J. Phys. Chem. 1995,99, 3532-3539
3532
Theoretical Studies of the Photolytic Decomposition of Vinyl Bromide at 193 nm Gilbert J. Mains and Lionel M. RafP Department of Chemistry, Oklahoma State University, Stillwater, Oklahoma 74078
Samuel A. Abrash Department of Chemistry, University of Richmond, Richmond, Virginia 23173 Received: June 20, 1994; In Final Form: December 16, 1994@
The decomposition dynamics of vinyl bromide upon single-photon excitation at 193 nm have been investigated by using classical trajectory methods on adiabatic excited-state potentials that have been obtained by using empirical and a b initio configuration interaction (CI) methods. The excited-state potential surfaces are represented by a global analytic hypersurface previously developed for the vinyl bromide ground state with the C-Br bonding Morse-type potential replaced with one of the repulsive C-Br interactions obtained in the empirical or ab initio calculations Energetic considerations suggest that the dissociation dynamics of vinyl bromide upon photolysis at 193 nm involves excitation to three or four repulsive C-Br states which include the A’A“(na*), 63A”(na*) and C3A’(no*) potentials. The effects of a vertical excitation from the ground state to the A’A”(na*) and E3A’(na*) states have been determined by the computation of 300 or more trajectories in each case. The results show that the only products for these excitations are vinyl radicals and either Br(2P3n)or Br(2Pln) atoms. No HBr is observed. This result is consistent with the hypothesis advanced in our previous study of vinyl bromide dissociation on the ground-state surface where we suggested that the HBr formed in previously reported beam experiments [Zsr. J. Chem. 1989,29,3831 is produced subsequent to internal conversion to the ground state. Combination of the trajectory results with the measured Br/HBr ratio of 1.28 indicates that the internal conversion probability lies in the range 0.44-0.64. The calculated translational energy distributions for C2H3 and either Br(2P3n) or Br(2Pln) atoms are peaked at energies significantly in excess of that observed in the beam experiments. This is interpreted to mean that the ab initio excited-state potentials are too repulsive. Comparison with the experimental data suggests that, in the region around the C-Br equilibrium distance, the ab initio energies are too large by about 16 kcdmol. The computed full width at half-maximum for all distributions is much smaller than the experimental result, suggesting that decomposition is occurring from more than one excited electronic surface. It is shown that a good fit to the measured translational energy distribution can be obtained from a linear combination of the distributions computed by using three empirical potentials whose energy at the equilibrium C-Br separation has been reduced by about 16 kcaYmol from that predicted by the ab initio calculations. The values of the expansion coefficients indicate that about 60% of the bromine atoms are formed in the 2P3n ground state. This is close to the statistical result based upon a simple count of available spin states.
I. Introduction
results indicate that the major decomposition channel is
The reaction dynamics for the bimolecular addition reactions of HBrDBr to C2HgC2D2 and for the associated unimolecular decomposition of vinyl bromide in the gas phase and under matrix isolation conditions have been shown to be particularly complex. Saito et al.’ have examined the thermal decomposition of vinyl bromide over the temperature range 1300-2000 K by using shock tube methods. Their results indicate that the initial decomposition proceeds solely via molecular elimination of HBr H,C=CHBr
A
HBr
+ HC=CH
The reported activation energy for reaction r l is 41.5 f 1.6 kcal/mol. It is not possible to determine from their data whether HBr is formed via a three- or four-center elimination reaction. In contrast, the dynamics of the gas-phase, photolytic reaction are much more complex. Wodtke et al.2 have photolyzed a molecular beam of vinyl bromide at 193 nm. The products were determined by mass analysis. Time-of-flight measurements permitted the product translational energies to be obtained. The @Abstractpublished in Advance ACS Abstracts, February 15, 1995.
0022-365419512099-3532$09.00/0
H,C%HBr
hv
Br
+ C,H3
Molecular elimination of HBr, reaction rl, is a secondary reaction channel. The measured Br/HBr product ratio is found to be 1.28 f 0.05. On the basis of the shape of the measured translational energy distribution, Wodtke et aL2concluded that C-Br bond fission occurs directly from the excited electronic state produced by the photolysis at 193 nm. It is further suggested that both Br(2Pln) and Br(ZP3n)atoms are produced by the photolysis. However, the data analysis presented does not give any estimate as to the Br(2P~n)lBr(2P3n) ratio. Like the shock tube measurements,’ the beam experiments2yield no information concerning the three- vs four-center nature of the HBr elimination reaction. The results of the photolysis experiments reported by Johnson and Price,3which employ xenon-filled flash lamps that emit in the 150-200-nm region, are in conflict with the data obtained by Wodtke et al? The mass spectrum of the photolysis products obtained by Johnson and Price3indicates the presence of a very low concentration of vinyl radicals. Consequently, it was 0 1995 American Chemical Society
J. Phys. Chem., Vol. 99, No. 11, 1995 3533
Photolytic Decomposition of Vinyl Bromide concluded that reaction r2 plays little or no role in the photolytic decomposition of vinyl bromide. No molecular hydrogen or bromoacetyleneformation was reported by either Johnston and Price3 or Wodtke et aL2 Photolysis of vinyl bromide in krypton matrices yields very different results from either of the gas-phase photolysis experim e n t ~ . ~Experiments ,~ reported by Abrash et al.495show that the only primary products are HBr and acetylene formed via reaction r l in either a three- or four-center elimination. No bromine atom formation, reaction r2, is observed. However, an important secondary channel leading to H2 and bromoacetylene is seen: H2C=CHBr
hv
H,
+ HCiCBr
(r3)
The shape of the HBr and H2 growth curves suggest that reaction r l is a primary, first-order process whereas r3 is a secondary reaction initiated by photolysis of the products of reaction rl. However, the experiments provide no information related to the molecular mechanisms involved in producing Ha and bromoacetylene via photolysis of a matrix-isolated HBr/acetylene pair. There is also no direct information available concerning the excited electronic states involved in these various processes. Abrash et have also examined the photolysis products obtained upon irradiation of matrix-isolated (HBr/C2H2/Kr), (HBr/C2D2/Kr), (DBr/HBr/CzHdKr), and (DBr/HBr/CzDz/Kr) mixtures using a medium pressure Hg source in which the principle emission is near 254 nm. The results raise numerous questions related to mechanism and the excited electronic states involved. For example, the measured band intensities suggest that photolysis of (HBr/C2Hz/Kr) gives ~
1
.
