum and difference transitions with low- frequency modes or complicated combinations, starting from an excited vibrational state. For example all the following transitions a--ise from the same initial state.They create dense homogeneous structure, if the frequency of C is low and if C and D have similar frequency (see also fig. 4 below): S(n + 1 9 4 C(m,m) D(Z,Z) S(n + 1,n) C(m + 1,m) D(U) S(n + 1,n) C(m - 1,m) D(Z,Z) S(n + 1,n) C(m + 1,m) D(Z - 1,l) S(n + 1,n) C(m - 1,m) D(Z + 1,Z). Obviously, many of the more complicated combinations are expected to have little strength. (iii) Inhomogeneous structure arises from the anharmonic shifts of complicated sequence transitions S(1,O) B(n,n) C(m,m) - * with respect to the " cold " transition S(1,O). If the anharmonic constants in the low-order term formula, eqn (ll), are known, one can calculate the corresponding inhomogeneous vibrational spectrum : However, they can be resonantly enhanced by appropriate couplings. We have performed such a calculation for a model set of constants in the molecule (CF,),C-CeC-H and the result for the broad Vibrational bandshape (disregarding rotation) is shown in fig.3 as a function of temperature. This temperature-dependent202 TIME-DEPENDENT PROCESSES IN POLYATOMIC MOLECULES v"- Fig. 3. Inhomogeneous vibrational model spectrum (without rotational structure) as a function of temperature (200-800 K as indicated). The model parameters correspond closely to values estimated for (CF3),C-CrCH, including the known value for the large CH stretching-bending anharmonic constant, which creates the " hot band " to the low-frequency side. behaviour and the fact that the width of such an inhomogeneous structure is propor- tional to An in S(n + An,n) will be used below.3. EXPERIMENTAL CF3H and CF3CCH were obtained commercially and showed no sizeable impurities in the gas chromatogram. (CF3)3CH and (CF3),C-CrCH were synthesized using perfluoro- isobutene as starting material as described elsewhere.16*20-22 They were purified by gas chromatography. The identity of the substances was in all cases obvious from the i.r. or n.m.r. spectra and from the physical properties. For band-strength measurements the substances were thoroughly degassed by freeze-pump-thaw cycles. In some runs using long absorption paths some water from the cell walls appeared in the spectra as an impurity; this did not perturb the interpretation and was in fact helpful for calibration purposes. The spectra were run on our BOMEM DA002 interferometric Fourier-transform infrared spectrometer system (evacuated), allowing for a maximum apodized resolution of 0.004 cm- ', although most of the spectra were obtained at lower resolution.The absolute wavenumber accuracy is mainly limited by the availability of suitable calibration Because of the nature of interferometric measurements by reference to the He-Ne laser wavelength, an ideally aligned system would give accurate wavenumbers and we have found that uncalibrated results were generally accurate to within the resolution used. This is not the maximum accuracy that could be achieved, but it is largely sufficient for the present purpose. Glass and stainless-steel sample cells of 9-20 cm length were used, fitted with KBr, sapphire or quartz windows.Spectra at low temperatures were measured in a cell of our own design, which could be cooled by flowing gaseous nitrogen to ca. 100 K at most, the actual limitation being rather the vapour pressure of the sample. Spectra at high temperatures (up to 550 K) were measured in a heatable cell (SPECAC). Temperatures were measured with copper- constantan thermocouples and were checked internally by measuring rotational line strengths of CO. Weak absorptions were measured using a variable-path cell, allowing for a maximumK. VON PUTTKAMER, H-R. DUBAL AND M, QUACK 203 length of ca. 22 m. Pressure broadening in the spectra was thus important only in the range of the second and third overtones (8000-13 OOO cm-l). 4. RESULTS 4.1. RESOLVED HOMOGENEOUS " COLD " STRUCTURE As an example of a resolved homogeneous structure we quote here briefly the classic example of CF3H, which was first investigated at high resolution in the overtone region by Bernstein and Her~berg,*~ and which we have reinvestigated recently, including the highly perturbed fundamental.The most prominent perturbation is a Fermi resonance between the CH-stretching and bending vibrational states S(n) B(0) and S(n - 1) B(2) with coupling matrix elements of the order of 70-100 cm-' for the whole range from the fundamental up to S(4). This corresponds to an oscillatory time evolution with periods of the order of 0.1 ps after hypothetical, ultra-short, pulsed excitation. This Fermi-resonance system occurs in a similar way for other saturated systems, C, F, H, and is discussed in connection with (CF,),CH below.The high-resolution results for CF3H (the spectra show rotational fine structure through- out) will be discussed in detail elsewhere.26 4.2. RESOLVED HOMOGENEOUS " HOT-BAND " STRUCTURE Fig. 4 shows a survey spectrum of CF3CCH in the region from the fundamental of the CH-stretching vibration to its first overtone. One observes weak, but by no means negligible, sum and difference transitions of the CHI-stretching fundamental (vl,S), the CH-bending fundamental (u,,B) and the C-C-C chain bending funda- mental (vlo,C). This is homogeneous structure of the second kind discussed in sec- c - 3000 Fig. 4. Survey spectrum of CF,CCH, 19.5 rn, 12 Torr. The crowded fine line structure is due to water (see text also).204 TIME-DEPENDENT PROCESSES IN POLYATOMIC MOLECULES tion 2.Let us consider as an example a transition starting from C(1). (See also fig. 5 later for a resolved presentation of the hot band sequences.) Then we have the following transitions, occurring about at the frequencies marked by yl, v1 + vIo and yr - vlo in fig. 4: S(1?0> C(1 Y 1) S(1,O) C(2,1) S(1,O) C(0J). The situation with the CH-bending vibration is perfectly similar. These transitions are not enhanced by resonance, but still they create an important homogeneous structure surrounding the main transition. A coherent, broad-band (short-time) excitation would lead to an oscillatory time evolution with characteristic times in the sub-picosecond range. The homogeneous structures created by off-resonant intra- molecular couplings are also important for narrow-band, stepwise multiphoton excitation, because they create a rich spectrum for near-resonant excitation.27 4.3.RESOLVED INHOMOGENEOUS FINE STRUCTURE Fig. 5(a) shows the spectrum of the CH fundamental region of CF3CCH at higher resolution. One recognizes fine rotational structure in the P- and R-branches, the hot band S(1,O) B(1,l) near 3310.35 cm-', and a very prominent set of hot-band sequences S(1,O) C(O,O), S(1,O) C(1,l) - - - S(1,O) C(n,n) in the Q-branch region, together with some less important hot bands. The assignment can be established via the temperature dependence 28 and via the combination differences : V(S(I,O) C(L1)) = 4S(1,0) CPJN + 4SI1,O) C(1,O)) - V(S(L0)). An important property of the inhomogeneous structure is the increasing coarse width with overtone quantum number v in S(v,O) C(n,n).According to the simple term formula, eqn (1 I), this increase should be linear in u. This is observed in the present case, as illustrated in fig. 5(b) for the band system S(3,U) C(n,n>, where the sequences up to n = 8 are spread out over the whole P-branch of the main transition. Because of the strong selection rule for optical transitions arising in inhomogeneous band structures, the time evolution after irradiation and the energy deposition during irradiation are quite different from excitation in a homogeneous band structure, even if the overall bandshapes look similar. In the statistical limit an inhomogeneous structure leads to eqn (8) with the relaxation dynamics of case C.I5 We may mention here that the unperturbed rotational band structure is also typically dominated by in- homogeneous contributions. 4.4.UNRESOLVED HOMOGENEOUS AND INHOMOGENEOUS STRUCTURE OF VIBRATIONAL CHROMOPHORE TRANSITIONS IN LARGE POLYATOMIC MOLECULES The above short discussions of resolved vibrational and rovibrationa1 fine struc- tures of band systems in " small " polyatomic molecules provide the background for an interpretation of the band structure and the dynamics of chromophore transitions in large polyatomic molecules. Fig. 6(a) shows experimental spectra for the CH- stretching region of (CF3)3C--C=C-H at 226, 300 and 523 K. The spectra show no rotational fine structure at the highest resolution used (0.007 cm-I apodized resolution), although J-structure with an expected spacing of ca.0.047 cm-I in the P and R branches should be easily resohable. Furthermore, the Q-branch is broad,K. VON PUTTKAMER, H-R. DUBAL AND M. QUACK 205 although its rotational structure is expected to be exceedingly narrow, much more narrow than even the 0.06 cm-l width observed for CF3CCH. It is clear that the apparent broadening arises from vibrationally congested structure, which can be of any of the homogeneous or inhomogeneous kinds discussed above. Phenomeno- 331 0 3320 3330 3340 v”/cm-’ 2.0 n % 1 W G CI 1 no 0 .o 9660 9670 968 0 9690 9 7c v”/cm- Fig. 5. (a) Vibrational sequence structure and rotational structure in the high-resolution spectrum of the CH stretching fundamental in CF3CCH ( p = 200 Pa, 1 = 10 cm, room temperature).(b) Sequence structure in the second overtone transition of the CH-stretching vibration in CF3CCH (20 kPa, 15 m, room temperature). logically this vibrational structure can be quite well represented by associating with each rotational line a Lorentzian with a temperature-dependent vibrational width (1.85 cm-l at 226 K to 4.5 cm-’ at 523 K). At the same time the effective band centres are shifted as a function of temperature.206 TIME-DEPENDENT PROCESSES IN POLYATOMIC MOLECULES 3310,O 3320.0 33 30.0 3340.0 Clem- 5.0 4 .O 3 . 0 2.0 1.0 0.0 331 0 3320 3330 3340 3350 v"lcm- Fig. 6. (a) Spectrum of the CH-stretching fundamental in (CF,),C-C=CH at 226, 300 and 523 K (the maxima decrease in that order). (6) Theoretical spectra for the conditions of the experimental spectra, see explanations in the text.It is our goal to analyse this structure in terms of homogeneous and in homogeneous contributions. From fig. 2 it is seen that the thermal vibrational populations are appreciable up to 3000 cm-l at 220 K and up to 12 000 cm-l at 540 K, This corres- ponds to a total number of appreciable vibrational lines in a purely inhomogeneous structure, which is ca. I .2 x lo9 at 220 K and 2.4 x 1019 at 540 K. In spite of these large numbers, the inhomogeneous band structure could be calcdatcd approximatdy if the simple term formula, eqn (1 l), were valid and if the anharmonic constants were known. The band structure in fig. 3 is the resuIt of such a calculation using model assumptions and some known constants.For instance, the sequence S( 1,O) B( 1,l) X(n,n) * * has a very large anharmonic shift and appears near 3309 cm-l, in a similar manner t o CF,CCH [see fig. 5(a)]. This the only sequence shift that can be measured directly. An indirect method allows for identification of the CCC chain-bending fundamental near 120 cm-l: fils( 1,O) C(n,n) X(m,m)] - c[S( 1,O) C(n - 1 ,n) X(m,m)].K. VON PUTTKAMER, H-R. DUBAL AND M. QUACK 207 The sequence shift for this vibration is found to be of the same order as in CF3CCH (-0.8 cm-*), from the combination differences: ;[S(l,O) C(n + I,n) X(m,rn)] + ~"[S(1,0) C(n - 1,n) X(m,rn)] - c[S(I,O) C(n,n) In these equations the mode X and the quantum numbers n and m are representative of the real, thermally averaged situation in the experimental spectrum.Because the calculated sequence shifts depend upon differences of broad-band maxima, the numbers obtained are rather uncertain. In practice it is not possible to go much beyond a few off-diagonal anharmonic constants by this procedure, one has to rely on very simple term formulae, and in addition the role of homogeneous structure would have to be dealt with. We have therefore developed a general method allowing us to evaluate approximately the temperature-dependent spectra in terms of a few, most relevant, parameters characteriz- ing the vibrational structure. The temperature-dependent absorption cross-section a(T,v) of a thermal ensemble is given by eqn (12) as a sum of the contributions from individual energy states with populations X(m,m)l.p j = exp( - Ej/kT)/Z(T) ( 1 2 4 and cross-sections oJ(v) ~ ( T , V ) = C p j o j ( v ) . i Making use of the density-of-states function, which is a sum of &distributions in a discrete picture : PSE) = 2 w - E,) (1 3) i one has a representation of o(T,v) as a function of s(E,v) with the continuous variable E : co o(T,v) = Z(T)-' a(E,v)p,(E)exp( --E/kT)dE (14) 0 the product o(T,v) Z(T) is thus the Laplace transform of the product a(E,v)p,(E): m, v)Z(T) = = m ( E VIP, (El I. (15) In principle, therefore, the homogeneous spectra a(E,v) = ok(v) at Ek could be re- covered from the temperature-dependent spectra by inverting the Laplace transform : a(E, v)p, ( E ) = 2- [ a( r, V)Z( T ) ] . (16) In practice, this inversion procedure, which would solve the rovibronic problem in one step, does not work unambiguously.W e use the following steps in an approximate treatment for large polyatomic molecules. (i) Rotation and vibration are treated separately, the rotational structure being calculated as a function of temperature in the usual way.29 (ii) The vibrational absorption from each vibrational energy shell is convoluted with this, using a simple, continuous vibrational bandshape function, for instance a Lorentzian. The bandshape is a function of two parameters for the position of the band centre and for the width. For the band centre one form would be208 TIME-DEPENDENT PROCESSES IN POLYATOMIC MOLECULES For the vibrational width one can take similarly: The general forms could be justified theoretically, although other, related functional forms are possible and have been The parameters Go and To are the vibrational band centre and the vibrational width (entirely homogeneous!) at zero vibrational energy or at a vibrational temperature of 0 K.We note that rv(Ev > 0) contains both homogeneous and inhomogeneous contributions due to the finite width AE of the energy shell at E,, containing many [ =pU(EU)AE] vibrational states. (iii) The weighted rovibrational spectra from each vibrational energy shell are added, which corresponds to an evaluation of the coarse-grained vibrational analogue of the integral in eqn (14) by quadrature. Fig. 6(b) shows a fit to the experimental results in fig. 6(a), using To = 0.45 cm-l and a linear approximation to eqn (18) (dE, < 1) with c = 7 x and with ;b = 3330 an-', a = 2 x b = 5 x cm, E, being expressed in cm-l (I CM-' = 11.962 J mol-I).The fit is quite reasonable and a better fit could be achieved using the non-linear form, eqn (18). Unfortunately, because of the smallness of To, this entirely homogeneous contribution remains fairly uncertain. There is, however, definite indication that it is smaller than the corresponding width in (CF,),CH, which was found to be ca. I ern-'.,' This would imply that resonance coupiing to the back- ground states of the frame vibrations is more efficient in the saturated compound than in the acetylene. This can be understood on a simple level for two reasons. First, the important Fermi resonance to the CH-bending overtone is absent in the acetylene. Secondly, the hydrogen during bending motion in the acetylene does not directIy interact with the bulky CF, groups, whereas this interaction should be sizeable in the saturated compound.Further, qualitative confirmation that the vibrational band Table 1. C--H chromophore transitions transition 2705 (2707) 3329.863 3328.1 2.8 2991 (2989) 3 .O 5688 (5678) 23 6557.865 6547.2 5.8 5880 (5877) 11.5 8559 (8543) 16.5 8685.66 9674.5 (5-7) 8680 (8681) 28 11 450d (11 460) d 12 717.19 11 280 (I 1 296) 55 Average room-temperature values. True band centre, however with absolute calibration at best to 0.005 cm-'. Second weak band at 5621 cm-I. Structure not simple. Highly asym- metric. A better fit can be obtained with a model including more interacti~ns.~~ structure in the acetylene is dominated by inhomogeneous structure, whereas in the saturated compound there is a dominant contribution from homogeneous structure, comes from the overtone spectra.For CF,CCH, which is given for comparison, accurate band centres could be determined so far for S(1,U) and S(2,U). All the other data are band maxima at room temperature. Simi- larly, the vibrational widths ry given in the table are effective widths at room temper- Table 1 summarizes the data for CH-chromophore transitions.K . VON PUTTKAMER, H-R. DUBAL AND M. QUACK 209 ature, the rotational structure being already taken into account. There is an almost linear increase of with u from u = 1 to u = 2 for the acetylene, less than linear for u = 3. This latter fact is possibly due to the high asymmetry, which is not yet taken into account in the deconvolution, but possibly there is also an interference narrowing from an increasing homogeneous width. In any case, for the Fermi-resonance polyads in (CF3),CH the width increases much more than linearly with u, and this can only be explained by a very substantial homogeneous contribution to the widths in this case.The table also shows the homogeneous structure created by the specific Fermi resonance of S(n) B(0) with S(n - 1) B(2). The values in parentheses are cal- culated with a very simple model, treating the stretching vibration as a Morse oscillator with C; = 3035 cm-' and x;l = -55 cm-l, and the bending vibration as harmonic with Ci = 1358 cm-', using for the coupling in addition one Fermi-resonance constant ksbb = 71 cm-I throughout.This also fits the intensity distribution. CF3H shows roughly similar behaviour, but with rotational fine structure and a number of further, most interesting rovibrational interactions which are discussed in detail elsewhere.26 An interesting feature in the ladder of Fermi resonances is the switching of zero-order weight (or approximate assignment) at S(4). This is different from the behaviour observed in CHBr, and CHC13.31 It should be mentioned that the band shapes are not as simple as one would expect from simple models invoking one or two optically active states which are coupled to continua, but this point and a number of other results contained in table 1 cannot be discussed in detail here. The main point of the present comparison is the dramatic difference between the acetylene (CF,),C-C_CH and the saturated compound (CF3)3CH.This indicates a much longer lifetime of a time-dependent, hypothetically localized highly excited state of the CH vibration in the acetylene. This difference in behaviour can be related also to the differences in the dynamics already found for CF3CCH and CF3H. 5. CONCLUSIONS The time-dependent processes occurring in polyatomic molecules during and after intense infrared irradiation depend in important ways upon the nature of spectral coarse and fine structures as a function of internal excitation. In the statistical limit, dominant homogeneous structure gives rise to stepwise, resonant multiphoton excitation with a linear intensity dependence [case (B)],15 whereas dominant inhomo- geneous structures gives rise to nonlinear pumping [case (C)].15 The origin of homogeneous and inhomogeneous vibrational structures can be identified in high-resolution spectra of small molecules such as CF3H and CF,CCH.The broad, temperature-dependent spectra of large polyatomic molecules can be interpreted as well in terms of these vibrational contributions to band structures as a function of vibrational excitation. In the case of (CF,),C-C=CH and (CF3),CH significant changes of the average vibrational energy, corresponding to ca. 5 or 6 C0,-laser photons, lead to small but significant changes in the vibrational band structure. The two molecular examples can also be used in an ideal way to demon- strate the important effects of molecular structure upon the dynamics. Both the temperature dependence of the spectra and the structure of the overtone absorptions show that the CH-chromophore in the acetylene is less well coupled by resonance interaction to the vibrational background states than it is in the saturated compound.In both compounds the total vibrational widths for the fundamental transition at low temperatures are fairly small, proving that decay times of locally excited CH- vibrational states are certainly larger than ca. 3 ps, which would be accessible to direct, time-resolved meas~rements.~ Extrapolation of the homogeneous width to zero2 10 TIME-DEPENDENT PROCESSES IN POLYATOMIC MOLECULES vibrational energy of the absorbing state indicates in fact that such lifetimes for an ensemble at 0 K would probably be ca. 5 ps for (CF3),CH and 10 ps or possibly more for (CF,),C-CzCH.Further experiments such as i.r. spectroscopy at very low temperatures in matrices and beams, time-resolved double-resonance spectroscopy and coherent laser spectroscopy in the picosecond domain will be able to establish these times more accurately. Although the decay times correspond to ca. 500-1000 classical periods of vibration, indicating localization of vibrational energy on this short, vibrational timescale, the times are much shorter than the typical nanosecond timescales for optical excitation in i.r. photochemistry, thus indicating delocalization on this latter time-scale in agreement with a large body of other experimental and theoretical evidence.' * 2 We are particularly indebted to R.Mews and A. Waterfeld for support during the synthesis of (CF,),CH and (CF,),C-CECH. Generous support of our work by J. Troe, the Fonds der Chemischen Industrie, and the Deutsche Forschungsgemein- shaft (SFB 93, Photochemie mit Lasern) is also gratefully acknowledged. We furthermore enjoyed help from and discussions with H. Burger, Chr. Mayer, G. Seyfang, E. Sutcliffe and H. J. Thone during the course of this work. M. N. R. Ashfold and G. Hancock, in Gas Kinetics and Energy Transfer, ed. P. G. Ashmore and R. G. Donovan (The Chemical Society, London, 1981), vol. 4. M. Quack, Adv. Chem. Phys., 1982,50, 395. A. H. Zewail, Ace. Chem. Res., 1980,13, 360. J. P. Maier, A. Seilmeier, A. Laubereau and W. Kaiser, Chem. Phys.Lett., 1977, 46, 527. C. S. Parmenter, J. Phys. Chem., 1982, 86, 1735. S. A. Rice, in Excited States, ed. E. C. Lim (Academic Press, New York, 1975). R. A. Marcus and 0. K. Rice, J. Phys. Colloid Chem., 1951,55, 894. H. M. Rosenstock, M. B. Wallenstein, A. L. Wahrhaftig and H. Eyring, Proc. Natl. Acad. Sci. USA, 1952,38, 667. J. Troe, in Physical Chemistry, An Advanced Treatise, ed. W. Jost (Academic Press, New York, 1975), vol. 6B, p. 835. lo B. D. Cannon and F. F. Crim, J. Chem. Phys., 1981,75, 1752. l1 D. W. Chandler, W. E. Farneth and R. N. Zare, J. Chem. Phys., 1982, to be published. l2 M. Quack, Nuovo Cimento, 1981,38, 358. l3 E. J. Heller, E. B. Stechel and M. J. Davis, J. Chem. Phjrs., 1980, 73, 4720. l4 M. Quack and J. Troe, Znt. Rev. Phys. Chem., 1981,1, 97. l5 M. Quack, J. Chem. Phys., 1978,69, 1282. l6 H. R. Diibal and M. Quack, Chem. Phys. Lett., 1980, '72, 342. l7 M. Quack, Ber. Bunsenges. Phys. Chem., 1981, 85, 318. l8 T. Beyer and D. F. Swinehart, Commun. ACM, 1973, 16, 379. l9 M. Bixon and J. Jortner, J. Chem. Phys., 1968, 48, 715. 2o H. R. Diibal and M. Quack, J . Chem. SOC., Faraday Trans. 2, 1982,78, 1489. 21 K. v. Puttkamer, H. R. Diibal and M. Quack, to be published. 22 E. P. Mochalina, L. Dyatkin, I. V. Galakhov and I. L. Knunyants, Dokl. Akad. Nauk SSSR, 1966, 169, 1346; L. L. Gervits, K. N. Makarov, Yu. A. Cheburkov and I. L. Knunyants, J . Fluor. Chem., 1977, 9, 45. 23 H. Burger and G. Pawekle, Spectrochim. Acta, Part A, 1979, 35, 565. 24 A. R. H. Cole, Tables of Wavenumbers (Pergamon Press, Oxford, 1977). 25 H. J. Bernstein and G. Herzberg, J. Chem. Phys., 1948, 16, 30. 26 H. R. Diibal and M. Quack, Chem. Phys. Lett., 1981, 80, 439; and to be published. 27 M. Quack, in Intramolecular Dynamics, ed. J. Jortner and B. Pullman (D. Reidel, Dordrecht, 28 H. R. Diibal and M. Quack, Chem. Phys. Lett., 1982,90, 370. 29 G. Herzberg, Molecular Spectra and Molecular Structure (Van Nostrand, Toronto, 1945 and 1966), vol. I1 and 111; J. M. Hollas, High Resolution Spectroscopy (Butterworths, London, 1982). 30 H. R. Dubal and M. Quack, to be published. 31 J. S. Wong and C. B. Moore, preprint 1981, H. L. Fang, and R. L. Swofford, J. Chem. Phys., 1982), p. 371. 1980,72,6382.

