J . Phys. Chem. 1984, 88, 3956-3964
3956
ordinary cw spectra. We attribute this to their direct dependence
on the T z j according to eq 1 . We expect that as 2D-ESE techniques are further developed, they will provide a very useful method to enable detailed studies of structure and dynamics in oriented media.
Acknowledgment. This work was supported by NIH Grant G M 25862, NSF Grants DMR 81-02047 and CHE 8319826, and by the Cornell Materials Science Center. Registry No. DPPC,2644-64-6.
FEATURE ARTICLE Chemical Dynamlcs Studied by Emlsslon Spectroscopy of Dissociating Molecules Dan Imre, James L. Kinsey,* Amitabha Sinha, and John Krenos‘ Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 021 39 (Received: November 29, 1983)
The use of absorption and emission spectroscopy of photodissociating molecules is discussed as a means of probing details of dissociation dynamics in extremely short-lived transient species. The study of photodissociation processes has special advantages which derive from the special ability to create well-defined initial conditions and from the simplicity of interpretation of experimental results. Casting the absorption and emission processes in a time-dependent formalism developed by Heller and co-workers enables intuitive connections to be made between spectroscopic features and the underlying dynamics. The absorptionspectrum of photodissociating molecules primarily contains information about very short-time dynamics, whereas the emission spectrum reveals more details and encompasses intermediate times as well. Information about both the excited-state and the ground-state potential surfaces is contained in the emission spectrum. Intensities of fundamentals, overtones, and combinations can be used to infer properties of the upper-state surface (such as forces and their gradients). The observed energies and band contours of the same features yield characteristics of the ground-state surface. Experimental results on methyl iodide and ozone are used to illustrate how emission spectra can be used to study reaction dynamics.
I. Introduction In every elementary chemical reaction the molecular system passes through a continuously evolving intermediate species that is neither reactant nor product but the former in the process of turning into the latter. No great insight is required to appreciate that the more we learn about these intermediate species the better we will understand the transformation. Theoretical techniques for treating dynamics of small polyatomics have advanced to the point where fairly accurate predictions can be What is still lacking is experimental data that can be used to supply information for these calculations and to test them. As experimentalists our goal is to devise a scheme which will enable a direct and “meaningful” observation of the reaction intermediate. Here the word “meaningful” refers to the ability to easily extract information which can be utilized as initial estimates in dynamical calculations. The hope, of course, is that by combining a few detailed experimental results with complete calculations, we can get a global picture of both intra- and intermolecular dynamics. In a recent elegant feature article in this journal, Foth et aL4 surveyed a variety of methods for studying photon emission from molecules and reaction intermediates in the process of falling apart. The purpose of our report is an elaboration, from a different point of view, of some of the aspects mentioned in the Foth paper, Le., the absorption and emission spectroscopy of photodissociating molecules. Our approach, which rests on a time-dependent formulation of photon absorption and emission developed by Heller and co-worker~,~ will emphasize the power in the inherent equivalence of time and frequency information in such experiments. We will use our results from methyl iodide and ozone UV photodissociation studies to illustrate how absorption and emission spectroscopy can be used to study reaction dynamics. We will Visiting Associate Professor 1982-83. Permanent address: Department
of Chemistry, Rutgers University, New Brunswick, NJ 08903.
0022-3654/84/2088-3956$01.50/0
show that even at a qualitative level very instructive information can be extracted. These two molecules were selected because they exhibit quite different nuclear motion on their path to unimolecular dissociation. We will start by discussing some of the general considerations to be taken into account when selecting a dynamical process for study. In section I11 we point out the advantages offered by the relative simplicity of photodissociating systems as compared to bimolecular reactions. Section IV describes the experiental approach which we have adopted for investigating photodissociation reactions. Here, we also make the connection between the spectroscopic data obtained experimentally and the dynamics in question. Section V discusses our experimental results for CHJ and 03.
