J . Phys. Chem. 1988, 92, 51 11-5120
5111
Unimolecular Dissociation Dynamics of 1,P-Difluoroethane and of the C2H,-F, van der Waals Complex Lionel M. Raff* and Robert W. Graham Department of Chemistry, Oklahoma State University, Stillwater, Oklahoma 74078 (Received: December 18, 1987; In Final Form: March 15, 1988)
Unimolecular decomposition reactions of 1,2-difluoroethane are investigated over the energy range 6.0 Q E Q 9.0 eV by using classical trajectory methods, Metropolis sampling procedures, and a previously formulated potential-energy surface. Vibrational predissociation of C2H4-F2complexes on the same potential surface is also examined. The decompositionchannels for 1,2-difluoroethaneare, in order of importance,four-center HF elimination, C-C bond rupture, and hydrogen-atom dissociation. The kinetics are found to be first order and the microcanonical rate coefficients fit a simple RRK form. The high-pressure limiting rates for HF elimination and C-C bond rupture are 4.39 X 10l2 exp[-2.775 eV/RT] and 2.44 X l O I 3 exp[-3.925 eVIRT] s-', respectively. For four-center HF elimination, the average fraction of the total energy partitioned into translation, internal HF motion, and internal modes of CH2=CHF are found to lie in the ranges 0.13-0.16,0.09-0.13, and 0.71-0.74, respectively, independent of the total energy. The HF vibrational energy distributions are noninverted and contain an average of 6.6-9.2% of the total energy. Comparison of the present results with those for the bimolecular C2H4 + F2 reaction to form 1,2-difluoroethane as a reaction intermediate shows that the energy distribution in the collisional intermediate is not completely randomized during the lifetime of the intermediate. Vibrational predissociation (VP) rates for C2H4-F2complexes are found to be in the range (1-3) X 10l2s-l. Mode specific rate enhancement is found for excitation of the nonplanar CH2 rocking mode of C2H4. The calculated product yields, microcanonical rate coefficients, and energy-partitioning results are shown to be in generally good accord with experimental data. The comparison indicates that the potential barrier for the C2H4 + F2 FH2C-CH2F reaction predicted by the empirical surface is too large. The energy-partitioning data suggest that the transition state for four-center HF elimination on the present potential surface is too productlike. Comparison of the VP rates with measured lifetimes for (C2H4)2dimers indicates that the C2H4-F2complex has greater stability than that predicted by the empirical potential surface.
-
I. Introduction In previous papers,'S2 we have reported the development of a global potential-energy surface for the [C2H4+ F2] system and computational studies of the bimolecular reaction dynamics of this system. Most of the important reaction and decomposition channels for this system are open on the global surface described in ref 1. These include reactions R1-R12. The accuracy of the C2H4 + F2
-
-
[CH2F-CH2F]* F2
+ C2H4
[CH2F-CH2F]*
+
CH,=CHF
+ HF +F
CH2-CH2F
+ C2H4 CH2-CHZF C2H4 + F2 CH,=CHF + HF CH2-CH2F + F CH2F-CH2F F
---*
+
CH2F-CH2F CH2F-CH2F
CH2F-CH2F CH2=CH2
+ F2
CH2=CH2
-
+
CH2F-CH2F
+ 2F CH,=CHF + H + F CH2F-CHF + H
+
-
+
CH2F-CH2F
+ 2H
CHF=CHF CH2=CH
+
+ HF + F
CH2F + CH2F
surface is such that equilibrium structures, reaction endo- and exothermicities, fundamental vibration frequencies, and some measured activation energies are predicted with fair-to-excellent accuracy. The trajectory studies of the bimolecular collision dynamics for the [C2H4 + F2] system2 showed the major reaction products to be CH2-CH2F F. The secondary products are CH2=CHF + HF. 1,2-Difluoroethane is found as a reaction intermediate
+
( 1 ) Raff, L. M. J . Phys. Chem. 1987, 91, 3266. (2) Raff, L. M. J . Phys. Chem. 1988, 92, 141.
0022-365418812092-5111$01.50/0
leading to CH2=CHF + HF but its lifetime is always less than s. The reaction cross sections for these processes 2.55 X were found to be uniformly less than 5 A2 even for relative translational energies more than 1 eV in excess of the reaction threshold. Most of the reaction exothermicity for all reactions is partitioned into the internal modes of the polyatomic product. HF is usually formed in the v = 0, 1, or 2 vibrational state. The center-of-mass differential cross section for fluorine atom scattering in reaction R3 exhibits a strong backward component along with an isotropic component. The first of these arises from a direct rebound mechanism; the second is the result of complex formation. Formation of fluoroethylene is shown to occur via a complex mechanism involving formation of 1,2-difluoroethane as an intermediate. Thermal rate coefficients are obtained for both the major and minor reaction pathways. Some mode-specific rate enhancement for reaction R3 is observed but not for reaction R5. The above results are in good accord with the gas-phase measurements reported by Kapralova et aL3 and with the general observed behavior of fluorine addition to 01efins.~*~ They are also in excellent agreement with the molecular beam results recently reported by Grover, Lee, and Shobatake6 who examined the dynamics of the F2 C6Hs system. Their results showed the major reaction pathway to be
+
C6H6 + F2
-
CsH6F + F
(R13)
They also observed the formation of HF via
C6H6 + F2
+
C6HsF + HF
(R14)
Reaction R13 exhibited a well-marked onset at 13.6 f 0.4 (3) Kapralova, G . A,; Chaiken, A. M.; Shilov, A. E. Kinet. Kutul. 1967, 8 No. 3, 485. (4) (a) Miller, W. T.; Dittman, A. L. J . A m . Chem. Sac. 1956, 78, 2793. (b) Miller, W. T.; Koch, S. D. J . A m . Chem. Sac. 1957, 79, 3084. (c) Rodgers, A. S. J . Phys. Chem. 1963, 67, 2199; 1965, 69, 254. (5) (a) Kapralova, G. A,; Shilov, A. E. Kinet. Kutul. 1961, 2, 362. (b) Kapralova, G. A,; Rusin, A. Yu.; Chaikin, A. M.; Shilov, A. E. Dokl. A N SSSR 1963, 1.50, 1282. (6) Grover, J. R.; Lee, Y. T.; Shobatake, K. Annual Review, Institute for Molecular Science, Myodaiji, Okazaki 444, Japan; Abstract IV-0-4, p 98.