HBr
~
9
~
+ HCSCH hv H2 + H C l C B r
0.4)
as the major product. Some C4HBr is seen which presumably arises from having matrix-isolated HBr in a matrix cage containing two acetylene molecules. Very little stable vinyl bromide product is obtained. In contrast, reaction r4 may not be the major reaction channel when (HBr/C2D2/Kr) is photolyzed. In this case, an important reaction is isotopic exchange:
+ DCECD hv DBr + HCECD
HBr
(r5)
The measured absorption intensities suggest that the channel forming HD and DC=CBr via reaction r4 is second in importance among reactions leading to C2 products. These conclusions, however, are somewhat equivocal since the relevant photon cross sections are unknown. Some, decomposition to D2 via HBr
+ DCECD
D2
+ HCECBr
(r6)
is also observed. The average r5h6 intensity ratio is about 1.7 f 0.3. Finally, a small amount of cis-DHC=CDBr is formed via a/3 addition HBr
+DClCD
*
cis-DHC=CDBr
(r7)
Except for reaction r7, the mechanisms involved in these reactions are, at present, unknown. If reaction r4 takes place by addition to form an excited vinyl bromide molecule which then eliminates Ha, it is difficult to understand why none of the gas-phase photolysis studies of vinyl bromide4v5have found H2 as a decomposition product if attempts were made to detect its formation. Another possibility is initial dissociation of HBr followed by atomic abstraction by hydrogen and Br atom
addition. Reaction r5 might occur via the sequence o$ addition followed by three-center elimination. The results obtained upon photolysis of (DBr/HBr/C2H2/Kr) and (DBr/HBr/CzDz/Kr) mixtures raise additional mechanistic question^.^ In the former case, the band intensities suggest that the decomposition products are, in order of importance, HC-Br, H C W D , DCWBr, and cis-HDC%HBr. No trans product is observed. In the latter case, the order of product importance is DCWBr, H C W D , cis-HDC=CDBr, and transHDC-CDBr. No vinyl-l,l-d2 bromide is seen. We have recently reported a classical trajectory study of the thermal gas-phase decomposition reactions of vinyl bromide on the ground-state potential energy surface: The global potential used in these studies is written as a sum of the different reaction channel potentials connected by parametrized switching functions. This potential was fitted to the results of ab initio electronic structure calculations and experimental thermochemical, spectroscopic, and structural data. The data base fitted includes measured endo- and exothermicities, equilibrium structures, fundamental vibrational frequencies, and the saddlepoint geometries and energies for several decomposition channels obtained by using 6-31G(d,p) basis sets for carbon and hydrogen and Huzinaga's (4333/433/4) basis set augmented with split outer s and p orbitals and an f orbital for bromine. Electron correlation is incorporated using Mtiller-Plesset fourth-order perturbation theory with all single, double, triple, and quadruple excitations included. The average absolute difference between AE values for the various decomposition channels obtained from the global surface and experimental measurement is 1.76 kcaY mol. Predicted equilibrium geometries for reactants and products are in good to excellent accord with experiment. The average absolute difference between the fundamental vibrational frequencies predicted by the global surface and those obtained from Raman and IR spectra vary from 10.2 cm-' for H2C=CHBr to 81.3 cm-' for HzC=CH. The potential barriers for seven decomposition channels agree with the ab initio calculations to within an average difference of 1.4 kcal/mol. The results of the trajectories calculations6 show the following: (1) The vinyl bromide decomposition dynamics follows a first-order rate law with a high-pressure limiting rate coefficient of 35.7 exp[-71.6 kcaYrnol)/RT] ps-'. (2) At thermal energies, the only decomposition product is HBr. The results indicate that the activation energy reported by Saito et al.' for this process is too small. (3) As the excitation energy increases, other decomposition channels become important. At E = 6.44 eV, the reaction channels are, in order of importance, H2 elimination (48.1%), HBr formation (44.5%), Br atom elimination (4.6%), and C-H bond fission (2.6%). (4) The percentage of the total excitation energy partitioned into product relative translational motion and HBr internal energy upon HBr elimination is a slowly increasing function of the total excitation energy. ( 5 ) Comparison of the calculated and experimental2relative translational energy distributions for product Br atoms and C2H3 formed upon C-Br bond fission and the time-of-flight (TOF) spectra for C2H2 upon HBr elimination indicates that Br atom dissociation is occumng on an excited electronic surface but HBr elimination is taking place on the ground-state surface subsequent to internal conversion. (6) Both HBr and H2 eliminations occur almost exclusively via a three-center mechanism. For both three- and four-center dissociation reactions, both C-X bonds rupture nearly simultaneously. In this paper, we examine the photolytic decomposition dynamics of vinyl bromide in more detail. In particular, we focus attention on the excited electronic states involved in reaction r2. The results suggest that Br atom dissociation occurs
3534 J. Phys. Chem., Vol. 99, No. 11, 1995 predominantly from repulsive 3A’ and lA’’ states which arise from excitation of the C-Br bond. By fitting the calculated distributionsof translational energies to the experimental results,z an estimate of the Br(2P1~~)/Br(zP3~2) ratio is obtained.
