J . Phys. Chem. 1990, 94, 1419-1425
1419
Properties of Activation Barriers from Thermal Rate Data on Forward and Reverse Reactions: OH H,, NH, 4- HprCH3 H,, and CH3 4- HCI
+
+
Hiroshi Furue and Philip D. Pacey* Department of Chemistry, Dalhousie University, Halifax, Nova Scotia, Canada B3H 4J3 (Received: February 28, 1989: In Final Form: June 27, 1989)
Experimental data on the temperature dependence of forward and reverse transfers of hydrogen atoms have been assembled. The following transition-state theory (TST) expressions, incorporating a factor, K , for tunneling through a one-dimensional Eckart barrier of effective forward and reverse heights Er and E, and of characteristic tunneling temperature, P,were fitted 7') Q,( T,wB)exp(-E,/RT). by least-squares methods to the data for each reaction: kr = KB,(7') Qv(T,wB)exp(-Ef/RT); k, = KB~( Here Ef, P,wB, and El - E, were adjustable parameters; wB is the geometric mean of the low-frequency vibrational term values of the transition species; and QV(T,wB) is the corresponding partition function. Br( 7') and B,(7') incorporate other TST factors, calculated from spectroscopic properties of reactants and semiempirical internuclear distances of the transition species. For the reactions OH + H2 == H 2 0 + H and NH2 + H2 * NH3 + H, most standard deviations are from 1% to 3% of the parameter values and the parameters agree well with independent quantum chemical or thermochemical estimates. The second reaction is 13 kJ mol-' exothermic at 0 K. For the reactions CH, + H2 + CH4 + H, Ef - E, disagrees with the values from the thermochemical tables, suggesting that there are errors in these tables or errors of 1 order of magnitude in the low-temperature rate constants. The latter possibility seems more likely, as we do find agreement between the established thermochemistry and recent kinetic data for the reactions CH, + HCI + CH4 + C1. The above TST expressions have also been fit to the results of variational TST calculations, incorporating more sophisticated tunneling corrections for the first and third reactions. The fitted parameters agree well with the properties of the tops of the vibrationally adiabatic barriers used in the variational calculations.
I. Introduction Chemical kinetic information is often used to determine changes in thermodynamic properties for chemical reactions.' For reactions involving polyatomic radicals, it has been argued that chemical kinetic studies provide the best thermodynamic information.' From the principle of detailed balancing, the ratio of forward and reverse rate constants, kr/k,, at a fixed temperature, T, is equal to the equilibrium constant, K . From the variation of K with T and the second law of thermodynamics, it is possible to find the standard entropy and enthalpy changes, ASoand W , for the reaction. Alternatively, from K a t one temperature and a third law calculation of ASo,it is possible to find AHo. Frequently, however, kf and k, have been determined at different temperatures, and it is necessary to have a model for the temperature dependence of kr and k,. Such a model could also be useful to harmonize the values of kf or k , from different laboratories. A possible model is the two-parameter Arrhenius law. However, we know that Arrhenius plots for hydrogen atom transfer reactions are often curved. In several such cases, a three-parameter transition-state-theory (TST) model, incorporating a tunneling factor, has been successfully applied.24 The three parameters are the effective activation barrier height, E f , a characteristic tunneling temperature, P,and a third parameter, which may be a constant facto^-^*^ or a bending f r e q ~ e n c y .Tunneling ~ is calculated for a one-dimensional Eckart barrier, where T* = hcw*/(2dB) and w* is the term value for vibration in a parabolic well with the second derivative equal but opposite to that of the barrier top, h is Planck's constant, c is the speed of light, and kBis Boltzmann's constant. The purpose of the present article is to extend this TST model to include both forward and reverse reactions by introducing a fourth parameter, Ef - E,, the difference between the forward and reverse barriers, equal to AHoo, When the model is fitted to forward and reverse kinetic and equilibrium data, it will be possible to determine Ef - E,, El, P,and W E , an effective mean vibrational (1) McMillen, D. F.; Golden, D. M. Annu. Rev. Phys. Chem. 1982, 33, 493; Brouard, M.; Lightfoot, P. D.; Pilling, M. J. J. Phys. Chem. 1986, 90, 445. Benson, S . W . J . Chem. SOC.,Faraday Trans. 2 1987, 83, 791. (2) Furue, H.; Pacey, P. D. J. Phys. Chem. 1986, 90, 397. (3) Rodriguez, A. E.; Pacey, P. D. J. Phys. Chem. 1986, 90, 6298. (4) Furue, H.; Pacey, P. D. J. Phys. Chem. 1987, 91, 4132.