ISSN:0301-7249    

DOI:10.1039/DC9837500197

出版商:RSC    

年代:1983

数据来源: RSC

摘要:

Faraday Discuss, Chem. SOC., 1983, 75, 211-222 Energy Distributions in the CN(X 2E+) Fragment from the Infrared Multiple-photon Dissociation of CF,CN A Comparison between Experimental Results and the Predictions of Statistical Theories BY J. Ross BERESFORD, GRAHAM HANCOCK AND ALEXANDER J. MACROBERT Physical Chemistry Laboratory, Oxford University, Oxford OX1 3 4 2 AND JOSEPH CATANZARITE, GOURI RADHAKRISHNAN, HANNA REISLER AND CURT WITTIG Departments of Chemistry and Electrical Engineering, University of Southern California, Los Angeles, California 90089, U.S.A. Received 20th January, 1983 Rotational and vibrational distributions in CN( X 'Z+) produced in the collisionless infra- red multiple-photon dissociation (MPD) of CF3CN have been measured by laser-induced fluorescence. Both distributions appear Boltzmann, and may be assigned " temperatures '' of Tvib = 2400 f 200 K and Trot = 1200 k 100 K.Phase-space theory (PST) and statis- tical adiabatic-channel theory (SACT) have been used to calculate the CN internal excitations. Both theories predict Boltzmann-like behaviour to within the availableexperimental resolution, with this being more pronounced in calculations using a distribution of CF3CN energies above dissociation threshold (as expected for the case of multiple-photon absorption) than in those using a single excited level of CF3CN. PST consistently predicted similar values of Tvib and Trot, in contrast to the observations. SACT calculations, however, reproduced the experi- mental temperatures using a parameter cc which describes the range of the angular potential between separating fragments and whose value lies in the range 0.5-1.0 A-l.The data are also qualitatively consistent with a simple model which assumes that fragment rotational and translational excitations derive from parent R,T motions in combination with the kinetic energies of those parent vibrations which are converted to product R,T excitations. Thus, statistical theories other than PST can be used to explain the experimental results, and such comparisons offer insight into details of the dissociation process. 1. INTRODUCTION For many years unimolecular decomposition theories have been successfully used to model the kinetic behaviour of gas-phase molecules excited to energies above the dissociation limit by thermal, chemical or photolytic means.'-3 One of the basic assumptions of such theories is that intramolecular energy transfer takes place rapidly amongst the internal degrees of freedom of the excited molecule, so that the rates of unimolecular decomposition can be calculated statistically using assumed properties of the activated complex.Detailed dynamics of the decomposition process (for example, the ways in which the available energy is partitioned amongst the degrees of freedom of the dissociation products) are not considered explicitly in transition-state theories such as R.R.K.M. However, such distributions can be computed using formalisms such as the phase-space 4-10 or adiabatic-channel 11*12 models, both of212 ENERGY DISTRIBUTIONS IN MPD which assume statistical behaviour of internal energy in the parent moIecule, but which contain different assumptions concerning the dynamical constraints associated with the decomposition. In PST, angular-momentum couphg together with the form of the radiaI potential describing the separating fragments are included, whereas in SACT a further constraint on the angular dependence of the potential is included.Experimental tests of these theories clearly need a method of producing excited parent moIecules with statistical distributions of internal energy. This would allow US to study simple bond-fission reactions, in which the reverse process has little or no activation-energy barrier which might affect the dissociation dynamics non-statistically , The technique of i.r. multiple-photon dissociation (MPD) is known to meet this requirement, with evidence for this corning both from experimental observations of a complete lack of any bond-specific dissociation effects and from theoretical models of the multiple-photon absorption process.13 Furthermore, the method has the advan- tage that molecules are prepared under collision-free conditions on the same (ground- state) electronic surface upon which they dissociate.The i.r. MPD method has the disadvantage that the CO, laser typically prepares an ensemble of excited parent molecules, with a range of energies and in a distribution of which only the gross features are known.13 Despite this restriction, studies of the fragments of i.r. MPD can, as we shall show, offer some insight into the behaviour of the excited parent molecule. Energy disposal in the fragments of i.r.MPD has been measured in a number of cmes using molecular-beam methods I4-l7 and laser-induced fluorescence (LIF) 18-31 for product detection. Although the latter technique is restricted to a limited number of diatomic or small polyatomic fragments, the internaLenergy dis- tributions (rotational, vibrational and in some cases electronic) can be characterized in detai1, and translational-energy distributions may also be measured by time-of- flight 1872s*27 or spectral-linewidth 31 measurements. The results obtained for the internal energies show two distinct features. First, rotational and vibrational distri- butions appear Boltzmann-li ke and thus for convenience can be characterized by “ temperatures ”.Secondly, even in instances where there is no significant barrier for the reverse reaction (e.g. the formation of two free radicals), and therefore exit channel effects do not control product distributions, the “ temperatures ” for these two degrees of freedom are markedly different. This study describes comparisons between experiment and theory for the internal- energy distributions in the CN(X 2E+) fragment produced via the i.r. MPD of CF,CN and observed using LIF. The experimental results obtained in two laboratories again show distributions which can be characterized by ‘‘ temperatures ”, with Tvlb % 2000 and Trot = 1200 K. The calculations indicate that Boltzmann like distributions amongst the degrees of freedom of the i.r. MPD fragments is predicted by statistical theories, and that SACT, but not the more extensively used PST, is able to reproduce the differences in vibrational and rotational “ temperatures ”.2. EXPERIMENTAL METHODS AND RESULTS CN(X 2E+) product distributions have been measured at U.S.C. and Oxford using similar experimental techniques, details of which have been described p r e v i ~ u s I y . ~ ~ * ~ ~ Low-pressure CF,CN vapour was dissociated under collision-free conditions using the pulsed output from a C 0 2 laser, and the nascent rotational and vibrational distri- butions of the CN fragment were determined by LIF of the B %+-X 2C+ system. The major experimental difference in the two laboratoties was in the type of CO, laser used, At U.S.C. this was a conventional multimode TEA laser (Lurnonics 103)operating on the (001)-(020)P14 transition at 1052 cm-'.The 0.8 .I output was focused to a spot of approximately constant fluence (ca. 102 J cm-2) over an area of ca. 0.5 mm2, At Oxford, a single-mode " tailored " pulse was used 33 with 10 ns rise and fall times and constant power during the 200 ns pulse length. The output from this arrangement [35 mJ, (001)-(100)P20, 944 cm-'1 was brought to a Gaussian shaped spot of area 0.3 mm2 at the e-l points, resulting in an " average fluence" Over this area of 7 J cm-2. With the tailored-pulse system, measurements were restricted to the (0,O) and (1,l) band regions of the B-X system, resulting in rotational distributions for u = 0 and an estimate of the ratio of the vibrational populations in u = 0 and 1 .More extensive measurements at U.S.C. enabled rotational distributions within v = 0, 1 and 2, together with relative vibrational level populations for u = 0, 1,2 and 3, to be determined. Where the two sets of results overlap, agreement is good. Fig. 1 0 200 400 600 800 1000 J ( J + 1) Fig, 1. Plots of the relative populations in the rotational €eveIs, J , of CN(X %*, u = 0) produced in the collision-free i.r. MPD of CF&N as a function ofJ(J + 1). A straight-line plot would be obtained for a Boltzmann distribution. Data were taken from experiments with the 200 ns " tailored " pulse (0) and the 200 ns multimode pulse (a), and show essen- tially the same temperature for the two sets of measurements. The pressure was 3 mTorr, TR = 1240 K. and the delay between the onsets of the two lasers was 1 p s .shows data for the rotational distributions in II = 0, pIotted in such a way that a straight line would be expected for a Boltzmann distribution. It is clear that the distributions from the two experimental arrangements can be represented by the same rotationa1 temperature of ca. 1200 K. Vibrational distributions were also found to be Boltzmann-like and the data are summarised in table 1 . Two comments on the experimental data are in order. First, although the rotational temperatures in the studies are identical, the vibrational temperatures differ. The more substantial body of data obtained with the mdtimode laser is probably more realiable, since in the tailored-pulse studies only the ratio of u = 0 to v = 1 populations could be estimated, using a wavelength region in which the overlap of the (0,O) and (1,l) bands seriously limits the accuracy.Secondly, it may initially appear surprising that the multimode measurements at high fluence (ca. lo2 J cm-2) and the single-mode measurements at lower fluence (7 J ~ m - ~ ) , both using similar (200 ns) pulse widths, give very simiIar214 ENERGY DISTRIBUTIONS IN MPD TQble 1. CN(X %+) energy distributions from the collision-free i.r. MPD of CFKN - multimode pulse, single-mode pulse, degree of freedom 1052 cm-l 944 cm-l rotational 1200& 100" 1240 & 100 vibrational 2400 f 200 ' 1900 f 300 a Rotational temperature was the same for v = 0,l and 2. Estimated from the relative popula- ions of t, = 0,1, 2 and 3.20 Estimated from the relative populations of II = 0 and 1.temperatures, as it is known that the laser intensities, which are very different in the two cases, control the energy available for partitioning into the fragments' degrees of freedom.23p29*34 For 200 ns multimode pulses the rotational temperature in CN is observed to increase with fluence (and hence intensity) up to ca. 20 J cm-2 but remains constant at higher fluences, owing to significant parent-molecule depletion.21 The dissociation yield (which is predominantly fluence dependent) is a steep function of fluence near 7 J cm-2,21 and since the single-mode experiments were carried out with a Gaussian fluence profile the predominant signal will be from those molecules dissoci- ated near the centre of the beam, at fluences of ca.15 J cm-2. Thus a single-mode pulse with a constant fluence of 15 J cm-2 and a multimode pulse of 20 J cm-2 would appear to produce the same CN distributions, indicating that at these fluences either the average intensities are similar for the two pulses of differing temporal behaviour within their 200 ns widths or the effect of intensity is minimal. One should also bear in mind that fluences which are estimated from the laser energy and the spot size are not very accurate for tightly focused geometries. 3. CALCULATIONS Both PST 4-10 and SACT 11*12 assume that a reaction complex A, produced with sufficient internal energy to decompose into fragments B and C , will dissociate with equal probability into each of the accessible product channels, thereby enabling the product-state distributions to be calculated statistically.Intramolecular energy transfer within the reaction complex is assumed sufficiently complete so that all of the available phase space is sampled, yet no transitions between channels occur as the complex dissociates, i.e. the motions are considered adiabatic.35 By accessible (" strongly coupled ") 35 channels is meant those that satisfy the normal conservation laws of energy and angular momentum between reactants and products, together with a constraint which is related to the dynamics of the separating fragments, namely that the reactant total internal energy E exceeds the maximum value of the effective channel potential V , i.e. The form of the channel potential distinguishes PST from SACT, as discussed below.E 2 V,,,. (1) PHASE-SPACE THEORY CALCULATIONS PST assumes that V takes the form W) = K1(r) + B(r)L(L + 1) + E m (2) where V,,(r) is the one-dimensional electronic potential as a function of r, the centre- of-mass separation of the fragments, B(r) is the effective rotational constant for theJ. R. BERESFORD et aI. 215 orbital motion (= h2/2pr2) whose quantum number is L, and Em is the internal energy of the separated products. Ve,(r) was deduced from the attractive part of the Lennard-Jones potential. (3) where Et is the relative translational energy of the separating fragrnents.‘-lo This condition simply requires that for the reverse direction the reactants have sufficient translational energy to surmount the centrifugal barrier to association.Fig. 2A illustrates the restrictions on the available phase space for the case of a parent moIecuIe (total angular momentum J,) dissociating into an atom and a linear molecule (angular- momentum J), showing the limiting value of the orbital angular-momentum quantum number L,, (which depends upon Et and hence upon J ) and the constraints imposed by conservation of angular momentum (L + J = Jo). For more complex cases the geometric interpretation is more laborious, but the principles and trends remain. the same. Energy distributions in CN were calculated by methods similar to those of ref. (8) and (9) using vibrational and rotational constants for CF3CN,36*37 CF, j8 and CN 39 from the literature, and C6 = 80 x 10-60erg c d . * Parent angular momentum (Jo) and disposable energy appearing in the degrees of freedom of the fragments (ES) were varied.produced by i.r. MPD, CN energies were calculated for the Gaussian function Eqn (I) and (2) reduce to the condition L(L + 1)h2 < 6pCtt3(E,/2>2i3 In an attempt to mimic the distribution of exp [ - ( I 3 - {E~})Z/2S2]dE~ (4) 1/2n 6 1 P(E1)dEt - where ( E l } is the average value of EZ, and S is the width of the distribution. Three such Gaussian distributions were used, with the foIlowing parameters: {Ex> = 10 000, 13 000 and 18 000 crnmf, and S = 4720 crn-l. The results are illustrated in fig. 2 and 3, and can be summarised as follows: (i) Rotational and vibrational populations at fixed Et show distributions which are well represented (within the resolution of the experimental observations) by Boltzmann ‘‘ temperatures.” (ii) Both vibrational and rotational temperatures show only a weak dependence upon the parent angular momentum Jo.(iii) For a given value of Et, vibrational and rotational temperatures are very similar, and such similarity is retained when using the P(E#) distribution. This is in striking contrast to the experimental observations. STATISTICAL ADIABATIC-CHANNEL-THEORY CALCULATIONS The form of the effective potential V(r) that is used in PST takes no account of any potential-energy barriers to dissociation that arise due to angular interactions of the separating fragments, and the statistical adiabatic-channel theory of Quack and Troe 11~12 attempts to rectify this by considering a different form of V(r).Since little is known of the details of potential-energy surfaces for poIyatomic moIecuIes, a simple interpolation procedure is used : w> = M-) + Eu(d &(p> = [E,(r,) - E,&xp[--a(r - re)] + E,, + B ( ~ ) P ( P + 1) (5) (6) (71 For a given dissociation channel a, &(re) is the parent internal energy at its bound equilibrium geometry [excluding the contribution B(r,)Jo(Jo + 1) which is added P = L + (Jo - L)exp[-a(r - re]. * C, was estimated using a Lennard-Jones potential. See also ref. (l), p. 134.60 50 40 30 20 10 0 L (A) L +J=J, L ma*a(E-E; - BJ (J* 1)) '1 3 for r - 6 attraction - 0 10 20 30 40 50 J E ,,(CN) := BJlJ -1- 1)/103 cm-l Fig. 2. Calculations indicating the effect of parent total angular momentum, Jo, on product V,R excitations.(A) shows the constraint imposed on the available product phase space by the conservation of angular momentum, for the case when the products are an atom and a linear molecule (see text for details), The shaded area indicates the allowed states for the case So = 10 and the dashed lines indicate the analogous region for the case Jo = 30. Clearly, low JO restricts the number of available product states. For more complex cases (e.g. CF3CN+CF3 + CN, JL -t J2 -I- L == Jo), the geometric interpretation is more laborious, but the principles and trends re- main intact. (B) shows the results of phase-space calculations of the CN rotational excitation (v = 0) which derives from the unirno- lecular reaction of CF,CN, for a fixed amount of disposable energy (18 000 crn-l) and different values of Jo.The curves are offset from one another for convenience and the " temperatures " associated with the curves are taken from the straight portions. (a) Jo = 70,3400 K; (b) Jo = 50,3430 K; (c) Jo = 30, 3450 K; ( d ) Jo = 10,3470 K. The trend suggested by (A) can be seen in the slowly changing slopes of the straight-line portions, and the results depend weakly on Jo. (C) shows the results of similar calculations for CN vibrational excitation. Energy is mcasured relative to the zero-point vibrational energy and, as with (B), the trend suggested by (A) is manifest in the calculations. 0, lo = 70, 3060 K; @, Jo = 50, 3110 K; 0, Jo = 30, 3140 K; I, Jo = 10, 3160 K.J. R. BERESFORD et al. 217 separately], E,, is the channel energy of the products in their specific quantum states, B(r) and L are, as in PST, the effective rotational constant for orbital motion and the orbital quantum number.Eqn (6) and (7) show that &(Y) interpolates smoothly t n c c) ._ ErO1(CN) = BJ(J + 1)/103 m-' E,(CN)/103 cm-' Fig. 3. Calculations of CN product vibrational and rotational distributions for different values of disposable energy, EZ, using single values as well as distributions over E*. (C) and (D) show rotational and vibrational distributions, respectively, for single values of ES [(a) and 0 , 1 8 000; (6) and 0 , 1 3 000; ( c ) and 0 , l O 000 cm-'1 and .lo = 30. The curves are offset from one another for convenience and the associated " temperatures " are taken from the straight-line portions. (A) and (B) show CN product rotational and vibrational distri- butions for cases where a distribution of E3 values is considered.The distribution function is a symmetric Gaussian whose width is 4720 cm-l for ( E s ) = 18 000 [(a) and 01, 13 000 [(b) and 01 and 10 000 cm-' [(c) and 01 and Es intervals of 944 cm-l are used (see text for details). Since the Gaussian is symmetric, ( E s ) = ELax. between limiting values at r = Y, and co. This exponential form of the potential reproduces that calculated for dissociation of a triatomic when effects of hindered rotation upon the barrier height are included,35 and this is used to justify its extension to polyatomic molecules, the value of cc thus being loosely related to the range of the angular potential of the separating fragments.It can be seen that PST is a special case of the morc general SACT by putting o! = co in eqn (6) and (7). In the present calculations, o! has been used as an adjustable parameter, and its magnitude in com- parison with that used in previous applications of the theory 1132p35*40 will be discussed later. The molecular constants used were the same as those for PST, with the excep- tion of the form of the electronic potential which was taken as a Morse function, Vel(r> = De(1 - exp[-p(r - re>II2* (8)218 ENERGY DISTRIBUTIONS IN MPD /3 can be calculated from the force constant F, of the bond corresponding to the reac- tion coordinate [p = (Fr/2D,)'/2 = 1.84 A-l], but since the Morse curve may not be a suitable representation of the potential for polyatomic molecules, being too flat at large r,iiJ2 p has also been used as an adjustable parameter. Calculations were per- formed as a function of Et, Jo and p for three values of 01, namely 0.5, 1 .O and 1.5 A-1.Details of the channel-counting procedures, similar to those described in the original formulation of the theory,L1,12 are given el~ewhere.~' Fig. 4. Rotational and vibrational distributions calculated using SACT. In (A) vibrational distributions are plotted for two values of the disposable energy Et corresponding to 10 and 18 photons above the dissociation limit [9440 (0) and 16 992 cm-' (J), respectively], for the highest value of c1 used (1.5 A-'). In (€3) rotational distributions are plotted as a function of J(J + 1) for Ez = 16 992 crn-', with straight lines indicating rotational temperatures.Note the decrease in Trot with decreasing a: a = [7, 1.5; 0, 1.0; ,0.5 A- l. (A) and (B) were both calculated for Jo :-= 44. Comparison of these calculations with those from PST [fig. 3(a) and 3(6)] show that cc = 1.5 A- appears to be close to the high cc limit of SACT. Representative results are shown in fig. 4 and can be summarised as follows: (i) As in PST, for each I 3 the distributions appear Boltzmann-like, but there is noticeable curvature in the rotational distributions at high energies [see fig. 4(b)]. Calculations with a distribution of I 3 values similar to that given for PST tended to remove this and produce a more linear Boltzrnann plot. (ii) Both variations in Jo (in the range 0-70) and p (values of0.84, 1.84 and 2.84 A-') produced <5"/: change in the observed temperatures.The calculations reported below were carried out at J , = 44 and B = 1.84 A-l. (iii) Vibrational distributions showed little change with a, vibrational temperatures and average energies decreasing by ca. 10% as a: decreased from 1.5 to 0.5 Ad'. (iv) At a I= 1.5 A-' and €$ = 16992 cm-l, Tvib and Trot are close in value and to the PST results, as can be seen in fig. 5,where calculations using both theories are presented. (v) Rotational distributions show a marked change with X , as can be seen in fig. 4(b) for Et I- 16 992 cm-I. Fig. 5 shows that when c1 is changed from 1.5 to 1.0 Awl, Trot decreases by 10% at = 16 992 cm-' and 26% at 9440 crn-l.J. R. BERESFORD et al. 219 Between a = 1.0 and 0.5 A-' the changes for these values of ES are more dramatic, with Trot decreasing by factors of 1.8 and 2.2, respectively.For a given a this ratio depends only weakly on Et (for a = 0.5 A-l, Tvib/Trot = 1.8 and 2.1 for a is the only parameter which significantly affects the ratio Tvib/Trot. 3600 320 0 k4 .P 2800 2 8 2400 --- n c.' +I I (d 0 ';= 2 0 0 0 ' z' 2 1600' c.' 5 z' 1200, I3 800 - .O P 0 Fig. 5. Calculated variations of CN product vibrational and rotational " temperatures " with the disposable energy ES for the reaction CF3CN-+CF3 + CN. Temperatures deduced from plots such as those shown in fig. 2 4 are plotted against ES. Circles show vibrational (0) and rotational ( 0 ) temperatures from PST. Squares show vibrational (0) and rotational (W) temperatures from SACT for a = 1.5 A- and triangles show rotational temperatures for SACT with a = 1.0 A-' (A) and 0.5 A-' ( v). As explained in the text, vibrational temperatures from SACT show little variation with a.Et = 16 992 and 9440 cm-l, respectively), and this suggests that distributions of Ez within this range should not affect the ratio unduly. Taking into account the un- certainties in the experimental values of the CN temperatures (table l), we conclude that our data can be reproduced by SACT using a value of a between 0.5 and 1 .O A-l. 4. DISCUSSION It is clear that the PST calculations lead to product V,R excitations which are different from the V,R excitations found experimentally in the CN fragments. Small differences aside, the PST distributions can often be ascribed " temperatures ", in which case T, Tv, no matter how the calculations are done (different Jo, average over Jo, single Et, distribution of ES values etc.).This is in sensible accord with the basic premises of the theory, in which all accessible states are equally probable, and similar results can also be obtained using the computationally simpler formalism of220 ENERGY DISTRIBUTIONS IN MPD Levine et al.,42 albeit with the loss of some rigour. As discussed above, the SACT calculations are capable of a closer match between experiment and theory. The SACT addresses the issue of correlating motions between reagent and products in a conceptually pleasing way, using a single parameter CC, but requires an equilibration between accessible states as the reaction occurs.This is a strong assumption, but makes the calculations tractable. The striking accord between the experimental results and the SACT calculations suggests that the physical picture is quite sensible, regard- less of any possible ambiguity in the assumptions necessary for its development. The value of a that we use to model the experimental results, 0.5-1.0 A-l, should be compared with those used in other SACT calculations. Thermal high-pressure- limit recombination-dissociation rate constants have been calculated for a series of molecules (including NOCl, NO2, 03, H20, CH4 and C2H6), with a = 1 A-l fitting all the experimental data to within a factor of In these cases there is no reason to expect a significant barrier for the reverse reaction.In contrast, translational- energy distributions for bimolecular reactions of halogen atoms with unsaturated hydrocarbons, in which statistical complexes are thought to be formed and significant exit-channel barriers may be present, are reproduced with cc > 1 A-' (e.g. 0: = 2 for F + C,H5Cl, 2-4 A-' for C1 + C2H3Br), although the molecular parameters of the intermediates involved in these cases are only estimated, and their values may affect the calculated distrib~tions.~~ The present experiments involve complexes whose character is far more similar to the former cases than the latter, and the range of values of cc used in the present work agrees well with values used previously. The results also suggest that for the present case, a = 1.5 A-' may be close to the limit where SACT and PST are equivalent.An alternative statement of the present agreement between theory and experiment is that a lack of complete intramolecular energy transfer, resulting in non-statistical behaviour, is not necessary to explain our results. However, an interesting perspective on this problem comes from consideration of the degrees of freedom of the CF3CN parent molecule prepared by i.r. multiple-photon absorption. The 12 vibrations are highly excited, while the rotations and translations are essentially those of the 300 K starting mate~ial.~''~~ Thus, the sample is prepared in such a way that parent excitation is strongly biased in favour of vibration, with much lower rotational excitation. The statistical calculations, on the other hand, equilibrate 15 degrees of freedom (e.g.the PST calculations deal with 6 vibrational and 3 rotational degrees of freedom of CF3, 1 vibrational and 2 rotational degrees of freedom of CN, and 3 degrees of relative trans- lational motion-2 orbital, 1 radial). It is not possible to occupy all of the available product states without energy flowing from the vibrational reservoir into the R,T degrees of freedom of the separated fragments, and in applying PST to the present system we assume implicitly that such energy-transfer processes are rapid on the time scale of the dissociation event. This, in fact, may prove quite presumptuous for an important number of physical and chemical systems. Note that if the parent had sufficient rotational excitation, this motion would correlate to produce R,T excitation, and the need for intramolecular exchange would be reduced accordingly.Thus, the manner in which we prepare the sample allows us to measure the flow of energy from vibrations into product R,T excitations, and this is a rather central issue to the matter of intramolecular reaction dynamics. In comparing our experimental results to the PST calculations, it is clear that there is an important difference, with a marked deficiency in measured product R,T excitations,20p21 relative to those which are computed. It follows that the picture of a " very loose transition state ", with equal occupancy of all states which are allowed by energy and angular-momentum conservation, is not realistic. In this context,J. R. 3ERESFORD et d.221 intramolecular energy transfer is incomplete on the pertinent time scale, which corresponds approximately to the time required for the CN and CF3 species to move from near the equilibrium geometry to some critical configuration (ca. s), despite the statistical nature of the excited parent, and we expect that such behaviour will prove quite common as more detailed experimental results become available. If motion from near the equilibrium geometry to the transition state is so rapid that intramolecular V+R,T transfer is completely inhibited, we can estimate the likely product R,T excitatiom2' First, we take the 5 vibrations which are being converted into product R,T excitations and estimate the nuclear kinetic energies with the simple formula This quantity is then combined with parent R,T excitation (300 K, 620 crn-l) in order to obtain the average amount of product R,T excitation, which can be ascribed a temperature if one so desires. Tn doing this, we find that with Tv = 2400 K (using CN as a vibrational thermometer), we predict TR,T E 1200 K.This is in surprising accord with the experimentally determined values* and suggests that the above considerations have merit. We also note that this procedure is in accord with other similar experimental observations and that it is so conceptually enticing as to inspire further thinking along the same lines. We are particularly indebted to Dr M. Quack for help and guidance on the calculations of product-state distributions via the statistical adiabatic-channel theory. Assistance with computation from K.G. McKendrick and C . G. Atkins is acknowledged. Support for the joint project from the Collaborative Research Grants Programme of NATO (grant no. RG. ISO.Sl> is gratefully acknowledged. W. Forst, Theory of UnimoZecuIar Reactions (Academic Press, New York, 1973). P. J. Robinson and K. A. Holbrook, UnimuIecuZar Reactions (Wiley-Interscience, New York, 1972). For a recent review of unimolecular reactions see M. Quack and J. Troe, Int. Rev. P h p Chem., 1981,1,97. P. Pechukas and J. C. Light, J. Chern. Phys., 1965,42,3281. P. Pechukas, C. Rankin, and J. C. Light, J. Chem. Phys., 1966,44,794. ' J. C. Light, Discuss. Faraday Soc., 1967, 44, 14. ' E. E. Nikitin, Theor. Exp. Chern., 1965, I, 144. C. E. Klots, J. Phys. Chem., 1971,75, 1526.C . E. Klots, 2. Naturfursch., Teil A , 1972, 27, 553. lo J. L. Kinsey, J. Chem. Phys., 1970, 54, 1206. M. Quack and J. Troe, Ber. Bunsenges. Phys. Chern., 1974,18, 240. l2 M. Quack and J. Troe, Ber. Bunsenges. Phys. Chem., 1975, 79, 170. l3 For a recent review see M. N. R. Ashfold and G. Hancock, lnfrured MultQle Photon Excita- tion and Dissociation Reaction Kinetics and Radical Formation, in Gas Kinetics and Energy Transfer, Senior Reporters P. G . Ashmore and R. J. Donovan (Special Publication, RoyaI Society of Chemistry, London, 1982), vol. 4, p, 73. l4 Aa. S. Sudbo, P. A. Schulz, E. R. Grant, Y . R. Shen and Y. T. Lee, J. Chem. Phys., 1979, 70, 91 2. Is Aa. S. Sudbo, P. A. Schulz, Y . R. Shen and Y . T. Lee, J. Chem. Phys., 1978, 69, 2312. l6 Aa. S. Sudbo, P.A. Schulz, E. R. Grant, Y . R. Shen and Y . T . Lee, J. Chem, Phys., 1978,68, l7 P. A. Schulz, Aa. S. Sudbo, E. R. Grant, Y . R. Shen and Y . T. Lee, J. Chem. Phyx, 1980, 72, 1306. 4985. * We also find 2o that TT = 900 K for the CN product, in accord with the above considerations.222 ENERGY DISTRIBUTIONS IN MPD J. D. Campbell, M. H. Yu, M. Mangir and C. Wittig, J , Chem. Phys., 1980, 69, 3854. l9 M. H, Yu, M, R. Levy and C. Wittig, J. Chem. Phys., 1980,72, 3789. 2o H. Reisler, F. Kong, A, M. Renlund and C. Wittig, J. Chem. Phys., 1982, 76, 997. 21 H. Reisler, F. Kong, C. Wittig, J, Stone, E. Thiele and M. F. Goodman, J . Chew. Phys., 1982, 22 M. N. R. Ashfold, G. Hancock, and A. J. Roberts, Faraday Discuss. Chem. Sor., 1979,67,247. 23 M. N. R. Ashfold, G. Hancock and M. L. Hardaker, J , Photochem., 1980, 14, 85. 24 M. L. Lesiecki and W. A. Guillory, J. Chem. Phys., 1977,66,4239; 1978,69,4572. 25 J. C. Stephenson and D. S. King, J. Chem. Phys., 1978,69, 1485. 26 D. S. King and J. C. Stephenson, Chem. Phys. Lett., 1977, 51, 48. 27 J. C, Stephenson, S. E. Bialkowski and D. S. King, J, Chem. Phys., 1980,72, 1161. 28 A. J. Grimley and J. C. Stephenson, J. Chem. Phys., 1981,74,447. 29 C. M. Miller and R. N. Zare, Chem. Phys. Lett., 1980,71, 376. 30 C. M. Miller, J. S. McKillop, and R. N. Zare, J. Chem. Phys., 1982, 76, 2390. 31 R. Schmiedl, U. Meier, and K. H. Welge, Chem. Phys., 1981, 80, 495. 32 M. N. R. Ashfold, G. Hancock, and G. W. Ketley, Furaday Discuss. Chem. Soc., 1979, 67, 204. 33 M. N. R. Ashfold, C. G. Atkins and G. Hancock, Chem. Phys. Lett., 1981, 80, 1. 34 A. M. Renlund, H. Reisler and C. Wittig, Cheni. Phys. Lett., 1981, 78, 40. 35 M. Quack, J. Phys. Chem., 1979,83, 150. 36 W. F. Edgell and R. M. Potter, J . Chem. Phys., 1955,24,80. 37 C. A. Burrus and R. M. Potter, J. Chem. Phys., 1957, 26, 391. 38 The rotational constant (Be) of CF, was calculated from moments of inertia, assuming CF3 to be The vibrational frequencies of CF, were taken from D. E. Milligan and M. E. Constants of 77, 328. a spherical top. Jacox, J. Chem. Phys., 1968,48, 2265. 39 K. P. Huber and G. Hertberg, Molecular Spectra and Molecular Structure ZV. Diatomic Molecules) Van Nostrand, Princeton, 1979). 40 M. Quack, Chem. Phys., 1980,51, 353. 41 J. R. Beresford, Part IZ Thesis (Oxford University, 1982). 42 R. D, Levine and J. L, Kinsey, Information Theoretic Approach: Applicafion to Molecular Collisions, in Atom-Molecule Collision Theory, ed. R. B. Berstein (Plenum Press, New York, 1979). 43 J. B. Halpern, Chem. Phys. Lett., 1979, 67, 284.

