J. Phys. Chem. 1996, 100, 7743-7764
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Resonance Raman Spectroscopy of Dissociative Polyatomic Molecules Bruce R. Johnson,* Carter Kittrell, Peter B. Kelly,† and James L. Kinsey* Department of Chemistry and Rice Quantum Institute, Rice UniVersity, Houston, Texas 77251-1892 ReceiVed: NoVember 22, 1995; In Final Form: February 1, 1996X
Resonance Raman spectroscopy as a probe of the early stages in the dissociation dynamics of polyatomic molecules has become a valuable complement to photofragmentation studies. While these spontaneous Raman experiments are obtained in the frequency domain, they often reflect evolution of the molecule during the first few femtoseconds of bond breaking. Coupled with progress in classical and quantum calculations of large-amplitude motion, unique insights have become available for a number of small polyatomic molecules. The development of this field to date is reviewed.
Introduction In resonance Raman spectroscopy (RRS), absorption of a photon may take a molecule to a higher electronic state from which it returns by spontaneous emission of a second photon. Since the experiments by Imre et al.,1-3 a number of investigations by this group and others have employed RRS as a tool for uncovering the dynamics of molecules excited to dissociative electronic states. Earlier work4-8 had shown that one can observe Raman scattering from diatomic halogens even if the intermediate state is excited into a continuum corresponding to bond rupture. This scenario is unlike the case in ordinary bound-state RRS where the excited molecule remains intact. Immediately after excitation of a (diatomic or polyatomic) molecule into a dissociative continuum, the nuclear coordinates begin to change in a manner which usually leads within tens or hundreds of femtoseconds to bond breaking. Since typical radiative lifetimes for spontaneous emission are on the time scale of 10 ns or longer, only a minute fraction of the molecules can radiate in time to frustrate dissociation. Nevertheless, the frequency spectrum of these emitted photons, reflecting the relative populations of final vibrational states of the molecule, can in favorable cases provide detailed information about the early course of dissociation. These time scales are also usually significantly shorter than collisions, so that the focus is on the isolated molecule. It is the purpose of this paper to review the sort of structural and dynamical information on ground and excited electronic states that has emerged from this method in the past several years. The natural perspective to take for study of rapid processes is the time domain formulation of quantum mechanics.9 Instead of using time-independent vibrational eigenfunctions for each excited electronic state, one uses dynamically evolving quantum wave packets. One also bypasses the familiar KramersHeisenberg-Dirac expression for the Raman intensity10-13 with its sum over all of the bound and continuous intermediate vibrational eigenstates. Instead, but fully equivalently, one calculates both absorption and Raman spectra by Fourier transformation of correlation functions Cfi(t).14-19 The latter are overlaps of vibrational functions φf* and φi(t), i.e., Cfi(t) ) 〈φf|φi(t)〉. Here φi ) µψi, where µ is the component in the direction of the initial polarization of the transition dipole between ground and excited electronic states and ψi is the ith vibrational eigenfunction of the ground state. Similarly, φf ) † Permanent address: Department of Chemistry, University of California, Davis, CA 95616. X Abstract published in AdVance ACS Abstracts, April 1, 1996.
S0022-3654(95)03436-8 CCC: $12.00
µψf. Evolution of φi for a time t under the forces of the excited state nuclear Hamiltonian H yields the vibrational wave packet φi(t) ) exp(-iHt/p)φi. The first experimental results obtained in this vein for a polyatomic molecule consisted of the emission spectrum of O3 photoexcited at 266 nm,1 within the continuous Hartley absorption band responsible for most of the stratospheric absorption of mid-UV solar radiation. The ground state potential energy surface (PES) of ozone has minima in C2V geometry and is of symmetry 1A1. Imre et al. found that the Raman spectrum was comprised of long progressions in both the symmetric (ν1) and antisymmetric (ν3) stretches and their combination bands, with essentially no contribution from the bending mode (ν2). The observed levels extended to within 500-1000 cm-1 of the dissociation threshold, reflecting the large changes in nuclear geometry taking place. The dynamical picture emerging from this initial experiment was of rapid wave packet motion on the 1B excited state PES in both the symmetric and antisymmetric 2 stretch coordinates. As illustrated in bondlike coordinates20 R1 and R2 in Figure 1, the center of the wave packet starts moving downhill toward a saddle point along the line R1 ) R2, while simultaneous motion in both directions perpendicular to this line causes the wave packet to bifurcate. After only a few femtoseconds, the bulk of the probability amplitude moves symmetrically out the two dissociation channels, never to return. The autocorrelation function C00(t) ) 〈φ0|φ0(t)〉, i.e., the overlap of the wave packet at time 0 with itself at a later time t, decays rapidly as the wave packet exits the Franck-Condon region. The broad, continuous absorption spectrum corresponds to the rapidly decaying autocorrelation function under the reciprocal nature of frequency and time variables in the Fourier transform.9 In the case of CH3I,2,3 an extremely long progression of overtones of the C-I stretch (ν3 ≈ 530 cm-1) all the way up to V3 ) 29 was observed (see cover of this issue). Each successive member of this progression was interpreted loosely as a tick of the clock in the dissociation process, gaining intensity as the molecular wave packet evolves toward greater C-I bond lengths and overlaps progressively more extended vibrational wave functions from the ground state. A secondary progression with a quantum in ν2 (≈1250 cm-1, the CH3 umbrella mode) was also observed to gain intensity with greater V3. The dynamical interpretation is that the wave packet initially leaves the FranckCondon region by increasing the C-I bond length and that, a few femtoseconds later, the CH3 fragment begins to convert from its tetrahedral geometry to its ultimately planar geometry. This provides an example of the sort of thing that can be determined by the Raman experiments and leads quite naturally © 1996 American Chemical Society
7744 J. Phys. Chem., Vol. 100, No. 19, 1996
Figure 1. Time evolution of the nuclear wave packet (absolute value shown) in 2D on the excited state 1B2 O3 PES of Sheppard and Walker.286 Potential contours are spaced by 2000 cm-1 increments.
to a description in the language of time-dependent wave packets; the alternative description in terms of multidimensional scattering states of the molecule would be much more complex. In benign cases it may be adequate to approximate the excited state potential by a local expansion truncated at the first or second derivatives (especially for a bound upper surface with a potential minimum close to that of the ground state). If this is done, it is possible to derive analytical representations of the multidimensional correlation functions21-26 or to use timecorrelator transform methods27-31 relating the absorption spectrum and the Raman spectra for different vibrational modes. In a loose sense these are time-dependent analogues to the timeindependent normal-mode calculations of vibrational frequencies. All of these methods which rely upon low-order expansion of the PES are extremely useful for cases where anharmonicities are not strong. In the case of photodissociation, however, we may experimentally be sensitive to large ranges of the PES which cannot be adequately represented by a quadratic polynomial in small-amplitude displacements (e.g., the PES in Figure 1). It then becomes necessary to adopt a perspective where nuclear motion is intrinsically large amplitude in at least some of the degrees of freedom. If there are only a few such coordinates, it is possible to use numerical methods to accurately propagate the time-dependent Schro¨dinger equation.32-34 The early diatomic experiments4-8 labeled the cases of excitation into the continuous regions of the excited state molecular curve as continuous Raman spectroscopy. In the extension to polyatomics, the larger number of vibrational modes can result in a quasi-continuum of discrete vibrational levels over certain ranges of excitation energy without actually leading to dissociation. In the following, we use the term dissociative resonance Raman spectroscopy (DRRS) to refer to the case that photoexcitation is into an unbound region of the excited state PES (or PES’s if there are more than one) since we are interested in resonance Raman spectroscopy as a complement to photofragmentation studies. Since the Raman spectra in both these cases are most sensitive to short-time dynamics, of course, one may not be able to distinguish on the basis of these spectra alone whether the molecule in the excited state is heading toward dissociation or not. In fact, the same techniques for analyzing the short-time dynamics behind Raman spectra were used early on both for isomerization23 and dissociation.1 By DRRS, we specifically refer to photoexcitation that leads to dissociation unless interrupted by the emission of a secondary photon. It is
Johnson et al. usually safe in this context (certainly for direct dissociations) to assume that the dynamics influencing the scattering intensities is so fast that one can ignore the possibilities of collisions in the gas phase, dephasing due to rotations,35 or distinct separation of the emission into prompt RRS and longer time resonance fluorescence components as has been seen and discussed for isolated bound-bound or broadened transitions.7,8,36 (For a very recent discussion, see ref 37.) For situations where the intermediate state is a vibrational continuum and nanosecond lasers are used, it has usually been assumed that no such distinction occurs; very recently, however, theoretical studies of the temporal characteristics of DRRS using shorter pulses have appeared.38-40 Since the earliest DRRS experiments, the photodissociation of a variety of other molecules has been studied, providing extended information about both ground and excited state PES’s. We will relate the progress to date, attempting to complement earlier reviews pertaining to Raman spectroscopy.13,36,41-46 Thus, attention is restricted in the following almost solely to resonance Raman spectroscopy of small dissociative systems. The literature of photodissociation is far richer than this, certainly. There are extensive Raman studies of biological chromophores, inorganic species, photofragmentation studies, recent experiments involving ultrafast pulses, and an exponentially growing number of time-dependent quantum mechanical calculations that all prove critical to fuller understanding of mechanisms of photodissociation. These studies are mentioned where relevant but are not discussed in depth in an effort to keep a manageable focus. After first reviewing the fundamental equations of absorption and Raman scattering within the framework of time-dependent quantum mechanics, several small dissociative polyatomics (CH3I and other iodides, H2O, H2S, CH3, etc.) are discussed in detail, particularly with respect to DRRS experiments and dynamical analyses. Other experimental and theoretical studies not discussed in detail are cited after that, and a discussion of work on inversion of Raman data to obtain excited state potentials and transition dipoles is given. Absorption Cross Sections The molecular cross section for absorption in weak fields can be obtained by time-dependent perturbation theory. We review the highlights in order to establish notation in the following and refer the reader to other works for derivations.18,47,48 For monochromatic light of frequency ω, the electromagnetic field in the dipole approximation can be written as
F(t) ) 1/2Foe exp(-iωt) + 1/2F0*e* exp(iωt)
(1)
where F0 is a constant and e is a polarization vector of unit normalization. This describes a continuous-wave light source, although the nanosecond laser pulses used in the typical DRRS experiment may also be accommodated by allowing F0 to have a variation slow compared to the optical period 2π/ω. Using semiclassical radiation theory in the dipole length gauge, the time evolution is governed by the Hamiltonian
Htot ) Hmol + d‚F(t)
(2)
where Hmol is the field-free molecular Hamiltonian and d is the instantaneous dipole operator for the electrons and nuclei. Within the Born-Oppenheimer approximation, the electronic portion of Hmol yields eigenfunctions χn(r;R) depending principally on the electronic coordinates r and parametrically on the coordinates R describing the nuclear configuration. (Here
RR Spectroscopy of Polyatomic Molecules
J. Phys. Chem., Vol. 100, No. 19, 1996 7745
r and R are used generically.) For each state n ) 0, 1, 2, ..., neglect of derivatives of χn with respect to R leads to a rovibrational Schro¨dinger equation
(Hn - En)ψn(R) ) 0
(3)
Hn ) TR + Vn(R)
(4)
where Vn is the PES of electronic state n and TR is the nuclear kinetic energy. The solution to the full time-dependent Schro¨dinger equation can be expanded in the electronic basis functions,
Ψ(r,R,t) ) ∑χn(r;R) ψn(R,t)
(5)
n)0
where ψn(R,t) is a nuclear wave packet, yet to be determined, which is governed by the dynamics due to both the molecular forces and the external field. Insertion of the Ansatz of eq 5 into the full Schro¨dinger equation and projection onto the different electronic states n then leads to a set of coupled timedependent equations for the ψn(R,t),
∂ ip ψn(R,t) ) Hnψn(R,t) + ∑ F(t)‚µnn′ψn′(R,t) ∂t n′)0
(6)
where µnn′, the transition dipole, is the electronic matrix element of the dipole operator between electronic states n and n′ and depends upon the nuclear variables R. At this point we have neglected nonadiabatic interactions between the different electronic states; these can be included, however, leading to additional diagonal and off-diagonal coupling terms. For short times and low field strengths, the coupled nuclear equations in eq 6 may now be solved by expanding in orders of time-dependent perturbation theory, subject to the initial value condition that the zeroth-order wave functions all vanish except for the ground state. We have
σiA )
ω
∑∫ dt exp[it(ω + 2pc n>0 -T T
0
