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Kinetic isotope effects in the reaction H + C2H4 → C2H5
Volume 78, number 2
CHEMICAL
PHYSICS LETTERS
1 March 1981
KINETIC ISOTOPE EFFECTS IN THE REACTION H -I-C2H4 + C,H, Ko-ichi
SUGAWARA,
Kiyoshl
OKAZAKI
and Shin SAT0
Deparrment of Applied Physics, Tokyo InsMute of Technology.
Ookayama. Meguro-ku.
Tokyo 152. Sapa-
Recerved 10 October 1980; in fmal form 9 December 1980
The high-pressure bmiting rate constants of the reactlons between H or D atoms and three isotopic ethylenes have been measured in the temperature range 206-461 K. PractxaUy no isotope effects due to the differences between the ethylefies could be observed This result does not agree with the prediction recently made by the activated complex theory.
1. Introduction
The reaction of H atoms with ethylene has been studied for the last 50 years fl ] . The reac-
extensively
tion mechanism
is now established
as
* +M
Here hl stands for a third body for the deactivation of the enerGed ethyl radicals, C,Hg. When H2 is used as a third body, 200 Torr is high enough to suppress the decomposition of C$z [2]. Recent development of experimental techniques made it possible to measure directly the high-pressure limiting rate constant of this reaction. Dorfman and co-workers [3,4] used the pulse radiolysis technique combined with the Lyman* absorption method. This technique was extended by Mihelcic et al. [SJ and in our laboratory [2,5] _ Oka and Cvetanovie 173 applied the phase-shift technique combined w&h HNO* fluorescence measurements. Lee et al. [S] used flash photolysis combined with the resonance fluorescence method. By using this technique, they measured the rate constants of this reaction over the temperature range 198320 K. Since this elementary reaction is rather simple, theoretical treatments have been carried out by many workers, especially in connection with the theoretical trearment of the unimolecular decomposition of C2Hg [5,9] _Ab initio calculations for drawing the potential energy surface for this reaction have also been carried out [lo--121. Nagase et al. [l I] performed ab iuitio 0 009-2614/81/0000-0000/S
02.50
calculations using the energy gradient method on this reaction system and predicted the structure of the activated complex and its normal mode frequencies. On the basis of these data, they showed that the theoretically calculated rate constants are in excellent agreement with the experimental results obtained by Lee et al. Encounraged by this success, they predicted several Isotope effects in the reactions between H or D atoms and various deuterated ethylenes. Recently our apparatus was modified so as to change the reaction temperature in the range of 200-500 K. We studied the temperature dependence of the rate constants of six reactions between H or D atoms and C2H4, C,H,D or C,D,, and found that the kinetic isotope effects thus obtained are quite different from those predicted by Nagase et al.
2. Experimental The experimental apparatus is the same as that described in a previous paper except that temperature is controlled [ 13]_ When temperatures lower than room temperature were used, the stainless steel reaction cell was covered with Styrofoam, in which a stream of nitrogen gas from boiling liquid nitrogen was introduced. Higher temperatures were attained by surrounding the reaction cell with heating tapes. The gas temperature in the cell was measured with a copper-constantan thermocouple at the center of the cell prior to pulse irradiation.
0 North-Holland Publishing Company
259
CHEMICAL PHYSICS LEnERS
Volume 78, numlxx 2
1 March 1981
HZ and I), were purchased from Takachiho Shoji Co. and used after passing through a trap at liquidmtrogen temperature. C2HG purchased from Takachiho Shoji Co., and CzH3D and C2D4 from Merck Co. were used as received. The nominal purities of the last two ethylenes were 98 and 99%, respectively, which were confirmed by mass spectrometric analysis.
3. Results About 700 Torr Hz or D, containing a small. amount of ethylene was pulse irradiated with highener,T electrons from a Febetron 706 and the concentration of H or D was followed by the absorption of Lyman-a by H or D. The decay curves observed were always first order. The decay rates obtained from the first-order decay plot in the D,--C2H, system are shown in fig. 1 as a function of the concentration of C2H4 at different tempratures. Similar observations
2
t
I
8
3
4
5
T-1 , 10-3 h-1
I-ig_ 2. Arrhenms plots for the reactions between H (open symbois) or D atoms (closed symbols) and CzH4 (0, l), CzH# [A, A) or CzD4 (4, I), X : the results of Lee et al [8].
were made with the other five reaction systems. The slopes of the lines shown in fig. 1 correspond to the rate constants at each temperature. Fig_ 2 summarizes the rate constants thus obtained in the form of an Arrhenius plot together with the results of Lee et al. The Arrhenius parameters calculated by the leastsquares method are summarized in table 1. it is noticed that the six reactions can be classitled into two groups, the H- and the D-atom reactions_ Practically no isotope effects due to the difference of ethylenes can be observed.
