5782
J . Phys. Chem. 1987, 91, 5782-5788
The Question of Enhancement of Bimolecular Reaction Rates by Selective Internal Excitation of Reactants in Polyatomic Systems I. Oref* Department of Chemistry, Technion-Israel Institute of Technology, Haija 32000, Israel
and B. S . Rabinovitch* Department of Chemistry BG- 10, University of Washington, Seattle, Washington 981 95 (Received: April 16, 1987)
A computational study is reported on the feasibility of enhancement of the rates of bimolecular reactions via vibrational excitation of the reactants. Butadiene and cyclohexadiene reactions with excited HC1 and excited butadiene and acetylene reactions with HC1 were investigated. It was found that rate enhancement is not feasible due to inefficient utilization of the excitation energy and competing efficient inelastic collisions which cause energy depletion in the reactants.
Introduction C-H local-mode laser intracavity excitation to higher vibrational levels of the ground electronic state manifold can produce a nearly monoenergetic population of molecules with high internal energ i e ~ . ’ - ~This method has been applied to investigate the effect of internal excitation of diatomic or polyatomic reactants in bimolecular reaction^.^,^ The immediate objective has been to ascertain whether reactive enhancement occurs upon selectively exciting the vibrational level of one of the species. One wishes also to learn and understand the nature of the dynamics.6 Put otherwise, where and when does it pay to invest vibrational energy. For the atom-diatomic case the answer is qualitatively known and depends on the potential energy surface features. An early barrier calls for translational excitation while for a late barrier case vibrational excitation does the most good. For polyatomic reactant systems, the question is more complicated. The addition of HCl to olefins has provided a suitable subject. Herman and Marlings (HM) studied the reaction of hydrogen halides with unsaturated hydrocarbons: 1,3-butanediene HCl* 1-chloro-2-butene
+
-
-+ +
3-chloro-1-butene 3-chlorocyclohexene 1,3 cyclohexadiene HCl* CzHz*
HC1-
CZH3Cl
(The asterisk signifies a vibrationally excited species.) No enhancement of reaction occurred when one reactant was prepared in a high vibrational state ( v = 5, 6). Klenerman and Zare4 (KZ) studied the reaction between HC1 and excited 1,3butadiene: 1,3-butadiene* + HCl 1-chloro-2-butene (6-center complex (6c))
-
-
3-chloro-1-butene (4-center complex (4c))
It seems reasonable’ in this case to assume that internal relaxation of the excited butadiene occurs before a collision with HC1, at the pressures (atm) employed. No enhancement due to C-H excitation ( u = 5) was observed. In the following we investigate the problem by examining various models for bimolecular reactions. We calculate the time (1) Chandler, D.W.; Farneth, W. E.; Zare, R. N. J . Chem. Phys. 1982, 77, 4441. (2) Jasinski, J. M.; Frisoli, J. K.; Moore, C. B. J . Phys. Chem. 1983, 87,
2209, 3826. (3) Reddy, K.V.;Berry, M. J. Chem. Phys. Lett. 1979, 66, 223. (4)Klenerman, D.;Zare, R. N. Chem. Phys. Lett. 1986, 130, 190. (5) Herman, I. P.; Marling, J. B. J . Chem. Phys. 1979, 71, 643. (6)(a) Polanyi, J. C.; Wong, W. H. J . Chem. Phys. 1969, 51, 1439. (b) Wolfrum, J. J. Phys. Chem. 1986, 90, 375. (7) Oref, I.; Rabinovitch, B. S. Acc. Chem. Res. 1979, 12, 166.
scales for some relevant processes that take place. Detailed trajectory calculations are impractical because of the uncertain nature and complexity of the potential surfaces involved in such reactions.
Rationale of the Computational Approach and Reaction Models Zmplusiue Collisions. If it is assumed that impulsive collisions are a prerequisite for a successful bimolecular addition reaction, it is required that the requisite energy should have already concentrated in the moiety which is involved directly in the formation of the reaction complex. The probability of the energy being in a moiety associated with the reaction site is P = p(E)(moiety)/p(E)(molecule)
As an example, consider the 4-center butadiene*-HC1 reaction. Here we have used only the frequencies associated with the reaction site HCl + C = C . We have used the following frequencies (cm-I): 1630 C=C stretch; 1438 CH2 scission; 1280 C H bend; 894 CH2 rock; 512 CCC deformation; 908 CH2 wag; and 522 CHI twist. The frequencies differ from the moiety of the long-lived complex discussed later on (and given in Table VI) by the fact that the impulsive model does not have transition modes which contribute significantly to the density of states. The probability of having energy of 12900 cm-’ (threshold energy internal thermal energy) in this moiety of the above complex is -2.0 X lo-”. Thus if one assumes an impulsive collision during which reaction takes place, the probability of finding the above energy in the “interesting” part is exceedingly small. Long-Lived Complex. More plausible are models wherein reaction proceeds via formation of a collision complex. In this case, energy redistribution can occur during the collision lifetime and the probability for successful reaction is enhanced. Bimolecular reaction may be assumed to take place in two steps. In the first, a collision complex is formed; in the second, a reactive complex (suitably energized configuration) is formed which results in chemical transformation. The question which underlies the possibility of reaction enhancement is the question of how the reactive lifetimes of the collision complex compare with the collision complex lifetime leading to collisional deactivation. This principle of the model is based on experimental results on intermolecular energy-transfer studies as well as on computational models.*-I’ The attractive forces result in a collision complex wherein three translation and two overall rotations are transformed into bending and stretching transition modes. In the intramolecular energy-transfer models it is assumed that during the
+
(8) Safron, S. A.; Weinstein, N. D.; Herschbach, D. R.; Tully,J. C. Chem. Phys. Lett. 1972, 12, 564. (9) Lin, Y.N.;Rabinovitch, B. S. J . Phys. Chem. 1970, 7 4 , 3151. (10) Oref, I. J . Chem. Phys. 1981, 75, 131. (11) Oref, I.; Rabinovitch, B. S. Chem. Phys. 1977, 26, 385.