0 1988 American Chemical Societv
5112
Raff and Graham
The Journal of Physical Chemistry, Vol. 92, No. 18, 1988
kcal/mol, which is in exact agreement with the 13.6 kcal/mol activation energy obtained for reaction R3.2 Frei, Fredin, and Pimente17have reported the results of [C2H4 + F2] reactions occurring in cryogenic matrices. The products obtained in their studies are very different from those obtained under bimolecular gas-phase collision conditions. Upon vibrational excitation in a cryogenic matrix, this reaction was observed to form 1,2-difluoroethane which subsequently was stabilized by energy transfer to the matrix or decomposed to yield hydrogen fluoride and fluoroethylene via reactions R1 and R2. The relative rates of stabilization by the matrix and decomposition via reaction R2 are dependent upon the nature of the matrix material. The quantum efficiency for formation of 1,2-difluoroethane is found to increase 5 orders of magnitude as the photon wavenumber increases from 953 to 4209 cm-I. However, the increase is neither smooth nor monotonic. There appears to be mode-specific rate enhancement in that excitation of the u2 uI2 combination band of C2H4at 3076 cm-l results in a quantum efficiency greater than that for excitation of u9 at 3105 cm-I. Knudsen and Pimental* reported similar results for the reaction of allene with F2 in N2, Ar, Kr, and Xe matrices at 12 K. The above discussion makes it clear that unimolecular decomposition reactions play a major role in the matrix reactions. The results of the bimolecular gas-phase calculations* indicate that such reactions are also of importance in the mechanism for H F formation. In this paper, we report the results of classical trajectory calculations of various unimolecular processes in the CZH4F2system. In particular, we focus attention upon the computation of microcanonical rate coefficients and energy partitioning for reactions R2 and R6-Rl2. Mechanisms for these reactions are also examined. In addition, we have previously shown that the reaction dynamics of vibrationally excited van der Waals complexes are intermediate between those observed for bimolecular gas-phase reactions and the corresponding system when matrix i ~ o l a t e d . ~The van der Waals complex resembles the matrix system in that the molecules are held in close proximity with the individual molecular rotations partially quenched. It resembles the bimolecular system in that there are no third bodies to which vibrational energy may be transferred and the van der Waals binding forces are much less efficient in holding the molecules together than is a cryogenic matrix. Studies of the 03.N0 complex have shown that the system exhibits mode-specific rate enhancement and structure spe~ificity.~ In this paper, we report the results of analogous studies of the C2H4-F2van der Waals system.
+
11. Methods A . I ,2-Difluoroethane. Trajectory methods are ideally suited for the study of complex reactions that occur on a time scale of several thousand molecular vibrations or less. Whenever 1,2difluoroethane is formed by the reaction of F2 with C2H4, the reaction exothermicity of 116 kcal/mol is primarily deposited in the internal vibrational modes of the molecule.2 Internal excitation to this level produces a variety of unimolecular decomposition reactions, each of which occurs on a time scale of 100 to several thousand molecular vibrations. Consequently, such reactions can be conveniently examined by using classical trajectory methods. All standard trajectory methods for the study of unimolecular reactions have been described in many references and need not be repeated here.IO The only real problem involves the proper averaging over the internal phase space of the molecule at the particular energy of interest. In the present study, microcanonical Metropolis sampling" is employed to effect this averaging. This method assumes that all phase-space points lying on the energy (7) Frei, H.; Fredin, L.; Pimentel, G. C. J . Chem. Phys. 1981,74, 397. (8) Knudsen, A. K.; Pimentel, G. C. J . Chem. Phys. 1983, 78, 6780. (9) Arnold, C.; Gettys, N. S.;Thompson, D. L.; Raff, L. M. J . Chem. Phys. 1986,84, 3803. (10) Raff, L. M.; Thompson, D. L. IR Theory of Chemical Reaction Dynamics; Baer, M., Ed.; CRC: Boca Raton, FL, 1985; Vol. 111, p 1. (1 1) Metropolis, N.; Rosenbluth, A. W.; Rosenbluth, M. Tu'.;Teller, A. H.; Teller, E. J . Chem. Phys. 1953,21, 1087.