ISSN:0301-7249    

DOI:10.1039/DC9837500211

出版商:RSC    

年代:1983

数据来源: RSC

摘要:

Faraduy Discuss. Chem. Suc., 1983, 75, 223-237 Product Energy Partitioning in the Decompositiosn of State-seIectively Excited HOOH and HOOD BY THOMAS R. RIZZO, CARL C . HAYPEN AND F. FLEMING CRIM * Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706, U.S.A. Received 30th December, 1982 Direct excitation of overtone vibrations is a highly selective energy-deposition technique which permits detailed studies of unimolecular reaction dynamics when corn bined with laser- induced fluorescence for state-resolved product detection. AppIying this method to hydrogen peroxide and its partially deu terated analogue (HOOD) provides vibrational overtone excit- ation spectra of the molecules in the region of the u = 6 level of the OH stretching vibration and determines the OH or OD product rotational energy distributions.Partially deuterating HOOH produces a dramatic change in the shape of the pure stretching transition while other features, which apparently involve the deuterated portion of the molecule, move to lower frequencies. The decomposition products are formed in rotational states up to the limit of the available energy but have a markedly non-thermal distribution, with the populations decreasing sharply at high rotational levels. Detecting the OD fragment following excitation of the OH stretching transition in the parent molecule reveals an energy disposal pattern which is similar to that in the undeuterated case. 1. TNTRODUCTION An important part of a General Discussion on intrarnoIecuIar kinetics is a con- sideration of unimolecular reactions since it is through reactions that intramolecular processes affect chemical systems.Careful study of the dynamics of unimolecular reactions, particularly the rates and partitioning of energy in the products, may provide a unique view of several aspects of the intramolecular processes themselves. Some of the questions that may be addressed experimentally are: Do the product-states from unirnolecular reactions reflect a statistical redistribution of energy in the excited molecule? Do they retain any memory of the excitation site of the parent molecule? Do either the product-state distributions or the unimolecular decay rates show any mode or site specificity ? Time- and state-resolved experiments which expIore the details of the decay dynamics are necessary to answer these questions and to test carefully theories of unimolecular decomposition.Experimental approaches to studying unimolecular reactions differ widely in the manner and specificity of the reactant excitation as well as in the means of product detection. Among the various excitation techniques are chemical activation both in bulk and in molecular beams,2 infrared multiphoton exci tat internal conversion following electronic ex~itation,~ and overtone vibration excitati0n.6~~ The latter technique is a particularly specific means of reactant preparation in that a precise energy increment can be introduced into a single vibrational mode of the molecule, Product detection techniques include mass-spectrometric or gas-chromatographic Alfred P.Sloan Research FelIow and Camille and Henry Dreyfus Teacher-Scholar.224 DECOMPOSITION OF STATE-SELECTED HOOH AND HaOD analysis of final products in bulk experirnents,'e6 angularly resolved mass- spectrometric detection in beam experiments,2 product absorption or chemilumines- cence- and time-resolved laser-induced fluorescence (LIF) detection of nascent frag- m e n t ~ . ~ This Iast technique is one of the most attractive in that it offers the possibility of both time- and state-resolved detection of the mimolecular reaction products. We have combined the site and energy specificity of overtone vibration excitation, with state-selective detection by laser-induced fluorescence, to perform time- and state- resolved studies of unimolecular reactions.A previous report described our first experimenta1 results on t-butylhydroperoxide, and most recently we have used this technique to determine product energy partitioning in the unimolecular reactions of hydrogen peroxide (H001-I) and its partially deuterated analogue (HOOD). We deposit energy in excess of the 0-0 bond strength in the molecule by exciting the v = 6 overtone vibration of the OH stretch and perform time- and state-resolved detection of the 0 H(OD) fragments using laser-ind uced fluorescence. Hydrogen peroxide is an interesting molecde for these studies of unimolecular reactions. From a theoretical point of view, the small size and relative simplicity of HOQH make it a suitable candidate for calculations of ab initio potential-energy surfaces for dynamical studies.From an experimental point of view, the 49.6 kcal rno1-I barrier l o for dissociation at the 0-0 bond in HOOH is low enough to permit overtone vibration induced dissociation, and the dissociation products are two OH fragments whose spectroscopy is well characterized." Excitation of u = 6 of the OH stretching overtone vibration in HOOH adds 54.2 kcal rno1-I of energy to the initial thermal energy of the molecule. This gives it ca. 4.5-6 kcal mol-' more energy than required to break the 0--0 bond. The excess energy must appear as translation and rotation of the resulting OH fragments since there is insufficient energy to produce OH molecules in the first vibrational state. Exciting the OH fragments from a particular level in the X2n state to thcA 'C+ state and monitoring the total fluorescence produces a signal proportional to the number of OH moIeeuIes formed in a single quantum level.There are three configurations of the experiment which each yield different types of information. In the first the excitation laser is set on the OH vibrational overtone frequency of the peroxide with the probe laser tuned to a particular transition of the OH fragment and the delay between the excitation and probe laser pulses is varied. In this way, the LIF intensity maps out the temporal evolution of the density of particular states of OH fragments formed in the reaction. If the unimolecular decay lifetime can be resolved in the experiment, a fit of the data provides a direct measure of that lifetime. For HOOH and HOOD the unimolecular decay is too fast to resolve on a nanosecond timescale; however, the temporal evolution of tle OH fluorescence provides useful information on the quenching and loss of the decom- position fragments.In the second type of experiment, the pump wavelength is scanned with the probe wavelength tuned to a particular OH transition and the delay time fixed so as to obtain an excitation spectrum of the OH vibrational overtone for those molecules which decompose. Finally, fixing the pump laser wavelength and delay time and scanning the probe wavelength over a series of OH levels measures the relative populations of the product quantum states resulting from the overtone- vibration-induced unimolecular reaction. Measurements on the partially deuterated peroxide, HOOD, using this technique can probe the fragment from the end of the molecole not associated with the vibrational overtone excitation, since OD is spec- troscopically distinguishable from OH.Fig. 1 shows an energy diagram for the experiment.T. R. RIZZO, C. C. HAYDEN AND F. F. CRIM 160 140 I30 60 50 - 40 - 30- 20- 10 - 0- 'JOH STRETCH 7- 511 'i 2 55 000 50 000 45 000 20 000 15 000 1 225 Fig. 1. Energy-level diagram for the overtone-vibration-induced decomposition of hydrogen peroxide. One pulsed laser excites HOOH molecules to t' = 6 of the OH stretching vibr- ation and a subsequent pulse from another laser interrogates the OH fragments by laser- induced fluorescence. The 5280 8, excitation photon adds 54.2 kcal mol-' over the initial thermal energy of the HOOH.2. EXPERIMENTAL The experimental apparatus is similar to that used in our previous mea~urements.~ A 6 ns pulse from a Nd : YAG-laser-pumped dye laser (Quanta Ray) having a bandwidth of ca. 0.3 cm-' excites u = 6 of the OH vibration of HOOH(D). Operating the dye laser with Coumarin 500 dye provides 10-15 mJ of pulse energy at the peak wavelength of the ZJ = 6 overtone vibration (5280 A). The 10 ns pulse from a frequency-doubled nitrogen-laser- pumped dye Iaser l2 (bandwidth ca. 0.1 cm- in the visible) counter-propagates collinearIy with the excitation beam through the room temperature Pyrex reaction cell and probes the fragments of the overtone-vibration-induced decomposition via LIF. A neutral density filter attenuates the probe beam to ca. 1 pJ in order to prevent saturation of the OH transitions.The OH fluorescence perpendicular to the beam axis passes through three Corning 7-54 filters and is imaged by a Iens onto a 10 mm slit in front of a u.v.-sensitive photomultiplier tube (EMI) whose output goes to a boxcar averager operating in the linear summing mode. A programmable digital delay generator (BNC) controls the timing between the two lasers.226 DECOMPOSITION OF STATE-SELECTED HOOH AND HOOD Its 10 ns step size along with the duration and jitter of the laser pulses produces 15 ns time resolution. The power of each laser is measured by sending a small portion of the beam into a photo- diode detector which stretches and amplifies the resulting electrical pulse and holds its peak value. In the case of the detector for the U.V.probe laser, a piece of fluorescent paper shifts the 3000 A light to visible wavelengths where the photodiode is most efficient. Careful tests demonstrate the linearity of the power measurements. A laboratory computer (PDP11-23) performs all the control and data acquisition functions in the experiment. In addition to serving as an external clock for triggering the lasers, the computer sequentially initiates analogue-to-digital conversion of the fluorescence signal and each of the laser powers, stores them every laser shot for later point-by-point normalization of the signal, and displays the data on a graphics t e r m i d . It aIso scans the waveIength of either Iaser or the time delay between the two laser pulses. Hydrogen peroxide (90%) which s used without further distillation, Rows slowly through the Pyrex reaction cell at pressures between 10 and 120 rnTorr * as measured by a capacitance manometer (MKS).At room temperature HOOH comprises 62% of the total vapour pressure. Because hydrogen peroxide catalytically decomposes on metal surfaces, contact with anything but Pyrex and Teflon is kept to a minimum. HOOD is produced simply by diluting the 90 % HUUH with D20 and distilling the mixture to higher peroxide concentration. Exchange of the hydrogen and deuterium is essentially instantaneous l 3 and produces an equilibrium mixture of HOOH, HOOD and DOOD in H20 and D20. A series of diagnostics determines conditions under which the signal arises solely from overtone-vibration-induced dissociation of peroxide molecules.Tuning the probe laser off an OH fragment resonance completely eliminates the signaI (except for a few photons of scattered U.V. laser light), indicating that OH is indeed the fluorescing species. Introducing the probe laser before the pump laser causes all but a few percent of the signal to disappear as well. The residual signal arises from excitation of the HOOH(D) moIecules to a dissociative electronic state by the U.V. probe with subsequent detection of the resulting OH fragments by the same laser pulse. Because this component of the signaI is strongly power dependent, we eliminate it by using low probe powers. Tuning the visible pump laser off the OH vibra- tional overtone transition while leaving the probe on an OH resonance reveals a small contribution of OH fragments which apparently comes from two-photon excitation of the HOOH(D) to a repulsive upper electronic state.14 This small component does not sig- nificantly affect our results.3. RESULTS 3.1. TEMPORAL EVOLUTION OF OH The temporal evolution of the density of OH fragments from the decomposition of HOOH(D) reflects both the unimolecular decomposition rate of the vibrationally excited peroxide molecules and the quenching of the nascent OH fragments. For molecules as small as HOOH(D) we expect the unimolecular decay rate to be too fast to resolve on a nanosecond timescale, even at relatively low levels of excitation above the dissociation barrier. However, the time-resolved observation of the OH state populations provides a convenient means of ensuring that the measured distributions are those of nascent products.Fixing the pump laser wavelength at the peak of the OH overtone vibration and scanning the time delay between the pump and probe lasers produces the series of curves shown in fig. 2. Each of these shows the fluorescence intensity from probing a particular OH quantum level as a function of time delay. The prompt rise in the fluorescence intensity reflects the fast unimolecular decay of the vibrationally excited peroxide molecules. This is consistent with an R.R.K.M. calculation I5vi6 using a * 1 Torr = 101 325/760 Pa.T. R. RIZZO, C. C. HAYDEN AND F. F. CRIM 227 variety of critical configurations all of which predict lifetimes t50 ps. Several processes determine the subsequent rise and fall of the fluorescence. One is transfer of rotational energy in OH by collisions with other molecules in the cell.This relaxes the rotational-state populations toward a thermal distribution with some levels L I L 1 I i l I I 1 1 1 1 1 1 1 1 1 1 0 0.5 1.0 1 . 5 2 .o t irnelps Fig. 2. Time evolution of the laser-induced fluorescence intensity for different rotationaI states of the OH fragments. The time is the interval between excitation of the overtone vibration in HOOH and interrogation by the probe laser. The initial rise in the signal reflects the rapid unimolecular decay of the excited HOOH, and the slower rise or fall arises primarily from rotational energy transfer of the OH molecules. The vertical arrows mark the deIay at which data on the nascent products are taken.228 DECOMPOSITION OF STATE-SELECTED HOOH AND HOOD emptying and others filling depending on their initial population and their population at thermal equilibrium.The series of curves in fig. 2 clearly display this movement toward equilibrium. The N = 1 level shows a small prompt rise due to unimolecular decomposition and a subsequent slower rise from the collisional redistribution of the molecules in the rotational manifold while N = 9 shows only a prompt rise and sub- sequent decay since its population at thermal equilibrium is small. The series of levels between N = 1 and N = 9 show a smooth progression in the manner in which they move toward equilibrium. A second process, flight of the nascent OH fragments out of the probe volume, prevents their detection, and therefore contributes to the decay of the OH fluorescence.For example, in the absence of collisions at 3 kcal mo1-I of translational energy, an OH fragment travels across the 3 mm diameter probe volume in 2.5 p s . Thus flight out of the beam could contribute significantly to the decay on the 2 p s timescale shown in fig. 2. Finally, reactive quenching of OH by HOOH l7 and H20 might affect the OH populations at long times, but these reaction rates are too slow to influence our measured distribution. Monitoring the evolution of the individual rotational-state populations enables us to choose the experimental conditions of pressure and delay between the excitation and probe pulses which allow measurement of truly nascent product-state distri- butions.The arrows in fig. 2 indicate the delay at which product spectra are taken at a pressure of 74 mTorr. Although the quenching and loss processes may change the OH rotational distribution on a microsecond timescale, as displayed by fig. 2, they produce a negligible change in the populations during the 20-30 ns delay used to obtain product-state data. 3.2. OVERTONE VIBRATION EXCITATION SPECTRA The technique of vibrational overtone excitation 6-9 is well suited to the study of intramolecular processes, particularly unimolecular reactions. Direct one-photon excitation of an overtone vibration or combination band involving an overtone deposits a precise amount of energy into an initially localized motion of the molecule. The local-mode picture of highly excited molecules describes overtone spectra of light- atom stretches in polyatomic molecules rather well.Particular functional groups exhibit remarkably similar stretching frequencies and anharmonicities which depend on their immediate chemical environment. For example, the methyl stretching over- tones in t-butylhydroperoxide,20 tetramethyldioxetan s and t-butyl alcohol 2o are almost identical, since each hydrogen is attached to a carbon which is bound to another carbon, whereas the difference in environment between the 00-H in t-BuOOH 7 9 9 and the CO-H in t-BuOH 2o is enough to shift significantly the OH stretching frequencies. These light-atom stretching motions seem to behave like local diatomic anharmonic oscillators and are described by the Birge-Sponer 21 relation, v" = Au + Bu2, where B is the anharmonicity and A - B is the mechanical frequency.The local-mode picture indicates that the OH overtone vibrations in HOOH should be very nearly the same as those in t-butylhydr~peroxide;~.~ however, the spectrum of HOOH above u = 3 of the OH stretching vibration has never been measured. A Birge-Sponer plot of the data available on the fundamental and lower overtones of HOOH is given in fig. 3 (solid points). The point at u = 1 is the average of the normal-mode asymmetric and symmetric fundamental stretching frequency, and the points at 11 = 2 and zi = 3 are averages of closely spaced rotational band origins in the corresponding vibrational overtone regions.22 Extrapolation of the points to u = 6 yields a value close to, but slightly shifted from, the Y = 6 overtone vibration in t-BuOOH.T. R.RIZZO, C. C. HAYDEN AND F. F. CRIM 229 Fixing our laser-induced fluorescence probe to the Q1(4) level of OH and scanning the visible pump laser about the u = 6 overtone region predicted by the Birge-Sponer plot produces the spectrum shown in fig. 4(a). The large broad peak, which we assign to the pure OH stretching overtone, falls at the value predicted by our extra- polation (open point in fig. 3) and has a width (86 cm-') which is similar to that ob- served in t-butylhydroperoxide. Several other features of this spectrum are particularly worth noting. There are three small broad peaks on the high-energy side of the main vibrational overtone transition, the most prominent of which is separated by ca.385 cm-l. We attribute 7 1 1 1 1 I 3200 t \ I 3100 c I 1 I I 1 1 I 1 2 3 4 5 6 7 vibrationaI level, ZI Fig. 3. Birge-Sponer plot for the ovcrtone vibrations in HOOH. The solid points are for the average of the symmetric and asymmetric stretch in u = 1 and the average of separate rotational origins in u = 2 and TI = 3. The open point is the maximum in the excitation spectrum of v = 6 as determined by monitoring the OH decomposition product. The solid line is a fit of the u = 2 and z1 = 3 points to the Birge-Sponer relation, Y" = Au + Bu2. A = 3701 cm-', B = -90.5 crn-l. these to a local-mode-normal-mode combination band. Similar features 23 have been observed in other molecules and seem to arise from a combination of several stretching quanta and one quantum of low-frequency bending motion.Zare and co-workers observe similar features separated from the main vibrational overtone by 429 cm-' at u = 5 and 449 cm-l at u = 6 in the t-BuOOH overtone spectrum. We suspect that these features in t-BuOOH and the higher-energy feature near the u = 6 overtone vibration in HOOH are a combination OH stretching and hydroperoxide torsional motion. The HOOH torsional motion has been extensively studied 24 and indeed one of the stronger of a number of transitions is centred at 370 cm-1.24c On an expanded wavelength scale, structure is clearly evident on top of the main stretching overtone. Other smalI molecules show rotational structure in the overtone spectrum (H,0,25 HCN 26 and C2H2 27 for example), and it is apparent in the lower-overtone transitions of HOOH.22 This structure indicates that there is an inhomogeneous contribution to the overtone linewidth of HOOH, perhaps arising from a progression of rotational states.230 DECOMPOSITION OF STATE-SELECTED HOOH AND HOOD HOOH l l l l l l l l r r r r l r l l r l l 5300 5250 5200 5150 wavelength/A Fig.4. (a) Overtone vibrational excitation spectrum of HOOH obtained by monitoring the Q1(4) transition of the OH decomposition product. (b) Overtone vibration excitation spec- trum of HOOD obtained by Q1 ( 6 ) transition of the OD decomposition product. Both spectra were taken at a pressure of 120 mTorr. The local-mode picture of overtone vibrations predicts that the u = 6 OH stretch- ing frequency in HOOH would not shift significantly upon substitution of a deuterium for one of the hydrogens.Fig. 4(b) shows the overtone excitation spectrum that we obtain for HOOD by detecting the OD fragment [Q1(6) transition]. The centre of the main overtone band falls at the frequency of its undeuterated analogue, and the band has the same overall width, but there are several important differences. The main v = 6 overtone is partially split into two broad peaks of roughly equivalent width. Also, the features we attribute to combinations of local and normal modes are shifted to slightly lower energy. This shift is consistent with the combination band containing a component of skeletal motion involving the OD end of the molecule. 3.3. OH(OD) PRODUCT-STATE DISTRJBUTIONS The spectroscopy of OH(0D) is complicated but well characterized.'l Angular- momentum coupling in the X211 ground state of OH (intermediate between Hund'sT.R. RlZZO, C . C . HAYDEN AND F. F. CRIM 23 1 cases a and b) gives rise to both spin-orbit splitting and Iambda doublet splitting. The A 'E+ upper state (Hund's case b) exhibits spin splitting, and the resulting tran- sitions between the states fall into six main branches and six satellite branches. The PI, Q1 and Rl branches originate in the lower spin-orbit component (2113!2>, and the Pz, Q2 and R2 branches arise from the upper spin-orbit component (2171,2). The Q1, R1, P, and Q2 branches have corresponding satellite branches, designated by primes, which arise from transitions with a common lower level to different spin components in the upper level.A peak and its satellite provide redundant information on the population of a particular quantum level, and serve as a convenient diagnostic in avoiding saturation of the transitions. A normalized spectrum of the R1 branch of OH which was taken at a pressure of 66 mTorr, with a 20 ns delay, and with the pump laser tuned to the centre of the OH v = 6 overtone vibration is shown in fig. 5. The entire spectrum contains 9600 data t 3065 3070 wavelengthjA Fig. 5. Laser-induced fluorescence excitation spectrum of R1 branch of the OH product from HOOH decomposition following excitation of ZI = 6 of the OH stretching vibration. The pump laser is fixed at 5280 A and the delay between laser pulses is 20 ns. The total pressure is 66 mTorr. There are 9600 points across the spectrum, and each is divided by both of the corresponding laser powers.points, each point normalized to both laser powers, and a peak contains ca. 25 points across (f.w.h.m.). We convert spectra to populations using peak areas from computer integration of the normaIized spectra in the expression of Kinsey and co-workers,28 which relates populations to intensities. In the limit of low probe power density and long collection gatewidth this expression becomes z - l 1 n c c I & - - where I is the integrated peak area, B12 is the Einstein absorption coefficient, z, is the radiative lifetime of the OH upper state, and T-I = z,-I + k,P is the total decay rate %2232 DECOMPOSITION OF STATE-SELECTED HOOH AND HOOD 0.2 0 t- 1 0.2 0 1 2 3 4 5 6 7 8 9 10 rotational level, N Fig.6. Product rotational-state djstributions from the (a) R1 and (6) QI branch LIF excitation spectra of the OH fragments produced by excitation oft’ = 6 of the OK stretching vibration in HOOH. The different symbols denote analyses from different spectra wjth the scatter reflecting the uncertainty in the determinations. The solid Iine is a smooth curv-e drawn through the points, and the broken line is the distribution at the indicated temperature. The temperature is a fit to the populations in N 5 6 where N is the angular-momenturn quantum number exduding spin. The total population is normalized to unity.T. R. RIZZO, C. C. HAYDEN AND F. F. CRIM 233 constant where k, is the quenching rate constant 29 for the 2Z+ state of OH by HOOH/ H20 and P is the pressure.Fig. 6 shows a plot of the populations of the lower spin-orbit component calcu- lated from the R, and Q1 branch transitions. A plot of a thermal distribution chosen to fit the populations at low N has been included as a point of reference but not to indicate that we expect the distributions to be thermal. The significant populations in fairly high N levels in each of these branches are notable, since an N = 9 molecule contains 4.73 kcal mo1-I of rotational energy. The 5280 A excitation adds only 4.6 kcal mol-1 of energy above the dissociation barrier of the HOOH to the 0.9 kcal mol-1 of average thermal energy of the HOOH molecules. Even though a significant number of peroxide molecules have more than the average thermal energy, an N = 9 1 2 3 4 5 6 7 8 9 10 rotational level, N Fig.7. Product rotational-state distribution from the Q1 branch LIF excitation spectra of the OH fragments produced by excitation of the higher-energy feature (6vOH + vx) in the u = 6 OH stretching region of HOOH. The other details are given in fig. 6 . OH molecule carries away a large fraction of available energy in its rotation with little remaining for rotation of its OH partner or for relative translation. The distributions as a whole are rather hot (on the average an OH fragment carries ca. 1.65 kcal of energy), although it is apparent that the high rotational levels drop off more quickly than a corresponding thermal distribution. This feature (hot distribution at low Nand fairly sharp drop off at high N) seems to be common to most of the distributions we measure and probably reflects the energy and angular momentum constraints of the unimolecular decomposition process of such a small molecule.There is no significant difference between population distributions obtained from the R, and Q, branches even though the temperature fits to the low-N components differ slightly. Since the two branches arise from different lambda doublet states, the similarity of the distributions shows that the populations in the two states of the lower234 DECOMPOSITION OF STATE-SELECTED HOOH AND HOOD spin-orbit component have the same IV-leveI dependence. An estimate for the relative populations of the different spin-orbit states comes from separateIy summing the populations in the levels probed by the R, and R2 branch transitions.Our measured ratio for the populations of 1.6 & 0.25 indicates a preference for the lower spin-orbit state. This ratio exceeds that of a thermal distribution (1.27) at 1400 K. In the context of the local-mode picture, excitation of a combination of a u = 6 stretching mode and a Iow-frequency bending or torsional motion in HOOH should prepare the molecule differently front excitation of the pure OH stretch. Exciting HOOH at the frequency of the observed combination-band feature (see fig. 4) and 30 72 3076 wavelengt h/8, 3080 I I I I I I I I I Fig. 8. Laser-induced fluorescence excitation spectrum of the OD product from HOOD decomposition followng excitation of D = 6 of the OH stretching vibration along with an OH spectrum from HOOH.probing the fragments yields the product-state distribution shown in fig. 7. The two major differences between this distribution and that obtained from the pure overtone- vibration-induced dissociation are the slight shift of the peak of the distribution to lower N levek and the greater population of very high levels. The net effect is to make the populations fit a thermaI distribution remarkably well, but this is likely to be coincidental. Exciting this combination band alters both the excitation energy and mode, and at present we cannot distinguish the role of these two factors in changing the measured product-state distributions from those obtained with pure local-mode excitation.T. R. RIZZO, C. C . HAYDEN AND F. F. CRIM 23 5 A potentially informative experiment in understanding the hydrogen peroxide dissociation is to excite one end of the molecule and selectively probe the fragment coming from the other end to determine whether the fragments retain memory of their excitation. In HOOD the fragments are spectroscopically distinguishable, and we can excite the OH overtone vibration and probe the OD product.Fig. 8 shows an LIF spectrum obtained from such a measurement. The lower curve is an OH spectrum from the decomposition of HOOH, and the upper curve displays OH and OD peaks from the decomposition of both HOOH and HOOD, which are in the reac- tion cell together. Fig. 9 shows the corresponding OD product rotational-state distribution. The smaller rotational constant of OD allows the population of higher N levels and makes the distribution appear broader than that for OH from HOOH, U 0 1 a a .* c, c1 0.1 5 0.10 0.05 0 c 1 1 2 3 4 5 6 7 8 9 1011 12 13 rotational level, N Fig.9. Product rotational state distribution from the Q1 branch LIF excitation spectra of the OD fragments produced by excitation of the u = 6 OH stretching vibration in HOOH. The other details are given in fig. 6. but if compared on the basis of energy rather than quantum number the two distri- butions are remarkably similar. The general features are the same with lower rotational levels fitting fairly well to a hot thermal distribution and a sharp drop occurring at high rotational levels. As before, the calculated temperature in the OD case is simply a reference obtained by fitting the low rotational-state populations and does not signal any important differences between the OH and OD distributions at the present level of analysis.4. CONCLUSION We have demonstrated that the technique of overtone vibration excitation of reactants combined with laser-induced fluorescence detection of product fragments permits detailed measurements of product-state distributions from state-selected hydrogen peroxide and its partially deuterated analogue. We have examined the effect of exciting slightly different but related modes of HOOH on the product distri-236 DECOMPOSITION OF STATE-SELECTED HOOEf AND HOOD bution and have selectively pumped the OH vibration in HOOD and probed the OD fragment from the initially unexcited end of the molecule. Our intent in applying these techniques to small molecules is to provide detailed dynamical measurements on a system that is highly constrained and theoretically tractable, but these same constraints make simple interpretation of the results difficuIt.We plan to explore the effects of these constraints on our results with the aid of statistical approaches such as phase-space calculations. Much work remains to be done on this system. In addition to obtaining more extensive data on the HOOD molecule at this level of excitation, we will also excite u = 7 of the OH stretch in HOOH(D) to explore both vibrational and rotational energy partitioning in the uni- molecular reaction. Finally, to refine the specificity of overtone excitation technique and to help interpret the details of the overtone spectra, we are pursuing experiments in which the averaging arising from the distributions of initial reactant energy and angular momentum is reduced by performing the overtone-vibration-induced decom- position in the cold environment of a pulsed supersonic expansion.We gratefully acknowledge the support of this work by the U.S. Office of Basic Energy Sciences of the Department of Energy. We particularly thank S. M. Penn for designing and assembling the probe dye laser and performing the R.R.K.M. caI- culations on HOOH. (a) D. W. Setser, MTP International Review of Science, ed. D. Herschbach (Butterworths, London, 1972), vol. 9; @) M. Quack and J. Troe, in Gas Kinetics and Energy Transfer (Specialist Periodical Report, The Chemical Society, London, 19771, vul.2; (c) H. M. Frey and R. Walsh, in Gas Kinetics and Energy Transfer (Specialist Periodical Report, The Chemical Society London, 1978), vol. 3. R. J. Buss, M. J. Coggiola and Y. T. Lee, Faraday Discuss. Chem. Suc., 1979,67, 162. D. S. King and J. C. Stephenson, J. Chem. Phys., 1980,72, 1161. (a) C. M. Miller, J. S. McKiIlop and R. N. Zare, J. Chem. Phys., I982,76,2390; (b) H. Reider, F. Kong, C. Wittig, J. Stone, E. Thiele and M. F. Goodman, J. Chern. Phys., 1982,77, 328. li (a) H. Hippkr, K. Luther and J. Trw, Faraday Discuss. Chern. Suc., 1979,67,221; fb) H. Hip- pler, V. Schubert, J. Troe and H. J. Hendelken, Chem. Phys. Lett., 1981,84,253. (a) K. V. Reddy and M. 3. Berry, Faraday Discuss. Chem. Soc., 1979,67,221; (b) K. V. Reddy and M. J. Berry, Chem.Phys, Lett., 1979, 66,223, D. W. Chandler, W. E. Farneth and R. N. Zare, J. G e m . Phys., 1982, '77, 4447. 3. D. Cannon and F. F. Crim, J. Chem. Phys., 1981,75, 1752. R. T. Rizzo and F. F. Crirn, J, Chem. Phys., 1982,76,2754. lo H. Okabe, in Photochemistry of SmalZ Mufecules (John Wiley, New York, 1978), p. 282. li (a) G. H. Dieke and H. M. Crosswhite, J. Quani. Spectrosc. Radiat. Tramfer, 1962, 2, 97; (b) W. L. Dimptl and J. L. Kinsey, J. Qrcanf. Specfuosc. Radiar. Transfer, 1979, 21, 223; (c) M. A. A. Clyne, J. A. Coxon and A. R. Woon Fat, J. Mu!. Spectrosc., 1973, 46, 146. l2 (a) M. G. Littman and €3. J. Metcalf, Appl. Opr., I978,17, 2224; (6) M. G. Littman, Opt. Lett.. 1978, 3, 138; (c) F. J. Durate and J. A. Piper, Appl. Opt., 1981, 20, 2113. l3 W. C. Schumb, C. N. Satterfield and R. L. Wentworth, Hydrogen Peroxide (Reinhold, New York, 1955), p. 297. l4 (a) L. T. Molina and M. J. MoIina, J. Phofochern., 1981, 15,97; (6) D. H. Volman, Adu. Photo- chern., 1964, 1, 69; (c) D. H. Volman, J. Chem. Phys., 1949, 17, 947. l 5 P. J. Robinson and K. A. Holbrook, Unimolecular RPacfiuns (Wjley, New York, 19721 l6 W. L. Hase and D. L. Bunker, Program QCPE-234, Department of Chemistry, Indiana I 7 P. H . Wine, D. H . Sernrnes and A. R . Ravishankara, J. Chem. Phys., 1981,75,4390. la B. R. Henry, Acc. Chem. Rex, 1977, 10, 207. l9 M. L. Sage and J. Jortner, Adc. Chem. Phys., 1981, 47, 293. '* T. R. Rizzo and F. F. Crim, unpublished results. 21 R. L. Swofford, M. E. Long and A. C. Albrecht, J. Chem. Phys., 1976,65, 179. 22 P. A. Guiguere, J, Chern. Phys., 1949, 18, 88. 23 H. L. Fang and R. L. Swoflord, J. Chem. Phys., 1980,73, 2607. University, Bloomington, Indiana 47401, U.S.A.T. R. RIZZO, C. C. HAYDEN AND F. F. CRIM 237 24 (a) P. Helminger, W. C. Bowman, and F. C. DeLuca, J. Mul. Spectrusc., 1981,85, 120; (b) L. Zumwalt and P. A. Giguere, J. Chem. Phys., 1941,9,458; (c) R. H. Hunt, R. A. Leacock, C. W. Peters, and K. T. Hecht, J. Chem. Phys., 1965,42, 1931 ; (d) R. L. Redington, W. B. Olson and P. C. Cross, J. Chem. Phys., 1962,36, 1311. 25 3-M. Fland and C. Carrey-Pegret, J. Mol. Specfrosc., 1974, 51, 142. 26 K. K. Lehman, G. J. Scherer and W. Klemperer, J. Chem. Phys., 1982, 77, 2853. 27 B. R. Henry, M. A. Mohamrnadi and A. W. Tarr, J. Chem. Phys., 1982, 77, 3295. 28 J. R. Cordova, C. T. Rettner and J. L. Kinsey, J, Chew. Phys., I981 75, 2742. 29 I. S. McDermid and J. B. Laudenslager, J. Chew. Phys., 1982, 76, 1824.