0022-3654/87/2091-5782$01.50/0 0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 22, 1987 5783
Enhancement of Bimolecular Reaction Rates SCHEME I
diatomic, A excitation
polyatomic, B excitation
B % B*
+
-
A B* A.B* A*B* AB' A.B' A.B* AB' AB* AB* + M - A B + M A*B' A+B B* + M - B + M +
-
+
ALA*
photoexcitation collision complex formation, k,,,, isomerization activated complex formation, k,,,, dissociation activated complex formation, kdlss excited product formation, k+ product stabilization, k,,,,' deactivation, kdcact+ deactivation of photoexcited species, k,,,,"
(estimated) 1-50-ps lifetime of the collision complex energy redistribution can occur, subject to angular momentum constraints. This model accounts satisfactorily for the fact that significant amounts of energy can be transferred between a highly excited polyatomic molecule and a suitable bath gas collider. Unlike the collision complex, the reaction complex depends on the intimate detail of the potential surface which, for polyatomic molecule reactions such as the present ones, are largely unknown. Using conventional wisdom, one can choose between an early attractive barrier or a late repulsive barrier. Successful reaction events, in the case of an early barrier, are favored by initial translational excitation,6 which is not the case in point and will not be discussed further. The reverse reaction to bimolecular association is unimolecular decomposition and detailed balance enables the calculation of the bimolecular rate coefficient from the unimolecular ones4 A late barrier in the bimolecular direction signifies vibrational excitation of the reverse, unimolecular decomposition products. This has indeed been found to be the case in several studies. l2-I7 Berry1* has estimated that, for 4-center dehydrochlorination, more than the statistical share is in HCl excitation. This conclusion was shared by Quick and Wittig', and by West et al.15 In another study, Lee et al.I7 found that only 20%of the available energy for the decomposition of chlorcethane goes into translation. As sparse as the data is for the 4c elimination it is nonexistent for a 6c elimination. We proceed by assuming a late barrier and exploring the consequences of this assumption.
Computational Details Next we discuss the general features of the calculations followed by detailed case studies. Consider the reaction scheme in Scheme I and the schematic potential energy profile of Figure 1. In Scheme I * indicates an excited molecule and an activated complex and k,, and kdWare the energy-dependent RRKM rate coefficients; A.B* and A*-B are collision complexes; AB+ is the isomerization activated complex (or its unimolecular dissociation reverse); A-B+ is the dissociation activated complex. Isomerization indicates product formation via bimolecular reaction and dissociation means a breakdown of the collision complex to the original reactants accompanied by deactivation of A* or B*. Either A or B may be vibrationally excited when the collision complex A-B is formed. Back reactions, k d m , signifies vibrational energy transfer involving an average ( A E ) of magnitude estimatedls to be in the range 0.5-10 kcal mol-I; energy is retained largely in the original partner site. Energy transfer is a highprobability process: but (&) is much less than the forward for kisomwhich signifies lower probability of a barrier Eo,eom successful addition reaction event to form AB; roughly speaking, the latter requires energy relaxation within A*.B or A-B* in amount of approximate magnitude Eo,imm. In order to make a quantitative evaluation, we proceed by estimating the relative magnitudes of the competitive unimolecular rate processes. For example, for polyatomic excitation we calculate kB*imm/kB*d,m. In both cases the activated complexes involve all
+
(12)Berry, M.J. J . Chem. Phys. 1976, 61, 3114. (13)Bauer, S. H.Chem. Rev. 1978, 78, 147. (14)Quick, C.E.;Wittig, C. Chem. Phys. 1978, 32, 75. (15) West, G.A.; Weston, R. E.; Flynn, G. W. Chem. Phys. 1978,35,2?5. (16)Polanyi, J. C.Acc. Chem. Res. 1972,5, 161. (17) Sudbo, Aa. S.; Schulz, P. A.; Shen, Y. R.; Lee, Y. T. J . Chem. Phys. 197a,69,2312. (18) Tardy, D.C.;Rabinovitch, B. S.Chem. Reu. 1977, 77, 369.
+
A* B A**B A**B AB' A**B A'.B AB* AB' AB + M AB* + M A+*B A + B A* + M - A + M +
-- -+
-
\I
A.-B*
-
\jE0 AB
Figure 1. Potential energy diagram of collision complex A.B*. A-B' and ABt are the activated complexes for dissociation and isomerization of the collision complex. eo is the well depth, Eois the bimolecular threshold energy for reaction, and AE, is the exoergicity of the products, AB. * indicates molecular and + indicates activated complex excitations.