Mains et al.
200
11. Excited-State Potentials Exploration of the electronic excited states of vinyl bromide was carried out via a series of ab initio calculations using the CIS (configuration interactions singles) portion of the GAUSSIAN 92 package of programs.’ The CIS equilibrium structure for a number of excited singlets and triplets of vinyl bromide were determined by using the 6-31G(d,p) basis sets for carbon and hydrogen and Huzinaga’s (4333143314) basis set* augmented with split outer s and p orbitals and a polarization f orbital, i.e. (433211432114/1), for Br. This is basis 11 in the preceding papere6 The molecular orbitals of the ground state (Xl A’ ), the f i s t CIS excited singlet state (@A”), and the lowest triplet state (g3A’ ) of vinyl bromide are relevant here. The promotion of an electron from the ground HOMO, essentially a mixed carbon-carbon n bonding and n Br orbital, to the excited singlet state SOMO, an antibonding C-Br orbital, is expected to result in a lengthening of both the C-C bond and the C-Br bond. The lowest CIS singlet state was found to be bound with a C-C bond distance of 1.38 b; (compared to 1.30 b; in the ground state) and a C-Br bond distance of 2.48 8, (compared to 1.96 b; in the ground state). This state is located 150.31 kcaVmol above the ground state, which is sufficiently close to the photolysis energy used in the beam experiments (148.5 kcal/ mol)2 that we might anticipate that this excited singlet is accessed by the photolysis. The lowest CIS triplet state (PA‘), which arises from promotion of an electron from the ground-state HOMO, shows a very different orbital behavior. The two singly occupied molecular orbitals (SOMO) are each very weakly bonding and result in a rotation of the CH2 moiety to make it orthogonal to the C-C-Br plane. The C-C bond length increases 0.22 8, to 1.52 A, but the C-Br bond length increases only 0.07 8,. Although the (g3A’) state lies only 86.7 kcaVmol above the ground state at the CIS level of accuracy, the unfavorable change in geometry lowers the Franck-Condon factor sufficiently that the state probably makes little contribution to the dynamics upon photolysis at 193 nm. A second CIS triplet state (G3A‘) was located 134.06 kcaYmol above the ground state. This state is unbound and dissociates to the vinyl radical and a bromine atom. The CIS calculations do not find all of the excited surfaces since other states arising from the interaction of the ground state of the vinyl radical and orientations other than with the singlyoccupied p orbital of the bromine atom are not found. In order to find these states, it is necessary to employ more sophisticated configuration interaction calculations such as CI, GVB-CI, or CASSCF. Attempts to do vinyl bromide calculations using the CASSCF section of GAUSSIAN 927 failed. While this research was in progress, we discovered that the vinyl bromide potential surfaces, in which the double bond was held in a singlet configuration, had been determined by Michl and Bonacic-Koutecky9 (MBK) using SCF-CI and GVB-CI methods. These calculations confirmed that the energy of the bound @A’) state was above the 148.5 excitation energy employed in the photolysis experimentsZ and provided the surfaces required to interpret the observed dynamics. Their results are shown in Figure 1. In these calculations, the vinyl radical is frozen in its equilibrium geometry and spin-orbit coupling is ignored. The equilibrium C-Br distance in vinyl bromide is 1.89 A. The lowest-lying, vertical, Franck-Condon
01
I
I
1
2.0
2.6
3.0
3.6 HZC=CH-Br R (A) H@CH + Br Figure 1. Ab initio CI potentials for vinyl bromide taken from ref 9. Reprinted with permission from ref 9. Copyright 1990 Wiley.