shell are equally probable. Since complex molecules tend to exhibit ergodic behavior when excited to energies near or above the dissociation limit, this assumption is expected to be valid. The techniques used to execute the procedure have been described in several references.12 Initially, 1,2-difluoroethane is placed in its equilibrium configuration and the desired internal energy E is inserted into the molecule as kinetic energy equipartitioned among the various momentum components. A trajectory is then integrated for a time sufficient to equilibrate the total internal energy between kinetic and potential energy. A Markov walk is then executed in which the momentum and position coordinates at the (nth 1 ) step are obtained from those at the nth step via
+
+ ( E - O.5)Aq p,("+l)= pl'"' + ([ - 0.5)Ap q,("+') = q,(")
(1)
(2)
where Aq and A p are scaling parameters chosen so as to produce an acceptable (acceptance/rejection) ratio of Markov moves and [ is a random number with a uniform distribution on the interval [0,1]. The new configuration is accepted as a move in the chain if
(3) where P [ q , p ] is, in principle, the 6 function 6[E-H(q,p)] with H being the system Hamiltonian. Such a choice, however, results in an unacceptably low ratio of accepted to rejected moves in the chain. To circumvent this difficulty, the 6 function is replaced by its prelimit form
P[q,pl = s/ Is2 +
iE - H ( q , ~ ) l ~ l ' if' ~I@ - H(q,p)ll f (4)
P[q,pl = 0
if 1iE - H(qJJ)ll 'f
(5)
where f is a cutoff factor greater than unity. The parameters used in the present Markov walk are 0.05 A and 0.05 mu (1 mu = 1.6309 X lo-'* (g cm)/s) for A q and Ap, respectively. In practice, a trajectory is integrated for a period sufficient to randomize the internal energy. This is followed by 10 000-50 000 Markov moves. One thousand additional moves are made between each initial phase-space point chosen for the calculation of a trajectory. A Runge-Kutta numerical integrator with a step size of 1.019 X s was used in all calculations. Trajectories are integrated until dissociation occurs or up to a maximum time of 2.548 X s. Since 1,2-difluoroethane reacts concurrently in several channels, we have
N = No exp[-k,(E)t]
(6)
k d E ) = Ck,(E)
(7)
where i
provided all reactions can be accurately described by a first-order rate law. The k,(E) are microcanonical rate coefficients for decomposition in channel i at internal energy E. The sum in eq 7 runs over all open reaction channels. N is the number of trajectories that have not reacted at time t and No is the total number of trajectories calculated. The individual k,(E) can be obtained by using Ni(t)/ N j ( t ) =
W E )/ k j ( E )
(8)
where N,(t) and Ni(t) are the number of reactions into channels i and j , respectively, at time t . For dissociation reactions leading to atomic products, the dissociation time is taken to be the time of the last inner turning point for the dissociated atom. For reaction R12, the time of the last inner C-C turning point is used. Whenever dissociation leads to the formation of HF, the time of the last inner turning point for both C-F and C-H vibration is computed and the dissociation (12) (a) Brady, J. W.; Doll, J. D.; Thompson, D. L. J . Chem. Phys. 1981, 7 4 , 1026. (b) Doll, J. D.J . Chem. Phys. 1982,74, 109.
The Journal of Physical Chemistry, Vol, 92, No. 18, 1988 5113
Dissociation Dynamics of 1,2-Difluoroethane
*6, 26.0 -0.7
-0.6
-0.5
-0.4
-0.3
Ln l(E-Eo)/EI I:
cc
2 2 53
125 3 C
187 50
'253
00
-IVE
Figure 1. First-order decay plots for the decomposition of 1,2-difluoroethane at the total internal energies indicated. The straight lines are least-squares fits to the data. TABLE I: Microcanonical Rate Coefficients rate coeff x lo-", E , eV
6.0 7.5 9.0
N'
65 127
73
SKI
kT
kRZ)
hR12)
k(R9)
2.60 6.50 12.80
2.51 5.64
0.09 0.86 3.60
O.Ob
7.93
0.0 1.26
aTotal number of trajectories computed. *Zero entries indicate that none of the trajectories resulted in the reaction. time is taken to be the smaller of the two. B. C2HpF2Complexes. The vibrational motion of the C2H4-F2 complex is described in terms of the normal modes for separated C2H4 and F2. The initial state selection corresponds to the excitation of one particular C2H4vibrational mode with one quantum of energy while holding all others at zero-point energy. The "stored structure" methodlo used in the study of bimolecular C2H4 + F2 collisions2was employed to effect the vibrational phase averaging. Vibrational predissociation was assumed to be complete whenever the C2H4-F2 center-of-mass separation exceeded 8.0 h;. Trajectories were integrated up to a maximum of 1.35 X s, which was sufficient for 80% of the trajectories to dissociate. 111. Results and Discussion 1,2-Difluoroethane. Microcanonical rate coefficients for the unimolecular decomposition of 1,2-difluoroethane have been computed at internal energies of 5.0, 6.0,7.5, 8.0, and 9.0 eV by using batches of 50-130 trajectories at each energy. Reaction R 2 is the principal decomposition pathway at every energy examined. At an internal energy of 7.5 eV, C-C bond rupture begins to compete with H F elimination. At 9.0 eV, some hydrogen-atom dissociation is obtained. Fluorine atom or F, elimination reactions were not observed in any of the trajectories even though both of these decomposition pathways are energetically open at the higher internal energies. Equation 6 describes the decomposition of 1,2-difluoroethane with good accuracy at all internal energies investigated in the present study. Figure 1 shows the resulting first-order decay plots for internal energies of 6.0, 7.5, and 9.0 eV. The lines are linear least-squares fits to the trajectory data. The negative slope of the line yields k T ( E ) . The use of eq 7 and 8 permits the rate coefficients for the individual reactions to be extracted from the trajectory data. The results are summarized in Table I. The internal energy dependence of the microcanonical rate coefficients for reactions R2 and R12 is well-described by an RRK expression
k ( E ) = u [ ( E - E,)/E]S4
Figure 2. RRK plot of the calculated microcanonical rate coefficients for four-center HF elimination reactions of 1,2-difluoroethane. The straight line is a least-squares fit to the data.