Fo,i/p)]∫dτR φ* n,i(R,0) φn,i(R,t) (10) It is understood that T must be large enough that the asymptotic value of the last integral is obtained (zero in the case of photodissociation). Thus, the focus transfers to the evolution of the wave packets in eq 9. Their overlaps with their initial images yield autocorrelation functions whose Fourier transforms are summed to yield the frequency-dependent cross section for absorption. As pointed out by Kulander and Heller9,18 and others,47-49 however, the wave packets φn,i(R,t) do not represent the experimentally prepared probability amplitude in the CW excitation limit. Instead, they are related to the corresponding components of the first-order wave functions by the time integral in eq 8, which extends over all of the dynamics of the φn,i(R,t) up to time T. As T f ∞, the half-Fourier transform of each φn,i(R,t) develops into a delocalized function (the “Raman wave function”21,47,49,50) spread over the range of R where the wave packet φn,i(R,t) has traveled. We have made explicit the possibility of excitation to multiple surfaces since, in practice, overlapping absorption bands frequently occur. We have also not averaged over orientations of the molecule even though this is usual for the gas phase (randomly oriented absorbers). If we assume that Hn approximately separates into vibrational and rotational contributions Hn,vib + Hn,rot, we may factor the wave functions ψ0,i and evolution operators exp(-iHnt/p) accordingly. The laboratoryfixed dipole moment components in µn,0‚e may then be expressed in terms of body-fixed components and functions of the Euler angles51 in order to facilitate integration over the rotational coordinates. In the approximation that Hn,rot is neglected, the integration corresponds to the familiar replacement of |µn,0‚e|2 by |µn,0|2/3. Equation 10 reduces to
σiA ≈
ω
∑∫ dt exp[it(ω + E0,i/p)] × 6pc n>0 -T T
0
ψ(0) n (R,t)
) δn,0ψ0,i(R) exp(-iEn,it/p)
(7)
3
∑∫dτvib ψ*0,i,vib(µ*n0)k exp(-iHn,vibt/p)(µn0)kψ0,i,vib
(11)
k)1
where the index i corresponds to a particular rovibrational solution of eq 3 for n ) 0. For the first-order response in the rotating wave approximation, we neglect the term proportional to exp(iωt) in eq 1 since this corresponds to stimulated emission. The response corresponding to absorption comes from the term proportional to exp(-iωt), and the first-order perturbed components of each state n are then obtained as “half-Fouriertransforms”
ψ(1) n (R,T) )
iF0 T ∫ dt exp[i(t - T)(ω + Eo,i/p)]φn,i(R,t) (8) 2p 0
If one uses a body-fixed coordinate system with one axis along the transition dipole, there is only a single term in the sum over k. For a diatomic molecule the situation is especially simple since the transition dipole lies either along the internuclear axis or perpendicular to it. For a polyatomic molecule it may also happen for geometries of specific symmetry that the transition dipole direction coincides with a specific body-fixed axis. In general, however, the absorption cross section consists of a sum of terms when allowing for large-amplitude excursions in geometry. Raman Cross Sections
where
φn,i(R,t) ) exp(-iHnt/p)µn,0‚eψ0,i(R)
(9)
The wave packets φn,i are thus obtained by multiplying the initial nuclear eigenfunction by the transition dipole µn,0‚e and propagating the result forward in time by the nuclear Hamiltonian Hn. One defines a cross section as the rate of photon absorption at large times T divided by the incident photon flux c0F02/2pω, where 0 is the permittivity of free space (1/4π in cgs units). This leads ultimately to the result18
The semiclassical treatment of the external fields can be extended to Raman scattering, except for the usual caveat that spontaneous emission must be treated in analogy to stimulated emission.19 A second field is added to account for the scattered photon,
Fs(t) ) 1/2Fs0es exp(-iωst) + 1/2Fs0*es* exp(iωst)
(12)
and only the term proportional to exp(iωst) is retained this time. Second-order time-dependent perturbation theory is used to obtain the contribution to the time-dependent wave function
7746 J. Phys. Chem., Vol. 100, No. 19, 1996
Johnson et al.
proportional to F0Fs0*. The overlap of this second-order component with the zero-order function ψ0f gives the probability amplitude at time t that the two-photon process leaves the molecule back in rovibrational state f of the ground electronic state. Therefore, the rate of populating state f is given by the time derivative of the square of this overlap. Ultimately, one finds that the differential cross section for scattering into solid angle dΩ with the molecule starting in state i and ending in state f is given by
dσfiR ωωs3 |e *‚r ‚e|2 ) dΩ 16 2π2c4 s fi
(13)
0
Here the molecular polarizability tensor rfi contains contributions from each intermediate excited electronic state which are half-Fourier transforms of cross-correlation functions (damping factors can be added for formal convergence of the time integrals),
(rfi)jk )
i
∑∫ dt exp[it(ω + E0i/p)]∫dτR ψ*0,f(R)(µ0,n)j × pn>0 0 ∞
exp(-iHnt/p)(µn,0)kψ0,i(R) (14) The product of the last three factors is the same as in eq 11 and represents a wave packet evolving on the nth PES. We see explicitly that the dynamics of exactly the same wave packets on each PES determine both the absorption and Raman spectra. There is an important distinction in the two cases, however; the relevant polarizability terms are squared in the Raman case, leading to interference effects between neighboring excited states even in the absence of any nonadiabatic interactions. As discussed by Loudon52 (p 293), the Raman cross section above corresponds to removal of energy from the incident beam which is deployed in the scattering process. In the actual experiments, however, one measures the energy per unit time and area of the scattered radiation. Since some of the energy of the inelastic process is left behind in the molecule, the cross section above must be corrected by the factor ωs/ω,
ωs4 dσfiR |e *‚r ‚e|2 f dΩ 16 2π2c4 s fi
(15)
0
This provides a general expression for the observed Raman intensities with no averaging over the distribution of molecular orientations. For gas phase samples we may again average over orientations if vibrational and rotational coordinates are explicitly separated.42,53 One then obtains the scattering intensity and depolarization ratio (ratio of scattered intensities perpendicular and parallel to the initial polarization) conveniently expressed in terms of body-fixed polarizability components. The Kramers-Heisenberg-Dirac expression10,11 for the polarizability tensor actually derives from such a time-dependent perturbation theory treatment even though it is frequently associated with the time-independent sum-over-intermediatestates picture of Raman scattering. By inserting a resolution of the identity in terms of the excited state eigenfunctions after the evolution operator in eq 14 and adding a phenomenological exponential decay term in the time integrations, the polarizability may be recast in its Kramers-Heisenberg-Dirac form. The two approaches are formally equivalent. Practically, however, the time-dependent approach is the natural choice for short time scales as in direct photodissociation.9,21 There are other, more complicated, effects on the Raman spectra which can occur when the excited states are nonadia-
Figure 2. 3Q0+ (dashed line) and total 3Q1-3Q0+-1Q1 (solid line) A-band CH3I absorption spectrum as deconvoluted by Gedanken and Rowe.65
batically coupled. Several recent investigations54-61 have dealt with the extension of the theory to incorporate dynamics under such circumstances. The type of effects expected due to variation of the transition dipole with nuclear geometry in largeamplitude motion have been investigated by Ling et al.62 CH3I A Band The A band of methyl iodide is a broad, featureless absorption continuum assigned by Mulliken63,64 to three excited electronic states labeled 3Q1, 3Q0+, and 1Q1. Only the latter two, respectively dissociating to CH3 + I*(2P1/2) and CH3 + I(2P3/2), were expected to have significant absorption strength. This was supported by the magnetic circular dichroism (MCD) experiments of Gedanken and Rowe,65 whose approximate deconvolution of the absorption spectrum (see Figure 2) ascribed the majority of the band intensity to the nondegenerate 3Q0+ state. I*/I ratios determined at various wavelengths throughout the UV differ somewhat from these predictions (see ref 66 for a summary of results to 1990), suggesting significant nonadiabatic interactions between the 3Q0+ and 1Q1 states during the course of dissociation. Furthermore, the angular distributions of photofragments appear consistent with absorption throughout the A band via a transition dipole moment parallel to the C3V symmetry axis of CH3I,67-75 and this is only expected for the 3Q 0+ state of symmetry A1. The picture that emerged was that the 3Q0+ state accounts for nearly all of the absorption (even on the high side of the band, contrary to the prediction of the deconvolution by Gedanken and Rowe65) and that production of I(2P3/2) occurs primarily through nonadiabatic 3Q0+-to-1Q1 transition.76,77 The only vibrational mode of the methyl photofragment found to be strongly excited in either dissociation channel was the umbrella mode (ν2),78,79 consistent with the transition from nearly tetrahedral angles in CH3I to planarity in CH3. Shapiro and Bersohn80 accordingly introduced the linear pseudotriatomic model: C-I stretching is represented by the distance from the I atom to the center of mass of CH3, and umbrella motion is represented by the distance from the C atom to the center of mass of the three H atoms. Quantum scattering calculations were used to obtain analytical 2D PES’s for the ground and 3Q 81 and 0+ states, which then served as input for dynamical semiclassical82 studies of the photodissociation. This original model also provided the interpretive framework for the first CH3I Raman experiments of Imre et al.2,3 The long Raman
RR Spectroscopy of Polyatomic Molecules progressions in the C-I stretch 3n and the parallel combination bands with the umbrella mode 213n seen on the cover were attributed to motion solely on the 3Q0+ PES. (The 3n emissions had already been seen from UV photoexcitation of CH3I and CD3I in rare gas matrices by Brus and Bondybey.83) The slow increase of 213n intensity with increase in n directly reflected the gradual preference for planar CH3 geometries as the C-I bond length increased on the 3Q0+ PES. Higher resolution CH3I and CD3I gas phase emission studies were subsequently performed at 266 nm excitation by Hale et al.84 to obtain reliably calibrated vibrational band positions and intensities used in a theoretical analysis by Sundberg et al.85 CD3I represented obvious complications in interpretation due to the presence of a 2:1 Fermi resonance between the CD3 umbrella and C-I stretch modes in the ground state; in fact, CH3I also represented (subtler) complications because of potential 5:2 Fermi resonance between the modes at some energy along the progressions. These issues were accommodated by performing variational calculations converged up to 20 000 cm-1 of vibrational energy using the complex Gaussian basis set introduced by Davis and Heller.86 The absorption and Raman spectra were calculated by semiclassical wave packet dynamics.16-19 The model potentials for the ground and 3Q0+ states were then adjusted to reconcile as closely as possible the absorption65 and Raman spectra and CH3/CD3 photofragment vibrational populations.69,87 Various other refinements have been made to the ShapiroBersohn model over the years. Kanfer and Shapiro88 performed their own modifications to the ground state potential to achieve better agreement with the vibrational level information of the Raman experiments. Shapiro77 included the 1Q1 excited state, model nonadiabatic coupling to 3Q0+, and non-Condon effects to try to reproduce the absorption and MCD data,65 vibrational state distributions of CH3 in the I and I* channels, and the wavelength dependence of the I*/I branching ratio.69,70,78,79,87 Coalson and Kinsey54 formulated an extension of the timedependent approach which could also allow nonadiabatic coupling between two excited state surfaces. Johnson et al.89 delineated how the coordinates in the linear pseudotriatomic model could be related to the curvilinear coordinate body frame vibrational coordinates in a fully large-amplitude treatment. Guo and Schatz66 used the numerical second-order-differencing propagation method of Kosloff and Kosloff90 to optimize the 2D coupled-surface model of Shapiro and Bersohn for agreement with the MCD deconvolution of the absorption spectrum, the I*/I branching ratios, and the ν2 vibrational distributions of CH3 available by 1990. The short-time theory of Raman scattering21 predicts that the ratio of the 32:31 emission intensities should be π/4, while the experimental results at 266 nm84 actually showed a weaker fundamental. This prompted an investigation into the excitation frequency dependence and polarization behavior (with rotational band contour analysis) of the 3n and 213n Raman features with up to four total quanta throughout a range of the UV.91,92 All of the Raman excitation profiles (REP’s) except for the fundamentals had simple smooth shapes that could be modeled using short-time theory for motion on a single repulsive PES. The 31 REP, however, had a bimodal shape. Polarization analysis at 266 and 280 nm found depolarization ratios for all 3n to be close to 1/3, the value expected for a parallel transition to one or more excited states.53,93 It was found that the observed REP’s could all be fit reasonably well by a model in which the 31 fundamental was subject to off-resonant interference from a higher electronic state or states with parallel transition dipole character. (An alternative explanation was given by Shapiro,94
J. Phys. Chem., Vol. 100, No. 19, 1996 7747 although off-resonant interference had also been identified in other alkyl iodide studies, see next section.) Since off-resonant scattering primarily interferes with fundamentals due to the shortness of its duration,21 the overtone and combination band REP’s could be used for extraction of the details of the resonant PES in the model. This investigation, though hardly the first to do so, highlighted the importance of both looking at more than one excitation wavelength and carefully examining the overtone and combination band intensities. Both of these can be critical in trying to extract the short time dynamics from DRRS experiments. Since, as mentioned above, the same wave packet yields both the absorption and Raman spectra, the absorption spectrum due to the single resonant PES in the model could be calculated. While too low in absolute normalization, the shape and position of the calculated absorption spectrum were found to be in very good agreement with the 3Q0+ component of the absorption band obtained by Gedanken and Rowe and shown in Figure 2. Firm conclusions are difficult because of nonnegligible errors in the overall accuracy of their fit to their MCD/absorption data. Nevertheless, the Raman results92 were taken to support the conclusion that the 3Q0+ component does not account for the whole of the absorption band; absorption by the 1Q1 states on the high-energy side appear to be very significant, despite the inferences from the angular distribution results67-75 that absorption throughout the A band is due to a parallel transition. Subsequent experiments at 266 nm by Lao et al.95 extended the studies of the 3n Raman progression and the depolarization ratios up to n ) 12. In the lower members of the series, the depolarization ratios derived from their measurements (∼1/3) agreed with those determined by Galica et al.91,92 However, a significant increase in the depolarization ratio was observed with increase in n which was taken to indicate emission from the 1Q states following initial absorption by the 3Q 1 0+ state. A qualitative correlation was then drawn between the depolarization and the amount of wave packet sampling of the 3Q0+-1Q1 conical intersection. Investigation of the polarization properties using 248 nm excitation58 showed stronger depolarization variation at lower n than for the 266 nm experiments, attributed to nonnegligible interference effects from 1Q1 absorption at 248 nm. Theoretical investigations of these effects were made.58-60 A more recent higher resolution (∼7 cm-1 monochromator band-pass) 266 nm resonance Raman study by Wang and Ziegler96 has changed this picture again. They find depolarization ratios that disagree somewhat with both the results of Galica et al.92 and of Lao et al.95 Wang and Ziegler also point out that angular momentum constraints forbid the ∆K ) (1 selection rules used by Lao et al. for Raman scattering between totally symmetric initial and final vibrational states if a change of electronic symmetry from A1 to E is involved. In other words, whatever amount of nonadiabatic transition there may be to the 1Q1 surface, it does not contribute to the 3n Raman intensities. In place of the coupled surface model, Wang and Ziegler propose that the depolarization ratios measured by them at 266 nm can be rationalized by interference, as discussed for eq 14 ff, due to two processes: (i) parallel absorption followed by parallel emission (3Q0+) and (ii) perpendicular absorption followed by perpendicular emission (1Q1). They then demonstrate that adopting the ratio of oscillator strengths predicted by Gedanken and Rowe’s analysis at 266 nm leads to depolarization ratios and rotational contours in substantial agreement with their own measured results. This in part challenges conclusions both of Lao et al. and of Galica et al. It is still unresolved how sensitive CH3I depolarization ratios in the A