11. Experimental Design Considerations The detailed study of nuclear motion during a reactive collision is an experimental challenge since the reaction time is typically less than 1 ps. Consequently, understanding the fine details would require knowledge of the dynamics on a femtosecond time scale. Or, to put it in a different perspective, during the time of interest the molecular system experiences structural changes on a scale of a few few angstroms. Knowledge of the time evolving structure with subangstrom resolution is equivalent to knowing the dynamics on roughly a femtosecond time scale. In order to yield the needed (1) S. Y.Lee and E. J. Heller, J . Chem. Phys., 76, 3035 (1982). (2) M. Shapiro and R. Bersohn, J . Chem. Phys., 73, 3810 (1980). (3) D. Truhlar, Ed., “Potential Energy Surface and Dynamic Calculations”, Plenum Press, New York, 198 1. (4) H. J. Foth, J. C. Polanyi, and H. H. Telle, J . Phys. Chem., 86, 5027 (1982). ( 5 ) (a) E. J. Heller, Acc. Chem. Res., 14, 368 (1981); (b) E. J. Heller, R. Sundberg, and D. Tannor, J . Phys. Chem., 86, 1822 (1982); (c) E. J. Heller, J . Chem. Phys., 68, 2066 (1978); (d) S. Y . Lee and E. J. Heller, ibid., 71, 4111 (1919).
0 1984 American Chemical Society
Feature Article
e
AB Figure 1. Schematic illustration for a radiative recombination process (A* + BC ABC + hu). The initial energy spread ( A E ) results in a broad and featureless emission spectrum.
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resolution the spectral fatures being monitored must be extremely sensitive to small changes of nuclear geometry. A very promising approach is to record the projection of the time evolving reaction, which occurs on one electronic surface, onto known vibrational wave functions of a different electronic surface. Emission or absorption amplitudes into discrete vibrational levels fulfill all the above requirements. This approach offers the advantage that experiments are now conducted in frequency space, thereby eliminating the need for subfemtosecond time resolution. For such spectroscopic information to be useful, however, the experiment must be designed in such a way that the spectroscopic details are not blurred. At first glance, the uncertainty principle would seem to pose an insurmountable obstacle to achieving a useful level of spectroscopic resolution for transition states with subpicosecond lifetimes. The loophole is that there are classes of measurement processes in which the inescapable uncertainty broadening appears in “uninteresting” variables. Consider a process that finds a molecule initially in a sharp molecular level and leaves it in another sharp level, with absorption and emission of a photon taking place in between. Conservation of energy requires that the frequency width of the emitted photon match that of the absorbed one to within the combined widths of the initial and final levels; i.e., if the source of absorbed light is narrow in frequency, the line shape of individual emission features will be determined by the energy spread of the initial and the dynamics of the final levels, not by that of the intermediate one. In this process the uncertainty broadening appears only in the variation of the scattering cross section with probe frequency. Another potential source of spectral blurring is the spread in initial properties of the state observed. In experiments probing a transition state generated by reactive collisions, the energy spread of the system is typically broad enough to eliminate the possibility of resolving discrete vibrrational lines (see Figure 1). Besides the desire for spectral resolution, there is another crucial reason for starting the system from a sharp molecular state. This relates to the simplicity of interpretation of the spectra obtained. In a full reactive collision, even if the energy spread could be reduced to a spectroscopically acceptable range, there would still
The Journal of Physical Chemistry, Vol. 88, No. 18, 1984 3951
RA-B
Figure 2. A photodissociation experiment. The laser transfers the ground-state wave function to the repulsive excited state where it evolves (dashed wave packets t,, t2, ..., etc.) into A* + BC*. Indicated in the figure by numbers are accessible experimental probes, (1) equilibrium geometry and spectroscopic constants of the final BC product, (2) internal-state, angular, and yelocity distributionsof the final products, (3) absorption (photodissociation)spectrum, (4) emission spectrum, (a) wing emission, (b) discrete emission.