6
4. Discussion According to Nagase et al., the calculated barrier height, V, for the reaction H + C2H4 + CzHs is 2.20
2
Table 1 The Arrhenius parameters obtained in the temperature range 206-461 K. A in lo-“’ cm3 molecule-’ S-I, E in kcal/mol H atom 0 0
8
4 fC..&I / 10
15
mlecule
l.2 cm
260
rates of the
A
E
A
E
C,H,D
4.6 f 0.3 4.3 f 0.4 4.6 =
3.4 r 0.2 3.5 _, 0.3 3.6 1- 0.3
2.19 +z0.02 218*0*U4
C2D4
2.15 f 0.03 2.12-c 0.05 2.17 r 0.04
-3
H atoms observed in the system of Hz at 700 Torr and CzD, at different tempemtures 8s a function of the concen~a~ion of C2D4.
Fig_ 1. Decay
D atom
C2H4
0.3
223 i 0.04
Volume 78, number 2
CHEMICAL
PHYSICS LETTERS
Table 2
Vibrational frequencies (in cm-‘) and moments of inertia (in au3 A6) for ethylenes CHa=CHa
CHa=CHD
vibrational frequency 935
CDa=CDs
843
1126
1163 1168 1387 1522 1640 1857 3305 3330 3376 3407
955 1141 1165 1270 1455 1592 1823 2478 3314 3356 3393
682 826 852 962 1106 1130 1216 1713 2387 2480 2518 2532
1611
4383
1 March 1981
kcaI/mol. At this saddle point, they calculated the normal mode frequencies and the moments of inertia of ah isotopically substituted activated complexes. The data necessary for the present discussion are summarized in tables 2 and 3. These results were kindly supplied by Dr. Nagase. It should be noted in table 3 that there are two configurations for the activated complex in the reaction with C,H,D. In the activated complex theory (ACT), the critrcal energy for reaction is the sum of the barrier he&t and the difference of zero-point energies between reactants and activated complex:
The E, values calculated are also listed in table 3. A small isotope effect due to the different ethylenes can be seen. On the other hand, the isotope effect in the pre-exponential factor is mainly governed by the dif-
rnn8n/rltof inertia (IAIgfc)
Table 3
Vibrational frequencies (iincm-r), moments cf inertia (in au3 a’) and path degeneracy for the activated complexes, and the critical energy (in kcal/mol) for the addition reactions CH2=CH2 H
+CH2=CHD D
vibrational frequency 404 328 432 383 915 923 980 977 1028 1042 1059 i036 1337 1341 1366 1368 1621 1626 1697 1699 3309 3310 3322 3320 3387 3388 3414 3416 587i 441i
CH2=CHD+
CD2=CDs
H
D
H
D
H
D
389 416 814 857 1021 1058 1236 1350 1521 1672 2469 3316 3358 3409 586i
318 354 813 854 1016 1029 1235 1347 1520 1671 2469 3316 3358 3404 441i
408 419 819 854 979 1048 1233
324 365 818 837 977 1032 1231
365 398 664 741 767 850 1067
308 312 663 736 761 821 1065
1350 1522 1672 2471 3314 3360 3402 584i
1347 1521 1671 2471 3314 3360 3402 441i
1110 1202 1458 2392 2432 2526 2541 5811
1202 1452 2392 2432 2526 2541 4391
4476
7877
9413
1110
15009
path degeneracy 4 4
2
2
2
2
4
4
critical energy 2.32
2.35
2.09
2.30
2.04
2 36
2.08
2.08
261
Volume 78, number 2
CHEMICAL PHYSICS LETTERS
ference in the mass of reactants.