frequencies of A.B* and of A-B'h and A.B+-. The calculational procedure for the rate coefficient for the "isomerization" of the collision complex khm to give the bimolecular reaction products was as follows: RRKM calculations were performed for the unimolecular decomposition of the bimolecular reaction product. Its activation complex parameters thus established (Table VI) were used without changes as the parameters of the isomerization activated complex. The details of the calculation are given below. The rate of dissociation of the collision complex was calculated by the RRKM procedure. Varying values of the well depth to (which is equivalent to the threshold energy for dissociation), available energies, and kdiss are given later on. In all cases the calculated dissociative lifetimes of the collision complex were orders of magnitude shorter than the reactive ones. In principle, there is a difference between deactivation of an excited polyatomic by HC1 and deactivation of an excited HC1 by polyatomic molecules. There are no experimental studies on the deactivation of HCl (u = 5,6) by polyatomic molecules. Zittel and Moore2s studied the deactivation of HC1 (u = 1) by CH, and found the rate coefficient to be 105/Torr s compared with gas kinetic cross section of 107/Torr s. The dipole-dipole relaxation by butadiene and other polyatomic molecules discussed in the present paper is much more efficient. Herman and Marling have considered the gas kinetic cross section to be realistic for the deactivation of the highly excited ( u = 5 , 6) HCl. In agreement with the above we have assumed kA'diss kB*dasin the present calculations. As mentioned before the RRKM calculations of kdlssdescribe the breakdown of the long-lived collision complex. Since it is a low-energy barrier one could use an alternative phase space or adiabatic channel model. Neither of the two models will alter significantly the conclusions discussed below. It should also be pointed out that repeated collisions will not change the sense of our conclusions. It is well established from other work7 that the initial chemical reaction activation event need not deposit reaction energy in the whole product molecule. The significant difference between diatomic excitation and polyatomic excitation discussed above is that the former is directly involved in the nascent moiety of A-B
-
5184
The Journal of Physical Chemistry, Vol. 91, No. 22, 1987
TABLE I: Energetics, Vibrational Temperature, and Number of Modes of the Reactant Polyatomics and Collision Complexes Ehv,
EintcmalP
EtotaI,
kcal/mol kcal/mol kcal/mol 40 38.6 44.6 45.1
C4H6* C2H2* C6H8*
+ HCI + HCI* C4H6 + HC1* moiety C2H2* + HCI C6H8 + HC1* C&* C4H6
41.18 38.92 44.92 46.61
1.18 0.32 0.32 1.51 3 3 3 3 3 2.1 2.1 3.3
43 41.3 48.1 41.3 48.1 40.7 46.8 48.4
Ea:
K s 1635 24 3783 7 4232 7 1362 36
s** 12 5 5.4 17
1343 1308 1448 2032 2306 2375 2640 1260
16 16 16 IO IO 9 9 19
30 30 30 13' 13 12 12 42
"Eintcrnal includes thermal energy, 1.2 kcal/mol of relative translational energy, and 0.6 kcal/mol of rotational energy. bActivemodes s* = EtOtaI/RTVib, 'The number of active modes in the moiety directly related to the collision center used in the calculations. TABLE II: Vibrational Modes (cm-I) of 1,3-Butadiene and the Average Enerev in Each Mode (kcal/mol)" ~~~
3087 1280 908 770 1381 3008
(E) 0.6257 1.7572 2.1236 2.2733 1.667 0.6569
a 1196 522 3101 1294 2992 894
(E) 1.8353 2.5614 0.6203 1.7444 0.6634 2.1385
a 162 3055 990 1630 512 976
(E) 3.0246 0.6382 2.0383 1.4591 2.5735 2.0527
TABLE III: Activation Energy, Total Energy, and ki,, Isomerization of the Collision Complex
Tvib*
Collision Complex 40 38.3 45.1 38.3 45.1 38.6 44.6 45.1
Oref and Rabinovitch
2984 301 1438 1013 912 1596
(E) 0.6666 2.8394 1.6172 2.0148 2.1194 1.4862
kcal/mol C4H6* + HC1 (4C) C4H6+ HC1* (4c)
33
C4H6* + HC1 ( 6 ~ ) C4H6 + HC1* ( 6 ~ )
29
ClH2* + HC1
36.4
C6Hs + HCI* 3CI 4C1
23.4 23.4
Vibrational Temperature of Reactants and Collision Complexes In each of the cases menti~ned?~ the total energy of the system was well above the barrier height for reaction. Since the energy and normal modes of the excited reactant molecules are known it is possible to calculate a vibrational temperature, Tvib,by iterating the quantum statistical expression (Evib) = -R d(ln & d / d T ' as well as to calculate the average content of each of the various vibrational modes. Table I shows the energetics of the various reactions, the vibrational temperatures, and the effective number of modes of the various species. For example, butadiene* at an excitation energy of 40 kcal/mol has a high TvIbof 1636 K, but the energy in the various individual modes is rather low as can be seen from Table 11; the number of effective modes, given by s* = (E)/RT,ib, is s* 12.7. Even at the high vibrational temperature, this number is only half the total number (24) of vibrational modes of the molecule. For the 1-chloro-2-butene molecule, with much higher average energy content and TYlb= 1693 K, s* is only -17, as compared with 30 molecular modes. Obviously even these high energy contents of the molecules do not signify classical behavior involving the full number of modes of the molecule. When the activation reaction, C4H6+ HC1*, was considered with the total initial vibrational energy localized in a nascent moiety having 13 vibrational modes, directly related to the reaction center, s* for the moiety was found to be 10-not much different from the C2H2*+ HC1 case, for which s* = 9. This is to be expected since the latter corresponds crudely to the moiety of the former. This similarity of results manifests itself below in the values of the various coefficients. It seems that even though the reactant moecule possesses enough energy to cross the barrier,
-
-
Eiotal,b
kcal/mol kimm(E), s-l 43 41.3 48.1 43 41.3 48.1 40.7 46.8
1.4 X 7.0 X 1.0 x 1.8 x 9.0 X 6.0 X 5.7 x 5.9 x
48.4 48.4
2.5 X IO4 3.0 X lo4
kisem(E)
(moiety),'
s-I
10' lo2 104 103
6.0 X lo4 5.5 x 105
lo2 10'
1.5 X lo4 8.3 X IO4
104 105
'Activation energy for bimolecular reaction, ref 4 and 5 . = Ehu + Einternal + Erotalional + Etranalational~ 'See Table I for the number of modes in the moiety. E indicates EtOtal.