7748 J. Phys. Chem., Vol. 100, No. 19, 1996 band may be to effects of the nonadiabatic interaction and how extensively direct excitation to 1Q1 contributes to Raman intensities. Ab initio calculations of increasing quality have been performed for the excited states in recent years.97-99 The extensive spin-orbit configuration interaction calculations of Amatatsu et al.99 have examined the behavior of both important excited state PES’s, particularly in the region of their conical intersection, and have been used to construct 6D PES’s including all internal coordinate motions except for C-H stretching. Classical trajectories were run and compared with experimental vibrational distributions of CH3 in the I and I* channels, as well as with recent results on the rotational distributions of the methyl fragment.100-103 These potentials were then used by Guo104 to perform a 3D wave packet calculation which included rigid bending of CH3 with respect to the C-I axis. The most ambitious investigations to date using these PES’s have been multiconfiguration time-dependent Hartree method calculations including a total of five vibrational modes by Manthe and Hammerich105 and by Hammerich et al.106 The 5D calculations, in a model similar in spirit to that by Johnson et al.,89 employed geometrically defined curvilinear internal coordinates for largeamplitude motion in CH3I instead of the fictitious atom of the linear pseudotriatomic model; among other things, even the effects of the Jahn-Teller distortion found99 in the degenerate 1Q level could then be investigated.106 Absorption spectra were 1 calculated in both the 3D (excitation to both 3Q0+ and 1Q1) and 5D (excitation to 3Q0+) investigations by Fourier transformation of the autocorrelation functions. The calculated absorption components were blue-shifted and wide compared to the results of Gedanken and Rowe65 but show qualitative agreement. Since much of the focus has been on the experimental I*/I and CH3 vibrational and rotational results (see ref 99 for a review to 1994), Raman correlation functions, cross sections and depolarization ratios from these ab initio PES’s have yet to be calculated. Zero kinetic energy (ZEKE) photoelectron spectroscopy has recently been implemented on both CH3I and CD3I107,108 using the dissociative A band as a resonant intermediate. Strobel et al.108 compare this to the Raman process in that evolution of the wave function occurs before the second photon event, in this case absorption of an ionizing photon. The resulting photoelectron spectrum of Strobel et al., which reflects absorption in the intermediate state, shows a progression in up to 10 quanta of the C-I stretch in the final ionic state (ν3+) and a parallel progression with one quantum in the umbrella mode (ν2+). Aside from the differences between these progressions and those observed in DRRS, there is also a progression with one quantum in the deformation mode ν6+. As discussed by Barry and Gorry70 for CH3I, this is one of the E-symmetry modes which will be active in nonadiabatic coupling between the 3Q0+ and 1Q1 states. Thus, ZEKE photoelectron spectroscopy holds significant promise in developing a more detailed picture of the dynamics of the nonadiabatic interactions during photodissociation. It is now clear that the A-band photodissociation of CH3I is anything but the prototype for simple, direct photodissociation that it once appeared. Nevertheless, a tremendous amount of new insight has been gained in the past few years, and this process stands as an example of how detailed a picture can be obtained by concerted experimental and theoretical efforts. Resonance Raman studies in the predissociative B ˜ state of CH3I have also been carried out.93,109-113 This is an intense Rydberg transition for which one of the Raman experiments111 was able to use a supersonic expansion of CH3I. Resonance
Johnson et al. hyper-Raman experiments (two-photon instead of one-photon excitation) have also been carried out for CH3I in both the B ˜ and C ˜ states.110,114,115 Alkyl Iodides: Solution versus Gas Phase Since the dynamics behind DRRS spectra occur on such fast time scales, the possibility arises of using such experiments as probes of solvent cage effects on photodissociating species, as well as of the effects of solvation on the electronic levels of the molecule. Sension and Strauss116 made a detailed investigation of I2 in hexane, focusing on the information provided by the REP. (See also refs 117 and 118.) More recently, a series of investigations have been made exploring the differences in solution and gas phase DRRS experiments for methyl and higher alkyl iodides. Raman spectra at 266 nm of CH3I and CD3I in hexane solution119 and of CH3I in hexane, hexadecane, and acetonitrile120 were obtained by Markel and Myers. The long C-I stretch progressions observed generally resembled those for the gas phase,3,84 though with certain differences. For CH3I in hexane, while overtones through 39 more or less matched the gas phase overtones, higher overtones were increasingly broadened and shifted in frequency. Consequently, the solution phase progressions were foreshortened, with the highest reported level being 316 instead of 329. The similarity between gas phase and hexane results up through 39 was taken to indicate the dominance of the single molecule photochemistry versus solvation dynamics for short times and for C-I bond length distortions out to ∼0.4 Å. Combination bands with a quantum in the umbrella mode were also observed and showed slightly more deviation in intensity from those in the gas phase. The CD3I differences were more pronounced and exhibited higher solution broadening, but interpretation was complicated by the 2:1 Fermi resonance between the umbrella and C-I stretch.84 Higher alkyl iodides were also studied by DRRS both in solution and in gas phase.121-124 Phillips and Myers121 examined absolute resonance Raman spectra for ethyl, isopropyl, and tert-butyl iodides in cyclohexane solution for several excitation wavelengths in the A bands and above. In each case, the C-I stretch fundamental intensity was determined to depend strongly on the excitation wavelength and to be anomalously lower than the first overtone for excitations near the center of the absorption band. This was assigned to off-resonant interference from a higher electronic state. The fact that the same situation was also found in the gas phase CH3I investigation of Galica et al.92 highlights the similarity of the iodine-based n f σ* electronic transitions in all of these alkyl iodides. Increase of the alkyl chain lengths did, however, tend to make a difference in greater mixing of the C-I stretch motion in other normal modes. Comparison of the solvated Raman spectra with gas phase ethyl, isopropyl, and tert-butyl iodide spectra123 at selected wavelengths showed strong similarities, although there were residual differences which could be attributed to dominance of the attractive portions of the solute-solvent intermolecular potentials.120 A comparison125 of the gas and hexane solution phase REP’s for CH3I also confirmed their similarities. Thus, all evidence indicates that the electronic states and short-time photodissociation dynamics near the FC geometries are essentially the same in the different environments for each alkyl iodide. A contrast to this is found in diidodomethane. A vapor phase A band (355 nm) DRRS study of CH2I2 by Zhang and Imre126 found significant symmetric and antisymmetric C-I stretching and weaker I-C-I bending activity. The stretching dynamics were subsequently modeled by 2D numerical wave packet
RR Spectroscopy of Polyatomic Molecules
Figure 3. Emission scans for C6H5I obtained by O’Brien et al.137 at excitation wavelengths throughout the B absorption band. The C-I stretch and its first two overtones are indicated by asterisks. Higher features are predominantly ring-based planar vibrations. Spectra are normalized to the intense peak at ∼1575 cm-1.
propagation.127 However, Kwok and Phillips128 have found the 355 and 341.5 nm Raman spectra for CH2I2 in cyclohexane solution to exhibit several other vibrational bands not observed in the gas phase spectra. I-C-I bending was particularly enhanced by the solvation. This was attributed to the bulkiness of the diiodo molecule and to slower photodissociation for two heavy fragments (CH2I and I), both of which allow for greater cumulative interaction with the solvent cage. C6H5I B Band The second absorption band of iodobenzene (∼210-235 nm) ˜ 1A1 r X ˜ 1A1 carbon has been assigned by Kimura129 as a B ˜ 1A1g (π* r π) ring transition corresponding to the B ˜ 1B1u r X transition in benzene. The lowest frequency mode is the C-I stretch which, at ∼265 cm-1, is approximately half that in CH3I. The broad room temperature absorption continuum therefore possesses substantial vibrational hot band congestion. There is still a residual diffuse structure evident which, in the corresponding B band of benzene, arises from a diffuse vibronically allowed progression in the symmetric carbon breathing mode (discussed by Ziegler and Hudson130). Photoexcitation in the B band leads to dissociation into C6H5 and I radicals.131 By analogy with results from photodissociation in the A and the merged C/D bands of C6H5I,132-134 it is expected that excitation to the B ˜ 1A1 state leads to predissociation on a time scale >0.5 ps. For the A band, which is complicated by the presence of two dissociation mechanisms,135 real-time studies have verified that both are of 0.4 ps duration or greater.136 These time scales are too long to be mapped out completely by DRRS, but B band studies were undertaken in an effort to understand the first part of the dissociation dynamics following excitation.137,138 Resonance Raman and hyper-Raman spectra of iodobenzene were also obtained by Bonang and Cameron.139 Figure 3 shows representative scans of the emission intensity observed by O’Brien et al.137 for C6H5I excited at a number of wavelengths throughout the band. Features with up to three quanta in the C-I stretch can be observed, indicating significant
J. Phys. Chem., Vol. 100, No. 19, 1996 7749 initial motion in this coordinate. The fact that this progression is so limited with respect to that found in the A band of alkyl iodides is in agreement with the interpretation of a delayed dissociation, although foreshortening due to other influences (e.g., transition moment coordinate dependence) cannot be ruled out. Furthermore, as is to be expected from the ring-based character of the transition, there is substantial activity in various ring modes around 1000-1200 and ∼1575 cm-1 and in some combination bands with a quantum of C-I stretch. The Raman spectrum is completely dominated by in-plane vibrations. Several of the levels observed are nearly degenerate, correlating to exactly degenerate levels in benzene. Analysis of the levels was aided by the work of Clark and McCaffery,140 who were able to make vibrational assignments using off-resonant circular polarization modulation Raman spectroscopy. A planar force field for C6H5I was constructed using the C6H6 force field of Ozkabak and Goodman141,142 as a starting point. Of key interest was the sensitivity of the C-I stretch fundamental and overtones to excitation wavelength. One can see from Figure 3 that the fundamental virtually disappears right in the middle of the resonance band. The effects of off-resonant interference as displayed in the CH3I and higher alkyl iodide REP’s initially suggested the possibility of similar interference for C6H5I. However, such interference from either higher or lower states would generally cause the fundamental REP to extend beyond the resonance region instead of decaying to zero as shown in Figure 3. A model was developed for this wavelength dependence in which the corresponding correlation function showed pronounced beating between the C-I stretch and a higher frequency mode (or modes) in the excited state for approximately one vibrational period of the C-I stretch. (See ref 45 for further discussion of and references to such phenomena.) Thus, in this case, the broad structure in the REP was assigned to dynamical effects. A deeper investigation into the behavior of the wavelength dependence of the dominant features was then made possible by a significant improvement in the experimental apparatus.138 A single computer was used to simultaneously step the laser wavelength, the angle of the frequency-doubling crystal, and the spectrometer grating angle. This allowed synchronized scanning of the absorbed and emitted UV radiation, thus locking onto one final vibrational feature of the emission spectrum at a time. In this way, REP’s could be collected for each particular vibrational state in a continuous scan instead of performing a separate experiment for each excitation wavelength as is usually done (e.g., as in Figure 3). Examples of these scans are shown in Figure 4 for particular vibrational features of iodobenzene. In order to explain the new REP data, the model of O’Brien et al.137 required further extensions. In order to treat the ∼1100 cm-1 spacing in the REP of the 265 cm-1 band, at least one of the modes in the 1000-1200 cm-1 frequency range was required. Furthermore, the most intense emission feature over most of the excitation region is that at ∼1575 cm-1. As observed in Figure 4, both the 1065 and 1575 cm-1 features have oscillations near the maxima of their REP’s with spacings close to the 265 cm-1 of the C-I stretching mode in the ground state. Thus, these three modes were included explicitly and the rest only implicitly as a source of smooth decay of the relevant time-dependent correlation functions. The excited state displacements and frequencies, as well as both constant (Condon) and first-order (non-Condon) terms in the transition moment, were optimized to bring all three calculated REP’s into simultaneous agreement with experiment. Hot band contributions from the C-I stretching mode were also included.