be a wide range of impact parameters, as well as spreads in relative orientation of the reactive pair. Hence, spectroscopic emission or absorption by the reaction intermediate would reflect a corresponding average over a bundle of trajectories spanning the phase space encompassed by the initial conditions. Unraveling the contributions of individual trajectories to the overall spectrum becomes a formidable task. The ideal system would be one in which the experimentalist could select a narrow subset of trajectories by generating initial conditions as well defined as possible, within the limits of the uncertainty principle. Such a system would afford the best chance of learning, in great detail, about a small subset of reaction paths. Knowledge of the dynamics for such well-defined initial conditions could then be used to characterize the forces bringing about the process. This paper illustrates how photodissociation is a particularly promising kind of process to study. By lowering our sights to “half-collisions”, rather than full collisions, we gain the ability to select an uncertainty-limited subset of initial conditions. Consequently, the subsequent dynamics can be followed on a femtosecond time scale. The following sections indicate the proper theoretical connections between the dynamics of a molecule undergoing photodissociation and the characteristics of light emitted during the dissociative process. For the present, let us work from the following rough picture: At time t = 0, the absorption of a photon has caused the initial ground-state vibrational wave function to be prepared on the excited-state potential energy surface. This wave function is very well localized and its form is usually well-known. Since this wave function is not an eigenfunction of the excited-state Hamiltonian, it becomes a moving wave packet on the upper surface. Its evolution in time constitutes the dynamic process of interest, which can be monitored by the extremely low yield of photons emitted as the process goes on. 111. Photodissociation
Figure 2 is a schematic summary of a photodissociation process, viewed in the spirit of the previous paragraph. The wave packet labeled to is the ground-state vibrationless wave function as prepared by a photon on the excited-state surface. As desired, it is defined to within the limits permitted by the uncertainty principle. No longer in an equilibrium position, it feels forces and
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Imre et al.
evolves on the surface as indicated by t,, t,, .... The time evolution is determined by the shape of the potential and the position of the wave packet at t = 0. The wave packet is at rest at t = 0, Le., (P),=,= 0, where P is the momentum. Typically, short-time behavior is dominated by forces ( d V / d q ) . These initially result in node development (evolution in momentum space) and subsequently cause motion of the wave-packet center. Spreading of the packet is governed by second derivatives (d2V/dq2)and usually develops somewhat more slowly. The overall motion and spreading of the initially prepared state is the reaction process: the transformation of the wave packet from t = 0 to t = results in the formation of products. Photodissociative processes can be studied in a number of ways, each of which is sensitive to a specific time scale and therefore to a specific region of trajectories. Some examples of different probes of photodissociation dynamics follow: 1. Equilibrium Geometry and Spectroscopic Constants of the Final Products. This information (which is available for most simple products of dissociation) is not sensitive to any particular time scale, but it does serve as an important guide in understanding the final result of the trajectory. The shape of the potential at infinite internuclear separation along the reaction coordinate is reflected in the equilibrium geometry and spectroscopy of the final product. 2. Internal-State, Angular, and Velocity Distributions of Products. These probe long-term dynamics (t on the order of tens of femtoseconds or longer). In these experiments the evolution is allowed to proceed all the way to completion. Measurements of product distributions provide information on the cumulative history of the molecule from t = 0 to probing time. 3. Photodissociation Absorption Spectroscopy. The absorption spectrum, t(w), is sensitive only to behavior in the local FranckCondon region, and thus to very short times ( t femtoseconds). Most chemists are used to seeing absorption coefficients formulated in terms of matrix elements of the transition moment between discrete bound states. A fully equivalent expression, which has the virtue of incorporating an explicitly dynamic entity? and which is equally appropriate for bound-bound or bound-continuum transitions, is given in eq l 6
acting on the wave packet in the Franck-Condon region. Typically, the absorption spectrum for short-lived molecules is featureless and can be used to determine only the magnitude of the gradient of the upper potential surface. The width of e(w) tells how fast the wave packet moves out of the Franck-Condon region. It contains no information about the direction or details of the motion. Emission spectra, on the other hand, can be used to extract these details. 4. Emission Spectroscopy. Two general spectral regions can be distinguished for photoemission (4a and 4b in Figure 2). In Figure 2, the single emission spectrum has been arbitrarily divided into the parts terminating on discrete (4b) and continuous (4a) ground-state levels. If one of the products is an excited atom capable of emitting at a fast rate, wing emission will be observed (see part 4a of Figure 2) to the red and/or blue side of the atomic emission line. This phenomenon, which has been described in detail in the Foth paper,4 is due to emission by the excited atom while the two fragments are still close enough together for there to be appreciable interactions. Observation of wing emission for NaI photodissociation has recently been reported by Polanyi et ale8 In this case the product is an excited-state N a atom. If one assumes a vertical Franck-Condon transition, the emission will be blue or red shifted relative to the atomic transition depending on the difference potential of the two surfaces involved. The spectral region of these “wing emissions” is expected to be broad and relatively featureless (see Figure 1). For systems whose atomic transition probability is very different from the molecular one, variation of the transition moment with internuclear separation could significantly affect the line shape. So far we have described emission into the ground-state continuum. The same spectrum (see part 4b, Figure 2) will show transitions into the bound part of the same electronic surface. The distinction between emission into discrete vibrational eigenstates, rather than into a continuum of product translational states, is nontrivial. It is precisely the ability to monitor emission into well-characterized vibrational eigenstates that provides the desired geometrical and temporal detail. This idea is developed in the following section.