TABLE IV: Well Depth, Energy in Transition Modes, and kdi,(E) for the Dissociation of the Collision Complex €0,' kcal/mol kcal/mol kdiss(Ediss),SKI C4H6 HC1 1 4.4 1.5 X 10l2 2.1 4.3 1.1 x 10" 2.7 5.0 1.0 x 1011 1.5 X IO" C2H2 + HCI 2.1 4.3 C6H8 + HCI 2.1 4.3 7.6 X IO'O "eo
is the well depth of the collision complex.
TABLE V Energetics, Frequency Factors, and Rate Coefficients for Reverse Unimolecular Decomposition of the Excited Product Ea?
"Total energy content of 41.2 kcal/mol and vibrational temperature of 1636 K. that includes those vibrational modes most directly associated with the reaction coordinate for isomerization. The effective molecule is thus much smaller and kiwiom should be relatively enhanced. Calculations of this type were done as well and are discussed below.
for the
A E o , ~ Etotai,'
kcall kcal/
kcal/
mol
mol 55.6 57.3 62.3 54.9 56.6 61.6 67.8 73.9
kuni(E),s-' A , s-' 2.5 X IO5 13.3d 3.9 x 105 2.6 X IO6 5.5 X IO5 12d 7.5 x 105 3.3 X IO6 e 3.2 X IO6
13.g
63.1 63.1
2.0 X IO5 4.0 X IO'
13.39 13.29
CH2=CHCHC1-CH3*
mol 42.6
14.2
CH2CICH=CHCH3*
38.3
13.5
C2H3CI*
73.3
27.1
C6H&1* 3C1 4CI
42.6 48.4
14.7 14.7
1%
"Activation energy. bExoergicity (see Figure 1). ' ~ t , t a l = Ehv + Eintcrnsl E,,, + E,,,,, AE,. dReferences 4, 21, 22. eTotal energy below E,. fReference 23. gSee text and ref 24.
+
+
the modes associated with the reaction coordinate, whose energies count most significantly, possess only a fraction of the energy needed to cross the barrier.
Case Studies Specific case studies of polyatomic and diatomic excitation in bimolecular reactions are discussed below. Details and results of the calculations are given in Tables 111-V and Table VI. The butadiene-HC1 system is the most extensively explored case. Six possibilities may be distinguished and they are listed in the following sections. A B*. Butadiene*-HCI; 4c Complex. We first assume that excited butadiene and HCI form CH,=CHCHCICH, via a 4centered, 4c, reaction complex. All the modes of the collision complex and isomerization and dissociation activated complexes (Table VI) are involved in the calculations of the rate coefficients kdiSand kisom(Tables I11 and IV). The value of kiWmis obtained by first calculating of the reverse unimolecular decomposition of 3-chloro- 1-butene. Its frequencies are estimated from butadieneigand chloroethane20 frequencies and are given in Table VI. In the isomerization activated complex AB' the 2946-cm-' CH
+
(19) Mui, P. W.; Grunwald, E. J . Am. Chem. SOC.1982, 104, 6562. (20) Shimanouchi, T. "Tables of Molecular Vibrational Frequencies"; NSRDS-NBS 39, 1972.
The Journal of Physical Chemistry, Vol. 91, No. 22, 1987
Enhancement of Bimolecular Reaction Rates
asymmetric stretch is taken as the reaction coordinate. The 666-cm-' C-CI stretch is reduced to 300 cm-', and the 8 16-cm-I C-C stretch is changed to 1200 cm-' as the double bond character increases. One of the C H 3 deformations is reduced from 1385 to 900 cm-' and the C-C-Cl bend is reduced from 256 to 130 cm-' since they are involved in the 4c stretched activated complex. Finally, the CHCl twist at 400 cm-' is increased to 1400 cm-' to take care of the increased character of the HCl bond in the activated complex. In addition there were minor changes in rocking, bending, and twisting. The frequencies thus chosen, all listed in Table VI, gave the experimental value of the frequency factor log 13.3 found by Thomasz' and Harding et a1.22 The collision complex A.B* which undergoes the isomerization is the "molecule" in the RRKM formulation of k,, and its frequencies are given in Table VI. The frequencies are composed of the unaltered butadiene frequencies and five transition modes (100 (3) cm-' and 50 (2) cm-I) correlating with the three translations and two rotations of the HCl molecule. The total internal energy of the collision complex (Table I) is found by adding the 40 kcal/mol of photon energy, 1.2 kcal/mol thermal energy, 1.2 kcal/mol of average translation, and 0.6 kcal/mol average rotational energies to a grand total of 43 kcal/mol. k,, (43 kcal/mol) is found to be 1.4 X lo3 s-l. kdlssis calculated by using the RRKM procedure with the molecular frequencies of the collision complex as discussed above for k,,,,. The barrier height to (Table IV) was varied from 1 to 2.7 kcal/mol as expected for a van der Waals complex. For the activated complex frequencies, one 100-cm-' transition mode is the reaction coordinate and one 100 cm-' is reduced to 50 cm-' allowing for greater looseness of the complex. The total energy in the transition modes (the internal modes associated with the van der Waals complex) moiety available for the dissociation of the collision complex, Ed,,,, was between 4.3 and 5.0 kcal/mol (Table IV). kdlssvaries between 1.0 X 10" and 1.5 X 10l2 s-I. The total energy in the transition modes is only a fraction of the total energy due to the conservation of total angular m o m e n t ~ m . ~ This limit on the "available" energy in the transition modes exremoved per collision between plains the low value of ( AE)down a highly excited molecule (sometimes over 100 kcal/mol) and a cold bath molecules. The value of Ed,=was chosen to be the same as ( h E d o w n ) . Finally, for a well depth of 1 kcal/mol and Edlss= 4.4 kcal/mol, the ratio kB*ISom/kB'dlss103/1012 For a well depth of 2.1 kcal/mol and energy in the transition modes of 4.4 kcal/mol kB*wm/kb'dlss 103/10" X lo-'. The large ratio of kdlssto k,,,, is due to the large differences in their activation energies. There can be no expectation of a detectable effect on the rate of reaction at any vibrational energy of butadiene in its ground electronic state. (It should be pointed out that larger values of