0022-3654/90/2094-1419$02.50/0
term value in the transition state. The thermodynamic significance of Ef- E, has been pointed out. The other three parameters provide valuable information regarding the transition state. For a three-electron transition state like DHH, it has been shown4that such information is as accurate as that obtained by a b initio quantum mechanical calculations. For systems with more electrons, ab initio methods become increasingly difficult, and the present method has a clear advantage. This advantage should be increased by the use of kinetic data on both the forward and reverse directions. The basic assumption of this work is the underlying assumption of TST, namely, from the point of view of classical mechanics, that systems do not recross the dividing surface between reactants and products. We also assume that a one-dimensional Eckart tunneling correction can successfully model the temperature dependence resulting from multidimensional quantum dynamics. We shall partially test this assumption by fitting the model to the results of variational TST calculations that involve more sophisticated tunneling calculation^.^^ We have also assumed that high-frequency vibrational partition functions do not change from reactants to transition state to products and that the low-frequency vibrations in the transition state may be grouped together with an effective mean term value, wB. Moments of inertia of the transition state are taken from semiempirical or ab initio calculations. Moments of inertia and vibrational frequencies of the reactants and products are taken from spectroscopic sources. Four reactions are examined in the present article. OH Hz H2O + H
+ NH2 + H2 CH, + HZ
+H CHP + H CH, + H C l e CH4 + Cl NH3
F=
(2f,r) (3f,r) (4f,r)
The experimental data for these reactions are critically discussed in section 11. The TST model is presented in more detail in section 111. The model is fitted to the data, and the resulting parameters are compared with a b initio calculations and with earlier exper( 5 ) Isaacson, A. D.; Truhlar, D. G. J. Chem. Phys. 1982, 76, 1380. (6) Steckler, R.; D. Dykema, K.J.; Brown, F. B.;Hancock, G.C.; Truhlar, D. G.; Valencich, T. J. Chem. Phys. 1987, 87, 7024. (7) Joseph, T.; Steckler, R.; Truhlar. D. G. J. Chem. Phys. 1987,87, 7036.
0 1990 American Chemical Society
1420 The Journal of Physical Chemistry, Vol. 94, No. 4, 1990 TABLE I: Summary of Experimental Data O H + H2 N H 2 + H2 CH,
+ H2
CH3
+ HCI
no. of points T range, K ref
37 250-2579 8-1 l o
Forward Reactions 60 38 673-1620 372-2166 12, 13" 19-26
11 253-495 43," 48, 49, 52
no. of points Trange,K ref
95 1246-2297 8
Reverse Reactions I45 52 502-1706 372-2300 12, 14, 15 27-42
42 200-504 43-49
" Forward rate constants for ref 8, 13,43,48, and 49 were calculated from reported equilibrium constants and reverse rate constants. imental estimates in section IV. The final section summarizes the results and presents recommendations for further experimental and theoretical work. 11. Data Sets The experimental data fitted in this work are summarized in Table I. Reaction 1 has been discussed recently by Michael and Sutherland.8 We have incorporated only the data they recommend, all of which were obtained since 1980. Included for the forward reaction are two flash-photolysis-resonance-fluorescence studies9J0 between 250 and 1050 K and a shock-tube atomic resonance absorption study at high temperatures." For the reverse rate constant and equilibrium constant, there are copious recent results obtained by flash photolysis in a shock tube with atomic resonance absorption measurements of H atom c o n c e n t r a t i ~ n . ~ ~ ~ ~ Reaction 2 is almost thermoneutral, which makes it less difficult to study in the forward and reverse directions. A study of both reaction directions in the same flow-discharge system has recently been achieved by Hack et a1.I2 Three rate constants