ISSN:0301-7249    

DOI:10.1039/DC9837500223

出版商:RSC    

年代:1983

数据来源: RSC

摘要:

Faraday Discuss. Chem. Soc., 1903, 75,239-250 Low -p o wer Infrared Laser Photo1 ysis of Tetr amethyldi oxet an BY SANFORD RUHMAN, ODED ANNER AND YEHUDA HAAS Department of Physical Chemistry, and The Fritz Haber Centre for Molecular Dynamics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel Receiued 2 1 sb December, 1 982 Previous experiments on the TEA CO, laser multiphoton dissociation of tetramethyl- dioxetan (TMD) have been extended to low fluence levels (<20 3 cm-2) and low pressure (ca. The reaction, followed by observing the accompanying luminescence, proceeds at a rate much slower than the laser pulse width. Thus direct determination of the unimolecular rate constant of this low-threshold-energy reaction fca. 25 kcal mol- I) is possible. The extent of activation can be estimated by comparing to rates measured on the same system using overtone excitation by Crim et al.[J. Chem. Phys., 1981, 75, 17521. Analysis of the results using R.R.K.M. theory is constrained by this comparison, and allows in principle the derivation of vibrational population distribution of the reacting molecules. A fourfold increase in the laser fluence leads to an almost lo3 yield increase. The average energy of the reacting molecules at the low-fluence end used is between 3000 and 4000 cm-' above the dissociation threshold. Better defined values can probably be obtained by either calibrating the overtone-excitation results, or by isolating the emission of a single species and using rate equations. The emission is shown to be due to at least two species: a fast-decaying component and the thermalized triplet.The former is strongly quenched by collisions, and its relative contribution to the total yield is increased upon increasing the fluence. Its emission spec- trum is very broad and apparently structureless. The thermalized triplet can be observed separately by using a red cut-& filter. It is formed by a unimolecular dissociation and not (up to pressures of ca. 40 mTorr) by colIisiona1 processes. Extrapolation to low-fluence, high-pressure conditions show that the main product is the triplet, in agreement with thermal, liquid-solution results. Torr *>. 1. INTRODUCTION Unimolecdar dissociation of molecules in the ground electronic state has been traditionally induced by collisional processes, heating or chemical activation.'J Lasers provide a convenient means for exciting an isolated molecule, as well as depositing the initial excitation in a predetermined vibrational mode.Two laser- based techniques that avoid electronically excited states of the parent are infrared multiphoton excitation (IRMPE) and overtone excitation (OTE). These methods can now be used to initiate reactions in a fast and clean way, and thus probe the mechanism of collision-free unimolecular reactions. In particular, the widely accepted hypothesis of fast intramolecular vibrational energy redistribution can be tested. If this assumption is correct, the same reaction path should be followed for any excitation mode, provided the same amount of energy is deposited in the molecule.In fact, the argument may be reversed ; Tf the current prevailing theory (often referred * 1 Torr = 101 325/760 Ps.240 I.R. PIIOTOLYSIS OF TETRAMETHYLDIOXETAN to as R.R.K.M. theory) l v 2 is correct, one mode of excitation can be used to estimate the energy content in molecules excited by another means. For example: OTE prepares a rather narrow distribution of excited molecules, particularly if a narrow-band light source is used. IRMPE on the other hand can produce a fairly wide distrlhtion of reacting molecules. One goal of this work was to compare OTE and IRMPE for a given molecule, and deduce the energy distribution of multiphoton excited molecules as a function of the fluence level. This method can, in principle, provide an '' experi- mental " IRMPE distribution function--a parameter that has so far not been directly measured and is needed for comparison with theoretical simulations of the IRMPE Unimolecular reactions leading to elcctronically excited products are of interest since they convert chemical energy directly to light.In the context of the present study they provide a facile means to follow the reaction progress in real time by monitoring the ensuing chemiluminescence. One of the best studied reactions is the decomposition of tetramethyldioxetan (TMD), which forms high yields of electronic- ally excited and found that correlation with thermal studies is not straightforward. At least two electronically excited species are involved: the well characterized acetone triplet and a species having a rather short decay time (ca.s) that could not be identified as either singlet or triplet acetone. In those studies a relatively high fluence level was employed (20-100 J cm-2), leading to large reaction rate constants and an appearance time that is shorter than the laser pulse width (ca. s). Comparison with R.R.K.M. theory could not be made as even the average excitation was not known. More recently, the same system was studied by Cannon and Crim, using C-H overtone ex~itation.~~-l$ They were able to show that with an excess energy of ca. 3000-5500 cm-l (excitation to D == 4 and 5) the observed unirnolecular reaction rate can be derived from a simple R.R.K.M.-based model. They also observed the two emitting species and were able to measure the pressure dependence of the rise and decay times of the fast component of the chemiluminescence.Since the identity of the short-lived component has not yet been established at the present time, it will be referred to as X. Using IRMPE one can in principle control the degree of excitation and observe reactions close to the energy barrier. We have recently extended the detection capability of our IRMPE set-up, and can conveniently follow reactions proceeding at a rate much slower than the inverse of the laser pulse width. In this paper we report IRMPE results obtained at low-fluence and low-pressure conditions. Comparison with OTE results, using only three independent excitation energies, is presented and its present limitations are discussed. The fluence and pressure dependence revealed in this work resolves the apparent discrepancy with thermal studies.Thus the prevalence of triplet acetone formation can be obtained by extrapolating our present results to high-pressure, low-fluence conditions. We have studied the IRMPD of TMD 2. EXPERIMENTAL The basic apparatus was described in an earlier work,li so only new features will be mentioned here. A pulsed COz laser was used as the light source. The pulse to pulse reproducibility and time jitter were greatly improved by replacing the spark gap with a thyration. The laser was operated in the TEMoo mode, on the R(20) line of the 00'1-10'0 transition at 10.247 pm. The output consisted of a nearly-gaussian shaped pulse (f.w.h.m. = 120 ns) the usual " tail " being eliminated by reducing the amount of nitrogen in the laser gas feed mixture.Pulse energies were typically 40 mJ. The beam was focused into the sample cell using a 50 cm focal-length lens. The Pyrex sample cell was 30 cm long and 30 mm dia-S. RUHMAN, 0. ANNER AND Y. HAAS 241 meter, fitted with BaF, windows. TMD was slowly flown through the cell at pressures up to 50 mTorr, measured by a MKS Barratron capacitance gauge (model 220-3A1-1, full scale 1 Torr). Observation was at right angles, the total lurninescencc being collected onto a photo- multiplier tube (EM1 6256s or 9558Q). The signal was amplified, fed into a transient digitizer (Biomation 8100) and averaged on a hard-wired averager (Nicolet 1170). Further data reduction and analysis were preformed on a VAX 750 computer. The laser energy incident on the sample was controlled by a liquid attenuation cell.The cell consisted of a stainless frame, in which the distance between two parallel, polished NaCl windows could be precisely controlled by a micrometer screw. Cyclohexane was found to be a convenient absorber at the laser wavelength used in this work. The cell width, controllable to 0.01 mm was varied between 0 and 5 mm. No change in the laser beam shape could be observed with this attenuator. 3. RESULTS Examples of the time-dependent luminescence following TMD irradiation by the CO, laser are shown in fig. 1. It is evident that the risetime of the signal, reflecting the reaction rate, is much longer than the laser pulse width (ca. 0.1 ps) Qualitative comparison with the data of Cannon and Crim show that the rate corresponds roughly to OTE to u = 4 or 5.Two distinct processes are clearly observed: a fast decay (due to X) which is strongly affected by the pressure, and a slower decay which is much less sensitive to pressure variations. The assignment of the long-lived com- ponent to triplet acetone, based on spectral and lifetime evidence,1°-12 is further supported by very effective quenching by molecular oxygen. l 6 Experimental separation of the total luminescence to the individual contributions of X and the triplet is not easy, since their emission spectra appear to be quite similar. Both are structureless, but the triplet emission extends further to the red. Using a 715 nm cutoff filter we were able to isolate almost completely the triplet emission. Under these conditions the signal is severely attenuated and thus far only relatively high- fluence data could be obtained, as shown in fig.2. It is clear from the figure that the triplet is formed at approximately the same rate as the total emission. At the pressure range used, its decay time is not strongly affected by collisions. The decay time is found to be ca. 140 p s . The total reaction yield, as given by the luminescence intensity, is strongly depen- dent on the fluence: the luminescence signal is increased by almost three orders of magnitude on quadrupling the fluence, as shown in fig. 3. At a given pressure the relative triplet yield is seen to increase on decreasing the fluence. An estimate may be obtained by integrating the areas under the fast and slow decaying portions.In the absence of absolute, or even relative, emission quantum yields the actual relative populations cannot be estimated. The trend, shown in fig. 4, is nevertheless quite clear. We define /? as yield of X ’ = yield of triplet and find that at higher pressures and lower fluence levels the triplet contribution becomes more and more important. At a given fluence, increasing the pressure leads to quenching of X 13wi4 accounting for the observed trend. This quenching can lead to a dark product, but in principle also to enhanced triplet formation. We checked this point by measuring the ratio of the peak intensity of X to the amplitude at 115 ps, where the triplet contribution is dominant. From the limited data we find that thc main factor determining the X/triplet ratio is the fluence.In any case it is clear that most of the decreased yield of X (due to colli- sional quenching) is not reflected in increased triplet signal. The results are shown in table 1.242 I.R. PHOTOLYSIS OF TETRAMETHYLDIOXETAN 1.00 1 I 1 1 -15.0 113 241 369 197 rlw I I I L -1.50 11.1 24*4 37.3 50.2 tlW Fig. 1. Time-resolved total cherniluminescence of TMD induced by IRMPE as a function of pressure and fluence. A11 intensities are normalized to unity the maximum. The actual intensity at 5.2 J cm-' was ca. three orders of magnitude smaller than at 18.4 J The laser line used was R(20) of OOol+lOoO transition. (a) The complete time history, including triplet state decay at 3 m Torr: (- ) 18.4 J cm-2; (- (b) Details of the rise and fast decay: (- ) 20 mTurr, 18.4 J (+ f- +) 20 mTorr, 5.2 J ~XI-~; ( a * * *) 3 mTorr, 5.2 J cm-z.a) 5.2 J CIII-~.S. RUHMAN, 0. ANNER AND Y. HAAS 243 1.00 x c v) .- 0) c.’ ._ C .- v) -iJ -13.0 115 2 4 3 3 70 L98 tlPS Fig. 2. Triplet emission at 18.4 J cm-’ and different pressures obtained by observing the luminescence through a 715 nm cutoff filter: (- ) 20 mTorr, 18.4 J cm-2; (. * - *) 6 mTorr, 18.4 J cm-’. I 0 0 4 8 12 16 20 COz laser fluence/J cm-2 Fig. 3. Total luminescence of TMD yield as a function of the laser fluence; 0, 3 mTorr; 0, 10 mTorr; A, 20 mTorr.244 - c 1OmTorr e I.R. PHOTOLYSIS OF TETRAMETHYLDIOXETAN 4 3 0 4 8 12 16 20 laser fluence/J Fig. 4. Ratio of the yield of the fast component X, to the triplet yield, p, as a function of fluence at some TMD pressures. 4.DISCUSSION Energetically, dissociation of TMD can lead to generation of both singlet and triplet acetone.' In the low-pressure gas-phase work singlet acetone was not directly identified. Both OTE and IRMPE reveal the presence of an electronically excited species, X, having a collision-free lifetime of ca. 100 ,us, and being strongly quenched by collisions. In addition, triplet acetone, T, is observed at longer timescales. The IRMPD of TMD can be represented by the following reactions: TMD + nhv --f TMDt TMDt + M -+ TMD TMDt -+ X TMDt + T Table 1. Relative triplet yield as a function of pressure and fluence pressure/mTorr fluence/J cmT2 3 6 10 20 5.2 0.13 - 0.13 0.13 9.6 0.09 0.08 0.08 0.08 14.4 0.05 0.06 0.05 0.07 18.4 0.03 - 0.04 0.045 a As determined from the peak signal amplitude to the amplitude at 115 ps.S.RUHMAN, 0. ANNER AND Y. HAAS 245 X + A c + h~ (5) X + M - + A c (6) X + M + T (7) T + A c + h v (8) where Ac is acetone in its ground electronic state and M any collision partner. The rate constants for collisional deactivation k2 and k6 by TMD have been deter- mined by Cannon and Crim to be 12.4 x lo6 s-' Torr-' and 5.6 x lo6 s-' Torr-', respectively. They have also shown that k3 + k4 (the unimolecular dissociation rate constant) can be calculated using R.R.K.M. theory. In the IRMPD experiments, the energy distribution of the reacting molecules is not known, and we wish to find out whether OTE data can be used to deduce it. Solution of the rate equations associated with reactions (I)-(7) leads to the follow- ing expression for X as a function of time, assuming that its initial concentration is zero : (1 - e-kr)e-kxr k,[TMDt], k X ( t ) = (9) where [TMDT],, is the initial concentration of vibrationally excited TMD and k = k2[MI + k3 + k4 - kx k, = k5 + (k6 + k,"].A similar equation holds for the triplet. 4.1. COMPARING IRMPE AND OTE RESULTS In distinction with most IRMPE data published to date, the reaction rate observed in this work is slow compared to the excitation rate.I7 At Auence levels < 15 J cm-2 we can thus separate these processes and assume that the excitation pulse is over by the time an appreciable chemical change takes place. The signal rise is determined by the rate of formation of excited molecules, which can be deduced for any energy from R.R.K.M.calculations and the collisional deactivation rates. In order to use eqn (9) we need to separate the triplet contribution from that of X. This work is now in progress, and it indicates that the triplet may be formed by a process having a lower barrier than X. At present the separation cannot be made at low Auence levels, and we chose to use the raw data of Cannon and Crim as a basis fur comparison of IRMPE with OTE. Our goal is to find out whether, and under what conditions, these techniques can be quantitatively compared. The procedure is as follows : Rise and decay curves for a given TMD pressure are obtained for several OTE excitation energies. These are used as a basis set for a linear combination that is fitted to produce the corresponding curve obtained by IRMPE: S(t, IRMPE) = c t l S ( f , ~ ~ ) (10) I S ( f , A ) is the signal intensity at time t , obtained by excitation means A .The co- efficients x of the individual components are constrained to be positive, in order to obtain physically meaningful results. The only detailed OTE data available to us were obtained at u = 3,4 and 5 of the C-H overtone with a TMD pressure of 10 mTorr. Relative absolute intensities were not available. The results reported below were obtained by normalizing each curve to have the same height at the maximum.246 I.R. PHOTOLYSIS OF TETRAMETHYLDIOXETAN When applied to the full rise and decay curve, the fitting procedure was found to be rather insensitive, possibly due to the large contribution of triplet-state decay, which varies little with excitation energy.We thus concentrated on shorter time intervals, for which the details of the rise and initial decay are more clearly displayed. Examples of the results of the procedure are shown in fig. 5. The fit is reasonable at low fluence levels, while at higher ones agreement is poor even for the best fit. In table 2 we summarize the results of two fitting procedures, one using only the rising portion of the curve (first 8 p s ) and the other extending to 44 p s . Table 2. Fitting coefficients obtained for four fluence levels and emphasizing two time intervals. See text for details. fitting extended over fluence level/ J cm-' first 8 ps first 44 ps a3 a4 a5 a3 a4 a5 5.2 0.66 0.32 0.01 0.26 0.71 0.01 9.6 0.05 0.94 0 0.08 0.84 0.07 14.4 0.01 0.67 0.34 0.06 0.51 0.42 18.4 0.01 0.58 0.44 0.005 0.27 0.72 The results show that even with a small number of relatively widely spaced excitation energies, OTE curves used can reasonably well reproduce our low-fluence data.At higher fluence the signal rises relatively slowly and decays at a faster rate than given by the basis-set functions. This may mean that one needs to include more basis functions, perhaps at higher excitation energies. OTE is restricted by the presence of an electronic transition at excitation wavelengths < 660 nm, preventing the measurements of u 2 6. However, the decay rate of X observed at 18.4 J cm-2 appears to be even faster than that obtained at 660 nm. Thus other factors (apart from the limited number of basis functions) need to be considered.One possibility is interference of excited-states interaction, such as energy pooling or triplet-triplet 1 .oo -0.10 I I I I -1.10 11.7 24.5 37.2 50.0 tills Fig. 5. For caption see opposite.S. RUHMAN, 0. ANNER AND Y. ftAAS m .M E G B .- v1 .- ‘5 -0.10 I 1 1 I - 0.90 11.9 24.6 37.4 50.1 ttPS 247 -0.10 I I L I rips -0.90 11,9 24.6 37.4 50.1 Fig. 5. Examples of the comparison of IRMPE results obtained in this work with OTE time profiles. The fitting procedure described in the text leads to the following ‘‘ best ” coefficients. (a) Laser fluence 5.2 J cm-Z, a3 = 0.26, a4 = 0.71, a5 = 0.01. (b) Laser fluence 9.6 J a3 = 0.08, cc4 = 0.84, cc5 = 0.07. (c) Laser Auence 18.4 Jcm-*, cc3 = 0.005; u4 = 0.27; as = 0.72. (- ) Best fit; (* - - -) experiment.TMD pressure is 10 mTorr.248 I.R. PHOTOLYSIS OF TETRAMETHYLDIOXETAN annihilation which may take place when the concentration of excited species becomes comparable to or greater than that of cold molecules. These conditions are never obtained for OTE but may hold for high-fluence IRMPE. The results of table 2 show, as expected, the gradual increase in the average energy of reacting IRMPE molecules on increasing the fluence. In order to obtain actual distributions, we need to know the distribution of reacting molecules obtained by OTE, and relative calibration factors for S(t,ui). All the experiments were conducted at room temperature, at which TMD has considerable vibrational energy-ca. 1000 cm-' on average. Furthermore, overtone excitation basically shifts the thermal population to energies around that of the light quantum.The shape of the resulting distribution strongly affects the chemiluminescence signal, since it is the molecules at the high-energy tail that contribute most to the product yield. This is particularly true for u = 3 and 4 as the unimolecular rate constant increases quite steeply at energies close to the reaction barrier. In table 3 we show the nominal photon energy Table 3. Energetics of OTE excitation of TMD starting at room temperature." All energies in cm-'. excitation 2, frequency E b E--EbC 3 8475 10 900 1900 4 11 050 12 800 3800 5 13 515 14 800 5800 a From ref. (13) and (15); B is the most probable energy of the reacting molecules at 10 mTorr; Eb is the barrier for TMD dissociation, 9000 cm-'.and the most probable energy of reacting molecules. These data are based on R.R.K.M. calculations by Cannon and C ~ i r n . ' ~ ? ' ~ Table 3 shows that u = 3 reaction is due only to molecules that were initially vibrationally hot. From the table we can conclude that at fluence levels up to 9.6 J cm-2, reaction is due mostly to molecules with less than ca. 4000 cm-l excess energy. The quality of the fit at low fluence seems to warrant a more quantitative estimate, which will be performed once the actual amplitudes of u = 3,4 and 5 OTE data are quantitatively comparable. 4.2. X, THE TRIPLET STATE AND THERMAL DATA The data provided by this work show that the thermalized triplet is not formed from X by collisions. Also, it appears that at a given pressure the contribution of the triplet to the total yield increases inversely with the fluence (table 1).These results are compatible with an independent route leading to the triplet, having perhaps a lower barrier than that leading to X. This point will be checked by comparing the kinetics of pure triplet formation (cf. fig. 2) with the total emission kinetics. While X can still not be positively identified, one possible assignment, that of a vibrationally hot triplet acetone, is not supported by our data. If that were the case, collisional deactivation of X would lead to an enhanced triplet emission on increasing the pressure from 3 to 40 mTorr. Increasing the pressure leads to strong quenching of X emission, without a comparable effect on the triplet.At low fluence levels the triplet contribution is increased for any Such enhancement is not observed. Finally, the data of table 1 correlate nicely with published liquid-phaseS . RUHMAN, 0. ANNER AND Y. HAAS 249 given pressure. Making the reasonable assumption that thermal excitation populated to a Iarge extent the same energy levels as low-fluence IRMPE, our data predict prevalence of triplet formation for thermal liquid-phase TMD chemiluminescence. 5 . CONCLUSiONS (1) The dissociation rate of TMD undergoing lRMPD was measured, Up to 15 J cmn2 laser fluence the risetime is >, 1 pus and can be conveniently separated from the laser pulse width. (2) Low-fluence IRMPE kinetics can be quantitatively compared with OTE kinetic obtained at u = 3,4 and 5 of the CH stretch.At fluences >12 J cm-2 the fit to this set of UTE data ispoorer. This opens the way to quantitative estimates of the energy distribution in IRMPE experiments. (3) The triplet state is not formed from X by collisional deactivation. Its relative yield is increased at low fluence levels and at high pressures. We thank Prof, F . F. Crirn for helpful discussions. This work was supported by the Israeli Commission for Basic Research and by the U.S.-Israel Binational Science Foundation. P. J. Robinson and K. A. Holbrook, UnimolecuIavReucrions (Wiley Interscience, London, 1972). W. Forst, Theory of Unimolecufar Reactions (Academic Press, New York, 1973). I. Oref and B. S. Rabinovitch, Acc. Chem. Rex., 1979, 12, 166. For a recent experiment iiivolving relatively low levels of excitation see A. B. Trenwith and B. S. Rabinovjtch, J. Phys. Chem., 1982,86,3447. A. Ben-Shaul, Y. Haas, K. L. Kompa and R. D. Levine, Lasers and Chemical Change (Springer VerIag, Heidelberg, 1981). M. Quack, J. Chem. Phys., 1978, 69, 1282. I’ (a) J . R. Barker, J . Chm. Phys., 19x0, 72, 3686; (b) S. Ruhman and Y. Haas, J. Chern. Phys., 1982, 76, 1317. D. J. Bogan, Gas Phase Dioxetan Chemiluminescence, in Chemi- and Bia-Energized Processes, ed. W. Adam and G. Cilento (Academic Press, New York, 1981). T. Wilson, Int, Reu. Sci. Phys. Chem., Ser. 2, 1976, 9, 265. W. Adam, Pure Appl. Chem., 1980,52, 2591. lo Y. Haas and G. Yahav, J. Am. Chem. Soc., 1978, 100,4885. ‘ I G . Yahav and Y. Haas, Chem. Phys., 1978,35,41. l 2 Y. Haas, Ado. Chem. Phys., 1981, 47(1), 713. l3 B. D. Cannon and F. F. Crirn, J . Chem. Phys., 1981,75, 1752. l4 B. D. Cannon and F. F. Crim, J . Am. Chew. Suc., 1981, 103, 6722. l5 B. D. Cannon, Ph.D. Thesis (University of Wisconsin, Madison, Wisconsin, 1981). l6 G. Yahav and Y . Haas, unpublished results. l7 A slow reaction was reported for the IRMPE of CF,CN, H. Reisler, F. Kong, C. Wittig, J. ’’ I . Oref, J. Chem. Phys., 1981, 75, 131. Stone, E. Thiele and M. F. Goadtnan, J , Chem. Phys., 1982, 77, 328.