internal energy in the transition modes will lead to even higher kdlssand thus make enhancement even less feasible.) A* B. Butadiene-HCl*; 4c Complex. If it were assumed that bimolecular reaction of butadiene and initially excited HCI involved total energy redistribution in the collision complex, then this case would not differ from the case A + B* discussed above. The frequencies of the molecule and activated complex are naturally the same (Table VI). The energetics are somewhat different: 41.3 kcal/mol and 48.1 kcal/mol total energy for excitation of the u = 5 and v = 6 levels yielding 7.0 X lo2 s-' and 1.0 X lo4 s-I for k,,,,, respectively. The values of kdlssdo not differ from the previous case; therefore kA*lsom/kA*dlss103/1012to 104/101' and again there can be no expectation for ento hancement of bimolecular reaction. A* B. Butadiene-HCI*; 4c Complex Moiety. Excitation of HCl can in principle be more productive than excitation of butadiene, since it can be argued that the HC1 energy is localized in a moiety which is involved with the reaction coordinate. This is not the case for the polyatomic excitation since energy distribution takes place on a picosecond time scale and therefore the whole molecule is automatically involved. To check this point
-
-
-
+
-
-
+
(21) Thomas, P . J . J . Chem. SOC. B 1967, 1238.
(22) Harding, C.J.; Maccoll, A,; Ross, R. A. J . Chem. SOC.B 1969, 634.
5785
we have assumed a moiety which includes only the modes associated with the 4c complex. The frequencies can be found in Table VI. They include those unmodified butadiene frequencies involved in the 4c complex: 1630-cm-' C=C stretch; 1438-cm-' CH3 and 5 12-cm-l C-C-C deformation; the 522-cm-' CH2 twist; 1013-cm-' C H bend; 301-cm-' C-C-C bend as well as the HCl stretch and five transition modes discussed before. The activated complex frequencies of the moiety are similar to some of those used in the calculation of k,,, discussed previously (Table VI). The 1630cm-' C=C stretch is reduced to 1200 cm-' to take care of the single-bond character in the activated complex. In addition the following frequencies were reduced: C-C1 bending to 130 cm-I; CH, deformation to 900 cm-I; C-Cl stretch to 300 cm-'. The CHCl twist was increased to 1400 cm-I to account for the formation of the HCl bond, while the 2886-cm-' stretch frequency was taken as the reaction coordinate. For activation energy5 of 33 kcal/mol and total internal energies of 41.3 and 48.1 kcal/mol, k,,,, equals 6.0 X lo4 and 5.5 X lo5 s-I, respectively (Table 111). kdlssdoes not change from its values in previous cases; therefore kA',,,/kA*dlss 105/10i2= to 105/101' = 10". Excitation of HC1 is thus more effective than is vibrational excitation of butadiene. At the highest energy that could be achieved, in principle, if not by present laser technology, i.e., at the HC1 100 kcal/mol-I, the ratio kA'lsom/kA*dlss dissociation level D 104-10-3, Le., a detectible effect might be just at the limiting edge of the best technique. A B*. Butadiene*-HCI; 6c Complex. The formation of 1-chloro-2-butene by HC1 addition via a 6-center complex, 6c, automatically involves most of the vibrational frequencies of the activated complex for product formation. The reaction complex is looser than the 4-center complex with a lower A factor22 (10l2 compared with Table V) and involves the skeletal modes of the whole molecule plus some C H and CH2 bending. The frequencies used in the calculation of k,,,, are all given in Table VI. The frequencies of the dissociation activated complex were chosen by calculating the frequency factor to agree with the value of 10l2reported in the literature.2z The major changes in 1-chloro-2-butene frequencies to form the activated complex are the following: 166 1-cm-' C=C stretch reduced to 1200 cm-' to account for the increase in single-bond character and C-C stretch at 894 cm-' increased to 1200 cm-' to account for increased double-bond character; C-CI stretch reduced from 746 to 300 cm-I; C=CI twist from 653 to 500 cm-I; C=C-C bend from 474 to 400 cm-I; C H wag from 998 to 700 cm-I; C H 2 (of the CHzCl group) twist from 1107 to 900 cm-'; CH, rock increased from 1051 to 1200 cm-I. The loose skeletal modes increased in frequency from 90 and 107 cm-I. A 1400-cm-' stretch was introduced to account for the increase H-CI bond character in the 6c complex. The reaction coordinate was the C H stretch as before. The "molecular" frequencies in the RRKM calculation of k,,,, are, in addition to the unaltered butadiene and HCI frequencies, all the collisional transition modes as discussed before in the butadiene*-HC1 4c complex case. kdlssis practically the same as for the 4c case and the same input numerical values are used (Table IV). The total energetics is almost the same as for the 4c case (Tables I, 111, and V). The major change being E, = 29 kcal/mol, the total internal energy is 43 kcal/mol and k,,,, = 1.8 X lo3 s-I. The ratio kB'l,m/kB*dlss 103/10'2 = and 103/101' = lo-* and as in the 4c case there can be no expectation of observing any enhancement of product formation. A* + B. Butadiene-HCI*; 6c Complex. Since there is total energy redistribution prior to reaction, this case is identical with the previous one in the details of the molecular and activated complex frequencies. The only differences is in total internal energy (Table 111) which is 41.3 and 48.3 kcal/mol for u = 5 and u = 6 excitation, respectively. k,,, (41.3 kcal/mol) = 9.0 X lo2 s-' and k,,,, (48.3 kcal/mol) = 5.5 X lo3 s-I. kA'lsam/kA*dlss 10-9-10-8 as for the butadiene excitation. This is to be expected since energy redistribution is faster than isomerization and the system does not distinguish between A or B excitation.