7750 J. Phys. Chem., Vol. 100, No. 19, 1996
Johnson et al.
Figure 5. A ˜ 1B1 r X ˜ 1A1 absorption spectrum of H2O (adapted from ref 145).
Figure 4. Continuously scanned REP’s for important vibrational features in the C6H5I B-band Raman spectra.138 The smoother lines in each case represent results of a best-fit model of the dynamics following photoexcitation.
The results are indicated by the smoother lines in Figure 4 and show that very good agreement can be obtained at this level. More detailed discussion of the vibrational assignments and correlation function calculations can be found in the original papers.137,138 The ability to continuously scan the REP’s should be strongly advantageous in many more applications than the lone case of iodobenzene. Aside from the obvious convenience that the change of excitation wavelength becomes automated, one may avoid calibration problems that typically occur between spectra taken at different times. Significantly higher resolution then also becomes allowed; this is probably unimportant for excitation in absolutely smooth and continuous absorption bands but should be of considerable value in the common case that finer scale vibrational structure is observed in absorption. A continuous-scan two-color variant of ZEKE spectroscopy has also recently been suggested in the recent extension to dissociative intermediate states.108 H2O A Band The first absorption band of H2O is a continuous transition extending from 185 to 145 nm, where it overlaps the low-energy side of the B band.143-145 Faint diffuse structure superimposed on the continuum, as seen in Figure 5, was originally assigned to a progression of excited state bending (ν2′) levels.145 Ab ˜ 1A1 initio calculations identify the transition to be A ˜ 1B1 r X with the upper state an isolated valence/Rydberg level and have resulted in an analytical PES146 which is directly dissociative into H + OH. A variety of theoretical and experimental investigations in recent years have converged on a consistent picture of the photodissociation dynamics. Indeed, dissociation in the A band of H2O is widely regarded as a prototypical case for direct dissociation of a polyatomic molecule on a single PES. The situation as of 1992 has been thoroughly reviewed in the article of Engel et al.,147 which should be consulted for greater detail. Resonance Raman scattering was obtained for excitation in the A ˜ state of H2O, D2O, and HOD at several wavelengths.148
The 266 nm Nd:YAG fourth harmonic was converted to shorter wavelengths by anti-Stokes Raman shifting, providing excitation at 184.5, 171.4, 160.0, and 150.0 nm (as well as 141.2 nm in the B band). For excitation near the A band center, where the longest progressions are usually expected, symmetric stretch (ν1) overtones up to (V1,V2,V3) ) (6,0,0) were observed in emission.148 The off-resonance excitation at 200 nm shows only a single peak, the ν1 fundamental. 149 (Other measurements have also been made in this preresonance region;150 these latter measurements have in fact obtained absolute scattering cross sections for water and other molecules.) The long on-resonance symmetric stretch progression provides direct experimental evidence that the initial stage of the photodissociation is simultaneous extension of both O-H bonds. No bending activity is observed in the Raman spectra, indicating negligible gradient of the excited state PES along the bending coordinate at the FranckCondon geometry. The antisymmetric stretch states with odd quanta are disallowed in the resonance Raman spectra by symmetry, but states with two quanta of ν3 are observed, both alone and in combination with up to four quanta of ν1. The wave packet in the dynamical picture can, in principle, spread quickly (bifurcate) along the positive and negative antisymmetric stretch directions, promoting strong ν3 activity as is seen in O3; however, this turns out in H2O to be minor compared to the motion along the symmetric stretch. The observed ν3 activity was attributed to Darling-Dennison coupling151 of ν1 and ν3 in the ground state although, of course, breaking of a single O-H bond ultimately requires large antisymmetric stretching distortions in the excited state as well. These results were in accord with the ab initio calculations of the excited state potential,146 which found a significant gradient along the symmetric stretch, but not the bend. Theoretical studies of absorption and photodissociation by Engel et al.152,153 which also calculated the (perpendicular) transition dipole had already found that the diffuse structure in the absorption spectrum could be reproduced even if the bending and stretching degrees of freedom were decoupled. (See also the book by Schinke.154) Thus, theory and experiment agreed that the diffuse progression in the absorption spectrum should be reassigned to excited state motion in the symmetric stretch instead of the bend. The lack of bending activity is furthermore in accord with the fact that rotational photofragment distributions are principally determined by the parent molecule Boltzmann distribution. (See ref 147 and references therein.) A number of theoretical calculations of the absorption and/
RR Spectroscopy of Polyatomic Molecules or Raman spectra were then made.149,155-159 Since the FC region starting from the lowest ground state vibrational level is ∼0.4 eV higher than the saddle point at longer (equal) O-H bond lengths, the early time motion is primarily in terms of symmetric stretching of the two bonds, giving rise to both the absorption progression and the strongest Raman overtone features. The gradient of the PES is quite strong, leading to rapid initial motion out of the FC region, rapid decay of the the autocorrelation function, and corresponding broadness of the absorption spectrum. A portion of the wave function propagating along the symmetric stretch returns to the FC region on a time scale of about 19 fs,158 but diminished in amplitude because of “leakage” along the dissociative antisymmetric stretch directions. This is in accord with a theoretical description of diffuse absorption structure for photodissociating symmetric triatomics put forth by Pack160 (see also the application to H2O by Braunstein and Pack161) and translated into time-dependent theory by Heller.17 The resulting damped autocorrelation function gives rise to the weak undulations observed in the absorption spectrum. The transition dipole moment, which could in principle strongly influence band shapes, was found to be only weakly dependent on nuclear coordinates in the FC region.152 Thus, the Condon approximation of a constant transition dipole is adequate for calculation of the absorption spectrum.155 However, its decrease with increasing O-H separation was found to be important for calculation of the higher Raman overtones since these final vibrational states extend outside of the FC region. An additional source of experimental data about the A state ˜ 1B1 dynamics has been obtained by observing C ˜ 1B1 f A 162 emission. Starting from (V1,V2,V3) ) (1,0,0) in the upper state, two emission features of different widths are observed which are attributed to evolution of the two lobes of the initial wave packet on the A ˜ state PES. One lobe starts well up on the repulsive wall and is quickly pushed out, leading to rapid decay in the autocorrelation function and a broad emission feature; the other starts further out toward the saddle point, is pushed out more slowly, and yields a narrower emission feature. That such a large change can be obtained by starting from neighboring locations along the C2V axis supports the picture that the important initial forces in the A ˜ state are along the symmetric stretch. The vibrational quantum numbers referred to above have been “borrowed” from the normal-mode numbering appropriate to low-lying vibrational states. As one goes to higher levels, higher anharmonicities inevitably become more significant. The simplicities of the normal-mode approximation then become lost, even though, in favorable cases, clearly identifiable progressions may still be found with normal-mode descriptions appropriate at the low-energy limits. In such cases, an approximate separability may hold for larger than normal displacements from the equilibrium geometry whether or not it is possible to identify the coordinates that best describe the separability of largeamplitude vibrational coordinates. A particularly important case arises in X-H stretches (X much heavier than H); the X-H bond length has long been known to be approximately decoupled from other vibrational degrees of freedom and to form a local mode163,164 with “good” quantum numbers up to several quanta. A local mode basis for the hydride stretches of a molecule then consists of (symmetrized) products of vibrational orbitals ψn(ri), where ri is the length of bond i. The parts of the PES relevant to these variables can be described by Morse or other potentials which try to accommodate realistic behavior at large distances from equilibrium in a way that low-order polynomial expansions cannot. One generally finds that the low-energy
J. Phys. Chem., Vol. 100, No. 19, 1996 7751 states are best described by a normal-mode basis but that, as the number of X-H stretching quanta increases, a local mode basis is more appropriate.165 It is well-known that H2O is an extreme case that is better viewed in terms of local modes if there are more than a couple quanta of stretching164,166-168 (though it is still possible to slightly improve upon bond coordinates for the description169,170). This led to adoption of the local mode interpretation of the higher vibrational levels seen in the resonance Raman spectra.149,158 In this description, the primitive stretching states |(nm)(〉 are of the form ψn(r1) ψm(r2) ( ψn(r2) ψm(r1), where ψn is usually a vibrational wave function for strongly anharmonic forces (e.g., for a Morse potential). Excited levels group into clusters (polyads) characterized by the total number of stretch quanta n + m. The levels observed in the Raman experiment were thereby assigned to states with very unequal sharing of the quanta between the two bonds (m * n).149 This represents an alternative to the usual interpretation of normal mode states coupled by Darling-Dennison resonance (product of quadratic terms in symmetric and antisymmetric stretch coordinates); the transition between these two points of view has been extensively studied.171-176 Thus, H2O represents a special case where a great deal of information is already known about the character of highly excited vibrations. High overtones and combination bands observed in DRRS of other polyatomics frequently provide new vibrational information which requires more extensive theoretical investigation. In addition to absorption spectroscopy, product state distributions have been probed after absorption of a 157 nm photon by using laser-induced fluorescence (LIF) to probe the OH product distribution.177-179 A theoretical treatment of product distributions is also provided by Engel et al.152 The undulatory structure observed in the absorption due to symmetric stretching also is manifested in the vibrationally resolved partial cross sections.152,180 For the isotopomer HOD, some selectivity in bond breaking is achieved as the excitation wavelength is varied.159 A number of studies use preparative vibrational excitation in the ground state to move the excitation outside the FC region. This also provides rotational selectivity, alignment, and bond specific excitation for HOD. An infrared preparative pulse selects a single rovibrational state and provides precise knowledge of the initial conditions prior to the 193 nm photolysis pulse.181 Stimulated Raman excitation (SRE) also provides one quantum of state-selected vibrational excitation. The rotational distribution of the OH product is sensitive to the initially selected rotational level;182 this leads to an estimated excited state lifetime of 40 fs.183 Infrared overtone pumping moves the excitation further from the FC region than pumping a fundamental. While rotational selection governs primarily only rotational distributions of products, vibrational state selection controls both vibrational distributions and wavelength dependence of the photodissociation cross section.184,185 (See also the review of Engel et al.147) State-selective photolysis has also been done for D2O and HOD by Cohen et al.186,187 Such overtone preparation can also place the wave packet at a location such that motion along a particular dissociation coordinate leads to 15-fold excess of OD versus OH;188,189 this process has been recently reviewed.190 SRE has also been used to achieve selective enhancement of OD photodissociation of HOD.191 H2O B Band The second absorption band of H2O, like the first, appears ˜ 1A1 absorption as a continuous transition. The B ˜ 1A1 - X spectrum ranges from overlap of the A band at 145 nm to that
7752 J. Phys. Chem., Vol. 100, No. 19, 1996 of the C bands at about 124 nm.143,145 Weak diffuse structure is superimposed on the continuum, but the features are larger and spaced closer than for the A ˜ state; it more closely resembles that of the Hartley band (D ˜ rX ˜ ) of ozone (see below). In spite of the superficial resemblance in absorption, the dissociation dynamics of the B ˜ state are very different than for either of these other two cases, as is revealed by resonance Raman scattering. Raman spectra have been recorded for only one excitation wavelength of 141.2 nm.192 Even so, the dramatic difference compared to A ˜ state Raman scattering provides indisputable evidence that the femtosecond dynamics of the molecule is very different. A bending overtone progression not seen in any of the A ˜ state spectra completely dominates the B ˜ state Raman spectrum, with five quanta observed. Conversely, the stretching motion overtone progression does not occur for this state, being restricted to the fundamental or one-quantum combination with bending overtones. While the A ˜ state initial motion is domi˜ nated by symmetric stretching motion along the C2V axis, the B state motion is dominated by bend with an admixture of stretching of one H-OH bond. In contrast to the interpretation of the absorption structure, the Raman data yield compelling evidence as to the nature of the initial dynamics of the dissociating molecule. A 3-dimensional ab initio PES193 is used in the analysis of the Raman emission data. The PES has the same symmetry as the ground state; these surfaces undergo a conical intersection, creating a well ∼3 eV deep and a linear minimum with one of the O-H bonds stretched to about 3 au.193 The gradient in the FC region therefore has a strong bending component, and “the dominant motion is the opening of the bending angle.”192 The deep well of the B ˜ state fails to strongly trap the wave packet because of efficient crossing to the ground electronic state in the vicinity of the conical intersection. This predissociation severely limits the B ˜ state lifetime and effectively damps the autocorrelation function. The tiny part of the wave packet which crosses the conical intersection both ways, i.e., retracing the (primarily bending) large-amplitude motion, gives rise to a recurrence and, hence, the fine structure of the absorption spectrum. This picture is supported by ab initio calculations and a dynamical interpretation.194 Photofragmentation studies that obtain OH in very high rotational states support the picture of high-amplitude bending on the B ˜ -state PES.193,195 The H atom is “ejected like a discus, leaving the OH radical spinning very fast...”154 H2S A Band The UV absorption spectrum of H2S is a continuous band approximately 6000 cm-1 wide peaking around 195 nm (51 000 cm-1),196-199 as shown in Figure 6.198 A single vibrational progression is observed (∼1150 cm-1 in H2S and ∼850 cm-1 in D2S) which was originally attributed to a bending progression in the excited state.196,197 The C2V ground state is of 1A1 symmetry. There are two excited singlet states in the energy range of the first absorption continuum:200 one of 1B1 and and one of 1A2 symmetry. The latter is dipole forbidden in C2V geometries; in Cs geometry, both are dipole-allowed and of A′′ symmetry. Photofragmentation studies have been performed by several groups,201-207 and the resulting angular distributions identify the absorption as due to a transition dipole perpendicular to the molecular plane. The absorption band was interpreted by van Veen et al.203 as absorption to a bound region of the 1B1 PES followed in a few vibrational periods by predissociation via the 1A2 PES; these states can be coupled by the b2 symmetry antisymmetric stretching vibrations.