In the present case, the factor is e2-1/2 for the two groups of reactions, the H- and the D-atom reactions_ Consequently, when the Arrhenius plots for the six reactions are calculated by the ACT using the data shown in table 3, six different curves can be obtained and clear isotope effects appear; for example, the calculated rate constant for the H + C2Dq reaction at 210 K is smaller than that for the D + C,H4 reaction_ This is in disagreement with the experimental results shown in fig. 2. Recently Garrett and Truhlar [ 141 calculated the absolute rate constants for the reactions D + H, and H + D, by using an accurate potential energy surface, and showed that the generalized ACT calculation is in excellent agreement with the experimental results obtained by Westenberg and de Haas. In that paper, they demonstrated that even the conventional ACT, which is used in the present discussion. gives good results if the tunneling effect is taken into account_ One of the simplest methods to take the tunneling effect into account is to express the transmission coefficient K by Wigner’s approximation: K =
i
+
&(h[Z’I/kn’,
where v is the imagmary frequency of the unbound normal mode at the saddle point. The v values for the
15
I
0 2
I
I
t
3
4
5
.p
262
reactions under consideration are also listed in table 3. Fig. 3 compares the ACT calculation including the tunneling effect with the experimental results. In this calculation, the experimental!y obtained rate constant for the reaction II + C2H, + C,H,, k,,,(T) = 4.6 X 10-l’ exp(-2_15/RT), was taken as the standard and the barrier height, V, was adjusted so as to fit the calculated rate constant to experiment at room temperature. The adjusted Vvalue was 2.43 kcal/mol. Of course, the same Vvalue was used for the calculation of the other five reactions. Very poor agreement between calculation and experiment was obtained_ This discrepancy cannot be explained as far as the normal mode frequencies and moments of inertia calculated by Nagase et al. are used. In the treatment of the RRKM theory on the unimolecular decomposition of ethyl radicals, Cowfer and Michael [9] estimated the structure of the activated complex and its normal mode frequencies together with some isotopically substituted ones. These data may be used for the estimation of the rate constants under consideration_ Fig. 4 shows the results of this ACT calculation, in which the adjusted Vvalue is 2.83 kcal/mol and the transmission coefficient is assumed to be unity. The agreement between calculation and experiment is again very poor. Further investigations are being carried out.
I
,
10-x
h-l
3_ Comparison of the ACT calculation including the tunneiing effect by usmg the data of Nagase et ai. with experiment_ Tire ratios between the cakurated rate constants and the rate constants observed for the reaction H f CTHa -+ DaHs,k,..J4 6 X lo-” exp(-2_15/RT), are plott&_~or symbols, see fg 2. Solid curves for H-atom reactions and dashed ones for D-atom reactions FE.
1 March 1981
0
2
I
I
1
3
4
5
T-r / lo-’ K-r Fig. 4. Comparison of the ACT calculation by using the data of Cowfkr and Michael with experiment. For symbols and curves, see figs. 2 and 3.
Volume 78, number 2
CHEMICAL PHYSICS LETTERS
References [l] [2] [3] (41 [S] [6]
E.W.R. Steacie, Atomic and free radical reactions, 2nd Ed. (Reinhold, New York, 1954). Y. Ishiiwa, M- Yamabe, A. Noda and S. Sato, Bull. Chem. Sot. Japan Sl(l978) 2488. W-P. Bishop and L.M. Dorfman, J. Chem. Phys. 52 (1970) 3210. T. H&id+ J.A. Eyre and L.M. Dorfman, J. Chem. Phys. 54 (1971) 3422. D. Miielcic, V. Schubert, F. HiiIfer and P. Potzinger, Ber. Bunsenges. Physlk. Chem. 79 (1975) 1230. Y. Ishikawa and S. Sate, Bull Chem. Sot. Japan 52 (1979) 984.
1 March 1981
[7] K. Oka and R.J. Cvetanovic, Can. J. Chem. 57 (1979) 777. [S] J-H. Lee, J-V- Michael. W.A Payne and L J. Stief, J. Chem Phys. 68 (1978) 1817. [9] J-A. Cowfer and J-V. hfichael, J. Chem. Phys 62 (1975) 3504, and references therein. [lo] W-L. Hase, G. Mrowka and R-J. Brudzynski, J. Chem. Phys. 69 (1978) 3548. [ll] S. Nagase, T- Fueno and K. Morokuma, J. Am_ Chem. sot. lOl(l979) 5849_ [12] 0. Nomura and S. Iwata, BuII Chem. Sot. Japan 53 (1980) 61. [13] K. Sugawara, Y. Ishikawa and S. Sato, BuIL Chem. Sot. Japan 53 (1980) 1344. [14] B.C. Garrett and D-G. Truhlar, J. Chem. Phys 72 (1980) 3460.