t(w) = c w J I m ( + l $ ( t ) ) exp(itAw) d t
IV. Light Emission during Dissociation When a molecule is excited into a dissociative continuum, it usually comes apart in roughly a molecular vibrational period or less (typically s). This is vastly shorter than the radiative s). Hence, dissociation is a powerful lifetime (typically destruction mechanism for molecular fluorescence. There is a tiny but finite photon yield, however, and the spectral characteristics of this emitted radiation turn out to be extraordinarily informative about dynamic processes on both the upper and lower potential energy surfaces. As it comes apart, the dissociating molecule sweeps through infinite displacements in molecular configuration, thus developing Franck-Condon overlap with highly excited vibrational levels of the ground state. This is reflected by unusually long progressions in the fluorescence spectrum. In 03, for example, we have reported vibrational states reaching to within 500 cm-’ of the dissociation limit.g We have recently observed levels in CHJ with as many as 29 quanta of vibrational energy in the C-I stretch (75% of the bond dissociation energy). This unique ability of a dissociating molecule to indicate the energies of ground-state vibrational levels is matched by the opportunities it provides to probe dynamic processes on the excited-state potential energy surface. The molecule leaves a “photograph” of its motion on the upper surface in the intensity pattern of the lines emitted during its dissociation. Let us now refine our rough picture of photon emission during photodissociation. Instead of an absorption coefficient, we need the amplitude, afi for the Raman process that carries the molecule from initial state i to final state f (in the ground electronic state)
Q)
-
(1)
where ($1 = (xlp; (XI is the ground-state vibrational wave function, and p the electronic transition moment. I+(t)) is defined by M t ) ) = exp(-ifiext/h)I+(0)) (2) Le., I$(t)) is the time-dependent wave packet evolvilg on the excited-state surface, where the nuclear Hamiltonian is Hex.-(Our convention for t_he zero of the excited-state Hamiltonian, Hex,is determined by He, Hex- ( ilHcxli),where Hexhas an arbitrary zero.) For most photodissociating molecules eq 1 can be approximatedsa,’ by t(w) =
cw e ~ p [ - ( A w ) ~ / 2 a ~ ]
(3)
where AU is the off-resonance detuning frequency from the center of the absorption band. The width parameter u is given by 2a2 =
cvkz/wOk k
(4)
where v k = dV/dqk. Vis the excited-state potential, and qk is the ground-state kth normal coordinate. The derivatives are evaluated at the ground-state equilibrium configuration. Thus, the spectral width of the absorption is determined by the forces (6) Lorquet et al. have inverted eq 1 to obtain experimentally determined correlation functions from photoelectron absorption spectra of a number of molecules. In particular, see A. J. Lorquet, J. C. Lorquet, J. Delwiche, and M. J. Hubin-Franskin, J . Chem. Phys., 76, 4692 (1982). (7) This approximation is valid under the following conditions: (a) The excited-state surface is well approximated by a quadratic in the local Franck-Condon region. (b) Short time dominates the spectrum, meaning that the wave packet does not revisit the Franck-Condon region. (c) The initial wave packet is well represented by a Gaussian. (For a detailed description see ref 5 . )
(8) H. J. Foth, H. R. Mayne, and R. A. Poirier, J. C. Polanyi, and H. H. Telle, Laser Chem., 2, 229 (1983). (9) D. Imre, J. Kinsey, R. Field, and D. Katayama, J . Phys. Chem., 86, 2564 (1982).