Johnson et al.
Figure 6. A ˜ 1B1 r X ˜ 1A1 absorption spectrum of H2S (adapted from ref 198).
Raman studies have been made of H2S by different groups in efforts to understand details of the absorption process and subsequent dynamics. Using excitation at 193 nm, Kleinermanns et al.208 obtained initial emission spectra from which, despite the low resolution and apparent fluorescence from other sources, nine bands were identified as H2S Raman features. This experiment was shortly superseded by Person et al.,209 who used higher resolution and eliminated interfering emission features due to molecules other than H2S. Formerly merged Raman features were thus partially resolved, new levels were found, and misassignments from the first study were corrected. The most notable features of the Raman spectrum are strong progressions in the ν1 (2611 cm-1) and ν3 (2684 cm-1) stretching modes. As is inherent in small hydrides like H2O (see above) and H2S, these levels appear in closely spaced polyads characterized by the total number of stretching quanta n1 + n3. Person et al.209 found ground state vibrational levels with up to seven quanta of S-H stretching, as well as parallel stretching progressions in combination with a single quantum of bending. (Two levels misassigned previously208 appear to require two less bending quanta and one more stretching quantum.) Higher levels far above the fundamental region were identified with the aid of local mode calculations by Halonen and Carrington.210 From these results, the early dissociation was identified as primarily S-H bond stretching with a small amount of HSH bending excitation. Furthermore, the ν2 bands in combination with ν3 were found to be enhanced compared to those in combination with ν1. It was pointed out that the small degree of bending activity in emission was inconsistent with the interpretation of the absorption structure as a bending progression. The higher vibrations were dominated by (symmetric) local mode levels with all quanta in one or the other bond, indicating the evolution to pure S-H bond breaking in the advanced stages of the dissociation process. Brudzynksi et al.211 obtained detailed Raman spectra at different resonant excitation wavelengths between 184 and 223 nm. The emission spectra were found to vary strongly with wavelength. At both the longest and shortest wavelengths, only the single-bond stretching states carried intensity. In the middle of the resonance region (200 and 204 nm) the relative intensities of the stretching features varied strongly, and the intensity of combination bands with one bending quantum increased substantially. This behavior was interpreted, in a reversal of the model of van Veen et al.,203 as direct transition to a dissociative 1B state and intensity borrowing by a bound or quasi-bound 1
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J. Phys. Chem., Vol. 100, No. 19, 1996 7753
1A 2
state. Such intensity borrowing would be evident in “vibronic coupling” or, using the more appropriate local mode terms, in the (observed) resonant enhancement of states with quanta shared between the two stretching modes. This reversed picture of the states was used in 2D wave packet calculations by Dixon et al.212 to theoretically model the observed SH photofragment distributions and the emission spectra obtained by Person et al.209 at 193 nm. Since then, Schinke and co-workers213-217 have performed both configuration interaction ab initio and quantum dynamical studies of the excited state potentials, verifying that the 1B1 PES is binding in the Franck-Condon region and is strongly predissociated by the 1A2 surface. Furthermore, there are two conical intersections between these surfaces at the ground state bending angle of 92°, one very close to the Franck-Condon geometry and one at longer S-H bond distances. Jet-cooled H2S absorption studies199 have shown that the spectrum is broadened only by the dissociation (not rotational congestion) and that both electronic states contribute in this band. These features and the diffuse absorption structure are well-reproduced in the recent calculations, with the latter assigned to motion along the symmetric stretch direction on the 1B1 PES209,213-218 instead of bending activity. The calculated Raman spectra, which are extremely sensitive to any inaccuracies in the ab initio PES and transition dipole calculations, are as yet only in partial agreement with the experimental Raman spectra and their wavelength dependencies.217 Browning et al.219 have examined the Raman spectra at 1 nm increments in the 199-203 nm range of excitation, arguing that the strong wavelength dependence of the bending and other features in this region reflects the presence of the 1A -1B conical intersection close to the Franck-Condon 2 1 region. It has become clear that these strongly coupled surfaces make H2S a very complex photodissociation problem considering that there are only three atoms. The emission spectra and their dependence upon excitation wavelength will represent a strong test of future ab initio and/or modeling calculations. CH3 B Band The absorption band of methyl radical was first investigated by Herzberg and Shoosmith.220 They observed a diffuse absorption band at 216 nm for CH3. Herzberg’s CD3 absorption spectrum, although broadened by predissociation, yielded ro˜ rX ˜ band tationally resolved structure.221 The analysis of the B indicated that both the ground state and excited state of the methyl radical are planar. The sharpening of the absorption spectrum upon deuteration was interpreted in terms of a tunneling predissociation on the excited state surface. The weaker features in the methyl radical absorption spectra were subsequently reexamined by Callear and Metcalfe222 and found to be due to absorption to ν2′, the out-of-plane bend, and hot bands involving ν2. Danon et al.223 examined the band origin (see Figure 7 for CH3) using MPI and estimated excited state lifetimes of 1.2 ps for CD3 and 0.12 ps for CH3. The B ˜ 2A1 state of methyl radical is similar to the A ˜ 1A2 state of ammonia (see below). The excited state surface of methyl radical has a shallow bound well in the FC region and an assumed modest barrier to dissociation to CH2 + H. The translational energy spectrum of the H atom fragment was recorded by Wilson et al.224 The measured time of flight of the resulting H atoms indicated that the CH2 fragment was ˜ 2A1, formed in the a˜ 1A1 state when CH3 dissociates from the B V ) 0 state. Within the past few years, RRS has been successfully applied to the study of several small gas phase hydrocarbon radicals.
Figure 7. MPI stepwise excitation-ionization spectrum of CH3I f CH3 f CH3+ (adapted from ref 223). This is essentially the absorption spectrum of CH3 for the band origin.
Raman spectra of the methyl,225-229 allyl,230-235 1-methylallyl,236 and 2-methylallyl237 radicals have yielded information regarding the excited state dynamics, ground state vibrational structure, and excited state frequencies of these elusive species. Pulsed lasers were used to generate and probe the radicals. Photolysis of halide precursors with either 266 or 213 nm radiation from a Nd:YAG laser yields momentary concentrations of radicals that exceed 1 Torr. Buffer gas selection, pressure, and delay time between photolysis and probe pulse control the cooling of the radicals. Methane is a useful buffer gas because it is nonreactive with methyl radical and more highly conjugated radicals. A buffer gas pressure of 1 atm and 15 ns delay of the probe pulse after the photolysis event yields spectra of room temperature radicals.227 Helium and short delay times were used when vibrationally hot radicals were to be examined. Resonance Raman spectroscopy has been used to probe the rovibronic specific predissociation rates corresponding to subpicosecond lifetimes of the 3 s Rydberg origin level of the ˜ methyl radical.227,229 Line widths of rotational levels in the B state were obtained from fitting Raman excitation profiles for individual S(J) lines with the same procedures used for ammonia.238 The CH3 lifetimes vary from 90 fs for J′ ) 4 to 70 fs for J′ ) 11. The methyl radical dissociation exhibits a large deuterium isotope effect. Corresponding CD3 lifetimes decrease from 760 to 340 fs as J′ increases from 2 to 15. The CH3 rovibronic lifetimes are about a factor of 2 shorter than the corresponding lifetimes of the analogous predissociated 3s Rydberg origin level of ammonia. The J′ photodissociation rate dependence is also less pronounced for methyl than for NH3. These results are consistent with a barrier to dissociation which is slightly lower and narrower for the methyl radical than in ammonia. Analysis of the tunneling rates using a cubic potential barrier places the barrier at 1.38 Å along the C-H dissociation coordinate with a height of 2200 cm-1.227,229 The 4-31G+ Rydberg+CI ab initio calculation by Yu et al.239 examined the C-H and C-H2 dissociation pathways for the methyl radical B ˜ state. This calculation was qualitatively correct but did not quantitatively capture the shape of the photoactive B ˜ state PES, overestimating the barrier height and position along the C-H coordinate. Recent multireference configuration interaction (MRCI) calculations by Botschwina et al.240 predict a barrier at 1.384 Å with a height of 2389 cm-1, in excellent agreement with experimental analysis.