have been deleted from this set of data because their residuals from a smooth curve were greater than 2 standard deviations. Sutherland and Michael13 have measured the equilibrium constant in a shocktube-flash-photolysis system. They have calculated values of kzf from these values of K 2 and their measurements of kZr.l4 Both these sets of values of k,, and kzr have been included in our data set, with values from a recent flash-photolysis-atomic resonance fluorescence study of the reverse reaction.I5 Most earlier results have been excluded, although a flash-photolysis-resonance-absorption studyI7 at low temperatures has been included in one fit. Values of k z f from this study were slower than other values at similar temperatures. Data from pyrolysis and photolysis for reaction 3f have previously been fit to a less sophisticated TST modeL2 The rate constants were obtained relative to that of the recombination reaction 2CH3 C2H6 (5) which was assumed to be independent of temperature. It is now known that the recombination rate constant decreases with increasing temperature,'* approximately in proportion to WZ. Fitting to the results of ref 18, we obtain k5 = 7.15 X lo1) L mol-' s-I K1l2.result^^^^^ for reaction 3f have been adjusted
-
(8) Michael, J . V.; Sutherland, J . W. J . Phys. Chem. 1988, 92, 3853. (9) Tully, F. P.; Ravishankara, A. R. J . Phys. Chem. 1980, 84. 3126. (10) Ravishankara, A. R.; Nicovich, J. M.; Thompson, R. L.; Tully, F. P. J . Phys. Chem. 1981, 85, 2498. (11) Frank, P.; Just, T. Ber. Bunsen-Ges. Phys. Chem. 1985, 89, 181. (12) Hack. W.; Rouveirolles, P.; Wagner, H. G. J . Phys. Chem. 1986, 90, 2505. (13) Sutherland, J. W.; Michael, J . V. J . Chem. Phys. 1988, 88, 830. (14) Michael, J. V.; Sutherland, J. W.; Klemm, R. B. J. Phys. Chem. 1986, 90, 497. (15) Fontijn, A. Private communication, revised values using the method of ref 16. (16) Marshall, P.; Fontijn, A. J . Chem. Phys. 1986, 85, 2637. ( 1 7 ) Demissv. M.: Lesclaux. R. J . Am. Chem. SOC.1980. 102. 2897. (18) Macphdrson, M T , Pilling, M J , Smith, M J C J Phys Chem 1985.89. 2268 (19) Davison, S.; Barton, M. J . Am. Chem. SOC.1952, 74, 2307. (20) Shapiro, J. S.; Weston, R. E. J . Phys. Chem. 1972, 76, 1669. (21) Kobrinsky. P C.; Pacey, P. D. Can J . Chem. 1974, 52, 3665.
Furue and Pacey slightly for this revised value of k S . The recent results of Moller et a1.26using ultraviolet absorption spectroscopy as the measure of CH, have also been included. Reaction 3r has been studied with electron spin resonance spectroscopy,z7~zs atomic resonance absorption spectro~copy,~~ hot wire calorimetry,)0 and various reference reactions3i42to determine the hydrogen atom concentration. Reaction 4r has been studied many times because of its importance in modeling C1 consumption in the stratosphere. Heneghan et al.43reviewed past work on this reaction and found that six recent studies, in which CI was monitored by resonance fluorescenceu46 or mass s p e c t r ~ m e t r y ,give ~ ~ room-temper~~~*~~ ature rate constants agreeing within *4%. We have adopted this data set and added a subsequent mass spectrometric result.49 In contrast, results for k4fare scattered by 1 order of magnitude. Early steady-state photolysis experiments gave slow rate cons t a n t ~evidently, ;~~ the reaction was too fast to be followed by this technique. Results calculated from klr and K4 obtained in very low pressure reactors (VLPR) were much faster.43.4s,49Here, a weakness is the fact that CH3 concentrations were not directly measured but instead were inferred from changes in CI concentrations. Pohjonen et aLsl monitored CH, by ultraviolet absorption spectroscopy, but second-order rate constants calculated from their work vary with the HCI pressure. Russell et al. directly monitored the decay of CH, by mass s p e c t r ~ m e t r y .Our ~ ~ data set includes the VLPR results and the results of Russell et al.
