J. Phys. Chem. 1994, 98,8673-8678
8673
Structural and Vibrational Kinetics by Stroboscopic Gas Electron Diffraction: The 193 nm Photodissociation of CS2 Anatoli A. Ischenko Lomonosou Moscow University, Moscow 119899,GSP Russian Federation
Lothar Schafer,' Jing Y. Luo, and John D. Ewbank' Department of Chemistry and Biochemistry, University of Arkansas, Fayetteville, Arkansas, 72701 Received: April 7,1994;I n Final Form: June 20, 1994"
A novel data analysis procedure is described, based on a variational solution of the Schrijdinger equation, that can be used to analyze gas electron diffraction (GED) data obtained from molecular ensembles in nonequilibrium (non-Boltzmann) vibrational distributions. The method replaces the conventional expression used in G E D studies, which is restricted to molecules with small-amplitude vibrations in equilibrium distributions, and is important in time-resolved (stroboscopic) GED, a new tool developed to study the nuclear dynamics of laserexcited molecules. As an example, the new formalism has been used to investigate the structural and vibrational kinetics of C+3, using stroboscopic G E D data recorded during the first 120 ns following the 193 nm photodissociation of CSz. Temporal changes of vibrational population are observed, which can be rationalized by collision-induced electronic-to-vibrational energy transfer from excited S(lD) atoms to ground state C=S and CS2. The time-evolution of the energy transfer is modeled by determining the vibrational distributions and mean internuclear distances (ra,*)of C+ as functions of delay time. Inverted (non-Boltzmann) distributions are observed, and the refined parameters of model distributions are presented. Introduction Time-dependent gas electron diffraction (GED) is a new tool that promises to be effective in investigations of the nuclear dynamics of laser excited molecules.' The essential experimental principles of stroboscopic GED were first developed a decade ago: including pulsed electron beams generated by photoemission with microsecond to picosecond time resolution. Recently, the method has derived new strength because the application of online data recording techniques, involving either photodiode array394 or CCDS detection, has enabled quantitative studies not possible before. First quantitatively modeled observations of chemical reactions involved the 193 nm photodissociations of CS2,4a tetrachloroethene,Ia and 1,2-di~hloroethenes,~~ the latter with a specific timedependent reaction characteristic: cis-trans isomerization was observed in the millisecond time regime but was not observed in the nanosecond time regime. These studies followed a number of earlier "before-and-after" investigations in which the effects of laser irradiation on the intensities of various target molecules were observed2v6without the possibility of quantitative model fitting. Very recently, a quantitative study was reported for the photodissociation of CFJ.5C Originally, the photodissociation dynamics and nonequilibrium vibrational distributions of laser excited species were studied solely by spectroscopy (see e.g. refs 7, 8) or time-of-flight (TOF) measurements, following the pioneering investigations of Wilson et. al.9 Compared to these methods, stroboscopic GED yields direct and complementary information on the time evolution of internuclear distances. This application of the diffraction phenomenon, including pulsed electrons or X-rays for solid state studies,1°establishes a new field of study that one may adequately call "structural kinetics".l An important new application of stroboscopic GED involves the study of vibrational redistribution in excited species. As a first example, in the present paper we describe one theoretical approach to such investigations, with specific application to
* Authors of correspondence. 0
Abstract published in Advance ACS Abstracts, August 1, 1994.
0022-3654/94/2098-8673$04.50/0
vibrationally excited carbon monosulfide, C=S, during the first 120 ns following the 193 nm laser-induced photodissociation of
cs2.