-
transition from the ‘A’ singlet ground state is a n n* excitation of the C-C n electrons to a bound g3A’(nn*) state, as identified in the CIS calculations. The energy of this transition lies well below the energy of the exciting photon at 193 nm (148.5 kcaltmol). Above the g3A‘(nn*) state lies an ensemble of repulsive states resulting from excitation of the u electrons in the C-Br bond and the lone-pair n electrons on the bromine atom. The lowest of these is a G3A”(nu*) state arising from excitation of a n electron on Br into a u* orbital. The corresponding singlet excitation to AIA”(nu*) lies slightly above it. A S3A’(nu*) state lies above the AIA“(nu*) state. This state is primarily a repulsive triplet which is the state located by the CIS calculation. The corresponding singlet BIA’(nu*) state is purely repulsive. Figure 1 shows that, on the basis of energetic considerations alone, we would expect Franck-Condon transitions to occur primarily from the ground state around R = 1.89 b; to either the AIA”(nu*), the h3A”(nu*), or the E3A’(nu*) state. Excitation to any of these repulsive states would be expected to lead to C-Br bond fission and the formation of Br C2H3 products. The results obtained by MBK9 and the CIS calculations indicate that the CIA’(nu*) state lies at an energy above the 193-nmphoton. We therefore do not expect it, or the higher energy states, to play a role in the photolysis dissociation dynamics. The b3A”(nu*) and AIA”(nu*) states are nearly equal in energy at all values of the C-Br distance of interest. We therefore assume that the vinyl bromide dissociation dynamics from these two states will be nearly identical and that only the spin-conserving excitation to the AIA“(nu*) state need be considered. Analytical expressions for the AIA”(nu*) and E3A‘(nu*) potentials have been obtained by fitting the MBK results9 to polynomial expansions in the C-Br distance. That is,
+
M vk(RC-Br)
= &(RC-Br)i
(1)
i=O
where M is either 5 or 9 and k denotes either the AIA”(nu*) or the c3A’(nu*) potential. The fitting coefficients are given in Table 1. Wodkte et aLzhave suggested that both Br(zPln) and B1f~P3n) are formed in the molecular beam photolysis experiments
J. Phys. Chem., Vol. 99,No. 11, 1995 3535
Photolytic Decomposition of Vinyl Bromide TABLE 1: Fitting Coefficients in Eq 1 and Parameters in Eq 2 for the Excited-State C-Br Potentials
150
Ab Initio GVB-CI Potentialsg
coeP
potential 1 potential 2 [‘A‘’(~ra*);~/2]~ [3A’(nu*);3/2]b 2 246.317 140 33 -601 560.905 722 -3 130.704911 44 2024 844.979 61 1 840.626 468 51 -2977 218.992 44 -550.369 126 729 2511 064.795 04 83.441 433 078 2 -1338 998.410 29 -5.112 596 596 67 468 132.452 547 -107 295.746 204 0.00 15 543.134 9747 0.00 0.00 -1290.881 077 23 0.00 46.804 086 7268
potential 3 [1A”(na*);L/2]b 2660.762 860 17 -3824.344 664 69 2268.960409 72 -670.326 992 369 98.427 246 5613 -5.739 332 446 26 0.00 0.00 0.00 0.00
100 *I
F
50
C
W
0 1.5
-
i A n
2.0
2.5
3.0
R(C-Br) (A)
. (B)
A
Param & kcaYmol) a cA-9 Re
(4
Empirical Potentials, Eq 2 potential S1 potential S2 potential S3 11A”(nu*);3/~lb11A”(na*);1/21b [3A’(na*);3/~lb 11.7322 8.2324 16.2043 1.7097 2.0262 2.3455 1.89 1.89 1.89 76.997 87.497 76.997
DO(kcaVmo1) “The units on coefficients ai are (kcaI/mol)/A’.bThe notation [‘A”(zu*);flrefers to the excited-stateC-Br potential involved in the dissociation to vinyl radicals + Br(ZPj)atoms.
although no estimate of the yield ratio has been obtained. Since the calculations reported by MBK ignore spin-orbit c ~ u p l i n g , ~ no results for the potential curves leading to Br(2P1/2) are available. However, a reasonable approximation to these potentials can be obtained by combining the results given in Figure 1 with the energies of the product limits. The splitting between the [Br(2P1/2) C2H31 and the [Br(2P3/~) CzH31 product limits is just the [Br(2Pl&Br(2P3n)]spin-orbit splitting, which is 10.5 kcdmol. If spin-orbit coupling were to be included in the CI calculations, we would expect these terms to have little or no effect on the AIA“(na*) potential at C-Br separations near the equilibrium distance since the total spin angular momentum in this state is zero. As R c - B ~increases, however, the spinorbit coupling would cause the AIA“(na*) potential to split into two states whose separation would increase monotonically with R c - B ~and asymptotically approach the Br(2P1/~)-Br(2P3/~) spin-orbit splitting of 10.5 kcal/mol as R c - B ~ 00. The AIA”(na*) and E3A’(na*) states are shown in Figure 2. The points for the excited states are taken directly from the MBK resultsggiven in Figure 1. The solid curves for the excited states are the least-squares fits obtained from eq 1. For the groundstate potential, the points are computed from the global potential described in ref 6 , while the solid curve is a cubic spline fit to these points. Figure 2 also shows a hypothetical splitting of the AIA”(na*) state which satisfies all of the criteria discussed above. The solid curve leading to the Br(2P1/2)product limit is a least-squares fit of eq 1 to the points shown. The fitting parameters for this potential are listed in Table 1. In order to obtain the excited-state, potential energy hypersurfaces required for the examination of the photolytic dissociation dynamics of vinyl bromide, we have assumed that dissociation occurs adiabatically on an excited-state hypersurface without surface crossing. We further assume that the various excited-state surfaces may be adequately represented by the analytic ground-state vinyl bromide potential6 with the C-Br bonding Morse potential replaced with one of the analytic potentials given by eq 1 and Table 1. As mentioned above, the dissociation dynamics from the AIA”(na*) and 63A”(na*) states are assumed to be identical.