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by absorption at frequency w and emission at w’ = w + ti - tp ( e i and cf are the energies of initial and final states, respectively.) Again, there is a dynamical expression exactly equivalent to the more common one involving sums over bound levels: (5)
As before 14m)= p 1 x m ) and the wave packet 141(t))is the initial-state vibrational waye function propagated by the excited-state nuclear Hamiltonian Hex. Given the usual approximations in expressions for t and aif (Born-Oppenheimer approximation, limitation to only two electronic states, etc.) eq 1 and 5 are exact equivalents of the more familiar expressions. N o new approximations have been incorporated. The dynamic kernel (+j4,(t))of eq 5 is what connects with our earlier picture, which we now improve as follows: Move 141) from the lower to the upper surface at t = 0 and let it evolve there as I + l ( t ) ) . Look at its overlap with final state (+A as a function of t and compute its half-Fourier transform to get a$ The absolute square of this quantity is proportional to the intensity observed at w’ = w tl - tp If we neglect for the moment the variation of p with respect to nuclear coordinates, the following picture emerges. At t = 0, the wave packet is still the initial vibrational wave function (let us assume it is that of the vibrationless state). It has no overlap with any other vibrational state at that time. As the wave packet starts to move, it will develop overlap with higher vibrational states, especially those with significant amplitude in the direction of motion. The differences in the configurations sampled by neighboring vibrational eigenstates (e.g., u = 0 and u = 1 or u = 1 and u = 2) are minute, yet the corresponding features occur at easily resolvable frequencies of the emitted light. In essence the emission spectrometer acts like an extremely high resolution microscope, where a small change in bond length is transcribed into a change in frequency of hundreds of cm-’. For a given vibrational progression, overlaps will temporally develop in a very simple order, starting with the lowest level and continuing in a sequence of increasing energy. At exact resonance in photodissociation (Aw = 0 in eq 5 ) each aofjust contains the integral of the dynamic quantity (+j+o(t)). This correlation function will decay on some time scale which is intrinsic to the system. This characteristic time is a molecular property. By moving off-resonance, one samples the dynamics on a time scale that decreases with increasing Aw. In the limit of very large Aw, only dynamical processes occurring on a time scale much shorter than the dissociation time contribute significantly to the observed intensities. (The question of observational time scale vs. detuning frequency is treated in some detail in a separate paper. The qualitative correlation of shorter times with larger detuning suffices here.) The spectra contain information about two potential energy surfaces. The frequencies and line contours of emission features are characteristic of the ground-state potential. The large geometric changes experienced during dissociation produce intensity into extremely high levels of the ground state, thus exposing regions of the corresponding surface not easily reached by other spectroscopic methods. Relative intensities of the various fundamentals, overtones, and combinations (and their dependence on excitation wavelength) reflect the dynamics of I@+(t))as it moves on the upper surface. Heller et al.5bhave shown that the dominant quantity determining the intensity of the kthfundamental (Zolk) is the force V, = aV/aqkalong the qk direction evaluated at the center of I+l(t=O)).Overtone intensities (ZoZk) are sensitive both to the forces and to the rapidity of wave-packet spreading (which involves second derivatives of V). Highly accurate dynamical calculations require more detail, of course, but these “simple” results are extremely instructive. In the examples discussed in following sections, we show how upper-state and lower-state information can be obtained from such data.