Theory To describe the time-dependent GED intensities which develop during the time interval in which the photodissociated molecular species equilibrate, two complementary levels of theory may be applied. One is purely statistical, Le. unconstrained by any model kinematic assumptions, and based on the cumulant expansion of the molecular intensity function." The other involves explicit parametrization of the scattering intensities in terms of the potential energy surface12 (PES). In the cumulant method the molecular GED intensities are represented by1l-12
where s = (4?r/A)sin(8/2), 8 is the scattering angle measured from the undeflected beam, A is the de Broglie wavelength of the electrons, gij(s) is the usual function of the atomic scattering amplitudes and phases,13 Im denotes imaginary, ri, denotes the internuclear distances, and the (Arif(t))c are the nth order c~mu1ants.l~ Then, averaging the M(s,t) function of eq 1 with an appropriate electron pulse profile function IO(tltd) gives the stroboscopicelectron diffraction intensitiesSM(8,td) as a function of the delay time td between the pumping laser pulse and the electron probe pulse
where T is the duration of the electron probe pulse. Refinement 0 1994 American Chemical Society
8674
The Journal of Physical Chemistry, Vol. 98, No. 35, 1994
Ischenko et al.
C-S Model Potentials "" I 1
Io;
Morse(appr0x)
k IHi
,
, , '
!(?/,
CS Intensity vs Vibrational Level (v = 0-10)
1
I
I
2
O1
1 3
Distance (A) Figure 1. Standard model potentials for c=Sderived from spectroscopic data (for details see ref 42).
of the cumulants in eq 1 provides a basis for modeling the experimentally observed intensities as a function of time. The cumulant expansion of eq 1 is rapidly convergent" and can thus be used to model any kind of probability density function through the Edgeworth series expansion.I4 For example, even a bimodal probability density of internuclear distances can be described with sufficient precision by the first four to six cumulants,15of which the first four have a clear meaning as the mean, dispersion, skewness, and excess of the probability density. By refining the cumulants from the GED data, one obtains information useful in determining the probability density function, the effective internuclear distances, and other parameters which characterize the vibrational and rotational kinetics.12 Thesecond method of modeling GED intensities involves either their explicit parametrization in terms of the PES2 or the direct solution of the radial part of the Schrijdinger equation for a given set of PES parameters. Once the vibrational eigenfunctions and eigenstates of the target species are determined, the molecular intensities can be calculated for individual vibrational states and then further averaged over any arbitrary vibrational distribution. In the present study the variational procedure of refs 16 and 17 was used. Some standard model PES for C=C are shown in Figure 1. After dissociation, the molecular fragments are likely highly rotationally excited. This effect can be included by using the procedure of refs 18-20. If the potential function is expressed as a Dunham-type21 polynomial series in dimensionless coordinates q = 2 7 r ( p c ~ , / h ) I / ~- r( er ) , then the following expression holds for the minimum q',(J):20
q:(J)
+ + 15a"J3(J +
a 3 J ( J + 1) - 3a7J2(J
-
+
3/2al(w,/2ao)1/2a6+ ~ 21)2 (~ -~ U , ( U , / ~ U ~ ) ~+ Y ~1)3J ~ ( J
27/2~l(we/2~o)1/2~10~3(~ + 1)3 + 9 / 2 a 1 2 ( w e / 2 a 0 ) ~ 9 J+ 3 ( 1)3 J ... ( 3 ) where CY = (2Be/we)1/2,Be is the rotational constant, we is the harmonic vibrational frequency, and QO, al, a2, ..., an are the coefficients of the Dunham polynomial expansion of the potential function. When the population of the rotational levels can be approximated by the Boltzmann distribution, averaging over rotational states J of eq 3 yields the rotational shift of the internuclear distance.20
0
100
50
150
200
250
s (l/nm) Figure 2. Theoretical ~ M ~ ( s ~ ~ ~ , a ~ , a ~ ,curves a ~ , .for . .C=S , u ~ )calculated for individual vibrational states from u = 0 to u = 10 (bottom to top) using eq 5 and the Dunham expansion coefficients42given in Table 2.
Once the vibrational wave functions have been derived, the molecular intensity functions for different vibrational states can be evaluated (see Figure 2 ) and corrected for vibration-rotation interaction through the potential energy parameters:l*-20
sM,(slr ;,ao,a1
P2,.