+
4.0
3.5
‘d 3 A /
E m c 5;
0
*,
I
Fc
W
70 1.5
1 a0
2.0
2.5
3.0
R(C-Br) (A)
3.5
4.0 Br(2P3/2)
,
E
, 1
s3
+
-
t
~~~
1
,
.5
2.0
2.5
R(C-Br)
3.0
, By 3.5
,
y,z ,) j 4.0
(A)
Figure 2. (A) Vinyl bromide potentials as a function of the C-Br interatomic distance, R(C-Br), with all other configuration variables frozen at their equilibrium values. The ground-state potential points are taken from ref 6. The associated curve is a cubic spline fit to the points. Excited-state potential points are taken from ref 9. The solid curves for the excited-state potentials are obtained from eq 1 and Table 1. (B) Expanded view of A for the region between 70 and 140 kcaY mol. (C) Empirical potentials, S1, S2, and S3, obtained from eq 2 and Table 1.
The Gaussian 92 calculations’ suggest that the above approximations should lead to reasonable results for the dynamics. All of the states above the ii3A’(nn*) state are associated with a very localized excitation of the C-Br moiety so that the excited state hypersurface should be nearly identical to the ground state except for the C-Br interaction term. Although the spin-orbit splitting of the AIA”(m*) state is purely hypothetical, it is unlikely that the precise details of this repulsive potential make a significant difference in the dynamics so long as the asymptotic limits are correctly represented. For reasons discussed in more detail in the subsequent sections, we have also examined the vinyl bromide dissociation dynamics using three other C-Br repulsive potentials that represent the spin-orbit splitting of the AIA”(na*) state and the E3A’(na*) state but which are less repulsive than those predicted by the GVB-CI calculation^.^ These potentials, which are shown in Figure 2c, have the functional form
Mains et al. 1.01 h
The parameter values for these potentials are also given in Table 1.
0.8-
a
s
III. Photolytic Dissociation Dynamics
A. Methods and F’rocedures. The photolytic dissociation dynamics of vinyl bromide have been investigated using classical trajectory methods.’O The initial states for the trajectories are prepared by first inserting zero-point energy into each of the vinyl bromide normal modes using projection meth0ds.l1-l3 Hamilton’s equations of motion are then integrated for a randomly chosen period r, given by tp = &
(3)
where 6 is a random number chosen from a distribution that is uniform on the interval [0,1] and T is the characteristic period of the lowest frequency vibrational mode in vinyl bromide. The numerical integrations are effected using a fourth-order RungeKutta procedure with a fixed step size of 2.038 x s. Equation 3 effectively averages over the vibrational phases of the molecule. Subsequent to the above integration, a vertical excitation to the desired excited state of vinyl bromide is attempted. If the difference between the excited-state and ground-state potential surfaces
(4) exceeds the energy of the exciting photon at 193 nm, the attempt is assumed to fail. In this event, the integration is continued for an additional random period after which another vertical excitation is attempted. When AE 5 hc/A ( A = 193 nm), excitation is assumed to occur and the potential is switched from the ground-state surface to Vk(RC-Br). The excess energy AE is then randomly partitioned among the 12 available vibrational modes using projection technique^.'^-^^ In all calculations, the initial rotational energy is zero. Subsequent to excitation, the trajectories are integrated until reaction occurs or until an upper limit of time, rm, is exceeded. Final-state determinations are made by using a combination of distance and energy criteria. B. Results. All of the reaction channels included in the ground-state potential6 are also present in each of the excitedstate surfaces. These include C-Br and C-H bond fission, three- and four-center HBr elimination, and three- and fourcenter H2 dissociation. When the excitation energy is primarily localized in the C-Br bond, neither C-H bond fission nor H2 elimination would be expected. No such reactions were observed in any of the trajectories computed in this study. In contrast, three-center HBr dissociation might occur. As the bromine atom dissociates on one of the repulsive excited potentials, much of the excitation energy will be converted into relative translational energy of the C2H3 Br products. The bromine atom will therefore possess sufficient energy to abstract the nearby hydrogen atom and produce a three-center HBr elimination reaction. On the ground-state surface, this is the major dissociation channel at internal energies below 6.00 eV.6 On the excited-state surfaces, however, we find that such dissociations do not occur. None of the 3700 trajectories computed in this study gave HBr as a product. The above result is consistent with the hypothesis advanced in our previous study of vinyl bromide dissociation on the
+
0.6-
0.01
1 . .
I
1
40
20
60
80
Relative Trans. Energy (kcal/mol) Figure 3. Relative translational energy distributions resulting from Br atom dissociation to form Br(*Psn) C& or Br(2Pln) C2H3. The solid squares are the experimental data taken from ref 2. The associated curve is a cubic spline fit. The trajectory results obtained by using the ab initio potential surfaces are shown by the points @,A,@). The dashed curves are th_efitted results from eq 5 using the surface; (A)[ALA”coefficients given in Table 2. (0)[A’A’’(J~U*);~/~] (n~*);~/2] surface; (e) [c3A’(na*);Y2]surface.