263
CHEMICAL
PHYSICS LETTERS
1 March 1981
KINETIC ISOTOPE EFFECTS IN THE REACTION H -I-C2H4 + C,H, Ko-ichi
SUGAWARA,
Kiyoshl
OKAZAKI
and Shin SAT0
Deparrment of Applied Physics, Tokyo InsMute of Technology.
Ookayama. Meguro-ku.
Tokyo 152. Sapa-
Recerved 10 October 1980; in fmal form 9 December 1980
The high-pressure bmiting rate constants of the reactlons between H or D atoms and three isotopic ethylenes have been measured in the temperature range 206-461 K. PractxaUy no isotope effects due to the differences between the ethylefies could be observed This result does not agree with the prediction recently made by the activated complex theory.
1. Introduction
The reaction of H atoms with ethylene has been studied for the last 50 years fl ] . The reac-
extensively
tion mechanism
is now established
as
* +M
Here hl stands for a third body for the deactivation of the enerGed ethyl radicals, C,Hg. When H2 is used as a third body, 200 Torr is high enough to suppress the decomposition of C$z [2]. Recent development of experimental techniques made it possible to measure directly the high-pressure limiting rate constant of this reaction. Dorfman and co-workers [3,4] used the pulse radiolysis technique combined with the Lyman* absorption method. This technique was extended by Mihelcic et al. [SJ and in our laboratory [2,5] _ Oka and Cvetanovie 173 applied the phase-shift technique combined w&h HNO* fluorescence measurements. Lee et al. [S] used flash photolysis combined with the resonance fluorescence method. By using this technique, they measured the rate constants of this reaction over the temperature range 198320 K. Since this elementary reaction is rather simple, theoretical treatments have been carried out by many workers, especially in connection with the theoretical trearment of the unimolecular decomposition of C2Hg [5,9] _Ab initio calculations for drawing the potential energy surface for this reaction have also been carried out [lo--121. Nagase et al. [l I] performed ab iuitio 0 009-2614/81/0000-0000/S
02.50
calculations using the energy gradient method on this reaction system and predicted the structure of the activated complex and its normal mode frequencies. On the basis of these data, they showed that the theoretically calculated rate constants are in excellent agreement with the experimental results obtained by Lee et al. Encounraged by this success, they predicted several Isotope effects in the reactions between H or D atoms and various deuterated ethylenes. Recently our apparatus was modified so as to change the reaction temperature in the range of 200-500 K. We studied the temperature dependence of the rate constants of six reactions between H or D atoms and C2H4, C,H,D or C,D,, and found that the kinetic isotope effects thus obtained are quite different from those predicted by Nagase et al.
2. Experimental The experimental apparatus is the same as that described in a previous paper except that temperature is controlled [ 13]_ When temperatures lower than room temperature were used, the stainless steel reaction cell was covered with Styrofoam, in which a stream of nitrogen gas from boiling liquid nitrogen was introduced. Higher temperatures were attained by surrounding the reaction cell with heating tapes. The gas temperature in the cell was measured with a copper-constantan thermocouple at the center of the cell prior to pulse irradiation.
0 North-Holland Publishing Company
259
CHEMICAL PHYSICS LEnERS
Volume 78, numlxx 2
1 March 1981
HZ and I), were purchased from Takachiho Shoji Co. and used after passing through a trap at liquidmtrogen temperature. C2HG purchased from Takachiho Shoji Co., and CzH3D and C2D4 from Merck Co. were used as received. The nominal purities of the last two ethylenes were 98 and 99%, respectively, which were confirmed by mass spectrometric analysis.
3. Results About 700 Torr Hz or D, containing a small. amount of ethylene was pulse irradiated with highener,T electrons from a Febetron 706 and the concentration of H or D was followed by the absorption of Lyman-a by H or D. The decay curves observed were always first order. The decay rates obtained from the first-order decay plot in the D,--C2H, system are shown in fig. 1 as a function of the concentration of C2H4 at different tempratures. Similar observations
2
t
I
8
3
4
5
T-1 , 10-3 h-1
I-ig_ 2. Arrhenms plots for the reactions between H (open symbois) or D atoms (closed symbols) and CzH4 (0, l), CzH# [A, A) or CzD4 (4, I), X : the results of Lee et al [8].
were made with the other five reaction systems. The slopes of the lines shown in fig. 1 correspond to the rate constants at each temperature. Fig_ 2 summarizes the rate constants thus obtained in the form of an Arrhenius plot together with the results of Lee et al. The Arrhenius parameters calculated by the leastsquares method are summarized in table 1. it is noticed that the six reactions can be classitled into two groups, the H- and the D-atom reactions_ Practically no isotope effects due to the difference of ethylenes can be observed.