..ran) = ,...,an)12(sin(sr)/r) d r ( 5 )
g(s)
If P,(t) is the vibrational population of state u, then the average molecular intensity function can be calculated M S J J
= Jr,(tlr,)[~p,(t)
x
U
sl$&lr :,ao,a ,a2,...,aJ2
( s i n ( s 4/ r ) drl d t ( 6 )
Different model vibrational distributions can be tested to fit the experimental data. When the photodissociation of, e.g., triatomic molecules involves excitation of the parent molecules from the ground state to a dissociative state, and the LandauTeller model is a p ~ l i e d , ~then 2 - ~ for ~ each channel of dissociation the final state vibrational distribution of the diatomic fragments may be represented by a Poisson distribution,l4
P ( v ) = (X"/u!) exp(-A)
(7)
where X is the mean number of X = ( E ) , / h c w , = ( 2 h c ~ w , ) - ' I j F ( t exp(iw,t) ) dt12 ( 8 ) and, in the classical approximation,
F(t) = - [ W ) / a r l , , , = PVO exp(-pr(t>)
(9)
where V(t)is the recoil potentia1,and p (the range parameter) and V, are constants for the Born-MeyerZ4 potential. The average vibrational energy can then be calculated:
6r( Trot)= r : - re zz 41;
cot [ (h/27r)(2ZkTr0,)' I 2 ]/ [re3(h / 2 x )(2Zk Trot)1/2] (4)
where 1,z = ( h / 2 ~ ) / [ 2 a ( 2 p D , ) 1 a/ ~is] the , Morse constant, p is the reduced mass, and I is the moment of inertia.
When the dissociation process is complete, ( E ( t ))vib is a regular function of time, and the parameter A(?) can be expanded in a series around the arbitrary time to:
The Journal of Physical Chemistry, Vol. 98, No. 35, 1994 8675
The 193 nm Photodissociation of CS2
Set #1: 20,40,120 us
where b,A, and B are the characteristic kinetic constants of the process. In this way the molecular intensities of eq 6 can be directly expressed in terms of the parameters that characterize the vibrational kinetics of the process. When the inverse electron diffraction problem must be solved, the kinetic constants may be determined from the time-dependent experimental data. Experimental Section Details of operation of the real-time pulsed beam GED apparatus have been described p r e v i o ~ s l y . ~In. ~the experiments a pulsed electron beam is scattered from a molecular beam or gas jet whose target molecules are irradiated in the scattering volume with optical pulses from a powerful tunable laser. The scattered electrons are recorded online with a suitable detector, e.g. a photodiode array or CCD camera. Time resolution is achieved because the diagnostic electron pulses arrive a t the excited species a well-defined and variable delay time after the exciting optical pulses. Thus, sequential electron pulses all encounter species with thesameage relative to the timeof excitation, and by varying the delay time, one can observe how and when molecular structures change after excitation. Under typical conditions in the Arkansas system, the electron pulses (duration -15 ns FWHM) are generated by photoemission and accelerated through a potential of 40 keV, producing -1 X 1OIo electrons per pulse. Typical pulse repetition rates are 20-40 Hz. For the current study, the CS2 target molecules were irradiated with 193 nm laser pulses (duration 15 ns FWHM, 50-130 mJ per pulse). Delay times, between excitation and electron scattering, ranged from 20 to 120 ns. The diffraction intensities were recorded online using photodiode array^.^^^ The target gases were admitted into the vacuum from the reservoir through a nozzle orifice, i.d. 200 pm, using a pushing pressure of 30-50 Torr. Scattering occurred in a volume immediately adjacent to the nozzle exit, in which the gas pressure is estimated to be 10 Torr. These conditions preclude the formation of clusters. The number of collisions, z , per particle in the target gas in 15 ns is estimated in the range loo C z C lo2. The data sets used for the current study are presented in Figures 3 and 4. Combined with a continuous-wave electron beam, the PDA GED detection system is one of the most precise currently existing tools for studying gas phase molecular structures,Ilb yielding bond distances with a precision of a few hundredths of a picometer. In contrast, the pulsed-beam curves (Figures 3 and 4) are still relatively noisy and short, illustrating the characteristic difficulties of stroboscopic GED experiments and the need for further improvements. Nevertheless, the existing data are entirely adequate for the present study, yielding unambiguous timeresolved results.