+
V. Specific Systems
In this section we present our results on two polyatomic systems, viz., CH31and Oj, which illustrate how information on nuclear
0
t=O
Rc.,:2.14A
O 1 (where Tdus is the characteristic molecular time) the integrand in eq 5 oscillates very rapidly. This results in domination of contributions of aoj by short-time dynamic^.^ Thus, excitation at the center of the absorption band produces an emission spectrum that reflects dynamics on the longest possible time scale: T 7dlss.By selecting A u # 0, the experimentalist
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can control times over which the dynamics of the system affects the observed spectral intensities. Emission features corresponding to late-developing dynamics, such as high overtones, will disappear more rapidly from the emission spectrum with detuning than the earlier-developing fundamentals and Rayleigh scattering. We have recently been able to formulate a well-defined “scattering time” 7idu)for the Raman process that takes the molecule from initial state li) to final state n.l4For the purposes of the present discussion, it suffices to state some of the qualitative results of these considerations: At A u = 0, ~~j 7dlss. If ti) is the ground level, T~~becomes slightly longer for successive states in a given progression. This is in accord with our qualitative understanding based on the observation that ( $ , l ~ $ ~ ( t )peaks ) later for higher n in a given progression. Figure 7 shows some typical correlation functions calculated from wave-packet dynamics on a one-dimensional quadratic potential. As Aw increases, each T~~ decreases, with 70, for the higher n in a given progression continuing to be somewhat longer (see Figure 8). As A u m all the T~~ eventually follow a Lorentzian dependence on frequency,I4 but they still preserve their order. The details of the connection between T~~ and A u are, of course, system dependent. The important fact is that an experimentally controllable parameter (Aw) can be used to control the time scale for observing the dynamics. Thus, frequency tuning can be a simple and powerful tool for improving the time resolution of events on short time scales. In our case the time development is simple. In Figures 4-6 we show emission spectra of CHJ for three different excitation wavelengths. The first of these (Figure 4 from
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(14) J. L. Kinsey, R. Sundberg, D. G. Imre, R. J. Silbey, to be submitted for publication.
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A
.
‘iXa_iyi*
“’ ,‘\
\ \
r 500-
I
1
I
0 I
0.0
2.0
4.0
6.0
I
I
q3
Q
440 420
Figure 9. Schematic illustration of the CH31 excited-state potential surface for q2 and q3 (kindly provided by Rob Coalson of Harvard University): (A) equipotential contour diagram with a photodissociation
400
trajectory; (B) sections for the potential along q2 at the ground-state equilibrium geometry (1) and at large q, (2).
1I
1
I
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8
IO
12
14
16
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2 0 22 24
n
ref 15) was obtained with excitation by X = 514 nm light ( A o 18500 cm-I). At the short observation time corresponding to this detuning, no overtones are seen in the spectrum. As indicated in the earlier discussion of the expected dynamics there is a large activity in the C-I stretch fundamental (4, with weaker intensities in the umbrella mode (v2) and the C-H symmetric stretching mode (vl). At such a large detuning from resonance, possible contamination of the spectrum by effects from other electronic states has to be suspected. Hence, one cannot expect to extract any definite conclusions about dynamics on the 300 surface from the relative intensities of the various symmetric fundamentals at this frequency alone. Likewise, observation of intensity in the antisymmetric e modes is not necessarily an indication of dynamics associated with these modes. Variation of the transition moment with the corresponding normal coordinates is a more probable cause of these features. This factor, which we have neglected so far, is minor for the present discussion and will be treated in more detail in a separate report. In order to increase the observation time,the laser was tuned close to resonance to give the spectrum shown in Figure 5 (X excitation 355 nm, A o 10000 cm-I). This spectrum is not very different from the previous one, as might be expected. The only significant difference is that a new band with two quanta in the C-I stretch can barely be seen. Thus, within less than 0.5 fs following absorption the wave packet has evolved (mainly in momentum space) enough to develop a small but observable overlap with u = 2. This substantiates our original expectation: The earliest motion of the wave packet is predominantly along the C-I coordinate. In Figure 6, we see a spectrum obtained with X = 266 nm ( A o < 1000 cm-I; Tobsd 7diSs). The spectrum is dominated by an astonishingly long progression in the C-I stretch (q,). Up to 29 quanta are observed, corresponding to a ground-state vibrational energy equal to -75% of the dissociation energy. The band intensities decrease slowly and monotonically. This pattern is consistent with a wave packet which is at rest at t = 0 (( P),=, = 0 ) and then accelerates along the C-I coordinate. Some activity in v l and v2 fundamentals is also noticeable, although without the appearance of overtones in these modes we cannot rule out their originating at least in part from other electronic surfaces. The long, intense v 3 progression, on the other hand, is an unmistakable signature of wave-packet dynamics on a resonantly excited surface.I6 The first several v3 features are pure v3 overtones. Farther along in the progression (viz., for later times), however, new types of bands appear. These are combination bands between vj and v2. This indicates that the initial motion is almost directly along q3 (the C-I stretch) and subsequently develops into motion in the q2 (umbrella-mode) direction as well. At even higher vibrational energies the spectrum broadens so that only envelopes of bands
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(15) B. Schrader and W. Meier, Eds., “Raman/IR Atlas”, Verlag Chemie, Weinheim, West Germany, 1974. (16) R. L. Sundberg and E. J. Heller, Chem. Phys. Lett., 93, 586 (1982).