6
4. Discussion According to Nagase et al., the calculated barrier height, V, for the reaction H + C2H4 + CzHs is 2.20
2
Table 1 The Arrhenius parameters obtained in the temperature range 206-461 K. A in lo-“’ cm3 molecule-’ S-I, E in kcal/mol H atom 0 0
8
4 fC..&I / 10
15
mlecule
l.2 cm
260
rates of the
A
E
A
E
C,H,D
4.6 f 0.3 4.3 f 0.4 4.6 =
3.4 r 0.2 3.5 _, 0.3 3.6 1- 0.3
2.19 +z0.02 218*0*U4
C2D4
2.15 f 0.03 2.12-c 0.05 2.17 r 0.04
-3
H atoms observed in the system of Hz at 700 Torr and CzD, at different tempemtures 8s a function of the concen~a~ion of C2D4.
Fig_ 1. Decay
D atom
C2H4
0.3
223 i 0.04
Volume 78, number 2
CHEMICAL
PHYSICS LETTERS
Table 2
Vibrational frequencies (in cm-‘) and moments of inertia (in au3 A6) for ethylenes CHa=CHa
CHa=CHD
vibrational frequency 935
CDa=CDs
843
1126
1163 1168 1387 1522 1640 1857 3305 3330 3376 3407
955 1141 1165 1270 1455 1592 1823 2478 3314 3356 3393
682 826 852 962 1106 1130 1216 1713 2387 2480 2518 2532
1611
4383
1 March 1981
kcaI/mol. At this saddle point, they calculated the normal mode frequencies and the moments of inertia of ah isotopically substituted activated complexes. The data necessary for the present discussion are summarized in tables 2 and 3. These results were kindly supplied by Dr. Nagase. It should be noted in table 3 that there are two configurations for the activated complex in the reaction with C,H,D. In the activated complex theory (ACT), the critrcal energy for reaction is the sum of the barrier he&t and the difference of zero-point energies between reactants and activated complex:
The E, values calculated are also listed in table 3. A small isotope effect due to the different ethylenes can be seen. On the other hand, the isotope effect in the pre-exponential factor is mainly governed by the dif-
rnn8n/rltof inertia (IAIgfc)
Table 3
Vibrational frequencies (iincm-r), moments cf inertia (in au3 a’) and path degeneracy for the activated complexes, and the critical energy (in kcal/mol) for the addition reactions CH2=CH2 H
+CH2=CHD D
vibrational frequency 404 328 432 383 915 923 980 977 1028 1042 1059 i036 1337 1341 1366 1368 1621 1626 1697 1699 3309 3310 3322 3320 3387 3388 3414 3416 587i 441i
CH2=CHD+
CD2=CDs
H
D
H
D
H
D
389 416 814 857 1021 1058 1236 1350 1521 1672 2469 3316 3358 3409 586i
318 354 813 854 1016 1029 1235 1347 1520 1671 2469 3316 3358 3404 441i
408 419 819 854 979 1048 1233
324 365 818 837 977 1032 1231
365 398 664 741 767 850 1067
308 312 663 736 761 821 1065
1350 1522 1672 2471 3314 3360 3402 584i
1347 1521 1671 2471 3314 3360 3402 441i
1110 1202 1458 2392 2432 2526 2541 5811
1202 1452 2392 2432 2526 2541 4391
4476
7877
9413
1110
15009
path degeneracy 4 4
2
2
2
2
4
4
critical energy 2.32
2.35
2.09
2.30
2.04
2 36
2.08
2.08
261
Volume 78, number 2
CHEMICAL PHYSICS LETTERS
ference in the mass of reactants.