(22) Gesser, H.; Steacie, E. W. R. Can. J . Chem. 1956, 34, 113. (23) Majury, T. G.; Steacie, E. W. R. Can. J . Chem. 1952, 30, 800. (24) Clark, T. C.; Dove, J . E. Can. J . Chem. 1973, 51, 2147, 2155. (25) Marshall, R. M.; Shahkar, G. J. Chem. SOC.,Faraday Trans. I 1981, 77, 227 1 . (26) Moiler, W.; Mozzhukhin, E.; Wagner, H. G. Ber. Bunsen-Ges. Phys. Chem. 1986, 90, 854. (27) Kurylo, M. J.; Timmons, R. B. J . Chem. Phys. 1969, 50, 5076. (28) Kurylo, M. J.; Hollinden, G. A.; Timmons, R. B. J . Chem. Phys. 1970, 50, 1773. (29) Roth, P.; Just, T. Ber. Bunsen-Ges. Phys. Chem. 1975, 79, 682. (30) Berlie, M. R.; LeRoy, D. J. Can. J . Chem. 1954, 32, 650. (31) Jamieson, J. W. S.; Brown, G. R. Can. J . Chem. 1964, 42, 1638. (32) Sepehrad, A.; Marshall, R. M.; F'urnell, J. H. J . Chem. Soc.,Faraday Trans. I 1979, 75, 835. (33) Peeters, J.; Mahnen, G. Symp. (In?.)Combust., [Proc.]1973,14, 133. (34) Walker, R. W. J . Chem. SOC.A 1968, 2391. (35) Dixon-Lewis, G.; Williams, A. Symp. (In:.) Combust., [Proc.] 1967, I I , 951. (36) Azatyan, V. V.; Nalbandyan, A. B.; Meng-Yuan, T.Kinet. Cata2. (Engl. Trawl.) 1964, 5, 1977. (37) Baldwin, R. R.; Norris, A. C.; Walker, R. W. Symp. (Int.) Combust., [Proc.] 1967, 11, 889. (38) Baldwin, R. R.; Hopkins, D. E.; Norris, A. C.; Walter, R. W. Combus:. Flame 1970, 15, 33. (39) Biordi, J. C.; Lazzara, C. P.; Papp, J. F. Combust. Flame 1976, 26, 57. (40) Biordi, J. C.; Lazzara, C. P.; Papp, J. F. Symp. ( I n t . ) Combust, [Proc.] 1975, 15, 917. (41) Fenimore, C. P.; Jones, G. W. J . Phys. Chem. 1961, 65, 2200. (42) Gorban, N . I.; Nalbandyan, A. B. Dok1.-Akad. Nauk Arm. SSR 1961, 33, 49. (43) Heneghan, S. W.; Knoot, P. A,; Benson, S. W. Int. J . Chem. Kinet. 1981, 13, 677. (44) Zahniser, M. S.; Berquist, B. M.; Kaufman, F. Int. J . Chem. Kinet. 1978, IO, 15. (45) Keyser, L. F. J . Chem. Phys. 1978, 69, 214. (46) Ravishankara, A. R.; Wine, P. H. J . Chem. Phys. 1980, 72, 25. (47) Liu, C. L.; Leu, M. T.; DeMore, W. B. J . Phys. Chem. 1978, 82, 1772. (48) Baghal-Vayjme, M. H.; Colussi, A. J.; Benson, S. W. J. Am. Chem. SOC.1978, 100, 3214. (49) Dobis, 0.;Benson, S. W. In:. J . Chem. Kinet. 1987, 19, 691. (50) Cvetanovic, R. J.; Steacie, E. W. R. Can. J . Chem. 1953, 31, 158. ( 5 I ) Pohjonen, M.-L.; Koskikallio, J. Acta Chem. Scand. A 1979, 33,449. (52) Russell, J . J.; Seetula, J. A,; Senkan, S. M.; Gutman, D. Int. J . Chem. Kinet. 1988, 20, 759.