ISSN:0301-7249    

DOI:10.1039/DC9837500239

出版商:RSC    

年代:1983

数据来源: RSC

摘要:

GENERAL DISCUSSION Prof. I. Yamazaki (Institute for. Molecular Science, Okazaki) said: In the paper presented by Prof. Rice and co-workers, the fluorescence lifetime of the fast-com- ponent decay is changed largely with the excited rotational level (see fig. 3). Re- cently Prof. Baba and co-workers ’ in Hokkaido University have demonstrated that, for pyrazine and pyrimidine vapours, the fluorescence quantum yield and the lifetime (for pyrimidine) are changed when the excitation wavelength is changed along the rotational contour of the 0-0 band at pressures < 1 Torr, whereas at pressures >10 Torr they are constant. The fluorescence component observed at higher pressures is regarded as due to the fast component. Hence Prof. Baba and I believe that, so far as the fast component is concerned, the lifetime as well as the quantum yield is constant irrespective of the excited rotational level.H. Baba, N. Ohta, 0. Sekiguchi, M. Fujita and K. Uchida, J . Phys. Chern., 1983, 87, 943. Prof. S. A. Rice (Uniuersity of Chicago) said: The results given by Prof. Yamazaki refer to gaseous pyrazine at room temperature, where many rotational states are thermally excited. Our experiments were carried out on very cold (ca. 1 K) molecules, so we could control the rotational transitions pumped. For most large molecules the rotational contour is made up of a superposition of rotational branches, so at any given energy in the contour a range of J and K will be excited. I do not see how Prof. Baba’s experiments can define the rotational quantum number well enough to give any indication of its value, hence I do not believe that Prof. Yamazaki’s con- clusion concerning the variation of quantum yield of fluorescence with J, from data on that yield as a function of position of excitation in the rotational contour, can be considered definitive, or even indicative. Prof.Y. Haas (Hebrew University of Jerusalem) said: Prof. Rice’s paper emphasizes the importance of phase relaxation and phase memory following a short laser-pulse excitation. Some photochemical reactions are extremely fast and involve bond fission in < s. Such processes are short compared with the time scales discussed in the paper and entail a rapid conversion of electronic energy to nuclear motion. Is there a possibility of preserving some phase information in this case, and could it be experimentally detected in some way? Prof.S. A. Rice (University of Chicago) said : I believe there are circumstances for which the answers to both of Prof. Haas’s questions are yes. To date very little attention has been focused on the relationships between the excitation process, the non-stationary state created by that excitation and the evolution of the non-stationary state. It is only in certain limiting cases that the preparation of a state and the evolution of that state can be considered to be independent processes. For example, the calculations described by Taylor and Brumer in their paper show clearly how the phase distribution in the excitation source must be accounted for in any detailed understanding of the initial decay of a prepared state.Turning this observation around, if the excitation process is coherent it ought to be possible to alter the time evolution of the system by tailoring the properties of that excitation process. That this is possible has been demonstrated in magnetic resonance spectroscopy :252 GENERAL DISCUSSION think, for example, of the spin-echo technique. It ought to be possible to execute a similar programme for molecular excitation on a time scale shorter than or comparable to the dephasing time for any particular excitation. It will be more difficult to carry out a sophisticated, controlled, coherent excitation process for a molecule than for a spin system because the energy-level structure for the former is much more complex than for the latter.Nevertheless, the principle that continuous control of the phases of the excitation source and molecule will permit control of the time evolution of an excited state is valid and I expect it to be used. Although J expect that control of the time evolution of a prepared state will lead to measurable changes in, say, the energy distribution or the ratio of yields of products of a reaction, 1 am uncertain as to whether the effects will be small or large and how the magnitudes of the effects depend on molecular parameters. Dr. D. M. Goodall (Utziuersity of York) said: In the van der Waals complex of s-tetrazine and argon, the argon is situated on the out-of-plane C, axis. I presume that the decomposition coordinate involves a lengthening of the distance between Ar and the ring along this axis.Motion along this coordinate is orthogonal to the group of in-plane vibrational modes, 6a and 6b (fig. 2 in Prof. Rettschnick’s paper). It was found that the 6a’ state does not dissociate directly. The modes from which energy transfers into the decomposition coordinate are both out-of-plane vibrations, 16a and 1621. Could Prof, Rettschnick comment on the relevance of geometric and symmetry factors in this decomposition ? Prof. R. P. H. Rettschnick (University of Arnstivdam) said : We have studied the dissociation process T”Ar --f T*f -I- Ar. The subscripts i and f refer to different vibronic states of the tetrazine molecule. The energy difference E,-E, is converted into dissociation energy of the complex and kinetic energy of the dissociation frag- ments.The energy of the initially excited state of the complex, Ei, may include vibrational energy absorbed by the external modes of the complex: 0 (stretching mode), /3y and pz (bending modes). The dissociation rate depends on both the kinetic energy of the fragments and the coupling between the vibrations of tetrazine and the external motions of the complex involving changes in the van der Wads bond length. The complex T-Ar belongs to the point group CZv. The symmetry species of the external modes 0, py and /Iz are a,, b, and b,, respectively, and the internal vibrations 6a, 6b, 16a and 166 belong to the representations a,, a2, a2 and a,, respectively. In our experiments the rotational temperature of the tetrazine molecule and the complex T-Ar was rathcr low (ca.5 K) and therefore the effect of Coriolis interaction is probably of minor importance. Rupture of the van der Waals bond may occur when a vibrational quantum of one of the internal modes is transferrcd towards the van der Waals stretching vibration. This process is symmetry-allowed if the product representation of the initial vibrational state and the perturbation term, which is a part of the Hamiltonian of the complex, contains the totally symmetric representation a,. The oul-of-plane mode 16b, as well as the in-plane mode 6a, interacts directly with the van der Wads stretching mode. Model calculations dealing with these inter- actions have been started recently, but reliable results have not yet been obtained. In my opinion the different properties of the vibrational modes 6a and 166 are primarily due to the different amounts of kinetic energy of the dissociation fragments (momen- tum-gap law).I have n o doubt that the 16n vibration is very effective in the dis- sociation process bccause of the low kinetic energy of the fragments after dissocia- tion. The conversion of one vibrational quantum of the torsional mode 16a into vibrational energy of the van der Waals stretching mode is a symmetry-forbiddenGENERAL DISCUSSION 253 process unless other vibrations are involved. If the bending modes by and pz are both involved in the energy-transfer process the symmetry restriction is violated, i.e. when the product representation for Q, Py and Pz equals the representation of the 16a mode.Energy flow towards the bending modes during the dissociation process can give rise to a rotationally hot tetrazine fragment (cf. fig. 5 of our paper). Dr. G. G. Baht-Kurti and Mr. I. F. Kidd (Uniuersity of Bristol) said: In their paper Ramaekers et al. study the photodissociation and redistribution of energy in the s-tetrazine-argon van der Waals molecule. We have been examining the analogous processes in the Ar-H, and Ar-HD van der Waals molecules using highly accurate theoretical methods. This system has the advantage that it is sufficiently simple to allow a detailed and accurate theoretical study to be undertaken. Good experimental data exist for these systems and potential-energy surhces and dipole-moment functions have been proposed for them. The experiments consist of measurements of the infrared absorption spectrum of the van der Waals molecules.The light is absorbed by the H, (or HD) portion of the van der Waals molecule. This then becomes vibrationally excited. The subsequent redistribution of the vibrational or rotational energy then leads to the dissociation of the complex. and present a few of our conclusions below. When the Ar-H, van der Waals molecule is excited to the state corresponding to Ar-H2(tl = 1, ,j = 0) and with total angular momentum J = 1, we calculate that the half width of the spectral lineshape is 1.41 x In contrast to this, if a small amount of additional rotational energy is also provided to the complex, so that it is now excited to its Ar-H,(v = 1 , j = - 2) state, the linewidth now increases to 5.07 x cm-l, corresponding to a very much shorter lifetime of ca. 1.0 x lo-'' s.The details of these calculations are to be published shortly.s has published the i.r. absorption spectrum of Ar-HD. In fig. 1 below we present our theoretical calculation of this spectrum over the wavenumber range 3866-3906 cm-l. Fig. 1 should be compared with fig. 8 of ref. (1). In general terms there is excellent agreement between our calculated spectrum and the experimentally observed one. There is slightly sharper structure in our calculated spectrum owing to the fact that we have included only the natural lifetimes of the states and no other broadening effects. There are two lines missing in our spectrum as compared with the experimental spectrum at around 3870 cm-l.These lines arise from quasibound states of the Ar-HD van der Waals molecule which are trapped by the centrifugal barrier.6 These states were not included in our present calculations. We have calculated accurate photodissociation cross-sections for these processes cm-l, corresponding to a lifetime of ca. 0.0004 s. In a previous Faraday Discussion McKellar A. R. W. McKellar, Faraday Discuss. Chem. Soc., 1982, 73, 89. R. J. LeRoy and J. S. Curley, Adu. Chem. Phys., 1980,42, 353. A. M.'Dunker and R. G. Gordon, S. Chem. Phys., 1978, 68, 700. G. C. Balint-Kurti and M. Shapiro, Chem. Phys., 1981, 61, 137. I. F. Kidd and G. C. Balint-Kurti, to be published. We thank Dr. J . M. Hutson for discussions on this point. Dr. T. Stephenson and Prof. S. A. Rice (University of Chicago) (partly communi- cated) : We have recorded the dispersed fluorescence spectra resulting from the excitation of helium-benzene van dcr Waals complexes.The vibrational relaxation pathways observed when the ]HeC,H, and complexes are excited to the 61,61162 and lo2 vibrational levels in the benzene lBzu state are shown in fig. 2, 3 and 4 respectivcly. Approximate branching ratios are presented in table 1. We find that in all cases the C6H6, HeC6H6 and He,C,H, absorptions overlap at our level of resolu-254 GENERAL DISCUSSION 65 6 0 5 5 50 45 2 40 n I ? 3 5 5 - 2 30 tl v b 2 5 % o l d 1 I I I I I I 38 65 3875 3085 3895 3905 photon energy /cm - Fig. 1. Calculated i.r. absorption spectrum of Ar-HD in the energy range 3866-3906 cm-'. The vertical scale corresponds to the photodissociation cross-section in units of A'.The spectrum corresponds to a temperature of 77 K. tion (excitation bandwidth ca. 1 cm-I). The data presented correspond to excitation at the absorption maxima of the complexes noted; no attempt has been made to separate the effects of overlapping transitions. In addition, because of the small frequency shifts involved, we are unable to distinguish between emission from bare benzene, resulting from vibrational predissociation of the complex, and the complex itself, wherein a change in vibrational state is ascribed to intramolecular vibrational relaxation. Several qualitative features of helium-benzene complex dynamics can be deduced from the data. First, the patterns of vibrational relaxation/vibrational predissociation are highly selective.This characteristic is demonstrated best in the 61162 and lo2 data. The 6l data provide an opportunity for comparison with collisionally induced vibrational energy transfer. Collisions of helium with 6l benzene at 300 K induce vibrational relaxation to the 11516' levels with an efficiency at least an order of magnitude larger than for relaxation to 162.1 This is contrary to the results presented here, in which energy redistribution proceeds most favourably to the 162 level when theGENERAL DISCUSSION 255 600 500 400 3 I !3 2 300 4 200 100 0 init ;a I level - f i n a1 levels 6' 6'- Fig. 2. Vibrational relaxation/predissociation pathways observed when HeC6H6 and He2C6H6 are excited to the 6' level. Table 1. Vibrational relaxation/predissociation pathways for HeC6H6 and He2C6Hs initial level final level approximate branching ratio 6', H&&(523) 1 62(475) 1 1'(517), 16'(238) 0" (0) 0" (0) 6l, H&6&(526) 1 62(475) 11'(517)? 16'(238) 6'162, HeC&,(1002) 6'16'(759) 6'1h2, He2C6H6(1008) 6l16'(759) 6l(521) 6'10'(1102) 4'11116'(1120) 1 64(950) 41162(840) 62( 1040) 0" (0) 1 02, HeC,H,( 1 164) 1 02, He2C6Hb( 1 166) 0.65 0.25 0.10 0.35 0.50 0.15 1 .o 0.40 0.20 0.40 0.70 0.30 0.40 a Energy, in cm-', of the specified level above the C6H, 'B2" origin given in parentheses.Re- mainder of relaxation of this level characterized by fluorescence transitions that have ambiguous assignments. Possible candidates are 6'111, 6'16', 5', 17', lo', 112, 16'11', 162, 4' and 6'10'.256 GENERAL DISCUSSION 1000 900 4 ' 800 1 8 P 4 700 60 0 50 0 i n i t i a l l e v e l f i n a l levels 4' 16' 10'16' \ \ 1 \ \ ! - 4l 16' ' \ -10' \ 11- c - 6' - 16' Fig.3. Vibrational relaxation/predissociation pathways observed when HeC6H6(-) and HeZC6H6 (- - -) are excited to the 6'1 62 level. the C6H6 is excited to the 6' level. Clearly the interplay between Franck-Condon-type effects (whereby pathways involving small vibrational quantum number changes are favoured) and energetic effects is different in these two experiments. In both cases relaxation to the lBzu origin is a relatively minor pathway. Secondly, the very different pathways observed for the relaxation/predissociation of HeC,H, excited to the 6l and 61162 levels indicates that the spectator-mode model which describes glyoxal-H, complex dynamics is not applicable to benzene com- plexes.Within the spectator-mode model one might expect, by analogy with the relaxation of complexes excited to the 6' level, to see significant relaxation to 1 64 when complexes are excited to 6l1@. Unfortunately, we are unable to clearly excite HeC,H, to the other partner in this Combination level, 1 fi2. A similar lack of correla- tion between the behaviour of combination levels and that of the relevant individual modes was observed in the case of Ar-tetra~ine.~ Finally, the dynamics of vibronically excited helium-benzene complexes are qualitatively different from those observed by Brurnbaugh et al. for Ar-tetra~ine.~ In the latter work the predominant mode of relaxation fur all vibronic levels of the complex was fluorescence from the complex level initially excited (branching ratio >0.74).We do observe such single vibronic level fluorescence when helium-benzene complexes are excited. We feel, however, that the majority, and perhaps all, of this emission arises from the overlap of benzene and helium-benzene absorptions. In any case, it is clear that for benzene complexes vibrational relaxationlpredissociation effectively competes with emission from the prepared level. It is unclear at this time IGENERAL DISCUSSION 1200 1100 1000 900 257 - - - - - - initial 1 l e v e l final tevets 4 I . E P ru‘ lo2 10‘16’----- 800 c 70 0 1 I 600 -- 4’16’ Fig. 4. Vibrational relaxation/predissociation pathways observed when HeC,H,(-) and HezCaHs(- - -) are excited to the lo2 Ievel.whether the difference in behaviour of the benzene and tetrazine complexes is due to variations in complex dynamics or simply reflects the vastly shorter fluorescence lifetime of tetrazine relative to benzene. We are extending our studies of benzene van der Waals complexes to additional 13211 vibrational levels, to complexes with neun and argon and to partially deuterated benzene derivatives. C. S. Parmenter and K. Y . Tang, Chem. Phys., 1978, 27, 127. N. Halberstadt and B. Soep, Chem. Phys. Left., 1982, 87, 109. D. V. Brumbaugh, J. E. Kenny and D. H. Levy, J. Chem. Phys., 1983, 78, 3415. Dr. R. Naaman ( Weizrnann Institute, Israel) said : We have studied the reactions of van der Waals (VDW) complexes with Ba atoms and found an interesting dependence of the amount of energy deposited in the product on the VDW complex lifetime.Two reactions have been studied: (CF,I), + Ba -+ BaI + CH,I*Ar + Ba -+ BaI + . (1) (2) In both cases the mechanisms of the monomeric analogues were studied, applying laser-induced fluorescence (LTF) and reactive-scattering technique^.^ These mechanisms are now well understood. The experiment was carried out using a crossed-beam arrangement, the clusters being formed by supersonic expansion through258 GENERAL DISCUSSION a pulsed nozzle. A flashlamp-pumped dye laser was used to excite the BaI and to obtain its excitation spectrum. In fig. 5 the LIF spectrum of BaI is presented as produced by reaction (1). The vibrational population peaks around Y" = 50 and V" = TO for the mono- meric and dimeric reactions, respectively.This decrease of ca. 20 kcal cannot be attributed to the change in the exothermicity of the reaction due to the VDW bond. On the other hand, as can be seen in fig. 6 only small changes in the vibrational population are caused in reaction (2), and its peaks for the VDW case are at Y" = 16, compared with I/" = 20 for the monomer. A simple model offers one possible explanation for the dramatic change in reaction (1 j. There are six extra degrees of freedom in the reaction complex which come from the dimer itself. They all have very low frequency, and therefore behave as phonons in the condensed phase. Because of their high contribution to the density of states in the reaction complex, significant portions of energy are deposited in them.Since these modes correspond to translational or rotational motion, once the dimer is dissociated much less energy is left to be placed into the vibration of BaI. In reaction (2) the number of' low-frequency modes is smaller; however, one could also expect here a significant decrease in the internal energy of the BaI. The fact that this is not the case points to fast dissociation of the VDW molecules, before the reaction really takes place. This may be explained by a weaker VDW bond and by the need to remove the Ar atom, which is located near the iodine, before the reaction occurs. ' G. P. Smith, J. C. Whitehead and R. N. Zare, J. Chern. Phys., 1977, 67,4912; Faraday Discuss. Chem. SOC., 1979, 67, 124. P. J. Dagdigian, H. W. Cruse and R.N. Zare, Chem. Phys., 1976,15, 249 S. M. Lin, C. A. Mims and R. R. Herm, J. Phys. Chem., 1973, 77, 569. (20,20) (30,3O)(LO,LO) (50,501 I I I 1 I I 530 I h m Fig. 5, LIF spectra of Bal produced by the monomeric reaction Ba + CFJ (a) or by the dimeric reaction Ba + (CF& (b).GENERAL DISCUSSION 259 1 I 1 I I 1 I (20,201 f 1 1 I I I I I I t 5 32 533 534 53 5 536 537 538 539 Alnm Fig. 6. LIF spectrum of Bal produced by the reaction of Ba + CH31 (A) and Ba + CH3- I-Ar. The contribution of the former is decreasing from (B) to (C). Prof. A. H. Zewail (California Institute of Technology, Pasadena) said: Since in Prof. Quack's work the relaxation time z is obtained from linewidth measurements it is necessary to ensure that the line is homogeneous in nature.How does one decide that the transition is homogeneous or inhomogeneous and what is the influence of rotations on relaxation ? Dr. E. Heller (Los Alumos) said: In his presentation Prof. Quack mentioned possible difficulty in the experimental measurement of lines with small intensity in an overtone-Fermi-resonance spectrum, and that these uncertainties might be a problem for the spectral criterion for quantum chaos we have put forward in our Discussion paper and elsewhere. I would like to point out that intensities which are very small contribute very little to the estimate of ergodicity for the spectroscopic zero-order state, which in the case discussed by Prof. Quack is a local C-H stretch. The reason for this is that the quantity P(ala), mentioned in my contribution and defined in eqn (6), is nearly unaffected by small line intensities (small pz) unless there are very many of them left unresolved.For example, a term with p i = 0.1 contributes 0.01 to P(ala), but a term with say 1/20th of the intensity, i.e.pi = 0.005, contributes only 2.5 x If quite a few such lines are buried in noise, etc., it still will not matter for the fraction of phase space covered or the degree of ergodicity calculated from the experimental spectrum. or <0.3% of the contribution of the stronger line. Prof. X. de Hemptinne (University of Leuven) said: 1 wish to make two comments on Prof. Quack's work. The first one is to recall that laser radiation is not a pure harmonic wave as is assumed in his eqn (2) and also in ref. (15). I refer here to my comment (p.165) on the paper presented by Taylor and Brumer. I have indeed shown in the paper which I mentioned there that the degree of excitation of oscillators260 GENERAL DISCUSSION (average number of quanta) is a function of two parameters: the intensity of the light beam and the entropy flux associated with the radiation. The latter parameter, which has not been considered so far by theoreticians in the field of MPE, depends on the physical and thermodynamic properties of the source. Taking the correct time dependence of the laser radiation, and applying an infinite- order perturbational treatment, pertinent conclusions may be drawn about MPE in coherent light, without using rate equations or master equations. (Rate equations or master equations are only a " must " with incoherent light, which laser light is not.) My second comment relates to the authors' discussion of MPE on the basis of high- resolution spectroscopy.In my opinion this claim is somewhat misleading. Let me take as an example the MPE of ethylene (J. Chem. Phys., 1980,73,3170). It is known that two i,r. active modes ( v , and vlo) resonate in the spectral range covered by the C 0 2 laser. It was shown that the C02 radiation at moderate intensity was able to " superexcite " (multiphoton) selectively one of the two modes, depending on which laser line was used for the excitation. On the other hand, the fundamental (v = 0 to v = 1) spectrum of ethylene is now known with great precision and all rovibrational lines which have been assigned.By comparing the two results, no correlation can, however, be found between the mode to which ethylene is " superexcited " with laser radiation and the assignment of the 0 to 1 transitions. However, if the claim is that all states of the irradiated molecules should be considered simultaneously, then 1 think this would be equivalent to a treatment of MPE by infinite-order perturbation of the molecular Hamiltonian, with which of course I agree. Dr. G. Hancock and Dr. A. J. MacRobert (Oxford University) said: Prof. Quack has indicated conditions under which rates of i.r. multiple-photon excitation can be expected to depend non-linearly upon laser intensity. Evidence for intensity- dependent i.r. multiple-photon absorption cross-sections and dissociation yields has been reported in the literature, but this has in almost all cases been qualitative, because the variation in laser intensity over the duration of the i.r.pulses used (dramatic in the case of mode-beating TEA pulses) has made accurate specification of its magnitude impossible. This can be remedied by the use of single-mode i.r. lasers whose output is shaped by electro-optic crystal switching to produce pulses with fast rise and fall times and for which the intensity remains effectively constant with time at any point over the Gaussian spatial output.' We have used such shaped pulses to determine separate fluence and intensity dependences of i.r, multiple photon absorp- tion in SF6, using optoacoustic detection of relative absorbed energies as a function of these parameters, together with long path absorption measurements to determine absolute values.Fig. 7 shows the measured optoacoustic signal as a function of peak laser fluence Q M for absorption of the P(20) CO, laser line at 10.6 pm in 100 mTorr SF, at two different pulse lengths of 50 and 200 ns, each having rise and fall times <lo ns. BM is defined by the expression @ = 0, exp(--2r2/uj2) where 0 is the fluence at any point a distance r from the centre of the Gaussian output beam; OM is numerically equal to the total beam energy E divided by rcto2/2. The data show clearly that, for a given fluence, the optoacoustic signal, which is proportional to the average number of photons absorbed per molecule ( n ) , is larger when that fluence is delivered in a shorter time, i.e.at a higher laser intensity. This effect is opposite to that expected from collisional effects during the different pulse lengths. In previous studies it has been shown that collisions increase the average number of photons absorbed in SF,, and measurements of energy deposition for the P(20) line indicate that at 100 mTorrGENERAL DISCUSSION 261 these effects should be small even for the longest (200 ns) pulses used in the present experiments.2 We attribute the dependence of absorbed energy on pulse length at constant to the effect of laser intensity, but stress that our measurements may underestimate the true intensity dependence because of a collisional contribution. Data for pulses of length 50, 100 and 200 ns were deconvoluted ovcr the Gaussian spatial distribution of fluence and combined with the long-path absorption measure- ments to yield the true dependences of ( n ) upon @.From these, the dependences of (n) upon the intensity I (constant @) and upon @ (constant Z) were obtained within a 0,o 1 0.1 peak fluence, OM/J cm-2 1.0 Fig. 7. Optoacoustic signal, proportional to the average number of photons absorbed per molecular, as a function of peak fluence aM for the i.r. multiple-photon absorption of P(20) C 0 2 laser line at 10.6 pm in SF6 (100 mTorr). Results for two '' shaped i.r. pulses " are shown, of lengths 50(0) and 200( X ) ns, both having fast (< 10 r2s) rise and fall times, with constant intensity at any point on the Gaussian output profile. Data were taken at room temperature, 293 K .limited range of these variables. For example, at @ = 100 mJ cmp2, ( n ) K 1''' in the range 0.5 < I/MW cmp2 < 2, and at I = 2 MW cm-*, ( n } cc @0'5 for 100 < @/mJ cmL2 c: 400. Absolute valucs of ( n ) for a 50 ns pulse were, for example, 0.5 at 50 mJ cmp2 and 3.4 at 500 mJ cmp2. It is hoped that further measurements of this kind, particularly with shorter pulses of well defined shape to reduce collisional effects, will allow more detailed theoretical modelling of the multiple-photon absorption processes to be undertaken. M. N. R, Ashfold, C. G. Alkins and G. Hancock, Chem. Phys. Lett., 1981, 80, 1; A. W. Pasternak, D. J. James, J. A. Nilsen, D. K. Evans, R. D. McAlpine, H. M. Adams and E. B. Selkirk, Appl. Opt., 1981, 20, 3849; J. C. Stephenson and D.S. King J. Chem. Phys., 1983. 78, 1867. J. G. Black, P. Kolodner, M. J. Shultz, E. Yablonovich and N. Bloembergen, Phys. Rev. A , 1979, 19, 704. Dr. R. D. McAlpine and Dr. D. K. Evans (Chalk River Nuclear Laboratories, Ontario) said: Following the presentations by Dr. Hancock and by Prof. Quack, we wish to describe some experiments which demonstrate the role played by laser intensity262 GENERAL DISCUSSION as against fluence and by collisions in the multiphoton decomposition (MPD) process. Using a variable-pulse-length C02 laser we can separate and study effects due to the important parameters pressure (P), fluence (9) and laser pulse width (AT). As well, of course, the laser can be tuned to different lines allowing the effect of laser wave- number (qL) to be probed, though not in a continuous manner.We use the single pulse photoacoustic technique,2 calibrated by transmission measurements, to study multiphoton absorption (MPA) and product analysis plus reactant depletion to study MPD. For restricted ranges of q, and for fixed QL, P and AT, the absorption cross-section, a(v,), and the average number of photons absorbed per molecule, ( n ) ( q ) , obey the empirical equations : 4 9 ) = KYb ( 1 4 (n)(v,) = Kv,(l+b)/hcQL. ( W MPA studies of CDF3,3y4 CH30H and CH3NH26 show that for sufficiently small values of PAT a log-log plot of a(q) or (v)(v,) against q shows a bend at q = qc. That is, the values of K and b change at this point. This is shown, for example, in fig. 4 and 5 of ref. (3). As PAT increases, the degree of change in K and 6 at pc decreases.For CDF33q4 and CH30H,5 q C z 1-10 J cm-2 and is insensitive to a change in AT. However, for CH3NH2,6 the bend occurs at qC/Az z 50-100 MW cm-2 and it is qC/Az rather than qc which is constant as AT is changed. For CDF3, CH30H and CH3NH2 b above qc is less negative than b below qc. Hence for v, > qc there is a reduction in a bottleneck for MPA. In the case of CH3NH2 this barrier is overcome with a particular intensity rather than a particular fluence, as is the case for CDFJ and CH30H. Varying q, P and AT, we observe, for CDF33i4 and CH30H that and for v, < qc, a(q, PAT) follows the 3-parameter empirical form Eqn (3) can be understood in terms of the following model. For " zero " collisions, some fraction of the ground-state rotational distribution is in resonance with the laser, causing a hole to be " burned " in this distribution and giving a cross-section o(v,,O).As PAT increases, collisional rotational relaxation fills the hole in the rotational distribution with a macroscopic characteristic constant z, and a(q,PAz) > a(p,O). For sufficiently large PAT, all of the ground rotational distribution that can be coupled to the laser is accessible via rotational relaxation, and a plateau value a(v,,PAz) = o(v,,a) is measured. For v, > v,,, eqn (2) is obeyed for CDF3 and CH20H; however, a(q,PAz) is more complex than eqn (3) in a way suggesting that very fast relaxation processes between high-energy vibrational levels are also important. CH3NH2 does not obey eqn (2), and we have not identified another reduction of the number of independent variables P, q and AT for this molecule.Studies in our laboratory confirm earlier conclusions '3' that the MPD of CH3NH2 is intensity- as well as fluence-dependent. A. W. Pasternak, D. J. James, J. A. Nilson, D. K. Evans, R. D. McAlpine, H. M. Adams and E. B. Selkirk, Appl. Opt., 1981, 20, 3849. S. L. Chin, D. K. Evans, R. D. McAlpine and W. N. Selander, Appl. Opt., 1982,21, 65.GENERAL DISCUSSION 263 D. K. Evans, R. D. McAlpine and H. M. Adams, J. Chem. Phys., 1982, 77, 3551. R. D. McAlpine, D. K. Evans and H. M. Adams, J. Chem. Ph-vs., 1983, 78, 5990. D. K. Evans, R. D. McAlpine, H. M. Adams and A. L. Creagh, to be published. D. K. Evans, R. D. McAlpine and H. M. Adams, Chem. Phys., in press.' G. Hancock, R. J. Hennessy and T. Villis, J. Photochem., 1978,9, 197. * M. N. R. Ashfold, G. Hancock and G. Ketley, Faruday Discuss. Chem. Soc., 1979, 67, 204. Ms. K. von Puttkamer, Dr. H.