-
-
-
+
-
-
5786 The Journal of Physical Chemistry, Vol. 91, No. 22, 1987
Oref and Rabinovitch
TABLE VI: Frequencies and Degeneracies of Excited Molecule and Activated Complex 2-Chloro-3-butene Collision Complex Moiety Molecule 1630 I 1438 1 894 1 512 1 522 1 2886 1 IO0 3 50 2 1013 1 301 1 300 800
1 1
1400 1000
2 1
1200 700
1 1
Activated Complex for Isomerization 900 1 1000 1 130 2 900 1
2881 256 912 1294
1 1 I 1
400 3008 830 770
1 I 1 1
2-Chloro-3-butene Unimolecular Decomposition, AB Molecule 990 1 3101 I 3055 1 441 1 100 1 329 1 2946 1 666 1 2986 1 1081 1 974 1 162 1
3008 130 912 1294
1 1 1
2881 1000 770 990
1 1 1 1
2986 900 3101 1400
1 1 I 2
1
Activated Complex, AB' 300 1 1000 1 900 1 130 1 3055 1 2984 1 327 1
-
A
+B
2984 653 816 1385
1 1 1 1
1596 1280 1463
1 1 1
976 1381 875
1
800 1200 162
1 1 1
1596 1280 900
1 1 1
700 1381 653
1
1 3 1
162 1596 50
1
1
2
1438 976 1381
1
1
1
1
1
3008 512 770 990
1 1 1 1
2992 1013 3101 301
2-Chloro-3-butene Collision Complex, A.B* Molecule I 1630 1 2886 1 2984 1 522 1 1196 1 100 1 3055 1 908 1 1280 1
3008 130 912 1294
1 1 1 1
2881 1000 770 990
1 1 1 1
2986 900 3101 1400
Activated Complex for Isomerization, AB' 300 1 1000 1 800 900 I 130 1 1200 1 3055 I 2984 1 162 2 327 1
1 1 1
1596 1280 900
1 1 1
700 1381 653
1 1 1
3087 894 912 1294
1
3008 512 770 990
1
2992 1013 3101 301
Activated Complex for Dissociation, A.Bt 1630 1 2886 1 2984 1 522 1 1196 1 100 I 3055 1 908 1 1280 I
1 1 1
162 1596 50
1 1
3
1438 976 1381
1 1 1
1 3
301 50
2
1
811 90 1369
1 1 1
1051 746 998
1 1 1
1000 500
5 2
1200 400
2 I
900 700
1
2984 100 1280
1
3
1 1
1
162 1596 50
2
1438 976 1381
1 1 1
5 2
1200 400
2 I
900 700
1
3087 894 912 1294
1 1
I
1
1 1
1
1 1
I I
1
1630 3101
1 1
1438 770
1 1
894 1280
1-Chloro-2-butene Collision Complex Moiety Molecule 1 512 1 1596 1 894 1 1196 1 162 1 100
300 800
1 1
1400 1000
1
1369 700
1 1
2881 1319 932 653
1 1
2946 1449 250
1
1 1
2
4
3008 1302 875 474
1 1 1
2881 1369
2
1
1
Activated Complex for Isomerization 900 1 1200 2 400 1 250 1
1300 500
-
I-Chloro-2-butene Unimolecular Decomposition, AB A Molecule 2946 1 1661 1 2986 1 107 1294 1 1234 1 974 1 1449 3101 1 3055 1 2984 1 1107 301 1 286 1 800 2986
1
2
Activated Complex, ABt 900 1 300 1 1400 1 1300 4
1
1 1
1
1 1
+B 1 3
1
1
1-Chloro-2-butene Collision Complex, A.B*
3087 894 912 1294
1 1 1
2946 1449 250
1
1
2
3008 512 770 990
1 1 1
2881 1369
2
1
1
2992 1013 3101 301 800 2986
1 1 1 I
1630 522 3055
Molecule 2886 1196 I 908 1 1
1 1 1
Activated Complex for Isomerization, AB' 900 1 300 1 1000 2 1400 1 1300 4 500 1
1
3374 50
1 2
3287 100
1
3374 100
2
3287 1972
1
1
1
1
1972 612
2
C2H,CI Collision Complex, A.B* Molecule 730 2 100 1 2886 1
612 730
2 2
Activated Complex for Dissociation, A.B+ 2886 1 50 2
1
1
Enhancement of Bimolecular Reaction Rates
The Journal of Physical Chemistry, Vol. 91, No. 22, 1987
5787
TABLE V I (Continued) 3000 300
2 1
1100 1800
3 1
1000 700
1 1
Activated Complex for Isomerization, ABt 720 1 200 1
-
3121 395
1 1
3086 941
1 1
3000 300
2 1
1100 1800
3 1
1000 700
1 1
3-Chlorocyclohexene Collision Complex, A-B* Molecule 1 468 1 298 1 1040 1 1577 1 1444 1 559 1 1050 1 994 1 1330 1 2884 1 2834 1 945 1 1111 1
850 1435 925 100
1 1 1 3
1 1 1 1
1602 1016 2886 1243
1 1 1 1
850 1435 925 100
1 1 1 1
1 1 1 3
945 2834 1040 559
1 1 1 1
1243 850 1602 1016
1 1 1 1
1 1 4 1
2834 1040 559 1243
1 1 1 1
850 1602 1016 677
1 1 1 1
1 1 1 4
945 2834 1040 559
1 1 1 1
1243 850 1602 1016
1 1 1 1
1 1 1 1
1602 1016 2886 1243
1 1 1 1
850 1435 925 100
1 1 1 1
1400 1111 298 1330
1 1 1 3
945 2834 1040 559
1 1 1 1
1243 850 1602 1016
1 1 1 1
4-Chlorocyclohexene Unimolecular Decomposition, AB A Molecule 2838 1 800 1 468 t 1111 1150 1 1050 1 1444 1 298 201 1 336 1 994 1 1330 1178 1 1165 1 2884 1 945 658 1
+B 1 1 4 1
2834 1040 559 1243
1 1 1 1
850 1602 1016 677
1 1 1 1
1 1 1 3
945 2834 1040 559
1 1 1
1243 850 1602 1016
1 1 1 1
2 1 1 1
658 2838 1150 201 1165
3050 1223 753 1377 745
4 1 1 1 1
50 2939 1178 506 1178
3 1 1 1 1
658 2838 1150 201 1165
1 1 1 1 1
3050 1223 753 1435 925
5 1 1 1 1
1200 1178 506 1377 745
1 1 1 1 1
2838 1150 130 1178
2
2939 1178 506 1377 745
1 1 1 1 1
3050 1223 753 1435 925
5
1200 1178 506 1377 745
1 1 1 1 1
1 1 1 1
Activated Complex, ABt 720 1 200 1
1 1 1 1
50 2939 1178 506 1178
5 1 1 1 1