(9)
where Eo is the critical energy for the reaction. For the simple C-C bond rupture occurring in reaction R12, Eo may be taken to be the carbon-carbon dissociation energy, 3.925 eV. For the four-center dissociation leading to HF, Eo is taken to be the potential barrier height of 2.775 eV previously computed for this process.2 Figures 2 and 3 show plots of In [&E)] vs In [ ( E E O ) / E ]for reactions R2 and R12, respectively. The line is a
2
-1.1
-1.0
2 1 -0.9 -0.8 -0.7 -0.6 -0.5 Ln l(E-Eo)/EI
Figure 3. RRK plot of the calculated microcanonical rate coefficients for C-C bond rupture reactions of 1,2-difluoroethane.The straight line is a least-squares fit to the data. TABLE 11: Energy Partitioning in Four-Center HF Displacement Reactions as a Function of Total Energy' E , eV (fit, v)H F V)OLfI" 6.0 0.156 0.094 0.738 7.5 0.139 0.126 0.731 8.0 0.159 0.132 0.716 9.0 0.130 0.118 0.744 (f, denotes the average fraction of the total energy.
least-squares fit to the data. The slopes of these lines yield s values of 5.57 and 8.48 for reactions R2 and R12, respectively. The intercepts give high-pressure limiting rates for reactions R2 and R12 of 4.39 X 10l2 exp[-2.775 eV/RT] and 2.439 X lOI3 exp[-3.925 eV/RT] s-l, respectively. Previous calculations2 have shown that the formation of H F in gas-phase collisions of C2H4 + F2on the present potential-energy surface proceeds via formation of 1,2-difluoroethane followed by a four-center elimination of HF. In contrast to the frequently observed result of very exothermic atom-molecule exchange reactions where the diatomic exchange product is usually formed in highly excited vibrational states, hydrogen fluoride formed in this reaction is most often in either the u = 0, 1, or 2 vibrational state. On the average, approximately 1 5 2 0 % of the available energy is partitioned into internal HF motion. Relative translational energy accounts for an additional 15%. The energy-partitioning results for unimolecular decomposition of 1,2-difluoroethane are very similar to those obtained in bimolecular collisions of ethylene and fluorine leading to HF. This is a reflection of the fact that the bimolecular process proceeds via 1,2-difluoroethane formation. Figure 4A-C shows the distributions of translational energy, internal H F energy, and internal CH,=CHF energy in (R2) decomposition reactions with 8.0-eV internal energy. The first moments of these distributions yield 0.159,O. 132, and 0.7 16 for the average fraction of the total energy partitioned into translation, internal HF, and internal CH2=CHF motion, respectively. The translational distribution is peaked at an energy of 20.0 kcal/mol rather than having an exponential form. This is the expected result whenever a back-reaction barrier is present. The energy partitioning in reaction R2 is found to be nearly independent of the total internal energy content of CHzF-CH2F.