0
50
100
150
200
250
s (lhm)
Figure 3. Experimental sM(s) curves, ranging from -40 to 130 nm-I, plotted on top of the least squares fitted model curves described in the text. Set 1 is shown (no CS2 present) recorded at delay times of 20 ns (bottom), 40 ns (middle), and 120 ns (top) after photoexcitation of CS2.
Set #2: 20,40,80,120 ns
-
N
Results and Discussion Since 1950,26the photochemistry of carbon disulfide has been thoroughly ~tudied~~-35 in the region from 180 to 210 nm. However, the results of different measurements are somewhat in disagreement, especially concerning the branching ratio of the S(3P) to SOD) states during the two-channel photodissociation of CS2 at 193 nm according to the schemes27-36
0
50
100
150
200
250
s (lhm)
Figure 4. Experimental sM(s) curves, ranging from -30 to 160 nm-I, plotted on top of the least squares fitted model curves described in the text. Set 2 is shown (with CS2 present) recorded at various delay times between 20 ns (bottom) and 120 ns (top).
For single-photon processes, the 193 nm radiation used in the present study cannot excite any higher electronic states of C=C or S. Thestructureoftheexcited state CS2(lB2lZu-) isconsidered to be q~asilinear,3~ but with different geometrical parameters than the ground state;36J7 further, predissociation occurs on a time scale of 1 ps.36 The available energy is defined as EAVL= hvL E,- Do,where hvL is the incident laser photon energy (-620 kJ mol-' at 193 nm), E , is the average internal energy of the parent CS2 molecule (-4.6 kJ mol-1 at room temperature), and DOis the ground state dissociation energy of the C=S double bond, (430.5 f 1.3 kJ mol-l;33 429.7 f 2.9 kJ mol-' 3*). Thus, if the sulfur atom is produced in the 3P2 ground state, the available energy will be 190 kJ mol-', and in principle, the C=C radical can be found in vibrational states up to u = 12. Alternatively, if the S atom is produced in the ID2 excited state, then EAVL 84 kJ mol-', and u = 5 will be accessible.
-
N
+
Ischenko et al.
8676 The Journal of Physical Chemistry, Vol. 98, No. 35, 1994 TABLE 1: Molecular Parameters. of C S 2 (Internal Standard) Used for Calibration of the Experimental Diffraction Intensities state XIZg+
TABLE 2 Dunham Expansion Coefficients. for the CS Radical Used in Calculating the Vibrational Wave Functions and Eieenvalues
wlb/cm-1
w2
w3
rc(CS)/Pm
672.573
398.210
1558.849
155.62
kl I f/cm-l
k122
kl33
kll3
k223
k333
-18.386
43.153
-130.295
-0.531
-1.195
-6.57
Xlld/cm-'
XI^
x 2 2
XI 3
x 2 3
x 3 3
-1 .oo
-2.49
1.00
-7.66
-6.45
-6.51
0 Values from ref 39. Harmonic frequencies. Force constants in dimensionlessnormalcoordinates. Anharmonicityconstants. For details of the calculations see ref 11b.