Figure 10. Birge-Sponer plot for
u3
levels observed in Figure 6 .
containing several vibrational eigenstates can be seen with our current resolution. Photodissociation Dynamics. Figure 9 shows a qualitative two-dimensional contour diagram of the excited-state surface for q2 and q3. This surface is repulsive along q3 with contour lines almost parallel to the q3 coordinate for small C-I bond lengths. The minimum along q3 is at about OHCH = 108’ (Le., the ground-state equilibrium bond angle). This is consistent with an n B* excitation where the CH3 part of the molecule is not expected to feel significantly new forces at its ground-state configuration. For large q3,however, the potential along q2 correlates to the q2 potential of free CH3. This potential has its minimum at the planar configuration (eHCH= l2Oo).l7 Thus, as the wave packet moves almost directly along q3,it feels new forces in the q2 direction, causing it to “turn”, increasing the H C H bond angles in the process. Not only does the potential minimum in q2 shift to a larger equilibrium angle as 9, increases, but its shape also changes. Since the w2 vibrational frequency is decreasing during the dissociation from 1200 cm-’ in CH31to -600 cm-’ in the free CH, product, the contours have to “open up” as q3 increases. A schematic photodissociation trajectory illustrating this is shown by the heavy line in Figure 9. At t = 0 the wave packet is only slightly displaced from the minimum along q2. The only strong force it feels is along q3. Hence, the trajectory will proceed mainly along this coordinate initially. In the process, overlaps with higher vibrational levels in q3 develop, leading to a spectrum dominated by v3 overtones. The intensities of these overtones decrease monotonically due to acceleration and spreading of the wave packet. As the C-I bond length increases further, the wave packet will begin to feel forces in the q2 direction. This will cause it to turn toward a larger bond angle, trading vibrational energy from q3 to q2, as is evident from the appearance of new v2, v3 combination modes. Eventually, the dissociation will lead to a CH, product vibrationally excited in q2 as has been found in the experiments of Leone and co-workers.” Ground-State Dynamics. We now turn our attention to the ground-state electronic surface. Figure 10 shows a plot of vibrational energy differences G(u3+1) - G(u3)as a function of v,. The data are consistent with a straight-line Birge-Sponer plot, indicating that the C-I mode is well described by a local Morse oscillator up to u3 = 23. A qualitative two-dimensional contour diagram for the ground-state potential along q2 and q3 is shown in Figure 11. For low energies q2 and q3 are only very slightly coupled. This is consistent with the known IR data’* and our observation of a clear progression in the C-I stretch. Like the upper-state potential surface, this surface also correlates asymptotically to CH3. Its minimum for large must also move
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(17) C. Yamada, E. Hirota, and K. Kawaguchi, J . Chem. Phys., 75, 5256
(1981).
(18) I. J. McNaught, J . Chem. Educ., 59, 897 (1982).
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0.0
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I % 4.0
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Figure 11. CHJ ground-state potential surface along q2 and q3: (A) schematic equipotential energy diagram (produced by R. Coalson), illustrating the change in q2 with q3 (a trajectory for a local q3oscillator at high energies is shown in heavy line); (B)sections of the potential
along the thermodynamic dissociation path (2), and along a local q3 oscillator (1). These sections illustrate why a Morse oscillator extrapolation overestimates the dissociation limit. toward BHCH = 120'. If a local C-I oscillator were prepared on this surface with energies