-R. Dubal and Prof. M. Quack (ETH, Ziirich) replied: Prof. Zewail has raised again the central question of the separation of homogeneous and inhomogeneous structure in the vibrational spectra (we prefer the term structure to width, because in the present case the underlying fine structure remains discrete). In our paper we have described in detail the method, which takes into account the rotational structure and allows us to separate homogeneous and inhomogeneous vibrational contributions by evaluating the temperature-dependent spectra. We might add here that this method has been tested on theoretical model spectra, for which all parameters were known by definition, and was found to give adequate results, for instance for the homogeneous width at 0 K (To) an accuracy of k0.2 cm-l.Further, improved models with asymmetric inhomogeneous line shapes, as shown in fig. 3 of our paper, are being applied to our spectra. Prof. de Hemptinne recalls that laser radiation is not a pure sine wave. This fact is known to and and has been pointed out by us [see eqn (2.2) of ref. (15) in our paper and the detailed discussion given there concerning the influence of laser properties]. It is, however, the task of theory to provide accurate descriptions of idealized limiting cases, which can be approached, if never reached, in laboratory experiments (the theory of free fall in vacuo is a classic case).Three such limiting cases lead to simple results: (1) excitation with monochromatic radiation, (2) excitation with " white " light over a certain bandwidth and (3) excitation with thermal radiation. These cases have been treated in our work and the numerical treatment of more com- plex intermediate situations is possible. Monochromatic radiation is, under certain conditions, an adequate limiting case for i.r. multiphoton excitation. Before philoso- phizing about the possible influence of laser properties one had better control them experimentally.lV2 We and others have shown that for some conditions not even the mode structure of the laser has an appreciable influence on i.r. photo~hemistry,~~~ although other situations are known as well and have been treated the~retically.~ Concerning the description of i.r.multiphoton excitation in terms of " spectro- scopic states " from high-resolution spectroscopy it is clear that not just the states of the fundamental transition but all molecular states have to be included [matrices W and V in eqn (2) of our paper, see also ref. (4)]. I can mention in this context recent quantum-mechanical calculations in which we have simulated the i.r. multiphoton excitation of ozone to dissociation threshold using the basis of spectroscopic ~ t a t e s . ~ These calculations, as in our previous work using this approach, have provided considerable insight in the mechanism of i.r. multiphoton excitation of polyatomic molecules and we are unaware of any better approach to this problem, although there are alternatives. Concerning the comments made by Drs Hancock and McRobert (Oxford) and by Dr.McAlpine (Canada) I can only congratulate these authors for their beautiful experimental work using controlled laser pulses for i.r. multiphoton excitation.' It is, of course, just these data which are needed for future comparison with theory. Among several possible experiments using their technique I would like to recall a particularly significant one, which has not, so far, been carried out: the determination of intensity-dependent rate coefficients in the non-linear regime of i.r. photochemistry.264 GENERAL DISCUSSION Using shaped pulses, this is possible even without real-time measurement of product or react ant concentrations .4*6 The comment made by Dr.Heller is addressed to a point made by us in the oral summary of our paper, namely concerning the importance of weak spectral lines for the understanding of the dynamics of molecules. We stress that we did not want to address by this the question of the validity of Heller's spectral criterion for quantum chaos in theoretical model spectra. Rather we wanted to stress the fact that a dynarnical interpretation of spectra on the basis of strong bands alone could be very misleading. It is probably best to illustrate this here with the example presented orally, which had not been included in detail in our paper. Fig. 8 shows the spectrum of the A,-band system of the vCH = 3 chromophore I i 1 I I t 1 I I 8000 8200 8400 8600 8800 F/cl-tl-' Fig.8.1.r. spectrum of CF3H in the range of the us = 3 CH chromophore Fermi-resonance band system. The weak bands A and B have been enlarged as shown. state in CF3H. This band system is dominated by Fermi-resonance interaction between S(3)B(U), S(2)B(2), S( 1)B(4) and S(O)B(6) and, indeed, disregarding weaker interactions, four bands can be observed, only two of which are strong and have been discussed previ~usly.~ The model Hamiltonian which allows us to establish the assignment is shown in fig. 9. This Hamiltonian is based on a simple, effective . 13 0 0' 1 2 2 O> 1140, 1060' , 0 J 0 0 - 3/ & k sbb E0(0,6,0) Fig. 9. HamiItonian for the A1 Fermi-resonance system of the CH chromophore in CX3H shown in fig. 8 [see text and ref. (S)].GENERAL DISCUSSION 265 anharmonic local force field for the CH chromophore and has been very successful in predicting band positions and intensities also for the E-band systems (with appro- priate changes) and for a number of molecules investigated in our laboratory ' (see also below).If one considers only the strong bands, one is tempted to treat the problem as a two-state Fermi-resonance. Hypothetical ultrashort pulse excitation of such a two- state system would essentially result in a fast beating phenomenon (" intramolecular energy transfer ") between two states S(3)B(O) and S(2)B(2). However, the time evolution using the full Hamiltonian with the parameters being determined from experiment is shown in fig. 10. This shows a very important contribution at least P N 1 .O 0.5 0 0 0.1 0.2 0.3 0.L 0.5 0.6 tips Fig.10. Time evolution for the population of separable basis states, assuming hypothetical ultrashort pulse local excitation at t = 0 and using the Hamiltonian in fig. 9 with the experi- mentally determined parameters. from the third state S(l)B(4) and a visible contribution from S(O)B(6), although the fourth band is hardly visible in the experimental spectrum. In fact this band was only detected after it had been predicted theoretically. The point is thus, that for any dynamical interpretation of spectra a careful search for weak lines should be undertaken. A good theoretical model of the spectrum and dynamics considered can be helpful in this context. The validity of our model for overtone spectra of the isolated CH chromophore has been tested on further molecules.Fig. 1 1 shows the frequency range correspond- ing to fig. 8 but for (CF3)3CH. The great similarity is immediately obvious and can be established by a detailed evaluation. Of course, further interactions lead to broad shapes for the large molecule, as discussed in our paper. The lower and next-higher overtones can be interpreted in a similar manner. Table 2 summarizes the main spectroscopic parameters evaluated for three particularly simple cases (the results for CD3H are still preliminary and have been mentioned also in relation to Prof. Zewail's ~ a p e r ) . ~ The main point of table 2 is the great internal consistency of the spectroscopic parameters. All three molecules show similarly large values for the effective diagonal anharmonicity xlSs of the stretching vibration,266 GENERAL DISCUSSION I I 1 I I I I I I I 7800 8000 8200 8400 8600 8I v"1crn-l 30 Fig.11. 1.r. spectrum of (CF3)3CH in the range of the us = 3 CH chromophore Fermi- resonance band system. See also text and fig. 8. for the effective off-diagonal anharmonicity X'sb and for the anharmonic constant ksbb inducing the Fermi-resonances. The " universal " local potential of the CH chromophore at large amplitudes can also be investigated by ab initio calculations.1° There is hope that the investigations of the spectra of fundamentals and overtones including weak features of the isolated CH chromophore in HCX3, which was started some years ago, will lead to a reasonably consistent understanding of the dynamics of this chromophore.ll M. N.R. Ashfold, C. G. Atkins and G. Hancock, Chem. Phys. Lett., 1981, 80, 1; A. W. Pasternak, D. J. James, J. A. Nilson, D. K. Evans, R. D. McAlpine, H. M. Adams and E. B. Selkirk, Appl. Opt., 1981, 20, 3849. M. Quack and G. Seyfang, J. Chem. Phys., 1982, 76, 955; M. Quack and G. Seyfang, Chem. Phys. Lett., 1982, 93, 442. M. Quack and G. Seyfang, Ber. Bunsenges. Phys. Chem., 1982, 86, 504. M. Quack, Ado. Chem. Phys., 1982, 50, 395. M. Quack and E. Sutcliffe, Chem. Phys. Lett., 1983, 99, 167 and to be published. M. Quack, J. Chem. Phys., 1979,70, 1069. H-R. Dubal and M. Quack, to be published. A. H. Zewail, Faruduy Discuss. Chem. SOC., 1983, 75, 315 and comments on this paper. lo M. Lewerenz and M. Quack, in preparation. l1 H-R.Dubal and M. Quack, Chem. Phys. Lett., 1980,72, 342. ' H. J. Bernstein and G. Herzberg, J. Chem. Phys., 1948, 16, 30. Table 2. Spectroscopic constants (in cm-') for the local model Hamiltonian of the CH chromophores (rounded). CF3H8 v", 3080 t b 1379 x s s - 60 Xbb -8 xs b - 25 gbb 7 lksbbl 96 (CF3)3CH8 3035 1358 - 55 0 -15 5 71 CD3H'O 3049 1290 - 60 -2.8 - 24.5 4.3 50.5 The constants have their usual spectroscopic meaning (see also text and main paper). The prime refers to an effective local approximation discussed in detail elsewhere.8GENERAL DISCUSSION 267 Prof. T. Baer (University of North Carolina) said : It was not clear from the paper presented by Dr. Hancock whether the final-state distribution of the products CF3 + CN is a result of the use of MPI, or whether one would obtain similar results if the reaction were carried out under conditions of thermal activation.Prof. C. Wittig (University of Southern California) said: In direct response to Dr. Baer’s question about whether IRMPD prepares the system differently than does collisional thermal activation, the answer is yes. Rotations are cold and vibrations are hot, unlike thermal activation. Also, in many instances the rate of reaction is controlled by the rate of optical pumping, and therefore reaction occurs from a group of energies with a rather small spread. This is quite unlike thermal systems except under certain conditions in the low-pressure regime. Most of the associated nuances were discussed in the previous reply, and it would be very useful to prepare parent species in thermal equilibrium and measure nascent V,R,T excita- tions in the reaction products (perhaps using very-low-pressure pyrolysis).Dr. G. Hancock (Oxford University) said : The final-state distributions presented in fig. 3(A) and (B) and 4(A) and (B) of our paper are those calculated for the CN(X2C+,v, J ) fragment under the assumptions of phase space theory (PST, fig. 3) and statistical adiabatic channel theory (SACT, fig. 4) for the unimolecular de- composition of CF3CN molecules which possess a specified value of E$ (the energy above the dissociation threshold which can be distributed amongst the degrees of freedom of the products; we call this the ‘‘ disposable energy ”) and Jo, the total angular momentum. In the i.r. multiple-photon dissociation experiments we observe dissociation from CF,CN molecules with distributions of values of E$ and Jo.The form of these distributions is unknown, but model calculations suggest that our assumptions of a Gaussian distribution for E$ and essentially a thermal distribu- tion for Jo are realistic ones. We present in fig. 3(C) and (D) as an example the PST calculation at a given value of Jo averaged over the assumed E$ distributions, but argue that these distributions are not of primary importance in the present calcula- tions, as all individual values of ET and Jo that we have tested give similar results, namely that PST predicts approximately equal vibrational and rotational “ tempera- tures ” in contrast with experimental data, but that SACT can overcome this defect whilst retaining the concept of energy randomisation prior to decomposition.The calculated CN internal-state distributions at given E$ and Jo for the two theories are independent of the method of preparation of energy randomised CF,CN molecules above the dissociation threshold, and thus can be applied to thermal decompositions. Energy distributions in the fragments would then be calculated by summing contribu- tions from molecules with distributions of E$ and Jo expected from thermal activation (distributions which generally will not be the same as those from i.r. multiple-photon absorption). Mr. S. Cohen and Dr. R. Naaman (Weizmann Institute, Israel) said: We would like to present an alternative model which explains why the rotational tempera- ture of a photodissociated fragment can be one-half of the vibrational tem- perature. The phenomenon can be understood by taking into account the change in heat capacity of the CN fragment upon passing from bound to free state.Rotational cooling of NO desorbed from Ru(OO1) has been accounted for in a similar fashion.’ Because at most one of the two rotations of a diatomic molecule is allowed in the268 GENERAL DISCUSSION adsorbed state, energy from this one rotation must be divided into two modes after desorption. The resulting Trot is Tsurf/2, A similar effect can occur in unimolecular decomposition. An important difference between desorption and decomposition is the nature of the " silent " fragment (the fragment not being spectroscopically analysed). In this unimolecular decomposition, CF3 is the silent fragment, whereas for the surface it is the Ru crystal.When the diatomic and silent fragments separate, the diatomic's moment of inertia must be small compared with that of the silent fragment in order for the rotational cooling to be observed. Desorption and dissociation represent two limiting cases. For desorption, there is clearly no rotational motion of the crystal as a whole. Therefore, the only contribution to diatomic rotation comes from the one rotational mode of the bound molecule. For dissociation, there is an additional rotation, that of the parent molecule. If the moment of inertia for the silent fragment is large compared with that of the diatomic, the diatomic inherits little energy from the parent and the result is similar to desorption.If the moment of inertia of the silent fragment is close to that of the diatomic, the rotational energy, inherited from the parent, will represent a significant fraction of the diatomic's rotational energy, so Trot will be larger than TVi,/2. Data from two recent works on photodissociation support this model. Lesiecki and Guillory have photolysed CH,CN.' They found Tvib of 425 K and T, of 664 K for the CN fragment. For CF3CN, Tvib is 2400 K and TR = 1200 K. Rotational constants for the fragments are as follows : B,(CN) = I .97 cm-' 3a B,(CH,) = 9.75 crn-l, B,(CH,CN) = 0.307 cm-1,3b B,(CF3) = 0.3 cm-', B,(CF3CN) = 0.0982 ~ r n - l , ~ A similar trend is seen in the rotational and vibrational temperatures of CF2 fragments resulting from the photolysis of CF2-X-Y.' For X-Y=Br2 and Clz, Trot = &Tvib.For X-Y = HCI, TR = 2Tvjb. Accordingly, B,(Br,) = 0.081 cm-', B,(Cl2) = 0.244 cm-l and B,(HCI) = 10.6 cm-'?" S. E . Bialkowski, J. Chem. Phys., 1983, 78, 600. M. L. Lesiecki and W. A, Guillory, J. Chem. Phys., 1977, 66, 4239. (a) G . Ilerzberg, lWolecuiar Spectra and Molecular Structure I : Spectra of Diatomic Molecules (Van Nostrand, New York, 1950); (b) G. Herzberg, Molecular Spectra and Molecular Struciure 11: Electronic Spectra of Polyafomic Molecules (Van Nostrand, New York, 1966). C. A, Barrus and R. M. Potter, J. Chem. Phys., 1957,26, 391. J. C . Stephenson and D. S. King, J. Chenr. Phys., 1978, 69, 1485. Prof. C. Wittig (Unitlersity of Southern Calvornia) said: The point raised by Dr.Naaman concerns the use of simple concepts and parameters, such as heat capacity and temperatures, to describe our observations. This is the essence of the last part of our paper, and I would like to elaborate on this, since once properly understood it is straightforward to develop the formal arithmetic required for caIcula- tions. It must first be appreciated that formalisms such as PST and SACT have embedded in them implicit assumptions concerning intramolecular energy transfer, namely that it is fast compared with the time required for the molecule to go from near the equili- brium geometry to some transition state ( 10-'2-10-'3 s). To appreciate this, consider the case of CF3CN. In our experiments, rotational excitation is low due to the sizable moments of inertia, and we expect parent rotations and translations to be essentially 300 K.Vibrational excitation is quite high, however, and the 12 vibrational degrees of freedom enjoy efficient coupling in the usual sense. Thus uur experiments prepare excited molecules with 12 degrees of freedom which are " hot '' and 6 degrees of freedom (rotation and translation) which are " cold ".GENERAL DISCUSSION 269 Now let us turn to the activated complex, in which it is assumed that all states are equally accessible within the constraints of conservation of energy and angular momentum. Relative translations are with respect to the parent centre of mass (c.m.). To simplify matters, we simply avoid the awful problems associated with finding constants of motion as the fragments are accelerated with respect to the c.m.while developing their own quantization axes. Within the conceptual framework of PST, the degrees of freedom being equilibrated are 7 for vibrations (6 for CF3, 1 for CN), 5 for rotations (3 for CF3, 2 for CN), 2 for the orbital motion of the fragments and one for radial translation. This totals 15, whereas the parent only had 12 degrees of freedom, which were originally excited. It is obvious in the case of PST calculations that the originally cold rotations are being equilibrated with the energized vibrations, and this is a strong implicit assump- tion. Both wagging and torsional vibrations, as well as parent rotation, lead to product rotation and translation, and if parent rotation is deficient in excitation, then product R, T degrees of freedom will appear deficient in excitation relative to product vibrations.Incidentally, because product rotations and translations are strongly coupled, and since kinematics is important in how the dynamics become manifest in product degrees of freedom (see our contribution on NCNO), we prefer to treat product R, T degrees of freedom together until a formalism for their separation evolves. Thus, the PST calculations may well sample too much phase space, since large values of orbital angular momentum, which correlates well with parent rotation, can be offset by rotational angular momentum of the fragments. Although the theory does not require that product motions be fully developed at a transition state, and although conservation of angular momentum is obeyed rigorously in the calculations, the theory implicitly requires that energy flows between parent vibrational and rotational degrees of freedom.Note that this is a flow and not a correlation as in SACT. It is here that we offer the simple arguments presented at the end of our paper using heat capacities and temperatures. As scattering into products nears completion (e.g. towards the top of the centrifugal barrier), we simply take the kinetic energy from the 5 vibrations which are being converted into product R, T motions and add this to the parent rotational energy in order to estimate the energy available for product R, T motions in the c.m. system. Including vibrational potential energy in this reservoir is physically unacceptable and leads to the unsavoury requirement of a large barrier for the association reaction.When applying this to the CF3CN system, we find that this approach predicts very nicely the Tv = 2400 K and TR = 1200 K experimental results. Also, because our measurements of translation energy [T,(CN) w 900 K] are in the laboratory and not the c.m. system, we expect our measured translational energies to be lower than 1200 K, since the relative motion is superimposed on the (300 K) c.m. motion of the parent. Thus, with rather straightforward arguments, we can reconcile our observations and we will develop this into a structured formalism as soon as possible. SACT, with its conceptually appealing emphasis on correlating certain parent vibrations with product angular-momentum states, has a built-in mechanism for blocking rotations, and it therefore comes as no surprise that our results can be fit with an SACT calcula- tion.However, the barriers in SACT will release energy along the exit channel and this will appear as product R, T motions, so it is not clear that product R, T excitations won’t be just as high with SACT as in the case of PST. Also, the arguments presented above concerning “ cold ” parent rotations and “ hot ” parent vibrations apply equally well to SACT.270 GENERAL DISCUSSION Finally, I would like to point out that the above considerations, coupled with a careful look at how kinematic effects can lead to cold product rotations, as in the case of NCNO dissociation, may well explain many of the results wherein species desorbed from a surface show rotational temperatures far below the surface temperature. Dr.K. Rynefors and Mr. J. Davidsson (Goteborgs Universitet) said: We would like to comment on the paper by Beresford et al. concerning the effects of total angular momentum conservation shown in their fig. 2(A). It has previously been argued that the representation of this conservation can preferably be done in energy space.' Many theories of unimolecular decomposition use phase space for the distribution of microstates. The density of states is then a function of energy and not, for example, of angular momentum. Often the primary experimental results are product energy distributions where also a representation in energy space is preferable. For further details, see ref. (1). In fig. 12 this representation has been used for the CF, and CN fragments con- I I EC Fig.12. Energy-space representation for the CF3 and CN fragments considered as a point mass and a diatomic system, respectively. sidered as a point mass and a diatomic system, respectively. In fig. 12 Erot is the rotational energy of CN and Ec is the centrifugal rotational energy. The electronic potential has been adopted from the phase-space theory calculations in the paper. Jo is set to 4 x A total energy of 1.88 x J, corresponding to the absorption of one photon above threshold, is used since the restriction curve comes very close to the Erot axis for higher values of total energy. We have also done some preliminary calculations on the effects of the CF, rotation. First, the allowed region is consistent with Boltzmann-shaped distributions for the rotational and vibrational degrees of freedom.Secondly, only low values of Ec are allowed in the diagram. Since Ec is transformed to translational energy in the product channel it is J s, since this is the most probable value for CF,CN at 300 K. From fig. 12 we believe that two conclusions can be drawn.GENERAL DISCUSSION 27 1 expected that this energy also is rather low, Both conclusions are in agreement with experiment a1 results.2 Note that these restriction curves can be drawn at any separation distance r between the fragments and not just at the peak of the centrifugal barrier as done previously.’ It is found that the restriction curves are displaced towards larger Ec values for higher r values but also that this displacement is reversed at a critical distance.This effect is closely associated with what Bunker calls bottlenecks in the number of micro- states as a function of Y. The connection between the restriction curves and bottle- necks has been described in more detail el~ewhere.~ K. Rynefors and P. A. Elofsson, Chem. Phyx Lett., 1981, 84, 343. ’ J. R. Beresford, G . Hancock, A. J. MacRobert, J. Catanzarite, G, Radhakrishnan, H. Reisler and C. Wittig, Faraday Discuss. Chem. Soc., 1983,75,211; H. Reisler, F. Kong, A. M. Renlund and C. Wittig, J. Chem. Phys., 1982,76, 997. D. L. Bunker and M. Pattengill, J. Chem. Phys., 1968, 48, 772. K. Rynefors, to be published. Prof, P. Brumer (Uniuersity of Toronm) said: A variety of different statistical models for birnolecular collisions has been discussed at this conference.Indeed, it is well known that a host of statistical models may be defined, each yielding different product distributions. This follows from the generality of the fundamental require- ments of a statisticaI model, i.e. that it satisfy microscopic reversibility and ‘ & zero relevance ”. The latter condition requires that the final distribution be independent of all initial conditions other than conserved quantities. dynamical approach to statistical behaviour in bimolecular collisions and to indicate its successful extension to unimolecular decay. The approach relies upon the extent to which neighbouring trajectories, initially separated in phase space by a distance d(O), diverge from one another with time.In particular, calculations have shown that the subset of reactant phase space which is characterized by trajectories displaying d(t)/d(O) > 103 evolves to a statistical product distribution. Such characterization can be readily made using short-lived trajectories. This being the case, a bimolecular collision can be studied, within the classical trajectory framework, using onIy short-lived trajectories as follows: Trajectories are numerically integrated until they are either compIeted or untiI they are shown to exponentially diverge from nearby neighbours by lo3. A similar calcuIation is carried out with trajectories initiated in the product channels to ascertain the product distributions associated with trajectories in the ‘‘ lo3 subset ”.The “ lo3 subset ” of the initial distribution is then assumed to evolve to yield the ‘‘ 103 subset ” product distribution. Combining the product distributions due to the direct and lo3 subsets, suitably weighted, yields the overall product distributions. Computational results using this approach have shown excellent agreement with the exact product distributions. The advantages of this approach are clear in providing an unambiguous definition of a “ collision complex ”, in displaying the relationship of trajectory instability to statistical behaviour and in avoiding long-lived trajectories which are a well known source of intractable computational error in such calculations. The two essential features noted above, i.e. the statistical features of the lo3 subset and its computational utility, have now been demonstrated for unimolecular decay.Two examples, to be discussed in detail el~ewhexe,~ are sketched below. Table 3 displays results related to the decay of a two-degree-of-freedom coupled Morse oscillator system. Each of the rows is distinguished by a mass ratio B; the potential is unchanged. Studies of product properties and lifetime distributions I wish to draw attention to a previously published272 GENERAL DISCUSSION show that B = 7/16 and 10/16 are non-statistical whereas B = 8/16 and 9/16 are statistical. Statistical lifetimes (7,) and times (2103) within which d(t)/d(O) = lo3 is achieved are shown in columns 2 and 3, respectively. The results shown that non- statisticality obtains when z, < 7103 whereas statisticality obtains when the two times are comparable.We emphasize that a comparison of these two numbers, for any reasonable system, can be made with little computational effort. Table 3. Results related to the decay of a two-degree-of-freedom coupled morse oscillator 7/16 41.7 45 8/16 39.0 78 911 6 36.8 70 10116 34.9 42 As the second example consider fig. 13 which shows, for two of the potentials introduced by Wolf and Hase4 to study CCH decomposition, the results of exact calculations of product properties (solid histograms) as well as the results (dashed) of the approach described above. Histograms in column 1 pertain to potential model IIC whereas those in column 2 relate to potential model IIA. The dashed histograms, obtained without computing any long-lived trajectories, are seen to be in very good agreement with the exact results.R. D. Levine and R. B. Bernstein, Adu. Atom. Mol. Phys., 1975, 11, 216; A. F. Wagner and E. K. Parks, J. Chem. Phys., 1976, 65,4343. I. Hamilton and P. Brurner, to be published. R. Wolf and W. Hase, J. Chem. Phys., 1980, 72, 316. ’ J. W. Duff and P. Brumer, J. Chem. Phys., 1977, 67,.4898; 1979,71, 2693; 1979, 71, 3895. Dr. H-R. Diibal, Dr. H. Hollenstein and Prof. M. Quack (ETH, Zurich) (communi- cated): In the paper by Drs Rizzo, Hayden and Crim (RHC) a beautiful new method of spectroscopy is presented, namely the vibrational predissociation spectroscopy of highly excited reactive states. We wish to comment here only on certain aspects of their spectroscopic results shown in fig.4 (we are also indebted to RHC for providing us with an improved spectrum during the meeting) which are related to current spectroscopic efforts in our laboratory. Our comment concerns both the vibrational structure and the rotational structure in these overtone spectra. From the rotational structure it should be possible to deduce the polarization of the transition, and from this one can conclude whether the vibrational bands arise from “ normal ” (symmetric or antisymmetric) stretching states or local states, which all give rise to different rotational structure. Fig. 14 shows a calculated B-type band, fig. 15 is a C-type band and fig. 16 a B-C hybrid (0.75 : 0.25 mixture), which corres- ponds to the local vibrational transition in H202. Fig. 17 shows a B-type band for HOOD, which is necessarily both “ local” and “ normal ”.From the coarse structure of the experimental bands one can conclude (i) that the widths of the bands observed are almost entirely of rotational origin and (ii) that the doublet structure for HOOD has a natural explanation from rotational structure. Unfortunately, one sees by inspection of fig. 14-16 that an unambiguous assign- ment of the polarization is only possible with a detailed analysis of the high-resolutionGENERAL DISCUSSION 273 0 *4 0.2 0.1 0 5 10 7 0 . 