The most important conclusion regarding the vibrational distributions in supersonic molecular beams of 193 nm irradiated CS2 is that the nascent vibrational populations of C* are strongly inverted for both the ID2 and 3P2dissociation channels and have a broad30 or bimodaP3 distribution with very low occupancy at u = 0 and u > 12. According to spectroscopic TOF m e a s u r e m e n t ~ , 3the ~ ? ~pho~ togenerated C=S fragments are also rotationally excited over a wide range of levels up to J = 99-98 for u = 4-3 (ID2 channel) a n d u p t o J = 74-73foru = 10-9(3P2channel),33withanaverage rotational energy of 15 kJ mol-'. The translational energy of the CES fragments has a broad distribution28-33 up to 188 kJ mol-I for u = 0 and S(3P2), and -75 kJ mol-' for u = 0 and S(lDz), with the maximum a t u = 3 corresponding to -46 kJ mol-'. To date, no observations have been reported of the timeevolution of thevibrational distribution of products when collisions are prevalent. In the current investigations two sets of experimental data were recorded and analyzed. In the first set the laser fluence delivered to the target molecules was so high that virtually all the CS2moleculesweredissociated. In the secondset, thelaser fluence was lower and the presence of undissociated CSZ remained, on the order of 10%. The measurements were repeated at delay times from 20 to 120 ns, and the gas flow rates were kept as constant as possible. We estimate that the pressure in the scattering area was on the order of 1-2 kPa. The intensities were compared directly with an internal standard,IIbusing the parent CS2 as calibrant (see Table 1). The equilibrium geometry of CS2 was determined using the cumulant method and the anharmonic force field of ref 39. The re(C=S) bond length derived from our data is 155.8(3) pm, whereas the spectroscopic value39 is 155.62 pm. At the first stage of data analysis, the theoretical molecular intensities were modeled in the form of the cumulant expansion of eq 1. The cumulants were calculated assuming Boltzmann vibrational and rotational distributions. The refined parameters were the common temperature T, the effective temperaturedependent internuclear distance ( r ( C = S ) )T = re + ( Ar) T,vib + 6rrot(T),and the index of resolution R.lIb These refinements led to physically meaningless solutions, i.e., yielding unacceptably low re distances and unreasonably high values for T , clearly indicating that the Boltzmann distribution does not apply to the present case. At the next stage of the analysis, the second modeling method was applied. Parameters of thevibrational potential function for C s S (Figure 1) were fixed at the spectroscopic values (Table 2). Because of its elasticity,I4 the Poisson distribution, eq 7, was chosen to model the vibrational distribution. For the rotational levels a Boltzmann distribution was assumed.40 The refined parameters were h(td) and the index of resolution R . In order to determine the rotational temperature Trot,a set of calculations were performed in the interval 1000-10 000 K. The downhill Simplex method4' was used for the X(td) refinements. The results are presented in Table 3 and Figure 5 .
-
-
-
state ao/cm-l az a3 a4 X'Z,' 503 515.1 -2.885 83 5.1241 -7.086 8.1 0 Values from ref 42. The minimum of the potential corresponds to rc(CS)= 153.5152(12) pm,inagreementwithearlierMW investigation^^^ rc(CS) = 153.4941 pm.