+
+
ground-state surface.6 In that investigation, we found that at internal energies equal to the photon energy in the photolytic experiments2 (6.44 eV), the simulated TOF spectrum obtained from the calculated distribution of translational energies subsequent to HBr elimination is in fair accord with the time-offlight measurementse2 As the excitation energy decreases, the degree of agreement between the computed and measured TOF spectra decreases. It was therefore suggested that the HBr observed in the photolytic beam experiments2 is being produced subsequent to internal conversion to the ground state. The failure to observe any HBr production in trajectories computed on the excited-state surfaces lends additional support to this hypothesis. All trajectories integrated on the excited-state potentials subsequent to a vertical excitation at 193 nm resulted in the production of Br atoms. Our previous calculations6 show that, at an internal excitation of 6.44 eV on the ground-state surface, 44.5% of the trajectories yield HBr provided the excitation energy is randomly distributed over all 12 vibrational modes. These results, combined with the measured2 Br/HBr ratio of 1.28 in the photolysis experiments, suggest that the probability of internal conversion subsequent to excitation at 193 nm is about 0.64. This value should be regarded as an upper limit since it is unlikely that internal conversion produces a random distribution of the excitation energy. A lower limit may be obtained by assuming that the energy distribution produced by internal conversion is such that all trajectories yield HBr. Under these conditions, the internal conversion probability decreases to about 0.44. Figure 3 shows the calculated distributions of C2H3 relative tfanslational energies subsequent to C-Br bond fission on the A’A”(m*) and the E3A’(nu*) surfaces to produce a vinyl radical and Br(2P3/2)or C2H3 Br(2P1/2). The points show the data obtained from the results of 300 trajectories after the distribution maximum are normalized to unity. In each case, these data are fitted by nonlinear least-squaresmethods to a two-term Gaussian distribution function
+
+
PE[’A”(nu*);3/2] dE = [OS0exp{-a,(E - u ~ ) ~ }
0.50 exp{ -a@ - u ~ ) ~ dE } ] (5) where the notation PE[1A”(~u*);3/2]means the dissociation occurs on the AIA”(rca*) potential to produce a BI(~PX) product
J. Phys. Chem., Vol. 99, No. 11, 1995 3537
Photolytic Decomposition of Vinyl Bromide TABLE 2: Fitting Coefficients in Eq 5 for the Calculated Translational Energy Distributions coeff al ((kcal/mol)-2) a2 (kcal/mol) a3 ((kcal/mol)-2) potentials 0.013 8264 48.598 [‘A”(zu*);’/$ 0.013 828 0.057 3985 57.1092 [1A”(na*);3/21” 0.005 529 11 0.176 399 [3A’(na*);3/2p 68.7577 0.010 2733 0.021 04 s2 33.8235 0.020 7673 42.5125 0.014 5308 s1 0.014 1327 52.1511 0.009 6848 s3 0.009 504 83
The notation [lA”(na*)~J refers to the excited-stateC-Br potential involved in the dissociation to vinyl radicals i- Br(zP,) atoms. a
+
with energy in the range E to E dE. The resulting coefficients for P~[’A”(nu*);~/2] and all other distributions are given in Table 2. The fitted data are shown by the dashed curves in Figure 3. The solid squares in the figure are the results calculated from the measured TOF data obtained in the molecular beam photolysis experiments.2 The solid curve is a cubic spline fit to the points. A comparison of the calculated and measured distributions of C2H3-Br relative translational energies suggests that the [A’A”(n0*);~/21 and [AIA”(nu*);l/~lpotentials are the most important surfaces in the dissociation process. However, it is apparent that the calculations predict that too much energy will be partitioned into relative translational motion of the products. This indicates that the excited-state potentials obtained from the GVB-CI calculationsg are too repulsive. Since variational calculations9 yield upper limits to the true energies, such results are not unexpected. This is particularly true since the &A ground-state potential employed in the calculationsis taken from the analytic ground-state vinyl bromide surface6 which is fitted to experimental data. Consequently, it lies below the results obtained in the SCF-CI and GVB-CI calculation^,^ which constitute an upper bound to this potential. The difference can be clearly seen by comparing the data shown in Figures 1 and 2A. At the C-Br equilibrium distance (1.89 A), the XIA ground-state energy obtained in the ab initio calculationsg lies 8.1 kcdmol above the experimental result. In addition, we expect the accuracy for the excited-state A’Afr and S3A’ potentials to be less than that for the ground state. In addition to the predicted energies being too large, the full widths at half-maximum (fwhm) for the calculated distributions are much smaller than the experimental result.2 It is possible that this disagreement is also due to inaccuracies in the electronic structure calculation^.^ Another possibility, however, is that C-Br bond fission does not occur exclusively from a single excited surface. This is suggested by the facts that the excited-state potentials shown in Figure 1 lie very close together with four of the states being energetically accessible upon excitation by a 193-nm photon and by the asymmetric shape of the measured relative translational energy distribution.2 A comparison of the peak position of the translational energy distribution obtained on the [A’A”(n0*);~/21 surface with the experimental peak maximum suggests that the GVB-CI potent i a l ~are~ to repulsive at C-Br separations around the equilibrium value by about 16 kcal/mol. The difference between the calculatedg and fitted6ground-state potentials accounts for about 8.1 kcal/mol of this amount. The remaining 8 kcaYmol is probably due primarily to the upper bound nature of the SCFCI and GVB-CI result^.^ To test this hypothesis, we have generated hypothetical potentials by using eq 2 for the [AIA”(n ~ * ) ; ~ / 2[A ] , * A”( no*);l/2] and [E3A‘(nu*);3/2] surfaces which are less repulsive in the equilibrium region by this amount. These potentials are shown in Figure 2c as S1, S2, and S3, respectively.