Activation Barriers from Thermal Reaction Rates 111. Transition-State Theory In this section, we will present the theoretical expressions that have been fitted to the experimental data. This will include discussions of tunneling and of the treatment of vibrational degrees of freedom. The TST expressions are as follows:
+ log Bf(T ) + log Qv( T,wB)- Ef/2.303AT + log B,(T) + log Q,(T,wB) - Er/2.303RT (6)
log kf = log K
log k , = log K
Here, R is the gas constant; K is the tunneling factor, Q,(T,wB) is the partition function for the low-frequency bending vibrations of the transition species, wB is an average low-frequency bending term value, Ef and E, are the effective forward and reverse barrier heights, and Bf(7‘) and B,( 7‘) are the remaining TST factors for forward and reverse reactions. Logarithms have a base of 10. The tunneling factors were calculated for Eckart barriers of forward and reverse heights, Ef and E,, and of characteristic tunneling temperature, P.At P, the average energy of reacting complexes is about half the barrier heights3 The tunneling factors were calculated by 40-point Gaussian quadrature with use of routines based on ref 54. Ef,E,, wB,and P were treated as variable parameters. This is a one-dimensional treatment of tunneling, which is really a multidimensional phenomenon. Given a complete potential energy surface, it is possible to perform a multidimensional calculation of the tunneling Such a surface would be described in terms of many parameters, whereas we can only hope to determine a few parameters from the available experimental data. Thus, we are forced to use a simple treatment of the tunnel effect. There is some evidence that a one-dimensional Eckart approach is a reasonable choice. Formulas similar to those used here were able to fit the results of an accurate multidimensional quantum dynamical treatmentSs of the reaction of H with H2 within 3%.s6 There was an unexplained discrepancy in the value of the barrier height, however. A similar approach has been used to fit experimental data for reactions of atoms with H2 and D2.4 The barrier heights obtained usually agreed with the results of ab initio calculations, within the combined uncertainties. Because of this experience we have some confidence that an Eckart treatment is a reasonable approximation to the true tunneling factor. It is necessary to be cautious when interpreting the parameters obtained. We will further test the one-dimensional approach by fitting the results of multidimensional theoretical treatments for reactions 1 and 3. Vibrations in the transition state are usually treated as harmonic oscillators and occasionally as anharmonic oscillators or hindered rotations. For the reactions of atoms with H2 and D2, we found that reasonable accuracy was obtained by considering high-frequency stretching vibrations to be unexcited and low-frequency bending vibrations to be excited, taking the bending frequency as a fitted ~ a r a m e t e r .A~ similar approach will be used here. The number of predominantly stretching vibrations does not change on going from reactants to transition state to products in these reactions. With the exception of reaction 4, all these frequencies remain high, so the partition functions will remain close to unity. Furthermore, the transition-state partition functions will tend to cancel with the reactant partition functions. Consequently, except for the symmetric stretch in reaction 4, we have omitted these degrees of freedom from our treatment. The number of bending degrees of freedom is different in reactants, transition state, and products; these low-frequency modes are significantly excited at experimental temperatures. The bending frequencies of the reactants and products are known from spectroscopy. It is not possible to treat all the bending frequencies in the transition state as fitted parameters; the experimental data are not sufficiently precise to distinguish between the many possible (53) Pacey, P. D. J . Chem. Phys. 1979, 71, 2966. 1981, 86, 357. (54) Brown, R. L. J . Res. Natl. Bur. Stand. (US.) (55) Schatz, G. C.; Kuppermann, A . J . Chem. Phys. 1976, 65, 4668. (56) Furue, H.; Pacey, P. D. J . Chem. Phys. 1985, 83, 2878.
The Journal of Physical Chemistry, Vol. 94, No. 4, 1990 1421
TABLE II: Summarr of Input Parameters OH + H2 NH2 + Hz CH3 + Hz CH3 t HCI n wllr cm-I w,, cm-I wrl. cm-I wC2.cm-I w,’,cm-’ LT#
3
5 1497
5 580
1595
1627 950
1306 1306
1 2
1 4 3 105.8
3
“reactant “product
2
I , f I z # I,#,
37.78
g’ .A6 mo1-l A, cm-’
12 12 261.8
139.7
6 580 2990 1306 1306 3019 3 6 12 23, 147 882.35
combinations of frequencies. Instead, we will take an idea from RRKM theory57 and group these frequencies and replace them by a single frequency. The partition function for bending vibrations in the activated complex then becomes Qv(T,w~)= [ I
- exp(-hcw~/k~7‘)]-~
(7)