7754 J. Phys. Chem., Vol. 100, No. 19, 1996 Resonance Raman experiments to examine the methyl radical predissociation dynamics of the higher lying vibronic levels in the B ˜ state were also performed.229,241 Rovibronic specific lifetimes for the (0,1,0,0) level of the Rydberg 3s state have been determined for CD3. The lifetimes for the (0,1,0,0) level vary from 350 fs for J′ ) 3 to 150 fs for J′ ) 10. The lifetimes for the (0,1,0,0) level of CD3 are 2 times faster than the lifetimes of the (0,0,0,0) level. This is in marked contrast to the observations of the predissociation rate of the 3s Rydberg state of ND3, where excitation of one quantum of the out-of-plane bend significantly increases the excited state lifetime.242 The fit to the excitation profile data yields a band origin for the (0,1,0,0)-(0,1,0,0) transition of 47 271 cm-1. The previous resonance Raman study227 determined the (0,0,0,0)-(0,0,0,0) band origin to be 46 635 cm-1. Using the ground state ν2 value of 457.8 cm-1 from Sears et al.,243 the frequency for ν2 in the Rydberg 3s state is estimated as 1100 cm-1.229 The ground electronic state vibrational structures of isotopically substituted methyl radicals were studied using resonance Raman spectroscopy.228 Stretching fundamentals, overtones, and combination modes were observed for these molecules as well as the first overtone of the wag. The quadratic, cubic, and quartic stretching force constants of the methyl radical were obtained by fitting CH3, CD3, CH2D, and CD2H stretching fundamentals and overtones derived from resonance Raman studies to a model potential. The local mode-coupled Morse oscillator model developed by Mills et al.244,245 was used to examine the methyl radical stretching potential. The Morse harmonic frequencies and anharmonic constants of the methyl radical are consistent with those of other molecules containing sp2-hybridized carbons. The interbond coupling in the methyl radical is larger than in ethylenic molecules, which indicates that the vibrational states of the methyl radical contain larger amounts of normal mode character than the ethylenic molecules. The quadratic, cubic, and quartic stretching force constants were derived from the local mode analysis of the methyl radical stretching vibrations. The quadratic force constant is in good agreement with the nonrigid invertor Hamiltonian analysis by Spirko and Bunker246 and Sears et al.243 The force constants derived using the Morse parameters from the CHn data are comparable to those calculated from the CDn data alone, confirming the validity of the Born-Oppenheimer approximation for the methyl radical. NH3 A Band System ˜ 1A1′ absorption band The room temperature A ˜ 1A2′′ r X system of ammonia extending from 180 to 220 nm consists of a predissociated progression in the umbrella mode ν2′ superimposed upon a broad continuum which diminishes strongly upon cooling by supersonic expansion247,248 (see Figure 8). The umbrella activity arises from the transition between the pyramidal geometry of the X ˜ state and the planar geometry of the ˜ system results A ˜ state.242,249 Absorption to the bands in the A in efficient predissociation to NH2 + H with rates increasing with umbrella quantum number V2′. This behavior is attributed to the presence of a barrier on the 1A2′′ PES for dissociation to NH2 + H.250,251 There also exists a conical intersection between the X ˜ and A ˜ surfaces at longer H2N-H distances that significantly affects the predissociation and the distributions of photofragments.252-255 No symmetric N-H stretch (ν1′) activity is directly observed in absorption, although such activity was expected earlier based on analyses of rotational constants which suggested significant lengthening of the N-H stretch in the A ˜ state,242 on FranckCondon analyses of the absorption bands,256,257 and on the
Johnson et al.
Figure 8. A ˜ 1A2′′ r X ˜ 1A1′ absorption spectrum of jet-cooled NH3 (adapted from ref 248). A single progression is observed in ν2′, the excited state umbrella mode.
observations of both ν1 and ν2 emission features from the ND3 V2′ ) 0 and 1 levels.258,259 Furthermore, Ziegler and Hudson260 observed several bands with one quantum of ν1 in the Raman spectrum of NH3 for excitation resonant with the V2′ ) 1 (21) level in the excited state, showing that ν1 is indeed FranckCondon active in RRS. The lowest V2′ levels in NH3 and its isotopomers, falling below the barrier, have significantly lower rates of predissociation and can be rotationally resolved spectroscopically (see refs 261 and 262 and references therein). By detailed analysis of the O, P, Q, R, and S scattering tensor elements for rotational RRS in a symmetric top, Ziegler et al.53,263 determined statespecific excited state lifetimes in the range 50-300 fs for several low-lying V2′ features in both NH3 and ND3. These lifetimes agreed with those determined from the absorption analysis264 and supported the importance of tunneling in the photodissociation mechanism for the lowest energy levels. REP’s were obtained for features of different J in the 22 band238 with lifetimes that were found to vary with J. Spectral widths for J ) 2 indicated a maximum excited state lifetime of ∼140 fs, taken to reflect primarily the predissociation rate due to some purely vibrational mechanism. Increasing J to 8 was found to decrease the lifetime to 70 fs, indicating the presence of a significant rotational mechanism as well. This was analyzed in terms of the model of Ashfold et al.,252 wherein centrifugal forces from rotation of a molecule about the breaking N-H bond axis produces an effective potential with diminished barrier height and increased tunneling rate. It was pointed out that the behavior of the Raman spectra could also possibly be explained by Coriolis coupling due to rotation about the symmetry axis. Subsequently, resonance hyper-Raman scattering (two-photon excitation to the A ˜ state followed by spontaneous emission) was observed and analyzed in NH3 and ND3, including studies of the excitation frequency dependence.110,265-267 The hyperRaman studies provided further support for the centrifugal model in the low-V2′ states.267 Thus, resonantly enhanced Raman spectroscopy for ammonia represents a case intermediate between completely bound and completely unbound excited states. Partial rotational resolution can be obtained and provides information about both vibrational and rotational aspects of the predissociation process. Quantum dynamics calculations for the absorption and emission processes in NH3 and ND3 were made by Tang et al.268,269 based purely on the two symmetric modes ν1 and ν2.
RR Spectroscopy of Polyatomic Molecules Adjustments were made to the double-minimum pyramidal ground state and planar excited state model potentials to bring the calculated spectra into agreement with experiment. The best fit produced an apparent single progression absorption spectrum due to persistent 3:1 Fermi resonance between ν1′ and ν3′, as suggested by Harshbarger.256 The calculated emission showed pronounced ν1 activity which, in a reversal of the usual descriptions of absorption, could be rationalized by wave packet motion off the planar geometry maximum of the ground state potential. A completely different time-dependent calculation was performed by Dixon,270 including all three N-H stretches in the excited state dynamics. Each of the stretches is approximately a linear combination of the ν1′ and ν3′ coordinates with the possibility of rapid dissociation upon excitation. This is an extension of the mechanism suggested by Avouris et al.,257 for which ν1′ resonance states would contribute only to the underlying continuum in absorption. Microwave optical double-resonance spectroscopy investigations by Henck et al.261,262 have obtained high-resolution absorption spectra of individual rovibrational levels in the 20, ˜ state of NH3 and its deuterated 21, and 22 levels of the A isotopomers, as well as 23 for NH3. Mode couplings and rotational effects were estimated using a local mode model for the N-H stretches in the excited state for which even one quantum leads to dissociation. The vibronic mechanism for the predissociation of the 2n series was attributed to ∼2:1 (not 3:1) Fermi resonance between the (formally unbound) N-H stretching and umbrella modes. The dominant rotational component of the predissociation was found to be either centrifugal or Coriolis effects,238,252 depending on the specific 2n band and isotope investigated. While much more has become known about the A ˜ state photodissociation from the recent work, there is still more to be learned. Because of the small size of NH3 and the fact that there are only six vibrational modes, it is reasonable to hope that extended PES’s and dynamics calculations can be performed within the next few years to build a more definitive picture of the dissociation throughout the entire band system. CH3SH The near-UV absorption of methyl mercaptan is continuous. Absorption begins near 310 nm and extends to shorter wavelengths.271 There is a broad plateau centered at ∼230 nm followed by a stronger maximum near 204 nm. Photoexcitation at any wavelength in this region (∼190-310 nm) leads to dissociation, with the main photoproducts being either CH3S + H (channel I) or CH3 + SH (channel II). The two broad features have been attributed to transitions from the ground electronic state to the first two electronically excited levels of 1A′′ symmetry (C point group). Ab initio studies of these two s electronic states272-275 indicate that the PES for the 11A′′ state is dissociative in the SH stretch coordinate, whereas that of the 21A′′ state is bound in both the SH and CS stretch coordinates. Despite the latter fact, photoproducts appear upon excitation into the 21A′′ state, and the absence of any structure in the absorption spectrum in the corresponding feature indicates that the excited molecule leaves the Franck-Condon region irreversibly in a time that is short compared to the period of the highest-frequency vibration in the electronically excited state. The quantum yield for H atoms has been found271 to be ∼0.5 for excitation at 193 nm wavelength (on the blue side of the maximum for excitation into the 21A′′ state) and ∼0.95 for excitation at 222 nm (near the very shallow minimum between the two peaks). The distributions in velocity and angle of photoproducts have been investigated by several groups using time-of-flight (TOF)
J. Phys. Chem., Vol. 100, No. 19, 1996 7755 techniques.273,276-279 The most recent of these, by Wilson et al.,279 using high-n Rydberg detection of H atoms, covers the widest range of excitation frequencies and has the highest resolution (∼50 cm-1 fwhm). Dissociative resonance Raman spectra have also been investigated at 222 nm273 and at 193 nm.277,280 The only features observed at 222 nm excitation, where the absorption is mainly into the 11A′′ state, were assigned as the fundamentals of the SH stretch and a methyl group hydrogen stretch. The region in which the CS stretch fundamental would have appeared was obscured by a large background signal. Thus, the long progressions in a bond-breaking coordinate that have often provided a characteristic signature for direct bond scission are absent. When these progressions appear, they tell a very clear story, but their absence cannot be used to rule out direct bond scission because the fundamentals’ intensities could have a large component from nonresonant higher electronic states. Indeed, the evidence from the TOF experiments supports a mechanism in the 11A′′ state involving direct cleavage of the SH bond, with modest excitation of the CH3S radical in its CS stretching mode or in combination with a 1040 cm-1 methyl rocking vibration.279 The extent of vibrational and rotational excitation increases as the excitation wavelength decreases, whereas the tendency to populate the upper (2E1/2) spin-orbit component of the 2E electronic state decreases as the available energy increases. The currently accepted picture for excitation into the 21A′′ state is an initial push, primarily along the CS stretching coordinate while still on the 21A′′ PES. After some extension in this direction, there is a substantial transfer of amplitude to the 11A′′ state via nonadiabatic coupling. Then dissociation proceeds on the lower state’s PES. This transfer seems to occur after sufficient displacement from the ground state equilibrium geometry that the wave packet finds itself primarily in a region on the 11A′′ PES where there is no barrier to cleavage of either the SH or the CS bond. The DRRS results support this picture.280 Excitation with a narrow-band 193 nm source (fwhm ∼1 cm-1) led to an emission spectrum with intensity into the ν5 fundamental (the CS stretching mode), 2ν5 and 4ν5. It was speculated that the second harmonic was suppressed in this sequence because of Fermi resonance with the first overtone of the H-C-S bending mode. In any event, the results seem clearly to indicate that the initial motion on the 21A′′ PES is predominantly in the direction of the CS stretch. Although there was a strong SH stretching fundamental, no observable intensity could be found in the first two overtones of this mode, suggesting that the fundamental intensity was dominated by nonresonant contributions. Both the work of Stevens et al.280 and that of Keller et al.277 encountered serious problems with emission from secondary processes involving photoproducts of the CH3SH photodissociation. For this reason, the narrow bandwidth and tunability of the source used by Stevens et al. were extremely important. The ability to investigate a number of distinct excitation wavelengths in the same vicinity allowed unequivocal identification of true Raman features from fluorescence of secondary products, since the former track with excitation frequency and the latter do not. The narrow bandwidth was also important in permitting unambiguous assignments of the most intense vibrational features. The ease with which these secondary processes can interfere in photodissociation studies was also noted in some of the TOF measurements.279 This points out the necessity in any DRRS study to be sure that the observed emission actually comes from the anticipated species. The CH3SH molecule thus provides a