5114
Raff and Graham
The Journal of Physical Chemistry, Vol. 92, No. 18, 1988 15
(A) TRANSLATION ENERGY
10 -
5-
d
1
0. 21
h
(8) HF INTERNAL ENERGY
14 -
HF VIBRATION
i
-
7 -
5Plr!dLJ
00
0 21
(C)
CH2 = CHF INTERNAL ENERGY
-
7 -
0
FRACTION
Figure 4. (A) Distribution of relative translational energies in four-center
HF elimination reactions of 1,2-difluoroethaneat a total internal energy of 8.0 eV. (B) Distribution of HF internal energies in four-center HF elimination reactions of 1,2-difluoroethaneat a total energy of 8.0 eV. ( C ) Distribution of internal energies in fluoroethylenefor four-center HF elimination reactions of 1,2-difluoroethaneat a total energy of 8.0 eV. TABLE 111: Partitioning of Internal HF Energy among Vibration and Rotational Energy in Four-Center Dissociation Reactions" mvib
0.066 0.085
0.092 0.079
content of 1,2-difluoroethane. The fractions appearing as vibration and rotation are 6.9-9.0% and 2.7-4.2%, respectively, at all energies investigated. Figure 5 , A and B, gives the calculated H F vibrational and rotational distributions for a total initial energy of 7.5 eV in 1,2-difluoroethane. The vibrational distribution is not inverted and both distributions are peaked at or near zero energy. Although the above results are very similar to those obtained for C2H4+ F2 gas-phase collisions yielding H F products,2 there are some important differences. The decay plots given in Figure 1 show that only 44.6%, 77.2%, and 97.3% of the 1,2-difluoros for internal ethane molecules have reacted after 2.55 X energies of 6.0, 7.5, and 9.0 eV, respectively. In contrast, the 1,2-difluoroethane formed as a reaction intermediate in the bimolecular reaction is never observed to live as long as 2.55 X s even though its total internal energy is only about 6.9 eV. Even more striking is the fact that only H F CH2=CHF products are obtained for the decomposition of the 1,Zdifluoroethane intermediate whereas in the present study reactions R9 and R12 are also observed. Clearly, the internal energy distribution in such collisional intermediates is not completely random even though the molecule may live for as many as 64 C-C vibrational stretching periods. Bintz, Thompson and BradyI3 have recently shown that energy redistribution in polyatomic molecules such as benzene is very rapid, occurring on a time scale of approximately 0.2-0.3 ps. These results, coupled with those obtained in the present study, show that either intramolecular energy transfer in 1,2-difluoroethane is much slower than that obtained for benzeneI3or, perhaps more likely, that while the energy-transfer rate out of a given bond in the molecule may be indeed be very fast, complete energy randomization in the molecule is not. The mechanistic details of the decomposition reactions of 1,2-difluoroethane may be determined by following the atomic motions throughout the trajectories. Figures 6-9 show plots of the time variation of various interatomic distances for reactions R2 and R12. Figures 6 and 7 show typical results for decompositions occurring via reaction R2. Time is given in units of 1.019 X s. Some of the curves are displaced upwards for purposes of visual
+
cn
rot
0.028 0.041 0.040 0.039
cf) denotes average fraction of the total energy. Table I1 shows the average fraction of the total energy partitioned into translation, internal HF, and internal CH2=CHF energy for different total energies. For total energies between 6.0 and 9.0 eV, 13-16% of this energy is always partitioned into relative translational motion whereas internal H F energy accounts for 9.4-13.2% of the energy. If the vibration-rotation coupling is ignored, the total H F internal energy may be separated into vibrational and rotational contributions by assuming that the rotational energy is given by that for a rigid rotor E,,, = L2/21
52
Figure 5. (A) HF rotational energy distribution in four-center HF elimination reactions of 1,2-difluoroethaneat a total energy of 7.5 eV. (B) HF vibrational energy distribution in four-center HF elimination reactions of 1,2-difluoroethaneat a total energy of 7.5 eV.
14 -
E , eV 6.0 7.5 8.0 9.0
13ENERGY26 (Kcalirnol)39
(10)
where L is the total angular momentum magnitude and I is the H F equilibrium moment of inertia. The vibrational energy can then be obtained by difference. Table I11 gives the average fraction of the total energy appearing as rotation and vibration of HF for different total anergies. The partitioning of H F energy between rotation and vibration is essentially independent of the total energy
(13) Bintz, K. L.; Thompson, 85, 1848.
D.L.; Brady, J . W. J . Chem. Phys. 1986,
Dissociation Dynamics of 1,2-Difluoroethane
The Journal of Physical Chemistry, Vol. 92, No. 18, 1988 5115
0
m
-a?
I
I
/C-C+5.0
1
0
-W
I
0
PF a ,H D
0
0.00
40.00
80.00
I
,
lbO.00
160.00
TIME Figure 6. Mechanistic details of a four-center HF elimination reaction of 1,2-difluoroethane. The C-C and C-F distances are displaced upwards by 5.0 and 0.5 ..&,respectively, for visual clarity. Time is given in units of 1.019 X s. Left-hand subscripts refer to atom numbers (see Figure 1 in ref 1).
Figure 9. Same as Figure 8. -6.71
I
0
m
/C-C*5.0 5 6 7 8 9 1 0 CENTER OF MASS RADIUSoBETWEEN F2 AND C2H4 ( A )
Figure 10. Potential energy curve for the C2H4-F2complex with structure 1. All distances and angles are those for equilibrium C2H4and F2.
_r
50.00
TIME Figure 7. Same as Figure 6 . 0
w1
"0' 00
10 00
20 00
30 00
40 0 0
TIME
Figure 8. Mechanistic details of a C-C bond rupture reaction of 1,2difluoroethane. The C-F distance is displaced upwards by 3.0 8, for visual clarity. Time is given in units of 1.019 X s. Left-hand subscripts refer to atom numbers (see Figure 1 in ref 1).