3 5 10 E R E R Fig. 13. (a) Translational, (6) vibrationati and (c) rotational product distributions for model potential IIC from exact (solid histograms) and short-lived-only (dashed histograms) computations. (d)-(f): as for (a)-(c) but for potential IIA.274 r I 18700 18 900 I9 too Flcrn-' Fig. 14.B-type band structure for an overtone transition in Hz02 (model calculation). spectra. We may point out that the experimental spectrum, although very noisy, seems to be more complex that the theoretical spectrum, indicating the occurrence of sphttings. These can arise from the torsional vibration or from the doublet splitting of the " local " mode, or it may be due to rovibrational perturbations. With noise- free spectra at high resolution these questions might be decided. Because for HOOD there would be no local-rnode splitting, good spectra on this compound would be very helpful, as would also be spectra of H180160€€. The second item of interest in the spectra of RHC are the vibrational side bands, that were suggested to be 6 vOH + v,, with v, being, for instance, the torsion.An alternative explanation would be that for the 0-0--H chrornophor there are Fermi-resonance structures of the kind 6 y S , 5 v s + 2 q,, 4 v s + 4 Vb etc. as we have definitely proved for the CH chromophore in a large series of fluorinated compounds.'GENERAL DISCUSSION 275 18 700 18 900 Flcrn- 19 100 Fig. 16. B-C hybrid band (0.75 : 0.25), corresponding to a “ local ” polarization in an over- tone transition of HzOz (model calculation) This would apply also to the spectra of tBuOOHm2 Whether this interpretation is correct can be tested by fitting the spectra of several overtone regions with one of the models developed in our work.’ Unfortunately, the H202 molecule is a highly non- rigid molecule which will make a detaiIed rotational and vibrational analysis compli- cated, but also challenging.18 700 19 100 Fig. 17. B-type band structure for HOOD, exhibiting the coarse structure with a minimum in the middle, similar to the experimental result (model calculation). Finally, we point out that from a simulation of the rotational band contour at high resolution it should be possible to obtain a reasonable value for the homogeneous vibrational predissociation width I-, which might be compared with lifetimes calculated from statistical theory.276 GENERAL DISCUSSION H-R. Dubal and M. Quack, to be published (see also comment by Dubal, Lewerenz and Quack at this discussion). M. C. Chuang, J . E. Baggot, D. W. Chandler, W.E. Farneth and R. N. Zare, Faraday Discuss. Chem. SOC., 1983,75, 301. Prof. J. P. Simons (University of Nottingham) said: In fitting the product rotational-state distributions to a statistical regime a possible source of error could be the occurrence of rotational alignment of the OH (OD) fragments. A consequence of this would be a reduction in the (2J + 1) degeneracy introduced by a constraint on the probability of accessing all possible MJ sub-levels. Prof. T. Baer (University of North Carolina) said : It would be most interesting to carry out Prof. Crim’s experiment at low temperatures at which the initial angular momentum is very low. Such an experiment might indicate whether the high rotational temperatures of the OH products are a result of the initial angular momentum contained in the system, or the result of the dissociation dynamics.Another way to do the experiment might be to tune the YAG laser to various rotational lines of the HOOD molecule. Prof. F. Crim (University of Wisconsin) said: The analysis and simulation of the overtone vibration spectra for HOOH and HOOD by Prof. Quack and co-workers are very informative. A later, higher quality, spectrum of the hydrogen peroxide overtone stretching vibration exhibits the difference in structure in going across the absorption feature even more clearly than fig. 4(a). The simulation recovers the essential aspects of the spectrum and nicely shows the separation of the two portions of the rotational contour in the case of HOOD. This analysis and its subsequent extensions will be an important guide to understanding the nature of the initially excited states in hydrogen peroxide. The suggestion that Fermi resonances involving the OOH bending motion are responsible for the higher energy features in the overtone excitation spectrum is quite interesting.This model certainly warrants further study to determine if it is consistent with the observed isotope shift upon partial deuteration. Data on other overtone vibrations in HOOH and HOOD as well as those in Bu‘OOH can help test the model as well. Prof. Simons’ comment on the possibility of product alignment reducing the availability of MJ sublevels and introducing a restriction in the statistical calculation raises an important point. We are planning polarization-dependence studies to explore the possibility of alignment being introduced by the excitation laser and selectively detected by the interrogation laser.A related point is the possibility that some vibrations in the excited HOOH(D) (a bend or a torsion, for example) selectively correlate with rotations in the separated OH(D) fragments. This leads to a more limited sampling of phase space than is included in the statistical theory. This is a possible explanation of the different shape of the product-state distribution following excitation of the combination band compared with that for excitation of a pure stretching vibration. Indeed, performing experiments on cold molecules with low angular momenta will be very interesting, as Prof. Baer suggests. We are currently planning such experi- ments in a pulsed molecular beam apparatus where the molecules are cooled in a supersonic expansion.We also intend to use the higher resolution obtainable with an etalon in our dye laser to attempt to excite individual features in the overtone excita-GENERAL DISCUSSION 277 tion spectrum. In particular, guided by the rotational analysis, we hope to select high- and low-angular-momentum states individually. Prof. R. N. Dixon (Uniuersity of Bristol), Dr. R. Vasudev and Prof. R. N. Zare (Stanford Uniuersity) said: In his paper Prof. Crim has posed a number of questions relating to energy randomisation in unimolecular reactions, and whether the product- state distributions show any mode or site specificity. We wish to report on an experiment concerning the photodecomposition of nitrous acid which we have recently carried out.' HONO has been dissociated by excitation at a number of discrete wavelengths within the vibrationally structured 3 'A"-f 'A' band system in the near ultraviolet.This is known to have a high quantum yield to give ground-state OH and NO frag- ments,2 with a minimum excess energy of 9200 cm-I to be disposed within these fragments. The photolysis has been initiated in several bands of the principal progression (2", upper state terminal NO stretching vibration) of trans-HONO. Laser-induced fluorescence excitation has then been used to probe the internal- state-population distribution and motional anisotropy of the nascent OH. The trans- lational recoil has been determined by measuring the Doppler profiles of the OH lines.The OH rotational distribution is found to be cold, but the transitions involving F2 spin levels of the ground state are all enhanced relative to those involving Fl levels when compared with a 300 K thermalised source of OH. Fig. 18 presents these data EJcm-' Fig. 18. Boltzmann plots of the relative populations of the F':(J" = N" + 3) and F,"(J" = N" - 3) levels of the OH fragment from photodissociation of HONO at 369 nm. The lines are calculated from the model discussed in the text. in the form of a Boltzmann plot, showing that the spin-orbit and rotational energies are not equilibrated. These observations can be quantitatively interpreted by assum- ing that the OH nuclear framework rotational energy is established while the spins of the OH and NO are still coupled to give a resultant singlet.The two theoretical lines in fig, 18 have been generated by projecting a nuclear rotational distribution character-278 GENERAL DISCUSSION ised by a " temperature " of 283 K, together with an infinite " spin temperature ", on to the Hund's intermediate case (a)/(b) coupling of OH(211). In addition to this lack of internal-state equilibration the rotational distribution shows a marked align- ment for the higher rotational quantum numbers (Nx 6). No vibrationally excited OH could be detected, placing an upper limit of one percent for the population of u = 1 relative to v = 0. The Doppler-split OH line profiles can be simulated by assuming a limiting translational anisotropy with /3 = -1 (recoil in the HONO plane), and a single OH recoil velocity equivalent to a Doppler full width of 0.61 cm-l.The effects of 300 K thermal HONO motion (f.w.h.m. = 0.063 cm-l) and laser line width (f.w.h.m. = 0.1 16 cm-l), convoluted on to the centre-of-mass Doppler shift, give a satisfactory simulation of the experimental line profile with photolysis at 369 nm. This Doppler width corresponds to an OH translational energy of 4720 cm-', which is 46% of the total energy available to the fragments. Conservation of linear momentum then requires that a further 26% must go to NO translation. In contrast, the OH internal energy corresponds to 2% of the total. Fig. 19 shows that there is no discernible change in the OH Doppler profile when f/cm-' 33000 30000 27000 24000 I 1 I Fig. 19.(a) The HONO(x-3) absorption ~pectrum.~ (6) P,(l) Doppler profile of the LIF excitation spectrum of the OH fragment obtained by photolysis at the frequencies shown by the arrows in (a). The f.w.h.m. of these peaks is 0.63 cm-'. up to two further quanta of terminal NO vibration are excited in the parent molecule. There is also no appreciable change in the OH rotational or vibrational distributions. The NO vibrational energy of HONO is therefore not available for partition into fragment recoil in the photofragmentation, despite the large mismatch between the NO vibration frequencies in the excited parent (1 120 cm-l) and the free NO molecule (1876 cm-I). Thus in HONO, even though the -N=O and breaking 0-N bonds are directly linked, energy over a range of 2200 cm-l does not appear to be transferred between them within the lifetime of the dissociation. The measured half-width of ca.60 cm-I for the HONO bands indicates that this lifetime is at least five vibrational periods of NO. The highly specific behaviour of this dissociating tetra-atomic molecule is clearly very different from that described by Prof. Crim for HOOH and HOOD. There is aGENERAL DISCUSSION 279 need for many more such experiments before our theories of unimolecular decomposi- tion can become truly predictive. ’ R. Vasudev, R. N. Zare and R. N, Dixon, Chem. Phys. Lett., 1983,96, 399. ’ R. A. Cox and R. G. Derwent, J. Photochem., 1976/7,6, 23. R. N. Zare and D. R. Herschbach, Proc. ZEEE, 1963,51, 173. G. W. King and D. Moule, Can. J. Chem., 1962,40, 2057.Prof. J. Troe (Universitat Gottingen) said: The article by Beresford et al. in this Discussion nicely demonstrates a typical feature of statistical theories of unimolecular processes. These theories often depend on only a small number of leading para- meters. In the statistical adiabatic-channel model this is, apart from known reactant and product properties, one interpolation parameter (alp). Therefore, one measure- ment may serve to fix this parameter, another measurement is then used to control the internal consistency and to analyse for statistical behaviour. In the elegant experi- ments of Prof. Crim’s paper on HOOH and HOOD, one piece of information is obtained, i.e. the product-energy distribution. A meaningful statistical description of these data can be obtained by taking advantage of a second experimental measure- ment of the same reaction: The thermal decomposition of H20z has been measured up to pressures where a transition to the high-pressure range just becomes visible (re-evaluation required) ; similarly the thermal recombination of OH has been studied in the fall-off range., These thermal data could be used to fix one parameter (CLIP), such that the product-energy distribution could be predicted and compared with these new data. ’ E.Meyer, H. A. Olschewski, J. Troe and H. Gg. Wagner, 12th Znt. Symp. Combustion (The ’ D. L. Baulch, R. A. Cox, R. F. Hampson, J. A. Kerr, J. Troe and R. T. Watson, J . Phys. Chem. Combustion Institute, Pittsburgh, 1969), p. 345. Ref. Data, 1980,9, 285. Dr. J. Pfab (Heriot-Watt University, Edinburgh) and Dr.I . Nadler, Dr. G. Radhakrishnan, Dr. H. Reisler and Prof. C. Wittig (University of Southern California) said: The experiments of Rizzo et al. with HOOH and HOOD are very important in that they resolve product rotations for a small system where a great deal of precision is possible. It is clear that further experiments, in which product vibrations and trans- lations are resolved for different initial-state preparations, will lead to a more refined understanding of vibrational predissociation for systems of this type. In our opinion, complete resolution of electronic, vibrational, rotational and translational degrees of freedom, for both fragments in a unimolecular reaction, is the most desirable circum- stance in experiments of this nature.In accord with this philosophy, we are presently studying several systems [HONO, NCNO, (CN), etc.] where this is possible, and we present here the results of experiments wherein NCNO dissociates following photon absorption under collision-free conditions. The energy-level structure of NCNO is “ rich ”, and there are several distinct electronic states which need to be considered when exciting the molecule in the region of the “ n* +- n ” system. The lowest excited singlet state (2 lA”) lies above the accepted dissociation energy of 29 kcal rnol-l,’ and an as yet unidentified triplet state lies somewhere between J I A ” and the f l A ‘ ground ~ t a t e . ~ . ~ In addition, there is a repulsive state whose accessibility to single-photon excitation is not known, as well as a state which correlates to CN(A ’n), and the associated spectra will be quite broad and (under the present experimental conditions) structureless.Following 2 l.4” t 8 ‘A’ excitation, significant wagging occurs, since the equili- brium bond angle changes from 114 to 134°,4 and, based on our experience with other systems, subsequent dissociation will partition energy into product rotations. Simi-280 GENERAL DISCUSSION lady, involvement of a low-lying triplet state should lead to significant product rotation. On the other hand, direct dissociation along a repulsive curve leads to very little rotation of the CN product, since repulsion is directed largely along the CN axis and parent rotation transforms efficiently into orbital motion of the products.Thus, by measuring CN internal degrees of freedom, it appears quite likely that we will be able to distinguish a direct-dissociation mechanism from one involving a bound intermediate which undergoes predissociation. In this contribution, we present experimental results wherein nascent CN rovibronic states are detected via laser- induced fluorescence (LIF) foIlowing the photodissociation NCNO, and by careful inspection of the spectra we are able to deduce the dissociation mechanism for the one-photon process. The experimental method uses unfocused pulsed laser photolysis (355, 532 and 670-732 nm) and pulsed LIF detection of CN (ca. 388 nm). The pukes are typically of 6 ns duration and the delay between the pulses is variable. Experiments are done under collision-free conditions (typically 5 mTorr, 50 ns delay) and signals are processed using conventional averaging techniques.Details of the experimental approach will be given el~ewhere.~ The visible and near-infrared absorption spectrum of NCNO is shown as the uppermost trace in fig, 20. The region used for dye-laser photolysis is expanded in the lower traces, where spectra are shown for the production of NCNO fluorescence, the CN product monitored by LIF at the (0,O) bandhead (J 25), and the CN product monitored by LIF at J = 2 (R branch). A typical CN LIF spectrum for these conditions is shown in fig. 21. Also shown in fig. 20 is the ratio of the CN bandhead and NCNO LIF signals, and the laser energy tuning curve, over the same wavelength interval. The NCNO LIF peaks correspond exactly to peaks in the absorption spectrum, as do also the CN bandhead LIF peaks.On inspecting these two traces, it is clear that they do not each follow the dye-laser tuning curve in exactly the same way, even though there is a one-to-one correspondence of the peaks. The noisy trace at the bottom is obtained by taking'the ratio of the CN bandhead LIF signal to the NCNO LIF signal, and this tracks the dye-laser tuning curve very well. Since the NCNO LIF signal varies linearly with the photoIysis laser energy, it follows that the CN bandhead LIF signal varies as the square of the laser energy, suggesting that the CN species being monitored derives from a precursor which has absorbed at least two photons. By measuring separately the power dependence for the production of CN, using several high-b states, while keeping the photolysis energy sufficiently low so that optical transitions are not saturated, we confirm that the CN prcduct with high J is produced via the sequential absorption of two photons, using the A lA" state as a gateway.This is a facile process, and we wish to emphasize that the present system is hardly unique. Etrects due to such processes may be manifest in many situations where laser excitation is used to prepare the initial excited ensemble. The spectra shown in fig. 21 show the " bimodal " nature of the CN distribution produced by 691.7 nm photolysis. The lower trace is obtained by photolysing at 355 nm, roughly twice the frequency of 691.7 nm. This allows similar energies to be accessed using either photolysis method, and since there are no symmetry restrictions we conclude that the " hot " portion of fig.21 is due to two-photon excitation, while the cold portion is due to one-photon excitation. This is confirmed by the observa- tion of a linear dependence of the production of CN(J = 2) with photolysis laser energy. The variation of the CN(J = 2) LIF signal with photolysis laser wavelength is shown at the bottom of fig. 20, and indicates that the CN produced via a single- photon process in the near-infrared is not corrdated to the 7 ~ * c n absorption. Taking the above into consideration, it seemed proper to obtain the cold CNGENERAL DIscussroN 28 1 distribution without interference from the two-photon process, and this was achieved as follows.By photolysing at 673.5 nm, considerable discrimination against two- photon excitation is achieved, as per fig. 20. A CN LIF spectrum obtained in this manner is shown as the upper entry in fig. 22. There are clearly both hot and cold components, with the cold component being dominant under these conditions. Further discrimination against two-photon excitation is achieved by lowering the wavelengthlnm 600 7 00 800 1 I 1 I 1 I I 660nm 732 nm Fig, 20. NCNO absorption spectrum and LIF signals plotted against photolysis wavelength for NCNO, CN (monitored at the bandhead) and CN (monitored at J == 2). The noisy trace is the ratio of the CN bandhead signal to the NCNO signal, and this ratio tracks the photolysis laser intensity very well. photolysis laser energy from 3.0 to 0.3 mJ.The high sensitivity of LIF detection allows us to do this whiIe maintaining adequate signal levels. The result is shown as the lower part of fig. 22, where the CN- LIF spectrum reflects an extremeIy cold distribution. This distribution is shown in fig. 23, and although temperature is an inappropriate parameter, two straight lines (30 and 160 K) are useful to the non- specialist when perusing the results. One particularly emphatic way to describe the results is to note that ca. 60% of the CN product molecules are in the lowest 5 rotationaI states and the associated temperature is 30 K.282 GENERAL DISCUSSION We believe that the very cold CN rotational distribution is a manifestation of direct dissociation following excitation to a repulsive potential-energy surface, as well as the efficient transformation of parent angular momentum into orbital angular momentum of the separating products.Lack of CN vibrational excitation is in accord with the projection of the CN bond distance in NCNO onto the CN bond length in the free species, and the lack of strong repulsion lying in the direction of the CN internuclear distance. Although we have not yet measured NO degrees of freedom, we anticipate that this species will contain more rotational and vibrational Fig. 21. CN LIF spectra obtained (a) with 691.7 nrn photolysis and (b) with 355 nrn photo- Iysis. Note the presence of rotationally cold CN in case (a). The " cold " CN Is due to one-photon excitation, while the " hot " CN is due to two-photon excitation.excitation than CN in the region near dissociation threshold. By using polarized photolysis radiation it should also be possible to detect specific orientations of product momenta, as per the lovely contribution by Dixon et al. in the poster session (reported in part on p. 277 of this Discussion volume). Finally, we note that this is an interesting way to avoid the use of nozzles in order to minimize spectral congestion. B. G. Gowedock, C . A. F. Johnson, C . M. Keary and J. Pfab, J. Chem. Suc., Perkin Trans. 2 1975, 351. S. Bell, J. Chem. SOC., Faraday Trans. 2, 1981, 77, 321. C. Bjurkman and P. S. Bagus, J. Chem. Phys,, 1982, 76, 31 1 I * J . Pfab, to be published. I. Nadler, J. Pfab, G. Radhakrishnan, H. Reisler and C. Wittig, to be published. Prof.T. Baer (Uni~ersity of North Carolina) said: I would like to ask Prof. Haas what fraction of the tetramethyldioxetane molecules dissociate to give electronically excited products? Are there some particular selection rules which enhance the production of excited states? Prof. Y. Haas (Hebrew Unirersity of Jerusalem) said: The fraction of excited acetone product molecules has not been determined by us. Steady-state studies inGENERAL DISCUSSION 283 P branch R branch -- I Fig. 22. Upper trace shows the CN LIF spectrum obtained with 3.0 mJ of photolysis energy at d = 673.5 nm. The spectrum is bimodal, with hot and cold components due to two- and one-photon excitation, respectively. With lower photolysis energy (0.3 mJ at 3, = 673.5 nm) cold CN dominates the spectrum.0 100 2 00 300 LOO 500 B,J(J+ 1) Fig. 23. Rotational state distribution for the LIF spectrum shown in the lower half of fig. 22. 0, from R branch (J = 0 - 16) and 0, from P branch (J = 1 - 14); ca. 60% of the CN is in J = O - 4 f o r T = 30Kandca.37%oftheCNisinJ=O-4forT= 160K.284 GENERAL DISCUSSION liquid solution indicate a yield of 30-50”/, in the case of TMD. This means that the production of an excited state is almost quantitative. Since our results extrapolate nicely to those obtained in condensed phases, we assume that the yields are similar upon laser excitation. Dr. J. A. Laramke (Warwick University) said: Could Prof. Haas comment on the change in relative population with excess energy for various laser fluences? In particular, could the larger pulse height, with its increased high-frequency components, influence the change in population? Prof.Y. Haas (Hebrew University of Jerusalem) said: We have changed the laser energy (and intensity) by less than a factor of four. This change is not expected to affect appreciably the frequency spectrum of the laser. The populations derived from our experiments are narrower than those obtained in many simulations based on rate equations. We have in the meantime used the rate-equation approach to derive the observed populations. As the dependence of the absorption cross-section on the internal energy is not known, we used various analytical forms to simulate it. This work is still under way, but the trend is clear; the cross-section must decrease appreci- ably within the excited molecule to create narrow distributions. Reasonable agree- ment is obtained with the expression on = oo(l + n)-’el, where n is the number of photons absorbed and oo the cross-section of the 0 -+ 1 transition.Dr. H. Reisler, Dr. F. B. T. Pessine and Prof. C. Wittig (University of Southern California) said: The experiments of Ruhman, Anner and Haas are interesting, in that they allow one to observe the unimolecular decomposition of an energised ensemble of molecules in real time. This can lead to qualitative estimates of the energy distribution of reactants produced by i.r. multiple-photon dissociation (IRMPD), and ultimately to serious tests of unimolecular reaction theories. In this contribution, we present data in which we detect ground electronic state fragments following the IRMPD of benzylamine: C6H5CH2NH2 + nhv --+ C6H5CH,NH2’ --+ C,H,CH, + (1) Such simple bond-fission processes transpire through the loosest of all possible transition states for neutral particles and therefore are most appropriate for detailed consideration.The direct observation of the buildup of products from reaction (1) allows us to estimate, with reasonable accuracy, the average energy in excess of reaction threshold. Also, the open rotational structure of NH, is amenable to determining product V,R,T distributions for molecules which have a well defined average energy in excess of reaction threshold and decompose with an average unimolecular lifetime. The experimental arrangement uses a CO, laser to energise molecules under collision-free conditions.’ Although both products can be detected by laser-induced fluorescence (LIF), it is most sensible to monitor NH2, and this is what we have done in the results presented here.The benzyl radical is formed with considerable vibra- tional excitation, and is excited even further by the presence of C02 laser radiation. This reduces the population of low vibrational states to such extent that the nicely structured LIF spectrum that one obtains with thermalized benzyl radicals is not detectable.’ Fig. 24 shows a benzyl LIF spectrum obtained using 1.5 Torr of Ar buffer in order to relax the nascent excitation. Without the Ar buffer no LIF signal characteristic of the benzyl radical throughout this region could be detected. In contrast, nascent NH2 contains modest internal excitation and is not excited further NH2, AHo = 71.2 kcal mo1-I.GENERAL DISCUSSION 28 5 wavelength Fig.24. Laser-induced fluorescence spectrum of benzyl, produced by the IRMPD of benzylamine. 1,5 Torr of Ar is used to relax the nascent excitation, so that this species can be identified via its structured absorptions. by the presence of C 0 2 laser radiation. Although we have not yet determined quantum statc distributions for NH2, this is certainly p~ssible,~ and we are very careful to discriminate against effects due to rotational relaxation. Each point represents an average of 8 laser firings (+25 ns jitter), and the vertical axes are independent for The essential experimental results are shown in fig. 25. 1 0 b 1OJ cm-' J 3 Fig. 25. Signals showing the build-up of NH2 following the excitation of benzylamine with a pulsed C 0 2 laser (upper left). Each point is the average of 8 laser firings (jitter = 25 ns), and the parent pressure is sufficiently low (1-2 mTorr) that collisional processes do not influence the rise of the signal.286 GENERAL DISCUSSION each of the 3 fluences. As the laser fluence rises from 10 to 45 J cmd2, the production lifetime shortens until it cannot be deconvoluted from the laser-pulse duration. It is clear that we are able to control the mean unimolecular lifetime, and therefore the mean energy in excess of reaction threshold. The signal decay is due mainly to transport out of the observation region, and the signals can be satisfactorily de- convoluted using the usual double-exponential form and two rate parameters, krise and kfal,. Fortunately, the thermal dissociation of benzylamine has been carefully studied using the very-low-pressure pyrolysis techniq~e,~ and we know that A , and E,, are 4 x 1014 s-l and 70.6 kcal mol-l, respectively. Using these data and the deconvolution expression given by F ~ r s t , ~ we can obtain the dissociation rate as a function of energy in excess of reaction threshold, and this information is presented in fig. 26, where the dashed lines show the region covered by the present experimental results. Our ability to fit the data with a single unimolecular reaction rate can derive from the large scatter in the data and/or a reasonably mono-energetic ensemble of reactants above reaction threshold. Given precise time evolution data, it should be possible to deconvolute the reactant-energy distribution, but this is not a trivial matter with the present experimental arrangement. The results are summarized in tabular form in table 4. Fig. 26. Benzylamine dissociation rate as a function of energy in excess of reaction threshold. A , and E,, are taken from the ref. (4) and the deconvolution expression is that given by F o r ~ t . ~ The dashed lines indicate the range covered by the experiments. The experimental arrangement is described in (a) H. Reisler, F. Kong, C. Wittig, J. Stone, E. Thiele and M. F. Goodman, J. Chem. Phys., 1982, 77, 328 and (b) H. Reisler, M. Mangir and C. Wittig, J. Chem. Phys., 1980, 47, 49. * T. Okamura, T. R. Charlton and B. A. Thrush, Chem. Phys. Lett., 1972, 88, 369.GENERAL DISCUSSION 287 K. Dressler and D. A. Ramsay, Philos. Trans. R. SOC. London, Ser. A , 1959, 251, 553. D. M. Golden, R. K. Solly, N. A. Gac and S. W. Benson, J. Am. Chem. SOC., 1972,94, 363. (a) W. Forst, J. Phys. Chem., 1972, 76, 342; (b) W. Forst, Theory of Unimolecdar Reaction (Academic Press, New York, 1973). Table 4. Unimolecular reaction rate of benzylamine laser fluence rate lifetime excess energy /J CM-~ 105s- 1 IPS /kcal mo1-1 10 3.4 f 0.5 2.9 f 0.5 52 13 5 4 ~ 1 2.0 & 0.4 55 15 7.7 & 1.2 1.3 f 0.2 58 20 14 &-2 0.7 f 0.1 62 27 50 10 0.2 k 0.05 72 48 > 100 <o. 1 > 78 Prof. Y. Haas (Hebrew University of Jerusalem) said : These elegant experiments reporting the relatively slow dissociation of benzylamine upon 1 RMPE show that infrared laser excitation can now be controlled to achieve a desired dissociation rate. Laser-induced fluorescence is a more general monitoring technique than chemi- luminescence, so that these experiments open the way to a much larger group of IRMPD reactions that could be characterized by methods similar to those proposed in our paper. I should add that more care needs to be practised upon using LIF than needed in chemiluminescent studies. It has been observed by us, and by others, that vibrationally hot parent molecules, prepared by IRMPE, may absorb the monitor- ing laser light and dissociate. This effect can be detected by checking the dependence of the signal on the monitoring laser power and, when the risetime is slow compared to the laser pulse-width, by checking the risetime at different energies.