7756 J. Phys. Chem., Vol. 100, No. 19, 1996
Figure 9. Hartley and Huggins absorption bands as measured at 195 K by Freeman et al.285
number of useful object lessons of general applicability for DRRS studies: (1) The excitation source should be sufficiently narrow banded to allow clear-cut identification of the intense features. (2) The ability to employ a number of different excitation wavelengths in the same region is useful in distinguishing between Raman scattering and secondary emission. (3) The appearance of long progressions in a specific normal mode can usually be assumed to indicate early motion in the direction of the corresponding normal coordinate, but the converse is not true. (4) The possibility of intense emission from photoexcitation of secondary products must always be borne in mind. In many cases, the intensity of this unwanted signal has prevented DRRS studies from being possible. O3 Hartley Band The UV absorption spectrum of ozone is one of the most studied of any molecule, due in large part to its importance in preventing harmful solar radiation from reaching the surface of the earth. The spectroscopy and kinetics have been reviewed as of the late 1980s by Steinfeld et al.281 and Wayne,282 although a significant amount of research continues through the present. There are several electronic states within a few electronvolts of the ground (1A1) state, and these have recently been the subject of extensive ab initio calculations by Banichevich et al.283,284 The intense Hartley band (200-300 nm) is shown in Figure 9 along with the merged Huggins band system on the red side from high-resolution 195 K measurements of Freeman ˜ 1B2 r X ˜ 1A1 in the et al.285 The transition is assigned as D C2V point group of the ground state. The excited state PES at the FC geometry is almost an electronvolt above the energy for dissociation into O2(1∆g) + O(1D). An early approximate form for the PES,286 adapted from earlier ab initio calculations,287 is shown in Figure 1. The absorption spectrum calculated286 from this surface by the semiclassical Wigner method16 was in excellent agreement with the overall shape of the experimental absorption spectrum,288-290 although the finer vibrational structure was not reproduced, and the vibrational distribution of the O2(1∆g) was found to peak at V ) 1 instead of V ) 0 as determined in the experiments of Sparks et al.291 The 266 nm DRRS study of Imre et al.1 provided new information about the short-time dynamics of the photodissociation. Experimentally, it was seen that both the symmetric (ν1, ∼1100 cm-1) and antisymmetric (ν3, ∼1040 cm-1) stretches were involved in long progressions and combination bands extending up to seven quanta (∼7500 cm-1 vibrational energy), which is almost to the ground state dissociation threshold for
Johnson et al. production of O2(3∑g-) + O(3P). No bending activity (ν2, ∼700 cm-1) was observed. Thus, the primary component of the photodissociation was identified as prompt motion both down the ridge toward the saddle point where both bonds are equally extended and perpendicular to the ridge in the two directions leading to unequal bond lengths. The initial motion was assigned to be primarily along the ridge since the first derivative of the 1B2 PES must vanish at the FC geometry. By analysis of the Raman features using the short-time-dynamics formulas of Heller et al.,21 an imaginary frequency of 1650i cm-1 was obtained for the antisymmetric stretch. Various attempts were made to calculate the absorption292-295 and Raman293,295 spectra with harmonic or slightly anharmonic models. Based upon the model of Pack160 or the time-dependent analogue described by Heller,17 dissociation in these calculations occurs along the antisymmetric stretch while bound motion is executed in the other modes, leading to diffuse structure in the absorption spectrum. None of these calculations could reproduce the structure observed in the actual absorption spectrum, however, and calculated Raman intensities were unreliable for higher overtones and combination bands.293,295 This arose from the large curvature required for the antisymmetric stretch, which led to quick exit from the FC region within 6 fs with no recurrence of the autocorrelation function. It was concluded by Johnson and Kinsey,295 as well as Ivanov et al.296 based on temperature analysis of the Hartley band, that a large-amplitude treatment was needed. Such a large-amplitude numerical propagation was performed in the two stretching degrees of freedom by Chasman et al.,297 using the Sheppard-Walker surface and variations. This explicitly demonstrated the exit from the FC region and the bifurcation of the wave packet without harmonic approximation, but also did not reproduce the absorption structure. An approach using only classical trajectories was then taken by Johnson and Kinsey.298,299 For classical mechanics in the regular regime, semiclassical quantization allows one to obtain information about energy levels (and spectra) through analysis of periodicity in the classical orbits.300 At the middle of the Hartley band, the high internal energy of photoexcited O3 ensures that classical trajectories are chaotic. In such situations, periodic trajectories, even when found, tend to be unstable to small changes in initial conditions and unsuitable for traditional semiclassical quantization. Nevertheless, Heller301 has shown that not-too-unstable periodic orbits can produce “scars” (regions of unusually high amplitude) in quantum eigenfunctions and, by extension, affect spectra calculated from these wave functions. In 1986, Holle et al.302 and Main et al.302 obtained a beautiful combination of experimental and theoretical results for excitation of the hydrogen atom in a magnetic field near the field-free ionization threshold. A classical trajectory search produced families of unstable periodic orbits whose periods corresponded precisely to recurrences seen in the correlation function obtained by Fourier transforming the observed excitation spectra. This provided irrefutable evidence that a classical correspondence held even in the highly chaotic energy regions. See also, for example, refs 303-305. Inspired by this, Johnson and Kinsey298,299 Fourier-transformed the absorption cross section of Freeman et al. The experimentally derived autocorrelation function is shown in Figure 10, where the focus is at significantly longer times than the initial decay due to the quick exit of the wave packet from the FC region (cf. Figure 1). The series of small recurrences up to 128 fs corresponds to the disorderly series of vibrationaltype features with average spacing 250 cm-1 seen across the Hartley band (Figure 9). Searches were then made on the
RR Spectroscopy of Polyatomic Molecules
Figure 10. Autocorrelation function derived from the O3 absorption spectrum measured by Freeman et al.285 The rapidly decaying shorttime component is normalized to unity and corresponds to the wave packet’s initial exit from the FC region. Later small recurrences have been argued298,299 to correspond to 3D unstable orbits returning to the FC region after one oscillation of the longer O-O bond and 1-4 oscillations of the shorter O-O bond.
Sheppard-Walker PES for 3D classical trajectories which, even if not fully periodic, returned to the FC region at least once before dissociating. Although it seemed likely that ridge-riding trajectories which retained C2V symmetry exactly would be particularly likely to return, only the simple symmetric stretch orbits with periods ∼41 fs returned within 150 fs. However, other trajectories starting with very slightly asymmetric O-O bond lengths were then found with return times that approximately matched the autocorrelation recurrences at 68, 99, and 128 fs. These constitute separate families of trajectories in which the longer O-O bond oscillates once while the shorter O-O bond oscillates 2, 3, and 4 times, respectively. While the bend angle changes during the motion, these special trajectories are primarily distinguished by their behavior in the O-O bond lengths. Thus, the primary autocorrelation function recurrences were assigned to be due to (the quantum analogues of) families of classical trajectories with different winding numbers in the oscillations of the two bonds, as shown in Figure 10. This time domain analysis, while limited by the approximate nature of the PES, provided the first specific “assignment” of the irregular structure in the Hartley band. There have since been several investigations by other groups, not all with the same opinions about the source of the spectral structure. It was argued by Farantos and Taylor306 that the important periodic orbits were those maintaining C2V symmetry. A subsequent quantum-and-classical study by Farantos307 found classical trajectories leaving the C2V symmetry ridge but different from those found earlier;298,299 his wave packet study freezing the bend (similar to that of Chasman et al.297) demonstrated that motion in two large-amplitude bond stretches was sufficient to produce small recurrences in the autocorrelation function, although not in close agreement with those shown in Figure 10. An earlier fully 3D large-amplitude investigation by Le Que´re´ and Leforestier308 had also found recurrences in the autocorrelation function, although differing significantly from experiment as well. A more fully converged 3D calculation was obtained309 by use of hyperspherical coordinates, although disagreement still remained. Each of the above calculations on the Sheppard-Walker PES produced recurrences too large in magnitude. A recent 3D quantum dynamical study by Balakrishnan and Billing310 reports much better agreement upon reaching full convergence. However, this surface is known to have limitations, e.g., minima that are too deep and in C2V
J. Phys. Chem., Vol. 100, No. 19, 1996 7757 instead of Cs geometry. More extensive PES and transition dipole calculations for the ground and excited states of the Hartley transition were made by Yamashita et al.311,312 and used in calculations for both the Hartley and Huggins313 bands. Both these calculations and those of Balakrishnan and Billing310 calculate autocorrelation function recurrences from the newer PES that are much too large. Thus, it is still unresolved precisely what is needed in a single-PES treatment to reconstruct the recurrences and Hartley absorption oscillations. It has been speculated311,312 that the ozone molecules which are delayed in their dissociation are more strongly influenced by the intersection with the repulsive 1B2 surface286 correlating to ground state products O2(3∑g-) + O(3P) (with quantum yield291,314 >10%) and that a single-PES treatment may simply be inadequate. Also possibly bearing on this issue is the discovery that O2(3∑g-) is produced in a bimodal vibrational distribution with very highlying (V′ g 26) O2 molecules present; this previously unsuspected portion of the distribution has been suggested to account for at least part of the “ozone deficit” problem in earlier kinetic atmospheric models.315 Further information to be integrated comes from a recent determination of the excitation profile for production of O2(1∆g) in low-lying vibrational states on the red side of the Hartley band, which finds oscillations intriguingly linked to the absorption oscillations.316 From the time-independent point of view, Joens317 has recently given a quantum number assignment in ν1′ and ν2′ for each of the features in the Hartley band with a root-mean-square error of 35 cm-1. This is interpreted in the framework of the model of Pack160 (see also refs 161 and 318) where the diffuse structure occurs from vibrations orthogonal to the dissociative coordinate (parallel to the antisymmetric stretch at C2V geometries). However, no reconstruction of the absorption spectrum was given, and earlier attempts293,295 with such models produced only a smooth spectrum due to the quick spreading off the C2V symmetry ridge. Instead, the recurrence picture that has emerged from the classical and quantal analyses described above is of two large-amplitude, strongly interacting, local bonds which (in conjunction with the bend) distort to geometries both along the ridge and over the Cs geometry wells and return to the original FC geometry before the final dissociation. Another example of diffuse spectral structure identified with unstable periodic orbits in which there is strong coupling between the breaking and nonbreaking bond was described by Schinke and Engel319 for linear CO2 photodissociation. Absorption in the Huggins band is much weaker. The vibrational bands, which appear predissociated, were shown by Sinha et al.320 to narrow substantially under jet cooling. This allowed a partial analysis of the rotational band contours identifying the dominant transition moment as that in the plane of the molecule and perpendicular to the symmetry axis. In view of the Cs geometry wells found on the 1B2 surface by Hay et al.,287 the absorption bands were assigned to weak (nonvertical) absorption into these wells, in which case both Huggins and Hartley bands represent different regions of the same 1B2 r 1A1 transition. However, the recent ab initio calculations of Banichevich et al.284 reassign the Huggins absorption to an excited 1A1 state. Using this alternative interpretation, Joens321 has recently provided a revision of Katayama’s322,323 of the vibrational structure. If this interpretation is right, the absorption is determined by the “vibronically allowed” component of the transition moment. This is substantiated by the ab initio calculations of Banichevich et al.284 The resonance Raman spectra of O3 were recently revisited by Chang et al.20 with significantly better resolution and with
7758 J. Phys. Chem., Vol. 100, No. 19, 1996
Figure 11. High-resolution ozone resonance Raman spectrum obtained by Chang et al.20 with 266 nm excitation. Only the (V1,0,0) levels of the polyads are labeled; unlabeled bands correspond both to other ozone Raman bands and features identified as fluorescence from other sources. The (V1,0,0) progression extends to (10,0,0), which is ca. 2000 cm-1 above the ground state dissociation threshold.