clarity. The H F distance being plotted initially oscillates about a value of 3.0 A. This distance is characteristic of a vicinal H-F distance. Consequently, H F elimination from 1,2-difluoroethane is a four-center process rather than a three-center one. The plots also show that the process involves first a hydrogen migration to the fluorine atom on the adjacent carbon followed by C-F bond cleavage to form the H F product. H F elimination is not concerted. Figure 6 shows that at 120 time units (tu) the C-H distance increases from its characteristic equilibrium value to about 3 8, while simultaneously the H-F distance decreases to its equilibrium value. The C-F distance, on the other hand, remains at its equilibrium value until 135 tu after which the C-F bond breaks completing the four-center dissociation reaction. The same mechanism is seen in Figure 7. Hydrogen-atom migration occurs at 30 tu, whereas C-F bond rupture is delayed by about 7 tu. The s values obtained from Figures 2 and 3 indicate that more of the vibrational modes participate in reaction R12 than R2. Figures 8 and 9 show the participation of C-H stretching and -CH2F rocking modes, respectively, in reaction R12. In Figure 8, energy is clearly seen to flow between the C-H stretch and the
C-C stretch. From 0-10 tu, the C-C stretch is highly excited. At 11-16 tu, the energy has flowed into one of the C-H stretching modes. At 22 tu, it has again moved into the C-C stretch causing bond rupture around 25 tu. The fact that the F2 distance increases in concert with the C-C distance shows that there is almost no rotation of the CH2F groups after dissociation. Consequently, the CH2F rocking modes do not contribute to this particular dissociation reaction. On the other hand, Figure 9 shows an R12 reaction in which the CH2F rocking modes are actively involved. The C-H stretching modes show no large excitation throughout the reaction. Nevertheless, at 25 tu, the C-C bond becomes highly excited resulting in dissociation around 32-33 tu. As C-C bond rupture occurs, we note that one vicinal H-F distance decreases to nearly the equilibrium H-F distance while simultaneously the F2distance decreases even though the C-C distance is increasing. This can only occur if the dissociation produces CH2Fgroups in excited rotational states which in turn suggests active participation of CH2F rocking modes in the reaction. Vibrational Predissociation ( VP) of C2H4-F2 Complexes. The global C2H4F2potential' has very shallow minima for C2H4-FZ center-of-mass separations between 5.25 and 6.73 depending upon the structure. The positions of these minima are similar to those expected for van der Waals minima, although the depth of the potential wells are probably too small. Nevertheless, their presence allows us to study the dynamic behavior of C2H4-F2 complexes whose structure and energetics are similar to those expected for van der Waals molecules. Table IV gives the equilibrium structures and stabilities relative to separated C2H4 + F2 of various C2H4-F2 complexes. These results were obtained by holding all bond lengths and bond angles fixed at their equilibrium values for C2H4 and F2 while varying only the center-of-mass distance. Consequently, the fully relaxed structures can be expected to have somewhat greater stabilities than those given in Table IV. As can be seen, structures 1 and 2 are predicted to be the most stable of those investigated with well depths of 0.091 54 and 0.074 13 kcal/mol, respectively, for center-of-mass separations of 5.25 and 5.26 A. The small well depths are not unexpected since dispersion forces were not explicitly included in the potential surface formulation and there are no dipole-dipole interactions. Figure 10 shows the C2H4-F2 well for structures 1 as a function of C2H4-F2 center-of-mass separation. We have studied vibrational predissociation (VP) of groundstate C2H4-F2 complexes (structure 1) produced by single-
5116
TABLE IV: Stabilities and Structures of Various C2H,-F2 van der Waals Complexes
notation
structure
well depth, kcal/mol
CM-C.M. distance, 8,
0.091 54
5.25
o.oo Raff and Graham
The Journal of Physical Chemistry, Vol. 92, No. 18, 1988
-p
-0.25
-0.50
z
-0.75
-m
-1.00
0
-1.25
0.074 13
5.26
0.045 00
5.94
0.022 50
5.95
0.022 so
5.95
5
0.01250
z
-g
6.69
-0.25
i -2.01
U
u t
-3.0
\
5o
U
100
150 Time
200
i
250
Figure 11. Decay plot for vibrational predissociation of C2H4-F2 complex with structure 1 with one quantum of excitation energy in (A) the C-H stretching mode, 0,; (B) the CH2=CH2 torsional mode. u4; (C) the CH2 0.011 11
6.13
nonplanar rocking mode, 07. have sufficient time to undergo intermode transfer and modespecific rate enhancement is the result.
0.01 1 11
6.73
a Very unstable complex, immediately dissociates (C.M. = center of mass).