Here, n is the number of vibrations treated in this fashion. This separation of vibrational modes is similar to the separation into conserved modes and transitional modes for unimolecular reaction^.^^ Here, we will call the modes constant modes and variable modes. We may test the accuracy of this approximation by considering reaction 3, for which ab initio calculationss9 are available. Here, there are five variable modes in the activated complex: two doubly degenerate bends with term values 592 and 1146 cm-’ and an umbrella bend with term value 995 cm-I. The doubly degenerate modes correspond to two translations and two rotations in the reactants and to two translations and two H-C-H bends in the products. The product of the vibrational partition functions for these five modes in the complex is 1.369 at 400 K and 5 1.6 at 2000 K. Substituting these values in eq 7 and solving for the effective average term value, W B , one finds 778 cm-l at 400 K and 842 cm-’ at 2000 K. These are less than the average of the term values, 894 cm-I. At high temperatures, one expects the product of partition functions to approach the product of the classical values, n i k B T / ( h c w B i )The . effective term value, wB,should approach the geometric mean value. In the present case, the geometric mean is 855 cm-I, very close to the calculated value at 2000 K. At lower temperatures, the partition function is dominated by the lower frequency vibrations and the effective term value is 9% lower. Our assumption that the six other vibrational partition functions remain constant may also be tested for this reaction. The quotient of these vibrational partition functions for the activated complex59 divided by the reactants at 2000 K is 1.239. For the activated complex divided by the products, the quotient is 1.147. Here, the major contribution is the 1960-cm-l stretching mode in the complex, which correlates with the H-H stretch in the reactants and a C-H stretch in the products. These modes do have a significant effect on the rate at high temperature, but a much smaller effect than the variable modes. If we multiply these quotients by the factor of 5 1.6 for the variable modes and solve eq 7 for the effective term value, we find the results are 5.6% and 3.7% less than the values obtained in the previous paragraph. Thus, we expect the present approximation will give a reasonable representation of the temperature dependence of the vibrational partition functions, but we expect the fitted term values to be somewhat less than the geometric mean of the variable term values. The numbers, n, of variable modes for the reactions are listed in Table 11. These modes are bending modes in the complexes, except for reaction 4, where the symmetric stretching mode, which involves the heavy atoms C and C1, is also likely to have a low frequency. The term values for variable vibrational modes in the (57) Marcus. R. A . J. Chem. Phvs. 1952., ~~, 20. 355 .~ ( 5 8 ) Wardlaw, D. M.; Marcus, R. Archem. Phys. Lett. 1984, 110, 230. (59) Walch, S. P. J . Chem. Phys. 1980, 72, 4932.
1422 The Journal of Physical Chemistry, Vol. 94, No. 4, 1990 TABLE 111: Parameters in Equation 6 for Reaction of OH with H2 from Fits to Exwrimental Data and from Theoretical Calculations
source
El
- E,,
kJ mol-’
Ef.
kJ mol-’
wB, cm-’
Furue and Pacey 30
i
OH*H2
P,K
expt (0.09)
-61.0 f 0.6 23.8 f 0.6 796 f 20 176 f 36 JANAFm -61.3 f 1.2 ab i n i t i 0 ~ ~ 9 ~ ’ -52.9 24.8 722 (379) SOSAGS(0.03) 27.6 f 0.3 729 i 12 288 f 6 saddle5 24.5 741 349 VAS 27.3 653-687 285
reactants, wfl and w,, and in the products, wrl to wr3,are also listed. These values are harmonic frequencies from the JANAF tables@ to ensure consistency with later thermochemical comparisons. The numbers of term values listed are less than the values of n because some vibrations in the transition state become translations or rotations in the reactants and products. The remaining term, log Bf(T) or log Br(T), in eq 6 may be calculated by the standard methods of TST.6’ Here BT. BR,Bv, and BE are contributions from translational, rotational, vibrational, and electronic partition functions. BV is the contribution from variable vibrational modes in the reactants. For reaction lf, this is unity. For reactions 2f, 3f, and Ir, it is the inverse of quantal vibrational partition function for frequencies wfl or wrl. For the other cases, it is the inverse product of the reactant variable vibrational partition functions. The quotient, BT, of translational partition functions can be calculated by standard methods from molecular masses.61 The quotient, BR,of rotational partition functions was calculated from classical formulas for linear or nonlinear molecules.6’ Symmetry numbers are listed in Table 11. Moments of inertia of polyatomic reactants were obtained from the JANAF tablesa The product, I , +12+Z3+,of the transition-state moments of inertia could have been treated as a fifth parameter. However, the experimental data are not sufficiently precise to determine five parameters. Therefore, we have used internuclear distances from a b initio calculations for reaction 162 and semiempirical calculations for reactions 2,63 3,64and 443to calculate the products of moments of inertia listed in Table 11. Semiempirical methods usually give consistent moments of inertia, even though they do not give reliable energies. The electronic quotient, BE,is unity except for reactions If and 4r. For these two cases, it is necessary to take spin-orbit effects into account.65 For reaction If, this factor is 2/[2 + 2 X exp(-hcA/kBT)] and for 4r, 2/[4 + 2exp(-hcA/kBT)]. Here, A is the spin-orbit coupling constant,60which is listed in Table 11. Use of these formulas assumes that there is no change in electronic state as the reactive collision proceeds.