Activated Complex for Dissociation, A.B* 468 1 298 1 1040 1577 1 1444 1 559 1050 1 994 1 1330 2884 1 2834 1 945 1111 1
Activated Complex for Isomerization, AB' 658 1 1165 1 1400 1 900 1 468 1 1111 1 1050 1 1444 1 298 1 400 1 994 1 1330
-
3-Chlorocyclohexene Unimolecular Decomposition, AB A Molecule 2838 1 1577 1 468 1 1111 1150 1 1050 1 1444 1 298 201 1 336 1 994 1 1330 1178 1 1165 1 2884 1 945 658 1 2838 1150 201 1178
2 1 1 1
Activated Complex, AB+ 658 1 1165 1 1577 1 468 1 1050 1 1444 1 400 1 994 1
1400 1111 298 1330
3050 1223 753 1377 745
4 1 1 1 1
50 2939 1178 506 1178
3 1 1 1 1
658 100 2838 1150 201
4-Chlorocyclohexene Collision Complex, A.B* Molecule 1 1165 1 1111 I 1040 1 468 1 298 1 559 1 1577 1 1444 1 1330 1 1050 1 994 1 945 1 2884 1 2834 1
3050 1223 753 1435 925
5 1 1 1 1
1200 1178 506 1377 745
1 1 1 1 1
2838 1150 201 1178
2 1 1 1
3050 1223 753 1435 925
5 1 1 1 1
2939 1178 506 1377 745
1 1 1 1 1
3050 1223 753 1435 925
5
1200 1178 506 1377 745
1
1 1 1 1
1 1 1 1
1 1
1602 1016 2886 1243
4 1 1 1 1
3050 1223 753 1435 925
1279 1030
1 1 1
3050 1223 753 1377 745
1
A
+B
C,H,Cl Unimolecular Decomposition, AB Molecule 3030 1 1608 1 1369 1 896 1 620 1 720 1
2838 1150 201 1178
2 1 1 1
Activated Complex for Isomerization, AB+ 658 1 1165 1 400 1 468 1 1050 1 1444 1 400 1 994 1
Activated Complex, AB+ 658 1 1165 1 400 1 468 1 1050 1 1444 1 400 1 994 1
-
1400 1111 298 1330
1
+B
1
5788
Oref and Rabinovitch
The Journal of Physical Chemistry, Vol. 91, No. 22, 1987
+
A* B. Butadiene-HCl*; 6c Complex Moiety. The principle of nascent moiety applies only to the case of HCl excitation. As previously discussed, only in this case is the energy in the "proper" location. However, unlike the 4c case, the nonrandom moiety which is formed during the 1,4-addition of excited HCl involves all the skeletal modes of the butadiene molecule which are also associated with the activated complex (Table VI). The frequencies of the moiety are 3101-cm-' C H stretch, 1630- and 1596-cm-I C% stretch; CHI 1438-cm-I cis, 894-cm-I rock, 770-cm-l twist; C H 1280-cm-l bend and 91 2-cm-I wag; 5 12- and 301-cm-I C-C-C deformations, C-C 1196-cm-' stretch and 162-cm-' torsion. In addition there are five transition modes (100 (3) cm-I and 50 (2) cm-I). The frequencies of the activated complex are kept unchanged from the full 6c complex case discussed before. They are listed in Table VI. kbm (41.3 kcal/mol) = 1.4 X lo4 s-' and kiSm(48.1 kcal/mol) = 8.0 X lo4 s-l, Table 111. The values of kisomfor the collision complex and moiety of the 4c are larger than those of the 6c complex as expected (Table 111). The value of kisom(41.3 kcal/mol) is an exception and kisom4c € kisom6c since the 6c activation energy is lower and its low frequency factor does not affect it strongly yet. At slightly higher energies always kiWm4c to 10" which is an > kisom6c. Finally kA*isom/kAdiss improvement over the previous case but still below possible detection. CZH2* HCl. The case of excited acetylene reaction with unexcited HCl should be the ideal case for rate enhancement of bimolecular reaction since the energy is spread over a small number of normal modes. Indeed, this system should be similar to the moiety of the butadiene-HC1* 4c complex case. The method of calculations is similar to that discussed before at great length. The collision complex frequencies are given in Table VI. The two rotations and three translations of each of the two linear molecules are transformed in the complex to three overall rotations and three translations, thus leaving four transition modes in the complex. The normal modesZoof acetylene remain unchanged. The value of kdiSat a well depth of 2.1 kcal/mol and total energy of 4.3 kcal/mol in the transition modes is 1.5 X 10" s-I (Table IV). A weaker van der Waals complex or a larger fraction of the energy in the transition modes will give higher values of kdiss. The activated complex frequencies for the calculation of kisom are chosen such that the A factor agrees with the experimental value 0P3 10'3.8s-I. The major changes in the frequencies are the 1608-cm-I double-bond stretch which is changed to 1800 cm to account for the increase in the C-C triple-bond character. C H bend, CHI wag, and C-Cl stretch were reduced as discussed before. The