TABLE V: Microcanonical Rate Coefficients for Vibrational Predissociation of C2H4-F2 Complexes with Equilibrium Structure 1
vibrational mode excited C-H sym str c', torsional u4 C2H4nonplanar rock L',
k x 10-12,
s-1
1.59
1.11 3.14
quantum excitation of the symmetric C-H stretch ( u , ) , the CH2-CH2 torsional mode (u4), and the nonplanar C H 2 rocking mode (u,). Batches of 200 trajectories were computed for each of the cases. Parts A, B, and C of Figure 11 show the first-order decay plots for VP of C2H4-F2 complexes with u,, u4, and u7 excited, respectively. The straight lines are least-squares fits to the middle portion of each plot. The initial and final regions are omitted in the fitting since it is expected that the initial region will be anomalous due to initial-state averaging bias while the final portions of the curve are inaccurate due to the small number of complexes remaining at that time. Microcanonical VP decay coefficients are obtained from the slopes of the least-squares fits. These results are given in Table V. The presence of mode-specific rate enhancement of the VP rates is clearly present. The nonplanar rock, u7, is significantly more efficient in promoting predissociation than is either the C-H stretch, u , , or the torsional mode, u4. These results are in accord with our previous findings for VP of 03.N0complexes where large mode-specific effects were noted.g In contrast, mode specificity was not found to nearly the same extent in our previous studies of the bimolecular reaction dynamics for C2H4+ F2 collisions.2 In the case of vibrational predissociation, the complex crosses the critical dividing surface and moves into the product configuration space at a much faster rate than is the case for bimolecular collisions. Consequently, the molecule's internal energy does not
IV. Comparison with Experimental and Other Theoretical Studies A. Comparison with Experimental Data. There has been only one experimental study of the bimolecular reaction of ethylene and molecular f l ~ o r i n eand , ~ very few experimental studies of the unimolecular decomposition dynamics of 1,2-difluoroethane have been reported. To date, there have been no experimental measurements of vibrational predissociation rates of the C2H4-F, complex. Nevertheless, there exist a significant amount of experimental data on closely related compounds which provide an excellent basis by which the qualitative and quantitative accuracy of the present trajectory results may be assessed. Qualitatively, the results for the bimolecular collision of C,H, + F2,*are in good accord with thermal data reported by Kapralova et aL3 and with the molecular beam results obtained by Grover et aL6 In both experiments, the major reaction channel was found to be addition of a fluorine atomm across a C=C double bond to produce a fluorine atom and a fluoroorganic radical. The trajectory calculations yield the same result in that reaction R3 is predicted to be the major reaction channel. As discussed in the Introduction, Grover et aL6 also find a secondary reaction channel which produces fluorobenzene and HF. Similarly, the calculations predict reaction R5 to be the channel of secondary importance. In this regard, it is interesting to note that Kapralova et aL3 do not report the observation of any H F product in their flame diffusion measurements. This result seems peculiar, not only because it is in disagreement with the trajectory results2 and with the crossed beam data,6 but also because, even if reaction R5 does not occur directly, fluorine atoms would be expected to undergo abstraction reactions to produce HF. The scattering data obtained by Grover et aL6 for the reaction of F2 with benzene suggest that the addition reaction to produce C6H6F F proceeds preferentially by a statistical mechanism, that is, through a C6H6-F-F complex. In contrast, the abstraction reaction leading to C6H5F+ HF appears, at least to some extent, to proceed via direct reaction that does not involve complex formation. The trajectory results2 agree with these observations only in part. Addition, reaction R3, occurs via a C2H4-F-F
+
Dissociation Dynamics of 1,2-Difluoroethane
The Journal of Physical Chemistry, Vol. 92, No. 18, 1988 5117
TABLE VI: Relative Addition Cross Sections as a Function of Relative Translational Energy
relative cross sections C2H4 + Fz C6H6 + F2 -+ C2H4F + F“ C6H6F + Fb -+
Elel,
eV
1.046 1.356 1.634
1.oo 1.71 2.74
1.oo 2.03 2.95
‘Reference 2. ’Extrapolated results from ref 6 . complex in many, but not all, trajectories. However, abstraction, reaction R5, is almost always observed to occur via formation of a complex and not by a direct mechanism. It could be that the abstraction reaction in the benzene F2 system is sufficiently different from the analogous reaction in the C2H4 + F2 system that the mechanisms are different in the two cases. The other possibility is that this difference reflects an inadequacy in the C2H4F2potential-energy surface. Additional molecular beam experiments on the C2H4 + F2 system are clearly needed. Quantitatively, it is more difficult to assess the accuracy of the trajectory results. The problem is that most of the data relate to systems that are analogous to, but not identical with, the C2H4 + F2 system. Consequently, it is difficult to determine whether agreement of theory with experiment confirms accuracy of the calculations or whether such agreement is merely fortuituous. Similar questions arise whenever there is disagreement. Grover et aL6 observe a well-defined onset at 13.6 f 0.4 kcal/mol for reaction R13. This is in exact agreement with the trajectory result for the activation energy of the corresponding addition reaction (R3).2 Grover et aL6 have also reported relative total reaction cross sections for the addition reaction as a function of relative translational energy over the range 13.6 6 Erel6 23 kcal/mol. Absolute cross sections for reaction R3 have been computed over the range 24.12 IErelI68 kcal/moL2 By extrapolation of the experimental data, a direct comparison of these results may be made. Such a comparison is given in Table VI. The trajectory calculations yield slightly lower cross section ratios for the ethylene-fluorine system than the beam data give for the benzene-fluorine reaction. The percent differences are 15.8 and 7.1% at 1.356 and 1.634 eV relative translational energy, respectively. The fact that the measured onset for reaction R13 is in exact agreement with the calculated activation energy for reaction R3 suggests that the barrier height predicted by the C2H4F2potential surfacel for reaction R3 is somewhat too high. Addition of a fluorine atom across the C = C double bond in benzene is not quite the same as addition across the ethylene double bond. In the former case, the addition would be expected to cause the loss of some resonance stabilization energy that is not present in ethylene. Consequently, the barrier to addition in benzene should be higher than for ethylene. The same conclusion may be drawn from the Kapralova et aL3 data which yield an activation energy for reaction R3 of 4.6 kcal/mol. Most of the experiments related to the unimolecular decomposition reactions of substituted ethylenes have been carried out on either CH3-CF3, CH3-CH2F, or various chlorine-substituted molecules. Qualitatively, it is found that upon either multiphoton excitation of CH3-CF2C1 or CH3-CC1314or chemical activation of CH3-CF, or CH3-CH2FI5 the major decomposition products are always HF or HCI olefin. The mechanism always involves four-center elimination. The trajectory results given in section I11 are in accord with these observations. Parks, Krohn, and RootI6 have also found that CH3-CF, formed by hot F atom displacement undergoes only
+
+
(14) Sudbo, Aa. S.; Schulz, P. A.; Shen, Y . R.; Lee, Y . T. J. Chem. Phys. 1978. 69. 2312. (1’5) Chang, H. W.; Craig, N. L.; Setser, D. W. J . Phys. Chem. 1972, 76, 954. (16) Parks, N . J.; Krohn, R. A,; Root, J. W. J . Chem. Phys. 1971, 55, 5785.