IV. Results and Discussion The four parameters in the TST model have been fit to the experimental data by a nonlinear least-squares method.66 Reaction 1. Parameters obtained by fitting eq 6 to the forward and reverse data for the OH, system are listed in the first line of Table 111. Here and elsewhere, quoted uncertainties are standard deviations. The number (0.09) in parentheses is the square root of the mean square residual (SRMSR) between experimental and fitted points, in log units. This corresponds to an absolute difference between observed and fitted rate constants of 23%. (60) Chase, M. W., Jr.; Davies, C. A,; Downey, J . R., Sr.; Frurip, D. J.; McDonald, R.A.; Syverud, A. N. JANAF Thermochemical Tables, 3rd ed.; US. Department of Commerce: Washington, DC, 1986, (61) Johnston, H. S . Gas Phase Reaction Rate Theory; Ronald: New York, 1966. (62) Walch, S. P.; Dunning, T. H., Jr. J . Chem. Phys. 1980, I I , 1303. (63) Calculated using the bond energy bond order method of ref 61. (64) Zavitsas, A. A,; Melikian. A. A. J . Am. Chem. SOC.1975, 97, 2757. (65) Truhlar, D. G. J . Chem. Phys. 1972, 56, 3189. (66) Ralston, M. In BMDP Statistical Software; Dixon, W. J . , Ed.; University of California: Berkeley, CA, 1983; p 305.
s/pm
Figure 1. Effective reaction barriers for reaction 1 as a function of the reaction coordinate: -, Eckart curve inferred by fitting eq 6 to exper-
e,
imental data; 0 , the sum, of potential energy and vibrational zeropoint energy as calculated in ref 5 from a surface fitted6’ to ab initio saddle point properties;62- -,Eckart curve inferred by fitting eq 6 to the results of sophisticated TST calculation^,^ which employed the same fitted s~rface.~’ The accepted internal energy change for this reaction at absolute zero is given in the second line. This agrees with the value inferred from the kinetic data, which gives confidence that the present method can give reliable thermodynamic values. The results of ab initio calculations62on this system are shown in the third line. The zero-point internal energy change, Ef - E,, differs from the values above it, reflecting the difficulty in performing accurate quantum chemical calculations on systems of this complexity. The values of El agree within 1 kJ mol-’ and of wB within 10%. In both cases, the agreement is within the accuracy of the ab initio calculations. The quoted ab initio value of Ef is the vibrationally adiabatic (VA) barrier height, including vibrational zero-point energy as well as electronic energy.6’ This is believed to give a more realistic barrier to reaction than the electronic energy alone. The ab initio value of T* is for the electronic barrier alone and so is not directly comparable with the experimental value. The a b initio value of wB quoted here and elsewhere in the article is the geometric mean for the variable modes. Isaacson and TruhlarS have performed canonical variational TST calculations for reaction If at eight temperatures. The fourth line in Table 111 shows the results of a fit of eq 6 to the rate constants obtained with one of their tunneling models, the SOSAG model, involving a second-order action angle treatment of the vibrationally abiabatic ground-state potential. Ef - E, and the product of moments of inertia were fixed at the values used in ref 5. The fit is excellent; the absolute difference corresponding to the SRMSR is 6%. Immediately below this line are properties of the saddle point of the potential energy surface on which the TST calculations were performed. This surface was based on the ab initio calculations quoted two lines earlier, and consequently, the parameters are very similar. The bending frequency also agrees with the fitted value in the line above, but the saddle p i n t value of Ef is 3 kJ mol-’ less. This difference is likely caused by the fact that the maximum of the sum of zero-point and electronic energies (VA energy) occurs along the reaction coordinate from the saddle point or maximum of electronic energy. The maximum of the former quantity is listed in the final line of the table. This is in excellent agreement with the fitted value, as it should be, since the VA surface was employed for the CVTST calculations. The values of wB listed in this line correspond to the canonical variational transition states at 0 and 2400 K. The value of T* on this line has been calculated from the VA maximum and points 0.1 bohr (67) Schatz, G . C.; Elgersma, H. Chem. Phys. Lett. 1980, 73, 21