In the present case, the factor is e2-1/2 for the two groups of reactions, the H- and the D-atom reactions_ Consequently, when the Arrhenius plots for the six reactions are calculated by the ACT using the data shown in table 3, six different curves can be obtained and clear isotope effects appear; for example, the calculated rate constant for the H + C2Dq reaction at 210 K is smaller than that for the D + C,H4 reaction_ This is in disagreement with the experimental results shown in fig. 2. Recently Garrett and Truhlar [ 141 calculated the absolute rate constants for the reactions D + H, and H + D, by using an accurate potential energy surface, and showed that the generalized ACT calculation is in excellent agreement with the experimental results obtained by Westenberg and de Haas. In that paper, they demonstrated that even the conventional ACT, which is used in the present discussion. gives good results if the tunneling effect is taken into account_ One of the simplest methods to take the tunneling effect into account is to express the transmission coefficient K by Wigner’s approximation: K =
i
+
&(h[Z’I/kn’,
where v is the imagmary frequency of the unbound normal mode at the saddle point. The v values for the
15
I
0 2
I
I
t
3
4
5
.p
262
reactions under consideration are also listed in table 3. Fig. 3 compares the ACT calculation including the tunneling effect with the experimental results. In this calculation, the experimental!y obtained rate constant for the reaction II + C2H, + C,H,, k,,,(T) = 4.6 X 10-l’ exp(-2_15/RT), was taken as the standard and the barrier height, V, was adjusted so as to fit the calculated rate constant to experiment at room temperature. The adjusted Vvalue was 2.43 kcal/mol. Of course, the same Vvalue was used for the calculation of the other five reactions. Very poor agreement between calculation and experiment was obtained_ This discrepancy cannot be explained as far as the normal mode frequencies and moments of inertia calculated by Nagase et al. are used. In the treatment of the RRKM theory on the unimolecular decomposition of ethyl radicals, Cowfer and Michael [9] estimated the structure of the activated complex and its normal mode frequencies together with some isotopically substituted ones. These data may be used for the estimation of the rate constants under consideration_ Fig. 4 shows the results of this ACT calculation, in which the adjusted Vvalue is 2.83 kcal/mol and the transmission coefficient is assumed to be unity. The agreement between calculation and experiment is again very poor. Further investigations are being carried out.
I
,
10-x
h-l
3_ Comparison of the ACT calculation including the tunneiing effect by usmg the data of Nagase et ai. with experiment_ Tire ratios between the cakurated rate constants and the rate constants observed for the reaction H f CTHa -+ DaHs,k,..J4 6 X lo-” exp(-2_15/RT), are plott&_~or symbols, see fg 2. Solid curves for H-atom reactions and dashed ones for D-atom reactions FE.
1 March 1981
0
2
I
I
1
3
4
5
T-r / lo-’ K-r Fig. 4. Comparison of the ACT calculation by using the data of Cowfkr and Michael with experiment. For symbols and curves, see figs. 2 and 3.
Volume 78, number 2
CHEMICAL PHYSICS LETTERS
References [l] [2] [3] (41 [S] [6]
E.W.R. Steacie, Atomic and free radical reactions, 2nd Ed. (Reinhold, New York, 1954). Y. Ishiiwa, M- Yamabe, A. Noda and S. Sato, Bull. Chem. Sot. Japan Sl(l978) 2488. W-P. Bishop and L.M. Dorfman, J. Chem. Phys. 52 (1970) 3210. T. H&id+ J.A. Eyre and L.M. Dorfman, J. Chem. Phys. 54 (1971) 3422. D. Miielcic, V. Schubert, F. HiiIfer and P. Potzinger, Ber. Bunsenges. Physlk. Chem. 79 (1975) 1230. Y. Ishikawa and S. Sate, Bull Chem. Sot. Japan 52 (1979) 984.
1 March 1981
[7] K. Oka and R.J. Cvetanovic, Can. J. Chem. 57 (1979) 777. [S] J-H. Lee, J-V- Michael. W.A Payne and L J. Stief, J. Chem Phys. 68 (1978) 1817. [9] J-A. Cowfer and J-V. hfichael, J. Chem. Phys 62 (1975) 3504, and references therein. [lo] W-L. Hase, G. Mrowka and R-J. Brudzynski, J. Chem. Phys. 69 (1978) 3548. [ll] S. Nagase, T- Fueno and K. Morokuma, J. Am_ Chem. sot. lOl(l979) 5849_ [12] 0. Nomura and S. Iwata, BuII Chem. Sot. Japan 53 (1980) 61. [13] K. Sugawara, Y. Ishikawa and S. Sato, BuIL Chem. Sot. Japan 53 (1980) 1344. [14] B.C. Garrett and D-G. Truhlar, J. Chem. Phys 72 (1980) 3460.
263