1.01 A
2c
0.8-
3
5
-Ee -5
O””.
0.4 -
0.2-
0.0
-
-_ 1 10
20
30
40
50
60
70
Relative Trans. Energy (kcal/mol) Figure 4. Relative translational energy distributions resulting from Br atom dissociation to form Br(2P3n) + C2H3 or Br(2Pln) CzH3. The solid squares are the experimental data taken from ref 2. The associated curve is a cubic spline fit. The trajectory results obtained by using the empirical potential surfaces are shown by the points @,A,.). The dashed curves are the fitted results from eq 5 using the coefficients given in Table 2. (0)S2 surface; (A)S1 surface; (0)S3 surface.
+
The relative translational energy distributions resulting from dissociation on surfaces S1, S2, and S3 were obtained by the computation of 500 trajectories on each surface. The results are shown in Figure 4. Again, the scaled trajectory data are shown by the points while the dashed curves are least-squares fits of eq 5 . Comparison with the experimental distribution2 supports the conjecture that the GVB-CI potentials9 are too repulsive by approximately 16 kcdmol in the region of the C-Br equilibrium distance. However, the computed fwhm for each distribution is still significantly less than the measured result., The results shown in Figures 3 and 4 indicate that Br dissociation is occurring from at least two excited potential energy surfaces rather than from a single surface. The asymmetric form of the measured distribution also suggests that the result is a weighted sum of distributions from different excitedstate surfaces. If this hypothesis is correct, the measured translational energy distribution should be a composite of PE[1A”(na*);1/2],P~[’A”(na*);~/2], and P~[~A’(nu*);~/2]. That is, we should have Pdexpt) = ClPE[’A”(no*);’/,1
+ C2PE[’A”(rco*);3/21+ C3PE[1A’(no*);3/2] (6)
where C1, C2, and C3 are fitting coefficients to Pdexpt). A leastsquares fit yields C1 = 0.669 051, CZ= 0.724 177, and C3 = 0.262473. Figure 5 shows a comparison of the computed composite translationalenergy distribution with the experimental result.2 Considering the approximate nature of the excited-state potentials, the agreement is reasonably good. The composite peak position is near that obtained from the measured TOF spectrum,2 and the computed fwhm is only sightly less than the measured result. The values of C1, Cz, and C3 required to fit the experimental translational energy distributionindicate that the ratio of Br(2P3n) to Br(2P1/2)product is 1.47. Thus, approximately 60% of the bromine atoms are formed in the ground spin state. This result is close to that which would be predicted if the process were statistical. The ratio of available spin states for Br(2P3n)to that for Br(2P1/2) is [2(3/2) 1]/[2(’/2) l)] = 2.00. If this were the sole factor governing the product ratio, we would expect 67% of the bromine atoms to be formed in the 2P3n state. It
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Mains et al.
3538 J. Phys. Chem., Vol. 99, No. 11, 1995
+
h
cn
C
I-
e
0.8 l * O l 0.6 0.4
trajectory results with the measured2 Br/HBr ratio of 1.28, we have determined that the internal conversion probability lies in the range 0.44-0.64. The calculated translational energy distributions for CzH3 Br(2Pln) products formed upon dissociation from the [AIA”(m*);’/2] surface is peaked at a translational energy that is about 7 kcdmol higher than the position of the experimental maximum.2 The calculated maxima for the distributions obtained on the [A1A”(m7*);3/2]and the [EA’(n~*);~/21 surfaces are 16 and 27 kcdmol higher than the experimental result,2 respectively. These results indicate that the excited-state potentials obtained from the GVB-CI calculations9 are too repulsive. When the [A’A’’(m~*);~/21,[A’A”(nu*); %I, and [E3A’(na*);3/2] potentials are replaced with less repulsive, empirical potentials, the peak positions of the calculated translational energy distributions are in much better accord with experiment.2 In all cases, the computed fwhm is much smaller than that obtained in the photolysis experirnenh2 It is therefore concluded that C-Br bond fission from several excited-state surfaces is being observed in the beam measuremenk2 The asymmetric shape of the measured translational energy distribution also suggests that this is the case. A least-squares fit of the computed translational energy distributions for the S1, S2, and S3 surfaces is found to yield good agreement with the measured result.2 The values of the fitting coefficients indicate that approximately 60% of the bromine product is formed in the 2P3/2 state, which is close to the statistical result (67%) obtained from the number of available spin states of Br(2P1n) and Br(2P3/2). It therefore appears that statistical factors play a role in the process provided we assume that non-adiabatic effects are unimportant.
1
1
ol 0.0
10
20
30
40
50
60
70
Relative Trans. Energy (kcal/mol) Figure 5. Composite translational energy distribution [- -1 obtained by fitting the distributions computed on the S1, S2, and S3 surfaces taken from ref (see Figure 4) to the experimental distribution [-.I 2. The associated curve is a cubic spline fit. The least-squares coefficients from eq 6 are given in the text.
should be borne in mind that the present calculations assume adiabaticity. That is, surface crossing from the [E3A’;3/2] potential to the [A1A”;l/2] surface is ignored. While we might expect the probability of such crossings to be small due to the difference in spin states, their presence would result in a Br(2P3~) to Br(2P1/2)product ratio shifted toward unity and, hence, less statistical. If such non-adiabatic effects are negligible, the present calculations suggest that formation of Br(2P3/2) and Br(2Pln) in the photolysis of vinyl bromide is primarily a statistical process.