molecular frequencies are those of the collision complex as discussed in the calculation of kda above. kiWm= 5.7 X lo4 s-l for u = 5 excitation (total energy 41 kcal/mol) and kbm = 5.9 X lo5 s-l for u = 6 excitation (total energy 47 kcal/mol) 4.0 X (Table 111). kB*isom/kB*dis 5.7 X 104/1.5 X 10" at 41 kcal/mol and 6.0 X 105/1.5 X 10" 4.0 X at 47 kcal/mol. These ratios are a 2 orders of magnitude improvement on the butadiene 4c and 6c complexes and similar to the butadiene-HCI* 4c complex moiety case, as expected. Thus no significant improvement may be further expected even in this seemingly "ideal" system for enhancement of bimolecular reaction via polyatomic excitation. Cyclohexadiene-HCl*. Cyclohexadiene resembles butadiene with its "hands tied behind its back" thus precluding formation
-
+
-
- -
(23) Cadman, P.;Engelbrecht, W.J. Chem. Commun. 1970,453.
of a 6c complex. We establish the activated complex frequencies used in the calculation of k,,, by calculating k,,, for the reverse unimolecular decomposition of chlorocyclohexene. 3-Chlorocyclohexene and 4-chlorocyclohexene are reported to decompose to cyclohexadiene and HC1 homogeneously and unimolecularly with Arrhenius rate coefficients 0p4 10" Z[exp(-36.950/R7')] s-I and lOI32[exp(-48.380/Rr)] s-I, respectively. The A factor for the 3-chlorocyclohexene is small compared to HCI elimination reactions of similar compound^.^^-^^ The A factor could not be reproduced by the RRKM calculations with any reasonable assumption of the activated complex frequencies. Therefore, the Arrhenius parameters were reestimated from the and E, = 42.6 raw data. The new parameters are A = kcal/mol, more in line with parameters for similar reaction^.^^-^^ The molecular and collision complex frequencies are given in Table VI. The major changes were 800-cm-' C-C stretch changed to 1200 cm-' to account for the increase in the double-bond character of the bond; 1330,677, and 201 cm-' reduced to 900, 400, and 130 cm-I as described before; 336-cm-I twist was increased to 1400 cm-' to take care of the increase character of the HCl bond; k,,,, (48.4 kcal/mol) = 2.5 X lo4 s-l, and for a well depth of 2.1 kcal/mol and total energy in the transition modes of 4.3 kcal/mol kdlss = 7.6 X 10" s-I. Finally, kA*.,,,/kA*dlSs = 2.5 X 104/7.6 X 10" 3X The molecular and activated complex frequencies of 4chlorocyclohexene decomposition are given in Table VI The major changes in forming the activated complex are C-Cl stretch reduced from 800 to 400 cm-I, C H bend changed from 1330 to 1400 cm-' to take care of the increased H-Cl character in the complex, and the 2939-cm-' C H stretch taken as the reaction coordinate. The value of k,, (48.4 kcal/mol) = 3.0 X lo4 (Table 111) and kdIss= 7.6 X 10" s-' (Table IV). kA'lsom/kA*d,rs= 3.0 X 104/7.6 X 1Olo 4.0 X low7and no enhancement should be expected for either the 3-chloro- or the 4-chlorocyclohexene addition products. Any decrease in the well depth or increase in the energy content of the transition modes will increase the value of kdlsssignificantly and thus reduce the ratio of k,,,, to kdlss.
-
-
Conclusions
The contribution of vibrational excitation to polyatomic and
HC1 bimolecular reactions rate enhancement was explored. Two cases, impulsive reactive collisions as well as long-lived reactive collision complexes, were investigated. No observable acceleration of the rate was indicated. Competition from inelastic "deactivating" collisions render the reactive outcome unlikely. Detailed studies of butadiene* + HCl, C2H2*+ HC1, butadiene + HC1*, and cyclohexadiene HC1* establish the above findings. The possibility that earlier workers KZ or H M failed to observe extra product formation simply because, being vibrationally excited, it decomposed promptly was considered; however at their pressures, collisional stabilization of the products would have occurred.
+
Acknowledgment. This work is supported in part by the USIsrael Binational Science Foundation and by the National Science Foundation. Registry NO. CHZ=CHCH=CHZ, 106-99-0; HCI, 7647-01-0;CZH2, 74-86-2; 1,3-cyclohexadiene, 592-57-4. (24) Holmes, J. L.;Dakubu, M . J . Chem. SOC.,Perkin Trans. 2 1972, 21 10. (25) Zittel, P.F.; Moore, C. B. J . Chem. Phys. 1973,58, 2004.