+
the four-center elimination reaction to form H F CH2=CF2even at energies sufficiently high that radical dissociation to CH3 CF, might have been expected to occur. The data contained in Table I shows that the trajectory calculations predict the same result in that radical dissociation was not observed at internal energies of 5.0 and 6.0 eV. Quantitative comparison of the trajectory data with experiment may be made with regard to the calculated microcanonical rate coefficients and associated critical energies and with regard to various aspects of the energy partitioning. The C2H4F2potentiall yields a critical energy for four-center H F elimination of 64 kcal/mol. Pritchard, Venugopalan, and Graham” and Pritchard and BryantI8 have examined the decomposition of hot 1,2-difluoroethane obtained by photolysis of CH2FCOCH2F. Benson and Haugen19 have used RRK theory to fit their data and have thereby obtained an activation energy of HF elimination of 62 f 3 kcal/mol. The two results are in excellent agreement. The measured barrier heights for four-center HF elimination in similar compounds are all close to these values. For example, Chang, Craig, and Setserl’ have obtained critical energies of 57 and 68 kcal/mol for H F elimination from CH3-CH2F and CH,-CF,, respectively. The critical energy for dissociation of CH3-CH2F to CH, CH2Fis known with good accuracy to be 87.2 kcal/mol. The C2H4F2potential’ yields a value of 90.5 kcal/mol for the corresponding dissociation reaction for 1,2-difluoroethane. Chang, Craig, and SetserI5 have reported chemical activation experiments on both CH3-CF3 and CH3-CH2F. These experiments yield k ( E ) values for four-center H F elimination reactions for each compound at energies of 92.1 and 102.4 kcal/mol for CH3-CH2F and CH3-CF,, respectively. For CH3-CH2F, the result is k(E=92.1 kcal/mol) = (1.8 f 0.3) X lo9 s-I. Comparison of this value with the trajectory results poses two problems. First, it is not clear to what extent the microcanonical rate coefficients for 1,2-difluoroethane should be similar to those for fluoroethane. In addition, it is not possible to calculate accurate values of k ( E ) at such low internal energies (relative to the dissociation endothermicities) using trajectory methods. Consequently, direct comparison requires that the fitted values in eq 9 be extrapolated over a 46 kcal/mol range. The danger of extrapolating so far beyond the fitted energy range is obvious. This problem may be avoided by comparing the trajectory results with the RRKM calculations reported by Chang et al.” The required frequencies for the four-center transition state were obtained by using experimental data for CH,-CH2F, cyclobutane, and ethylene. Inplane frequencies were obtained from assigned bond orders. The measured activation energy was used to adjust the critical energy. At the experimental energy of 92.1 kcal/mol, the RRKM calculations gave a rate coefficient of l .24 X lo9 s-l, which is in good accord with the measured value. At 138 kcal/mol, the RRKM result is 4 X 10” s-I. The corresponding trajectory result from Table I is 2.5 X 10” s-I. The extent of agreement is clearly satisfactory considering the differences to be expected between the four-center dissociation of 1,2-difluoroethane and fluoroethane. Several experimental studies of energy partitioning in fourcenter unimolecular dissociation reactions have been reported to which the trajectory data given in Tables I1 and 111 may be compared. Holmes and Setser2’ have measured the fraction of the total energy remaining in the organic product upon four-center dissociation of HC1 from several substituted cyclobutanes. Their results show that an average of 60% of the total energy remains with the olefin after dissociation. The trajectory results for 1,2difluoroethane show that between 71 and 74% of the available energy remains with CH,=CHF after H F dissociation. This result is independent of the total internal energy present over the range of 6.0 < E < 9.0 eV. The small difference between the experimental data and the trajectory results is not surprising in
+
+
(17) Pritchard, G. 0.;Venugopalan, M.; Graham, T. F. J . Phys. Chem. 1964, 68, 1786. (18) Pritchard, G. 0.; Bryant, J. T. J . Phys. Chem. 1965, 69, 1085. (19) Benson, S. W.; Haugen, G.J. J . Phys. Chem. 1965, 69, 3898. (20) (a) Holmes, B. E.; Setser, D. W. J. Phys. Chem. 1975, 79, 1320. (b) Holmes, B. E.; Setser, D. W. J . Phys. Chem. 1978, 82, 2461.
Raff and Graham
5118 The Journal of Physical Chemistry, Vol. 92, No. 18, 1988 TABLE VII: Relative HF Vibration-State Populations in Four-Center Dissociation Reactions" n
0 1
2
calcdb
exptl'
n
2.05 1 .oo
1 .36d 1.oo
3 4
0.71
0.39
5
calcdb 0.19
exptl' 0.11
0.05 0.00
0.027 0.00
"The result for the n = l state is arbitrarily set to unity. bPresent work.