rotational band contour analyses, determining vibrational band origins to an accuracy of a few cm-1. As before, strong activity was seen in vibrational levels in the symmetric stretch (V1,V2,V3) ) (n,0,0), neighboring bands with antisymmetric stretching of the form (n-2,0,2) and (n-4,0,4), and the (0,0,6) band. This is shown in Figure 11, where several high-resolution emission scans are assembled (relative intensities approximately correct). Features corresponding to fluorescence of photoproducts (especially excited O2) were distinguished from true O3 resonance Raman features by comparison with results from experiments using 270 nm excitation; the anomalous intensity in (9,0,0) for 266 nm excitation, for instance, was thus determined to be due to overlap with a fluorescent feature. The new Raman spectra show the surprising fact that vibrational levels in the symmetric stretch progression (n,0,0) extend ∼2000 cm-1 aboVe the ground state dissociation threshold (∼8500 cm-1). These higher levels are therefore vibrational resonance states of the ground state PES, although they do not show appreciable broadening over lower members of the sequence. However, a careful search did not find any trace of the (11,0,0) level. Ozone is a molecule for which neither normal nor local mode approximations are particularly good. Nevertheless, stretching energy levels may be calculated by diagonalizing matrices based on Darling-Dennison or related coupling.171,173-176 The 21 stretching levels observed up through (10,0,0) were all fit to within less than 4 cm-1 with both a Darling-Dennison model and large-amplitude calculations on a model PES. Here, as in calculations based on the earlier Raman observations,324 the model PES predicts binding in the two stretches to energies significantly higher than the thermochemical dissociation energy. The spectroscopic results also provide no evidence of strong coupling with the bend over the extended regions sampled by the eigenfunctions of the observed vibrational levels, although this presumably does occur elsewhere. Hopefully a much broader picture will emerge for the character of the ground state PES reflecting the different regions sampled by the DRRS experiments, photodetachment in O3-,325 O2 + O recombination,326 etc. The emission experiments have thus yielded unique information about the ground state. The diffuse structure in the absorption spectrum, on the other hand, partially opens a window to details of excited state sojourns out of and back into the FC region. There is more spectroscopic information which may be gained to open this window much further, i.e., detailed
Johnson et al. investigation of the excitation frequency dependence of the Raman intensities for the various symmetric and antisymmetric stretch bands. This is not an easy matrix of data to obtain since resonant excitation extends over 10 000 cm-1, there are a number of observed vibrational bands which should all be accurately registered with each other, and the resolution of excitation frequencies should be fine enough to resolve the fine structure which results from the same dynamics as that in the absorption spectrum. The continuous-scan REP techniques first used for iodobenzene are ideal for application to ozone, and our first exploratory efforts exciting on the red side of the Hartley band indeed show vibrational-state-specific structure.327,328 An extended set of REP’s,329 in whole or in part, will surely provide useful criteria by which to judge future theoretical calculations and will hopefully contribute to the ultimate goal of understanding the UV photodynamics of ozone. Further Studies In addition to the work detailed above, several other molecules have been investigated by DRRS. Bell and Frey330 identified ν2 and ν3 progressions in the NOCl Raman spectrum for excitation at 266 nm. Gas phase and solution studies have been made for the S3 r S0 transitions in CS2 by Myers et al.331-333 and in SO2 by Yang and Myers.334 Nitromethane has been studied at 200 and 218 nm in the gas phase by Lao et al.335 and in cyclohexane, acetonitrile, and water solvents (with gas phase and perdeuterionitromethane comparisons) by Phillips and Myers.336 Ketene photodissociation via the lowest 1B1 state has been studied by Liu et al.337 for different excitation wavelengths between 217 and 200 nm. Berryhill et al.338 have observed strong vibronic activity in the Raman spectra of acetylene excited at 204 and 178 nm (A and B bands). Bonang et al.339 have examined liquid methanol, ethanol, and ethylene glycol at different wavelengths in the UV. Rolfing and Valentini340,341 examined NO2 predissociation via the 11B2 state, and more recently, Fan and Ziegler342 have made a study of mode-specific subpicosecond lifetimes in the photodissociation in the 22B2 state. Chiu and Chang343 have measured the resonance Raman spectra of S2Cl2 at 514.5 nm at different temperatures with high-temperature observations of additional (Raman and fluorescence) bands attributable to the decomposition product S2Cl. Lenderink and Wiersma344 have recently used DRRS to determine the dynamics of dimethylnitrosamine photodissociation in the S1(n,π*) r S0 transition. Incorporation of absorption, fluorescence, and resonance Raman spectroscopies in electron-transfer studies have been investigated by Myers345 and Kulinowski et al.346 Johnson and Myers347 have examined I3- in ethanol by both absorption and Raman spectroscopies. Competition between different dissociation mechanisms has been assigned to CH3NH2 photoexcited in first UV absorption band at 222 nm by Waschewsky et al.348 CH2ICl in cyclohexane solution has been examined for several excitation wavelengths between 532 and 282 nm by Phillips and Kwok,349 and Man et al.350 have obtained both A- and B-band Raman spectra for CH2IBr in cyclohexane. Arendt et al.351 have examined predissociative excited state dynamics at 199 nm of acrolein, acrylic acid, and acryloyl chloride. Shang et al.352 used 313 nm excitation DRRS to distinguish between two proposed dissociation mechanisms on the first excited singlet surface of methyl azide. As mentioned in the Introduction, isomerization in the excited state is an important photochemical alternative to dissociation for which the practice of RRS is in principle the same (i.e., there are still very few photons emitted if the molecule never returns to the FC region!). Ethylene, for example, displays
RR Spectroscopy of Polyatomic Molecules significant geometry changes upon photoexcitation.353-355 Hexatriene twisting has been investigated by RRS by Westerfield and Myers356 and references therein. An unusual example is 1,3-cyclohexadiene, for which Trulson et al.357 have used RRS as a probe of the dynamics in the direction of ring breaking following excitation in the 260 nm 1B2 absorption band. This case exhibits not only geometry changes but also breaking of a chemical bond. Another such investigation is that into ultrafast intramolecular proton transfer in heterocyclic aromatic compounds by Pfeiffer et al.358 On the theoretical side, Jacon et al.359 have investigated the emission spectra and photodissociation fragmentation of ICN excited in the UV. A variant of the reflection principle so wellknown from absorption spectroscopy was proposed for DRRS by Kolba et al.360 and proven within the harmonic model by Lee.361 Shapiro38,39,362 has presented a uniform theory of DRRS excitation emission in which the laser pulse is not necessarily long in duration compared to emission lifetimes. Keller and Atabek40 have also presented a coherent-state-based theory for the case of short laser pulses. Kroes and van Hemert363 have presented predicted resonance Raman spectra of photodissociating 3CH2.363 In addition to the polyatomic molecules discussed above, there have been several DRRS studies of diatomic molecules. O2 has been examined theoretically by Williams and Imre364 for excitation in both the bound and unbound regions of the B3∑ustate and experimentally at predissociated discrete bands of this (Schumann-Runge) system by Zhang and Ziegler.365,366 Hartke367 has shown explicitly in the case of Br2 excited in the 450500 nm range the equivalence of time-dependent and timeindependent calculations of Raman spectra, as well as their good agreement with experiment. High-resolution measurements for excitation at wavelengths between 330 and 500 nm were used by Strempel and Kiefer368 to determine accurate forms for the excited state potentials (see also refs 369 and 370). Time delays and transition rates were formulated for continuum resonance Raman scattering by Hartke et al.371 IBr excitation emission and photofragmentation mapping were studied by Levy et al.372 A wave packet investigation of nonadiabatic coupling effects in the predissociation of IBr photoexcited near 500 nm has been made by Guo.373 The 530 nm resonance Raman spectrum of I2 has recently been used as a probe of predissociation dynamics in liquid Xe and CCl4.374,375 The femtosecond dynamics of a wide variety of photoexcited molecules have been obtained in the gas phase, in solution, and in solids, using resonance Raman spectroscopy. However, one very important category that has not been represented is the dynamics of molecules adherent to surfaces. Nonresonant and surface-enhanced Raman scattering have been used in a number of studies of molecule-substrate systems, but far fewer studies have focused on resonant Raman scattering, and none has led to an analysis in terms of important dynamics of the adsorbate and/or substrate. Given the potential importance of this information, it appears well worth attempting to apply DRRS to both physisorbed and chemisorbed species even though it will clearly be experimentally and theoretically challenging. Physisorbed iodine and bromine are attractive candidates for an initial study. These molecules have been well studied by RRS and will adhere to many surfaces. Resonance Raman spectra with several overtones have been obtained for iodine adsorbed onto silica gel.376,377 Larger changes in the Raman frequency shifts are observed for bromine.378 Both iodine and bromine adsorbed on porous Vycor have been subjected to RRS.379 RRS of the triatomic ions Br3- and I3- on a zeolite substrate has also been reported.380 Bromine adsorbed onto
J. Phys. Chem., Vol. 100, No. 19, 1996 7759 various metal surfaces has also been studied by RRS,381 although semiconductor and insulator surfaces are more natural candidates for DRRS studies. Other promising adsorbates are, for example, hydrogen and alkyl halides and possibly ozone on silica gel.382 These previous Raman studies using fixed frequency lasers have shown that one can indeed obtain Raman emission spectra for (at least some) physisorbed species. Application of tunable lasers to these (and chemisorbed species) offers the possibility of exploring their REP’s and attempting to extract dynamical information on the short-time molecular interactions.383 As far as we are aware, this would represent a completely new application of DRRS. Inversion Methods In the case of absorption cross sections, the relevant time correlation functions C00(t) can be obtained directly by inverse Fourier transformation of the data. (See refs 298, 299, 384, and 385 and references therein.) This is not possible in the same way for the correlation functions relevant to Raman cross sections because the observed quantity depends on the absolute square of the (half) Fourier transform of the correlation function.19 The phase of the Raman amplitude, which is necessary for recovery of the correlation function by Fourier inversion, thus appears to have been lost. This is unfortunate, because the Raman correlation functions are rich in information about the dynamics on the excited PES. The correlation function C00(t) obtained from the absorption spectrum permits a quite precise answer to the question of “how fast” the system left the Franck-Condon region. In fact, |C00(t)|2 is precisely the survival probability at time t for the wave packet to overlap with its appearance at time t ) 0. This quantity is entirely silent, however, as to the direction of motion in the multidimensional space of nuclear coordinates. The Raman-related correlation functions Cn0(t) have the ability to provide exactly that missing detail. The usual route to dynamical information from Raman studies has therefore been to work from parametrized models for the upper-state PES and the transition moment. There are a number of powerful and beautiful “transform” methods developed primarily for use with Raman spectra of nondissociative large molecules.27-31 These methods begin with a power series expansion of the upper PES up to quadratic terms in the ground state normal coordinates and neglect of the transition moment’s dependence on these coordinates (Condon approximation) and then build on that simple picture, as required, by adding further terms. In dissociative molecules, however, an explicitly largeamplitude approach is called for, both in description of the PES’s and of the transition moment. Johnson and Kinsey386,387 have shown that the short-time behavior of the C0n(t)’s, together with a knowledge of the ground state PES and its vibrational eigenfunctions, in principle allows a determination of the shapes of both the excited state PES and the transition dipole in a neighborhood of the FC region. (From a time-independent point of view, see also the Raman data inversion for I2 by Williams et al.388 and the fluorescence data inversion for Na2 by Shapiro.389) Tests were made in numerical simulations for a diatomic asymmetric double-well problem with nontrivial coordinate dependence of the transition moment386 and a twooscillator model387 based on the Sheppard-Walker ozone PES286 and a hypothetical bimodal transition moment. The results of these numerical simulations were quite encouraging since no restrictions to small-amplitude motion, the Condon approximation, or diatomic (1D) molecules were required. This still leaves the question of how to obtain the Cn0(t)’s from experimental data. The possibility of recovering the
7760 J. Phys. Chem., Vol. 100, No. 19, 1996 missing phase of the Raman scattering amplitude is far from a lost cause. This is because it is the Fourier transform of a causal function.390,391 Consequently, the real and imaginary parts of the amplitude are not independent quantities but are Hilbert transforms of each other. Remacle and Levine392-394 proposed and tested methods for inversion of REP’s to time correlation functions, using both a maximum entropy formalism and an inversion employing Fourier series expansion of the dispersion relation. Their proposed methods were tested with calculations based on the two-mode model previously used to describe the excitation frequency dependence of the C-I stretching REP in iodobenzene.137,138 The calculations produced impressively good recovery of the shapes of the correlation function for most relevant times. The short-time behavior of the recovered Cn0(t) was not highly accurate, however. This is not too surprising, since the behavior near t ) 0 is so strongly affected by the high- and low-frequency tails of the cross sections, which were assumed not to be available as input information. The good ability to determine the correlation functions at later times is auspicious. A method needs to be found that can take advantage of this later-time information for recovery of the PES and transition moment. One approach to the calculation of Hilbert transforms that has recently arisen is the application of orthonormal wavelets by Beylkin et al.395 (see also references therein). Wavelet analysis is useful for decomposition of spectra or functions which require different levels of resolution in different locations. For example, Modisette et al.396 have examined the use of a wavelet basis in a quantum-mechanical variational context for a double-well problem with nearly singular wells. The use of such techniques for Hilbert transforms for inversion of REP data is expected to be advantageous in cases where the REP’s exhibit significant structure superposed on broad continua. Conclusion The use of RRS has proven to be a valuable tool for investigation of the dissociation of several small polyatomic molecules, including not only stable gas phase cases but also radicals and species in solution and matrices. The inherent sensitivity to short-time dynamics and the emerging technologies for computing such dynamics have proceeded hand-in-glove to enlarge our understanding of the photodissociation process in these cases. While the earliest DRRS investigations focused on direct dissociation during the first few femtoseconds, attention has increasingly been given to dynamics on longer scales. This is particularly of interest in the gas phase where dissociative absorption continua sometimes exhibit diffuse structure reflecting dynamics on the 100 fs scale or longer. Such structure will also certainly be reflected in high-resolution REP’s as these are obtained, opening new prospects for very specific vibrationally selective information and insight. Acknowledgment. It is a pleasure to acknowledge the aid of and interactions with Bor-Yu Chang, Chih-Wei Hsiao, Jeffrey L. Mackey, and Richard Stevens. Acknowledgment also goes to Reinhard Schinke for suggesting that a review of this field was in order. This work was supported by the Robert A. Welch Foundation and National Science Foundation Grant CHE-9220278. References and Notes (1) Imre, D. G.; Kinsey, J. L.; Field, R. W.; Katayama, D. H. J. Phys. Chem. 1982, 86, 2564-2566. (2) Imre, D.; Kinsey, J. L.; Sinha, A.; Krenos, J. J. Phys. Chem. 1984, 88, 3956-3964.
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