IV. Summary The decomposition dynamics of vinyl bromide upon singlephoton excitation at 193 nm have been invesitgated by using classical trajectory methods on adiabatic excited-state potentials that have been obtained by using ab initio SCF-CI and GVBCI methodsg and the Gaussian 92 system of program^.^ Three empirical excited-state potentials are also employed in the dynamics calculations. The excited-state potential surfaces are represented by the global analytic potential previously developed6 with the C-Br bonding Morse-type potential replaced with one of the repulsive C-Br interactions obtained in the ab initio calculations9 or one of the empirical potentials. Energetic considerations suggest that the dissociation dynamics of vinyl bromide upon photolysis at 193 nm involves excitation to three or four repulsive C-Br states which include the AIA”(nu*), h3A”(m*), and E3A’(nu*) potentials. The molecular beam photolysis experiments reported by Wodtke et ~ 1 suggest . ~ that both Br(2P3/2)and Br(2P1/2) are formed in the dissociation process. Since the ab initio electronic structure calculations7 did not include spin-orbit coupling, we have developed a hypothetical potential leading to Br(2P1/2)products which has the correct asymptotic limits.This potential is utilized to investigate the expected dynamics when excited-state Br(2Pln) atoms are formed. The effect of a vertical excitation to the [‘A’’(n0*);~/21, [lA”(m*);l/2], and [3A’(na*);3/2] states have been determined by the computation of 300 or more trajectories in each case. The results show that the only products for any of these excitations are vinyl radicals and either Br(2P3/2) or Br(2P1/2) atoms. No HBr was observed. This result is consistent with the hypothesis advanced in our previous study of vinyl bromide dissociation on the ground-state surface? where we suggested that the HBr formed in the beam experiments2 is produced subsequent to internal conversion to the ground state. By combining the
Acknowledgment. We are pleased to acknowledge financial support from the National Science Foundation under Grant CHE-9211925 and from the Petroleum Research Foundation under Grant 25424-GB6. Financial support from the Halliburton Corp. in the form of a travel grant to G.J.M. to attend the Theoretical Symposium on Structural Chemistry, Austin, TX, is gratefully acknowledged. G.J.M. acknowledges a generous allocation of IBM 3090 CPU time at Oklahoma State University, a grant of time on the CRAY YMP at the National Center for Supercomputing Applications (NSCA), and time on the RS/ 6000 cluster at the Cornel1 Theory Center. We thank Professor Michl for correspondence regarding the excited electronic state surfaces for vinyl bromide. We are grateful to Professors Michl and Bonacic-Koutechy and to John Wiley & Sons for permission to reproduce Figure 1 from their book Electronic Aspects of Organic Photochemistry. References and Notes (1) Saito, K.; Yokubo, T.; Fuse, T.; Tahara,H.; Kondo, 0.;Higashihara, T.; Murakami, I. Bull. Chem. SOC.Jpn. 1979,52, 3501. (2) Wodtke, A. M.; Hintsa, E. J.; Somorjai, J.; Lee, Y.T. Isr. J . Chem. 1989,29,383. (3) Johnston, G. R.; Price, D. Dyn. Mass Spectrom. 1973,3, 183. (4) Abrash, S. A. Ph.D. dissertation, University of California at Berkeley, 1987. (5) Abrash, S. A.; McMahon, M. T.; Zehner, R. W. J . Phys. Chem. 1994,98, 11909. ( 6 ) Abrash, S. A.; Zehner, R. W.; Mains, G. J.; Raff, L. M. Theoretical Studies of the Thermal Gas-Phase Decomposition of Vinyl Bromide on the Ground-State Potential-Energy Surfaces. J . Phys. Chem., accepted for publication. (7) Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.; Wong, M. W.; Foreman, J. B.; Johnson,B. G.; Schlegel, H. B.; Robb, M. A,; Replogle, E. S,.; Gomperts, R.; A n h s , J. L.; Raghavachari, K.; Binkley, J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.;
Photolytic Decomposition of Vinyl Bromide Stewart, J. J. P.; Pople, J. A. Gaussian 92, Revision A; Gaussian, Inc.: Pittsburgh, 1992. (8) Huzinaga, S.; Andzelm, J.; Klobukowski, M.; Radzio-Andzelm, E.; Sakai, Y.; Tatewaki, H. Gaussian Basis Sets for Molecular Calculations; Elsevier: Amsterdam, 1984. (9) Michl, J.; Bonacic-Koutecky, V. Electronic Aspecrs of Organic Photochemistry; Wiley: New York, Chichester, Brisbane, Toronto, Singapore, 1990; p 385.
J. Phys. Chem., Vol. 99, No. 11, 1995 3539 (10) Raff, L. M.; Thompson, D. L. The Classical Trajectory Approach to Reactive Scattering. In Theory of Chemical Reaction Dynamics; Baer, M., Ed.; CRC Press: Boca Raton, FL,1985; Vol. III, p 1. (11) Raff,L. M. J. Chem. Phys. 1989,90, 6313. (12) Raff, L. M.J. Chem. Phys. 1991, 95, 8901. (13) Raff, L. M. J. Chem. Phys. 1988,89, 5680.
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