Analyses of the first set of intensity curves (Figure 3), recorded when virtually all of the parent CS2 was dissociated, yielded vibrational energies for the C=C fragments which increased with time (seeTable 3), with a strongly invertedvibrationaldistribution, that broadened as time progressed (Figure 5 ) . The rotational temperatures, found at 7000 f 1500 K, remained approximately constant. Analyses of the second set of intensity curves (Figure 4), recorded when undissociated CS2 was present, also yielded an inverted vibrational distribution, as above, but in contrast to the former, the average vibrational energy of the C=C fragments was essentially independent of delay time (Table 3). An average h(td) value of 1.5 f 0.3 was found independent of td, for 20 < Id < 120 ns. Rotational temperatures were also fairly constant a t -4000 f 1000 K. In previous spectroscopic30 and TOF investigations33 of the 193 nm photodissociation of CS2, two different nascent vibrational distributions were found for the fragment C Z C . When these distributions were used in our calculations to fit the experimental data, no acceptable agreement was obtained. Both distributi0ns30,~~ give average vibrational energies in C=C that are too high to fit our data. The distribution derived from ref 33 gives (E), 100 kJ/mol and ( E ) , 74 kJ/mol from ref 30. Comparison with our data (see Table 3) shows that the essential part of the vibrational energy has been redistributed to translational and rotational degrees of freedom even at the shortest delay time. Refinements of our data with a bimodal distribution of vibrational energy, P,(Xl,h2) = PP,(hl) + (1 - IB)P,(Xz),were also performed, using several starting values for the branching ratio of S(3P)/S('D) reported in the literature; Le., /3 132 or /3 2.5.31~33 In each case refined distributions resulted in which XI = Xz. In this case, as in all the other refinements, the values obtained for X were only negligibly correlated with other refined parameters, such as re(C=S) or Trot. To explain these results, we suggest the possibility of inelastic collisions of electronically excited S(lD) atoms with C Z C and CS2, after the photodissociation is complete, leading tovibrational excitation according to the following scheme:
-
-
-
-
-
+
S (3P,) C=S (X'Z;, u'> u ) + E,,
(14)
where Ekn corresponds to the energy released into translational degrees of freedom, and E[S(lD2)] - E[S(3P2)] = 1.145 eV.27 An alternative explanation for the observed time evolution of vibrational population is possible which considers the formation of a plasma and collisions of the highly excited ions with C d in the high-fluence laser experiments (set 1) but not at lower intensities (set 2). Formation of a plasma could explain the difference in rotational temperatures found for sets 1 and 2, for which we do not have an explanation, except that the values obtained from the current data are highly uncertain and perhaps within error limits. Additional experiments, including fluorescence spectroscopic investigations, may help discern which of the
The 193 nm Photodissociation of CS2
The Journal of Physical Chemistry, Vol. 98, No. 35, 1994 8677
TABLE 3: Structural and Vibrational Parameters of the CS Radical vs Time Delay, 4, After tbe 193 nm Photodissociation of C S 2 , As Determined from Stroboscopic Electron Diffraction Intensities' X
tdb
ra
(E),
Y3
( W C ' 1 2
B '
Y4
Set 1
20 40 120
1.4 2.1 3.2
28 41 55
154.7 155.0 155.5
20 40 60 80 100 120
1.3 1.1 1.8 1.2 1.8 1.6 1.5 f .3
29 24 35 27 36 31 30& 5
154.0 154.6 154.8 154.0 154.9 154.6 154.5& .4
Av .
155.0 155.6 156.2 Set 2 154.3 154.9 155.2 154.3 155.4 155.0 154.9f .4
6.9 9.9 10.6 7.2 6.9 8.5 7.0 8.6 8.1 1.7f .8
0.42 0.73 0.83
-0.33 482 -0.99
0.44 0.41
-0.35 -0.32 -0.54 -0.32 -0.56 4.48 -0.43 .ll
0.51
0.42 0.58 0.53 0.49& .08
The upper part of the table refers to the experiments with no parent CS2 present after photodissociation (set 1). The lower part corresponds to experiments (set 2) in which CS2 was present in mole fractions of approximately 0.1. (E), is given in kJ/mol; r,, rB,(A9)c1/2,in pm. 73 and 7 4 are Xis the mean number of vibrational quanta in the Poisson distribution (see text). Note dimensionless cumulant coefficients, = (AF)c/(@)cn/2.11b the increase in X with time in set 1 and its constancy (1.5 f .3) in set 2, and the increase in r, (>155 pm) and rB(>l56 pm) with time in set 1, in contrast to set 2. 0
Nascent, Set #1, Set #2
Set #1: Radial Distributions
set 2
120 ns
40 ns
k L
20 ns
t;: set 1
nascent refs. 30,33 0
2 4
6 8101214 V
Figure 5. Vibrational distributions for generated by 193 nm photodissociation of CS2. The nascent distributions described in the literature30J3 are shown at the bottom. The distributions determined from the time-resolved electron diffraction data of this study are shown in the central section (set 1, no CS2 present, 3 curves) and in the top part of the figure (set 2, 4 curves, CS2 present). Note the broadening of the distribution (increased population of higher u-states with time) in set 1 which is in contrast to set 2.