ISSN:0301-7249    

DOI:10.1039/DC9837500251

出版商:RSC    

年代:1983

数据来源: RSC

摘要:

Faruday Discuss. Chem. SOC., 1983, 75, 289-299 Unimolecular Reactions Induced by Vibrational Overtone Excitation B Y JOSEPH M. JASINSKI,~ JOAN K. FRISOLI AND c. BRADLEY MOORE Department of Chemistry, University of California and Materials and Molecular Research Division of the Lawrence Berkeley Laboratory, Berkeley, California 94720, U.S.A. Received 301h November, 1982 A continuous-wave dye laser has been used to activate molecules above threshold for unimolecular reaction. Visible photons selectivity excite high overtone transitions of inequivalent CH oscillators. Thus, a known amount of energy is deposited directly into vibrational degrees of freedom of the mdecule in its electronic ground state in a single photon absorption. The rate of unimolecular reaction has been measured as a function of internal energy, type of CH overtone transition excited and pressure to test for non-statistical effects.Results are presented for the isomerization of cyclobutene and 1-cyclopropylcyclobutene to the corresponding buta- 1,3-dienes and the isomerization of 2-methylcyclopentadienc to 1 - methylcyclopentadiene. No evidence for significant deviations from statistical behaviour has been observed. A fundamental problem in the study of unimolecular reaction dynamics is to understand how total internal energy and site of excitation influence unimolecular reaction rates. One of the most important aspects of the problem is to identify conditions under which unimolecular reaction rates are not well described by statistical unimolecular rate theories, since this provides useful information on rates of intra- molecular vibrational relaxation (i .v.r.), coupling between vibrational degrees of freedom in highly excited polyatomic molecules, and possibilities for carrying out quantum-state or chemical-bond selective unimolecular reactions.Experimental approaches to addressing these questions have generally employed chemicaI act i- vation, electronic excitation or infrared multiphoton excitation to prepare and study vibrationally excited molecules. These approaches have been extensively reviewed.'-' The general condusion from most of this work is that for most molecules, excited to vibrational energies sufficient to overcome typical activation barriers for uni molecular reaction, i.v.r. is rapid compared with the rate of reaction, and therefore statistical unimolecuIar reaction rate theories provide an adequate description of the results.Deviations occur when the molecule has an unusually weak bond, such as for van der Waals cornplexe~,~ or when the time-scale of the experiment is made very short (of the order of picoseconds), such as in the high-pressure chemical activation experiments of Rabinovitch and c o - w o r k e r ~ . ~ ~ ~ Recently a new technique for the preparation of highly vibrationally excited molecules has become available. Reddy and Berry have demonstrated lo that by t Present address: I.B.M., Thomas J. Watson Research Center, Yorktown Heights, New York 10598, U.S.A.290 REACTIONS INDUCED BY OVERTONE EXCITATION using laser excitation of high overtone transitions of XH stretching motions (X = C, N, 0) it is possible to prepare optically molecules in the ground electronic state with substantial amounts of vibrational energy via absorption of a single visible photon.This provides a method for studying the rate of unimolecular reaction for a given molecule as a function of total internal energy and of the particular XH transition excited. Some of the questions which arise are: Is the initially prepared vibrational state significantly non-random and, if so, on what time-scale? Are there molecules for which the nuclear motions excited by photon absorption are more strongly coupled to the unimolecular reaction coordinate than to other nuclear motions, i.e. can overtone excitation be used to induce mode-selective vibrational photochemistry? Thus far, overtone excitation has been used to study four unimolecular reactions. Reddy and Berry have used overtone activation combined with steady-state kinetic experiments to deduce values of the unimolecular rate constant, k(E), for the isomeri- zation of methy1 isocyanide ' v 9 and allyl isocyanide." Zare et a1.I' have used a similar technique to study the overtone-induced dissociation of t-butylhydroperoxide.Crim and co-workers have used real-time detection of product fragments to study the over- tone-induced dissociation of tetramethyl dioxetan '' and t-buty1hydropero~ide.l~ For two of these molecules, allyl isocyanide lo and t-butylhydroperoxide," the experimental data have been interpreted as exhibiting evidence for non-statistical reaction on chemically useful time-scales following overtone excitation.This paper summarizes work on the following overtone-induced unimolecular reactions : Ll Full experimental details for each of the molecules studied appear el~ewhere.'~-'~ C yclo butene, l7 1 -cycIoprop ylcyclo bu t ene and 2-methylcy clopent adiene l9 were prepared and spectra recorded. 20*21 Phot oisomer izat ion experiments were performed by filling a photolysis cell to the desired pressure and placing the cell intracavity in a C.W. dye laser for photolysis. Following photolysis, the sample was analysed by gas chromatography. Values of the unimolecular rate constant for isornerization follow- ing excitation of various CH overtone transitions were obtained from the pressure dependence of the forward rate constant over a substantial range of pressures and photon energies.None of these reactions shows effects which are readily attributable to deviations from statistical behaviour over the range of experimental conditions tested. SPECTROSCOPY High-overtone spectra of XH-containing molecules exhibit a progression of broad, weak absorption bands in the visible. These spectra have been analysed in terms of aJ. M. JASINSKI, J. K. FRISOLI AND C. B. MOORE 29 1 local-mode model which considers the XH bonds as a set of uncoupled anharmonic o ~ c i l l a t o r ~ . ~ ~ - ~ ~ Spectroscopic transitions are assigned as 0-v excitations of individual XH oscillators, where u is the vibrational quantum number of the excited oscillator. This picture has proven quite useful in explaining band positions, intensities and iso- topic substitution effects in high-overtone spectra. This suggests that the concept of an XH local mode has some utility, at least as a zero-order spectroscopic state.For hydrocarbons with more than one type of CH bond, the spectrum at each overtone consists of a number of bands each of which may be identified as a local- mode transition for a different type of CH bond or a different local environment. There is a good correlation 2o between bond length, isolated CH fundamental fre- quency and CH overtone transition frequency for a large number of hydrocarbons. The general ordering 20.21 of overtone transition energies by bond type is methylenic < methyl < olefinic, aryl < acetylenic.The overtone transitions which are most readily accessible for study with currently available C.W. dye lasers are the 0-5, 0-6 and 0-7. The integrated absorption cross-section per CH bond for most 0-6 tran- sitions in hydrocarbons varies over about a factor of two around the average value 2o of 1 . 1 x cm2 cm-l molecule-l. Typical peak cross-sections 20p24 are in the cm2 range for 0-5 transitions, the lou2$ cm2 range for 0-6 transitions and the cm2 range for 0-7 transitions. PHOTOISOMERIZATION KINETICS The photoisomerization kinetics can be described ' 9 ' ~ ~ by ( 5 ) (9 k(E) A* - products. The steady-state approximation gives the forward rate constant k = kak(E)/{k(E) + ks[Mll. The rate constant for photon absorption by reactant A is k,; k , is the rate constant for collisional deactivation of excited molecules A* by bath-gas molecules M, k(E) is the unimolecular rate constant for reaction of A* to products at total internal energy E, and [hw] is the effective photon concentration inside the photolysis cell and is propor- tional to the laser output power.Values of k are measured as a function of pressure by performing timed irradiations. (ii) where @ is the quantum yield. A value for k , is obtained from the intercept of a Stern-Volmer plot of the data ( k - * plotted against pressure). The ratio k,/k(E) is then obtained from the slope of a plot of l/@ against pressure. A value for k(E) can be extracted from this ratio if k , can be measured or calculated. Under the assump- tion that a single collision deactivates A* sufficiently to preclude further reaction, ks is simply the gas-kinetic collision rate constant.In this type of experiment collisions serve two purposes. The collision rate constant provides a reference against which k(E) can be measured, and the collision frequency (k,[M]/s-l) defines the time-scale of the experiment. As the pressure is increased, the average time between collisions decreases and therefore the average time during which a photoactivated molecule may react before it is collisionally deactivated decreases. Deviations from statistical behaviour may manifest them- Then k(E) is obtained from = k,/k = {k,[M]/k(E)} + 1292 REACTIONS INDUCED BY OVERTONE EXCITATION selves in one of two ways. The values of k(E) derived from linear Stern-Volmer plots may show a non-monotonic increase with increasing energy, as has been claimed for ally1 isocyanide,'O or the averge value of k(E) may change with increasing pressure as an increasing fraction of the reacting molecules do so from a non-random vib- rational energy distribution.This leads to curvature in the Stern-Volmer data at high pressures, as has been claimed for t-butylhydroperoxide.'l In order unam- biguously to characterize such effects it is desirable to obtain data over as wide a range of pressures, quantum yields and overtone transition types as possible. CYCLOBUTENE The isomerization of cyclobutene to buta-l,3-diene [eqn (l)] was chosen for study for several reasons. Cyclobutene is a small, structurally simple hydrocarbon with a completely assigned vibrational ~ p e c t r u m .~ ~ * ~ ~ Its thermal isomerization kinetics have been well ~ t u d i e d . ~ ' - ~ ~ Both reliable Arrhenius parameters for the thermal reaction and model R.R.K.M. calculations 30-31 of k(E) are available. Cyclobutene has two distinct types of CH bonds, methylenic and olefinic, which have well separated over- tone transitions. Excitation of CH stretching motions of these two types of bonds may Iead to different coupling to the reaction coordinate, which is believed 30*32 to be a simultaneous breaking of the carbon-carbon bond connecting the methylenic carbons and a rotation of the methylene groups to establish the n-electron system of butadiene. Finally, a large number of substituted cyclobutenes are known, thereby providing a large family of molecules with different structures, vibrational-state densities and CH bond types which can be explored once the parent has been studied.The main features of cyclobutene overtone spectra are readily assigned (fig. 1). At each overtone the lower-energy transition is the methylenic CH stretch, the higher the olefinic. The shoulder to the low-energy side of the 0-5 methylenic transition has not been unambiguously assigned. Based on its position in the u = 5 spectrum and its absence in the v = 6 spectrum, and assuming that its absence is due to over- lap with the = 6 local-mode transition, a possible assignment is as a combination band involving one less quantum of CH stretch plus two quanta of an 1100 cm-I vibration. Candidates are CH2 twisting and ring-breathing modes, which appear at ca.1100 cm-l in the i.r. spectrum of cy~lobutene.~~ The activation energy for the thermal isomerization 29 of cyclobutene to butadiene is 32.9 kcal mol-I (11 500 cm-I). Therefore, the critical energy for isomerization is well below the available vibrational energy when cyclobutene is activated by overtone absorption using any of the transitions shown in fig. 1. Values of k(E) have been measured near the peak of each transition shown in fig. 1 and at several wavelengths across the u = 5 methylenic peak. Data for irradiation in the u = 5 spectral region gave linear Stern-Volmer plots over the range of pressures (typically 0.5-60 Torr *) and quantum yields (typically 0.95-0.05) studied. The u = 6 plots were linear to 700 Torr, where the average time between collisions is 100 ps.Values of k(E) were calculated from the Stern-Volmer slope and intercept using a value of 4.3 x 10-lo cm3 molecule-I s-' fork,. This assumes a hard-sphere collision diameter30*33 of 5.3 A. The data (table 1) show k(E) to be a monotonically increasing function of energy, There is no obvious difference (other than scaling with total energy) between excit- ation of methylenic or olefinic overtone transitions or between excitation of the low- energy shoulder of the 0-5 methylenic transition compared to the main peak. The values of k(E) listed in table 1 are in reasonable agreement (a factor of 2-3 larger) with R.R.K.M. values of k(E) calculated for cyclobutene by F r e ~ . ~ ~ The deviation * 1 Torr = 101 325/760 Pa.J.M. JASINSKI, J. K. FRISOLI AND C. B. MOORE 293 I I I I I I I I I (A) n w .3 3 -$ v 2 13 200 13 400 13 600 13 800 14000 14200 .& 5 15400 15600 15800 16000 16200 16400 16600 16800 wavenumberlcm- was 50 Torr. Fig. 1. (A) Fourth and (B) fifth CH overtone spectra of cyclobutene. The sample pressure cannot be taken as evidence for non-R.R.K.M. behaviour since there are a number of factors, such as a different choice of k,, which could improve the agreement. 1 -CY CLOPROPY LCYCLOBUTENE A well precedented approach to studying energy randomization and to looking for deviations from statistical behaviour in unimolecuIar reactions is to attempt selectively to excite “part ” of a molecule and study the competition between reaction or fluorescence from this part with i.v.r.into the rest of the molecule. This technique has been used extensively by Rabinovitch and co-workers to observe reaction from non-random vibrational energy di~tributions.~.’ This idea can also be applied to the study of energy randomization in overtone- excited molecules,l’ The overtone-induced isomerization of l-cyclopropylcyclo-294 REACTIONS INDUCED BY OVERTONE EXCITATION butene (CPCB) is an example. Excitation of the v = 6 methylenic CH overtone transition in cyclobutene was shown in the last section to result in a unimolecular reaction rate of 5 x 10' s-l. One can estimate from R.R.K.M. calculations that at the same energy, fully randomized CPCB should isomerize with ~ ( E ) F z 10s s-'* Therefore, CPCB can be used to test for energy randomization between the two rings on a nanosecond time-scale. While chemical activation studies 2*7 suggest that the appropriate time-scale for energy randomization at high internal energies is 1-0.1 ps, studies on the overtone-induced isomerization of ally1 isocyanide have been inter- preted as exhibiting observable non-statistical behaviour on a microsecond time-scale.lo Table 1.Isomerization rate constants frequency moIecule 1crn-I spec t t oscopic assignment it(€)/ 10's - I cyclobutene 1 3 346 13 420 13 446 13 500 14 096 14 120 15 706 16 602 combination band 0-5 methylenic 0-5 methylenic 0-5 methylen ic 0-5 olefinic 0-5 olefinic 0-6 methylenic 0-6 olefinic 3.5 If: 0.8 4.3 i 0.5 4.0 f 0.5 3.5 fU.7 9.1 f 1.4 7.4 f 1.8 49 f 6 82 f 11 cyclopropylcyclobutene 15 646 0-6 cyclobutenyl CH2 0.027 f.0.008 16 470 0-6 cyclopropyl CH2 0.10 5 0.04 2-methylcyclopen tadiene 13 221 0-6 methylenic 1.3 f 0.3 1 3 396 0-5 methyl out-of-plane 1.8 & 0.6 13 596 0-5 methyl in-plane 4.2 f 0.9 14 200 0-5 olefinic 6.1 j= 2.7 If this interpretation is correct, and if the phenomenon is fairly general, then CPCB should show significant differences in k(E) for reaction (2) depending on whether a cyclobutenyl or a cyclopropyl CH overtone transition is excited. The fifth CH overtone spectrum of CPCB is shown in fig. 2. Based on the fifth CH overtone spectra of cyclopropane 34 and cyclobutene (fig. l), the lower-energy transition is assigned to the cyclobutenyl methylenic overtone, while the higher-energy transition is assigned primarily to the cydopropyl methylenic overtone.The cyclo- butenyl olefinic transition is probably completely obscured by the cyclopropyl tran- sition. The small shoulder at I6 300 cm-' has not been assigned, but may be due to the unique cyclopropyl CH bond. The thermal activation energy for reaction (2) is 34.14 kcal mol-' (1 1 940 ern-'). Photon absorption at either overtone transition provides CPCB with internal energy well in excess of the critical energy for reaction. Values of k(E) were measured for irradiation near the peak of each transition (table 1). A value of 4.2 x lo-'' cm3 m~lecule-~ s-' was used for k,, corresponding to a hard-sphere collision diameter 35 of 6.0 L$, intermediate between cyclobutene (5.3 A) and n-heptane3' (6.9 A). The value of k(E) for excitation of the cyclopropyl methylenic (and possibly also the cyclobutenyl olefinic) overtone transition is larger than the value of k(E) for excitation of only the cyclobutenyl ring via the cyclobutenyl methylenic overtone transition.The magnitude of the increase is in good agreement with values calculated 36 from R.R.K.M. theory as are the absolute magnitudes of k(E). The experimental values at both energies agree nearly quantitatively with the calculated values.J. M. JASINSKI, J. K. FRISOLI AND C. B. MOORE 295 In order to determine whether there might be a fast component to the reaction corresponding to isomerization prior to complete energy randomization between the two rings, photolyses at 15 646 cm-l were carried out up to a pressure of 10 Torr, where the time between collisions is 10 ns and the quantum yield is 0.002.The Stern- Volmer plot remains linear, indicating that the average value of k(E) does not change noticeably even when >99% of the photoactivated molecules are deactivated prior to reaction. Experiments at higher pressures were not carried out since at 10 Torr a 15500 15700 15900 16100 16300 16500 16700 wavenumber/cm - Fig. 2. Fifth CH overtone spectrum of cyclopropylcyclobutene. The sample pressure was 15 Torr. photolysis time of 7 h was required to produce 0.7% conversion to products. The fact that no change in k(E) is seen down to a quantum yield of 0.002 combined with k(E) = 5 x lo8 s-l for cyclobutene allows one to estimate that the full amount of vibrational energy deposited by photon absorption is localized in the cyclobutenyl ring for (4 ps.2-METHY LCY CLOPENTADIENE One might expect that deviations from statistical behaviour in overtone-induced reactions would be most pronounced for reactions which involve significant hydrogen atom motion along the reaction coordinate. This type of reaction might allow for particularly efficient coupling between the nuclear motions excited by the optical transition and those motions which lead to reaction. None of the reactions thus far induced by overtone excitation meets this requirement, largely owing to the difficulty of finding reactions which involve substantial CH motion but which still have suitably low activation energies to be isomerized by overtone excitation. A possible candidate is the isomerization of 2-methylcyclopentadiene (2MCPD) to 1 -methylcyclopentadiene (IMCPD), reaction (3).The reaction is an example of a sigmatropic [1,5] hydrogen ~ h i f t , ~ ~ , ~ ’ and thus the reaction coordinate should involve substantial (but not exclusive) hydrogen-atom motion of one of the methylenic hydrogen atoms. The lowest- energy transition is assigned to the methylenic CH overtone, the next two transitions to the out-of-plane and in-plane methyl-group transition^,^^ which are not motionally The fourth CH overtone spectrum of 2MCPD is shown in fig. 3.296 REACTIONS INDUCED BY OVERTONE EXCITATION averaged by methyl-group rotation,34 and the highest-energy transition to the olefinic overtones. The Arrhenius parameters for reaction (3) have not been measured in the gas phase, but Frey 39 has estimated that the activation energy is 27 kcal mo1-I (9445 cm-l) assuming an A factor of The estimate is based on rates of equilibration of 1- and 2-MCPD in solution.The values are not entirely reliable since the solution equilibration rates show some solvent dependence.19 Values of k(E) were obtained 40 near the peak of each transition and are shown in table 1. A value of 3.7 x cm3 molecule-l s-l was used for k,, calculated from a collision diameter of 5.4 A which in turn was estimated from the value for The values of k(E) increase 13000 13200 13 400 13600 13800 14000 14200 14400 wavenumber/cm - was 60 Torr. Fig. 3. Fourth CH overtone spectrum of 2-methylcyclopentadiene. The sample pressure monotonically with increasing energy. Most importantly, excitation of the methylenic CH overtone transition at 13 221 cm-' results in the slowest reaction. The values of k(E) are in order of magnitude agreement with R.R.K.M.calculations based on the Arrhenius parameters given above.41 The values of k(E) were determined from Stern-Volmer data in the pressure range 1-5 Torr. At pressures significantly above 5 Torr of pure 2MCPD, a pressure- dependent dark reaction (presumably Diels-Alder dimerization on the cell walls) precluded accurate measurement of values of k. This problem could be overcome by using a mixture of ca. 1.5% 2MCPD in n-pentane. Using this mixture, values of k were determined up to a total pressure of 100 Torr for irradiation of the methylenic CH overtone transition at 13 221 crn-l. The Stern-Volmer plot is linear over the full range 10-100 Torr studied.The high-pressure data exhibit no obvious curvature and give a value of k(E) = (2.5 4 2.1) x lo7 s-'. This is in reasonable agreement with the value of (1.3 0.3) x lo7 s-' found for pure 2MCPD. The slightly higher value for k(E) derived from the high-pressure data may indicate that n-pentane is a less efficient deactivator of vibrationally excited 2MCPD than is 2MCPD itself. The major conclusion is that there is no evidence for an increase in k(E) relative to k , at pressures up to 100 Torr when the methylenic CH overtone transition is excited.GENERAL DISCUSSION 291 DISCUSSION The data presented above demonstrate that cyclobutene, 1 -cyclopropylcyclobutene and 2-rnethylcyclopentadiene isomerize with rates which are consistent with the assumption that the vibrational energy introduced by overtone excitation is fully randomized prior to any significant amount of reaction.In all cases k(E) increases with increasing energy and with a functional dependence on energy that can be ade- quately modelled by R.R.K.M. theory. Systematic deviations between experimental and calculated values of k(E), such as the factor of 2-3 deviation for cyclobutene, cannot be taken as evidence for non-R.R,K.M. behaviour because of uncertainties in the most realistic valuc of k , to use, in the transition-state parameters for the calcu- lation, and in how to best account for the thermal vibrational energy in the reactant molecules. Up to the highest pressures studied no evidence has been found for an increase in k ( E ) relative to k, as a larger fraction of the photoactivated molecules are collisionally quenched.The shortest collisional time-scale in any of the experiments was 100 ps. The results are therefore consistent with the majority of chemical acti- vation e~perirnents,~'~ which suggest that energy randomization occurs on a 0.1-1 ps time-scale for large molecules at relatively high levcls of vibrational excitation. The results presented here do not aid in understanding the non-monotonic dependence of k(E) on energy reported for ally1 isocyanide.1° They do suggest that this observation is not readily carried over to structurally unrelated molecules. Throughout the course of this paper it has been assumed that overtone excitation prepares a molecule with a significantly non-random vibrational energy distribution.This point deserves some discussion since the vibrational state or states prepared when a molecule is irradiated at an overtone transition with a C.W. dye laser is not presently very well defined. The hypothesis that no non-random energy distribution is prepared could equafly well explain the experimental results presented above. Most current theoretical models for overtone absorption spectra and spectral linewidths are cast in terms of a zero-order XH local-mode state which carries all of the oscillator strength from the ground As discussed above, this provides an adequate explanation of the band positions. The ca. 100 cm+' linewidths observed for these transitions are explained in terms of coupling between the zero-order local- mode state and a bath composed of the remaining vibrational states of the molecule.The assumption that the linewidths are dominated by uncertainty broadening leads to the conclusion that the XH local mode state, if prepared, dephases and/or relaxes into bath modes (but not necessarily all bath modes) on a ca. 50 fs time-scale. Therefore, preparation of a local-mode state would require a transform-limited laser pulse of 50 fs duration. This requirement has not yet been met in any study of overtone photo- chemistry. By the arguments given above, C.W. irradiation with a narrow bandwidth laser cannot prepare a local-mode ~ t a t e . ~ Rather it must prepare some superposition of energy eigenstates of the true molecular Hamiltonian.Which nuclear motions arc excited and to what degree depends on which eigenfunctions are optically coupled to the ground state and how strongly. Nothing more quantitative can be stated without a more detailed picture of the eigenstates. Unfortunately, very little information on realistic vibrational wavefunctions for polyatomic molecules at high levels of excitation is as yet available. In the extreme case one might hypothesize that all available states at a given energy are equally coupled to the ground state and hence that all possible vibrational states within the 1 cm-' bandwidth of the laser are excited. This seems unlikely given that the majority of these states probably do not involve significant CH motion and thus do not contain a significant amount of the zero-order character which298 GENERAL DISCUSSION makes the spectroscopic transitions allowed.It seems more likely that C.W. laser excitation within an overtone absorption band results primarily in excitation of nuclear motions which are close in space or frequency to CH stretching motions, and therefore, that at least in some sense the initial excitation is non-random. If this is the case, then the fact that no evidence for non-random reaction has been observed for the molecules discussed in this paper is best attributed to a lack of sufficiently stronger coupling of the optically excited nuclear motions to the reaction coordinate than to other vibrational motions. CONCLUSIONS Laser excitation of high-overtone transitions provides a novel method for the preparation of highly vibrationally excited molecules in the ground electronic state.While the amount of energy introduced is well characterized, the nature of the vib- rational motion excited by C.W. irradiation is not, at present, well defined. Isomeri- zation reactions of three hydrocarbons have been studied over a range of experimental conditions. The systems were chosen to provide a test for whether overtone excit- ation might give deviations from statistical expectations on longer time-scales than those required for such observations in chemical activation systems, either because of slower i.v.r. rates or because of more effective coupling of the excited nuclear motions to the reaction coordinate. No evidence for such behaviour has been found, This work was supported by the U.S.Army Research Office, Research Triangle Park, North Carolina. J. D. McDonald, Annu. Rev. Phys. Chem., 1979, 30, 29. I. Oref and B. S. Rabinovitch, Acc. Chem. Res., 1979, 12, 166. C. B. Moore and I. W. M. Smith, Furuduy Discuss. Chem. Suc., 1979,67, 146. H. Hippler, K. Luther and J. Troe, Furuduy Discuss. Chem. Suc., 1979, 67, 173. R. E. Smalley, J. Phys. Chem., 1982, 86, 3504. P. A. Shultz, Aa. S. Sudbra, D. J. Krajnovich, H. S. Kwok, Y . R. Shen and Y . T. Lee, Annu. Rev. Phys. Chem., 1979,30, 379. K. V. Reddy and M. J. Berry, Chem. Phys. Lett., 1977, 52, 1 1 1. K. V. Reddy and M. J. Berry, Furuduy Discuss. Chem. SOC., 1979, 67, 188. lo K. V. Reddy and M. J. Berry, Chem. Phys. Lett., 1979, 66, 223. D. W. Chandler, W. E. Farneth and R.N. Zare, J. Chem. Phys., 1982, 77, 4447. B. D. Cannon and F. F. Crim, J. Chem. Phys., 1981, 72, 1752. ' A. B. Trenwith and B. S. Rabinovitch, J. Phys. Chem., 1982, 86, 3447. l3 T. R. Rizzo and F. F. Crim, J. Chem. Phys., 1982,76, 2754. l4 J. M. Jasinski, J. K. Frisoli and C. B. Moore, J. Chem. Phys., in press. l5 J. M. Jasinski, J. K. Frisoli and C. B. Moore, J. Phys. Chem., in press. l6 J. M. Jasinski, J. K. Frisoli and C. B. Moore, J. Phys. Chem., in press. l7 A. C. Cope, A. C. Haven, F. L. Ramp and E. R. Trumbull, J . Am. Chem. Sue., 1952,74,4867. l8 D. Dickens, H. M. Frey and R. F. Skinner, Trans. Furuduy Soc., 1969, 65, 453. l9 W. E. Farneth, M. B. D'Amore and J. I. Brauman, J. Am. Chem. Suc., 1976, 95, 5546. 2o J. S. Wong and C. B. Moore, J . Chem. Phys., 1982, 77, 603. 21 J.S. Wong, PhB. Thesis (University of California, Berkeley, 1981); J. S. Wong and C. B. 22 B. R. Henry, Ace. Chem. Res., 1977, 10, 207. 23 M. L. Sage and J. Jortner, Adv. Chem. Phys., 1981, 47, 293. 24 R. G. Bray and M. J. Berry, J. Chem. Phys., 1979,71,4909. 25 R. C. Lord and D. G . Rea, J. Am. Chem. SOC., 1957,79, 2401. 26 E. M. Suzuki and J. W. Nibler, Spectrochim. Acta, Part A , 1974, 30, 15. 27 W. Cooper and W. D. Walters, J . Am. Chem. Soc., 1958,80,4220. W. P. Hauser and W. D. Walters, J. Phys. Chem., 1963, 67, 1328. 29 R. W. Carr and W. D. Walters, J. Phys. Chem., 1965, 69, 1073. Moore, in Lasers and Appfications (Springer-Verlag, West Berlin, 1981), p. 157.GENERAL DISCUSSION 299 3D C . S. Elliot and H. M. Frey, Trans. Faraday SOC., 1966, 62, 895. 31 M. C. Lin and K. J. Laidler, Trans. Faraduy Soc., 1968, 64, 94. ” R. B. Woodward and R. Hoffmann, The Conservation of Orbital Symmetry (Academic Press, 33 Estimated from the collision diameter of cis-but-2-ene; G. H. Kohlmaier and B. S. Rabinovitch, 34 J. S. Wong, R. A. MacPhail, C. B. Moore and H. L. Strauss, J. Phys. Chem., 1982,86, 1478. 35 S. 0. Chan, B. S. Rabinovitch, J. T. Bryant, L. D. Spicer, T. Fujimoto, Y . N. Lin and S. P. Pavlou, J. Phys. Chem., 1970,74, 3160. 36 W. L. Hase and D. L. Bunker, QCPE, 1973, 11, 234. Vibrational frequencies estimated from those for cyclopropane and cyclobutene. State sums and densities were calculated using the Whitten-Rabinovitch semi-classical algorithm. New York, 1971). J. Chem. Phys., 1963, 38, 1692. 37 C. W. Spangler, Chem. Rev., 1976,76, 187. 38 These assignments are based on analogy to the assignment of the methyl-group transition in propene [ref. (20)] and on a consideration of the interaction between the methyl-group CH bond orbitals and those of the ring n cloud. See D. C. McKean, Chem. SOC. Rev., 1978,7, 399. 39 H. M. Frey and M. C. Flowers, J. Am. Chem. Soc., 1972,94, 8636. 40 Values of k(E) for 2-MCPD were calculated using a kinetic scheme which includes the possi- bility of nascent 1 -MCPD isomerising back to 2-MCPD prior to collisional stabilisation. 41 W. E. Farneth, Ph.D. Thesis (Stanford University, 1979, gives a set of vibrational frequencies for the molecule and the transition state. R.R.K.M. calculations were performed using the program cited in ref. (36).

ISSN:0301-7249    

DOI:10.1039/DC9837500289

出版商:RSC    

年代:1983

数据来源: RSC