possibilities, reactions 14 and 15 or dissipation of a plasma, is actually occurring. Without additional data we prefer reactions 14 and 15 for two reasons: There was no visible emission from the reaction volume during the experiments, and the changes in radial distribution with time, as shown in Figure 6,are nearly symmetrically distributed about re, which is characteristic for vibrational excitation. If our interpretation in terms of reactions 14 and 15 is correct, then it is an important aspect of our results that, within the error limits, the average value found for X(td) in the second data set (CS2 present) is the same as that found for the initial (20 ns) intensity curve of the first data set (X(td) = 1.4, Table 3, no cs2 present). This observation seems to indicate that the electronic to vibrational energy transfer from S(1D) to CS2 (reaction 15) completes on a time scale, i.e., within the first 20 ns, at which the same process involving C=C (reaction 14) has barely begun. Thus, our data indicate that the cross section of the inelastic collision process of S(1D) with C=C is much smaller than with CS2. This compares to the quenching efficiency reported for O(lD2) in collisions with C = O in comparison with CO2,z7even
100
120
140
160
180
200
Distance /pm Figure 6. Experimental radial distribution curves of C=S obtained by Fourier inversion of the intensity data of Figure 3 (set 1). The Fourier transforms were calculated without artificial damping and without theoretical intensity data at inner s-values. Differences,experiment minus theory (E- T), for the 20,40,and 120ns curves are shown at the bottom; differences between experimental curves are shown in theccntral section; the experimental Fourier transforms, from 100 to 200 pm, are shown in the top part. Note the increase in both short and long radii a t 40 and 120 ns compared to 20 ns, illustrating the splitting caused by increasing populations of higher vibrational states with time.
though the advantage of C02 is much less than the order of magnitude required for this aspect of our data interpretation. Whatever the exact interpretation of the observed phenomena may be, our investigations illustrate, in a general way, how stroboscopic gas electron diffraction may be used to study vibrational kinetics. In the specific case of C=C, additional experiments are in preparation to obtain a more detailed description of the processes involved and specific values of the cross sections and rate constants of the S('D)/C=C electronic to vibrational energy transfer process. Conclusions The conventional data analysis methods used in gas electron diffraction are inapplicable in the analysis of stroboscopic GED data of laser-excited species,because they are based on expressions
8678 The Journal of Physical Chemistry, Vol. 98, No. 35, 1994 whose derivation restricts them to equilibrium systems and molecules with small-amplitudevibrational motions (for a detailed discussion see ref 11b). The results presented in this paper demonstrate that molecular GED intensities can be expressed in terms of the parameters that characterize the vibrational kinetics of a nonequilibrium system. Thus, together with related formulations of time-dependent molecular GED intensities of dissociativeelectronic states,lb,c the current paper provides a much needed basis for future experimental work in stroboscopic gas electron diffraction. For the specific example selected for analysis, the 193 nm induced photodissociation of CS2, we conclude that collisioninduced electronic-to-vibrational energy transfer is indicated by our data for the reaction products, involving excited S(lD) atoms and ground state CeeC and CSz molecules. The cross section for this process very likely is significantly larger for CS2 than C=C. Acknowledgment. The authors thank Prof. C.R. Geren, Vice Chancellor for Research and Dean of the Graduate School, University of Arkansas, for his support. This work was supported by NSF Grants ECS-9002677and CHE-93 14064. References and Notes (1) (a) Ischenko, A. A.; Spiridonov, V. P.; Schifer, L.; Ewbank, J. D. J . Mol. Struct. 1993,300,115. (b) Ischenko, A. A.; Ewbank, J. D.; Schlfer, L. J. Mol. Strucr. 1994,320, 147. (c) Ewbank, J. D.; Schlfer, L.; Ischenko, A. A. J . Mol. Srrucr. 1994, 321, 265. (d) Ischenko, A. A.; Ewbank, J. D.; Schlfer, L. 15th Austin Symposium on Molecular Structure, Abstracts, pp 10 and 33, University of Texas, Austin, TX, March 21,1994. (2) (a) Akhmanov, S. A.; Bagratashvili, V. N.;Golubkov, V. V.; Zgurskii, A. V.; Ischenko, A. A.; Krikunov, S. A,; Spiridonov, V. P.; Tunkin, V. G. Sou. Tech.Phys. Lett. 1985,11, 63. (b) Ischenko, A. A.;Spiridonov, V. P.; Zgurskii, A. V.; Tarasov, Yu. I. Structure and Properriesof Molecules; Ivanovo:USSR, 1988; p 63. (c) Vabishevich, M. G.; Ischenko, A. A. Methodfor Inuestigating the Sfructural Kinetics of Ultra-Fast Processes; USSR, Patent 1679907, 1990 (priority on Oct. 14, 1988; registered Apr. 16, 1986). (3) (a) Ewbank, J. D.; Schlfer, L.; Paul, D. W.; Benston, 0. J.; Lennox, J. C. Reu. Sci. Instrum. 1984,55,1598. (b) Ewbank, J. D.; Schifer, L.; Paul, D. W.; Monts D. L.; Faust, W. L. Rev. Sci. Instrum. 1986, 57, 967. (c) Ewbank, J. D.; Paul, D. W.; Schlfer, L. IR 100 Award, Research and Deuelopment, October 1985. (4) (a) Ewbank, J. D.; Faust, W. L.; Luo, J. Y.; English, J. T.; Monts D. L.; Paul, D. W.; Dou, Q.; Schlfer, L. Reu. Sci. Instrum. 1992,63, 3352. (b) Ewbank, J. D.; Luo, J. Y.; English, J. T.; Liu, R.; Faust, W. L.; Schifer, L. J . Phys. Chem. 1993,97,8745. (c) Faust, W. L.; Ewbank, J. D.; Monts D. L.; Schifer, L. Reu. Sci. Instrum. 1988,59,550. (d) Ewbank, J. D.; Faust, W. L.; Monts D. L.; Paul, D. W.; Schifer, L.; Bakhtiar, R.; Dou, Q.Mol. Cryst. Liq. Cryst. 1990, 187, 351. (5) (a) Williamson, J. C.; Dantus, M.; Kim, S.B.; Zewail, A. H. Chem. Phys. Lett. 1992, 196, 529. (b) Williamson, J. C.; Zewail, A. H. J . Phys. Chem. 1994,98,2766. (c) Dantus, M.; Kim, S.B.; Williamson, J. C.; Zewail, A. H. J . Phys. Chem. 1994, 98, 2782. (6) (a) Ischenko, A. A,; Golubkov, V. V.; Spiridonov, V. P.; Zgurskii, A. V.; Akhmanov, A. S.;Vabischevich, M. G. Appl. Phys. B 1983,32,1661. (b) Ischenko, A. A.; Golubkov,V. V.; Spiridonov,V. P.; Zgurskii, A. V.; Akhmanov, A. S. Vestn. Mosk. Uniu. Khim. 1985, 25, 385. (c) Rood, A. P.; Milledge, J. J. Chem. Soc. Faraday Trans. 2 1984, 9, 1145. (7) Andresen, P. The Dynamics of the Photodissociation of Small Molecules; Alves, A. C. P., Ed.; Frontiers of Laser Spectroscopy of Gases, Kluwer: Dordrecht, The Netherlands, 1988.
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