The Journal of Physical Chemistry, Vol. 94, No. 4, 1990 1423
Activation Barriers from Thermal Reaction Rates TABLE IV: Parameters in Equation 6 for Reaction of NH2 with H2 from Fits to Experimental Data and from Theoretical Calculations
TABLE V Parameters in Equation 6 for Reaction of CH3 with HZfrom Fits to Experimental Data and from Theoretical Calculations El
expt A (0.10)12-15 -13.3 f 0.03 -12.6 f 0.2 exut B (0,10)12-15J7 adinitid1 ’ J ANA F72 -16 f 6 Demissy” -8 f 6 Hack12 -16 f 7 Gibson” -14.5 f 1.2 Sutherland” -15.4 f 1.2
60 f 1 56 f 1 66.6
975 f 31 1034 f 25
951
406 f 60 162 f 86 (567)
on either side of i t 5 It is in excellent agreement with the value inferred two lines above. Some results for this reaction are summarized in Figure 1. The circles show points along the VA barrier as calculated in ref 5 from the fitted surface of ref 67. The dashed curve is an Eckart curve inferred in the present work from the TST rate constants of ref 5. The top of the barrier is reproduced almost perfectly. In the middle range of energies, the Eckart curve is shifted somewhat toward the product side. The solid curve is an Eckart barrier inferred herein from experimental data. It is somewhat broader and lower than the theoretically based barriers. Absolute rate constants for the barriers would be very similar, but an Arrhenius plot for the higher, thinner barrier would be more curved. In preparing this graph, the zero of energy was taken as the zero-point energy of the reactants. The zero of the reaction coordinate, s, was taken at the VA barrier maximum. The scale of the reaction coordinate is appropriate for motion of a hydrogen atom. Data for reaction 1 f have previously been fitted by an expression of the log kf = log F
+ ( C / R ) log T - G/2.303RT
(9)
Values of C, the heat capacity of activation, lay between 11 and 15 J K-’mol-’. The other parameters do not have a simple significance. Reaction 2. The results of fitting high-temperature data for reaction 2 are listed in the first line of Table IV. The second line shows the results of including also the flash photolysis results of Demissy and Lesclaux17 from 400 to 500 K. These results are somewhat slower than a curve extrapolated from the high-temperature data, and accordingly, they give a lower barrier height and tunneling temperature. The values of E,, wB,and T* from ab initio calculations of Melius’l are in better agreement with experiment if the results of ref 17 are excluded than if these results are included. (Note that E, is quoted for this reaction instead of Ef in order to facilitate this comparison.) The value of T* from the full data set seems particularly low, although the ab initio value of Tc is not corrected for zero-point energy. This provides evidence that the partial data set, represented by expt A, is preferable. Based on these considerations, we recommend -13.3 kJ mo1-I as the value of El - E,. Combined with other quantities from the JANAF table^,^,^^ this corresponds to a bond dissociation energy (De) in NH3 of 445.3 kJ mo1-I and standard enthalpies of formation (AHr’) of NH2 of 190.4 kJ mol-I at 0 K and 187.5 kJ mol-’ at 298 K. The value of Ef - E, agrees with most earlier results, listed in Table IV, within the quoted uncertainties of the earlier results. (68) Gardiner, W. C.; Mallard, W. G.; Owen, J. H.J. Chem. Phys. 1974, 60, 2290. (69) Zellner, R. J. Phys. Chem. 1979, 83, 18. (70) Cohen, N.; Westberg, K. R. J. Phys. Chem. Ref Data 1983,12, 531. (71) Melius, C. F. Quoted in ref 14. (72) Chase, M. W., Jr.; Curnutt, J. L.; Downey, J. R., Jr.; McDonald, R. A.; Syverud, A. N.; Valenzuela, E. A. J. Phys. Chem. Ref. Data 1982, 11, 695. (73) Gibson, S.T.;Greene, J.; Berkowitz, J. J. Chem. Phys. 1985, 83, 43 19.
source expt (0.19) JANAF60 POICIS9 M R6 ICVT/MR6 (0.008) J37 ICVT/J3’ (0.02)
- E,,
kJ mol-’ 5.5 f 0.5 0.1 -9.3 28.5 28.75 f 0.04 0.1 0.3 f 0.1
El, kJ mol-l 61.0 f 1.5
wa. cm-’ 772 f 37
55.8 54.8 55.6 f 0.1 50.5 51.0 f 0.2
855 569 844 f 5 889 970 f 9
71. K 460 f 41 (223) 327 309 f 5 (249) 312 f 5
(In preparing Table IV, we have used values of AHf’ or De from the cited work and other quantities from the JANAF tables,60 as needed.) The present value of Ef - E, is 2 kJ mol-’ less negative than the result of Sutherland and Mi~hae1.l~This requires comment, as about half the data used in the present work came from Sutherland and Michael’s study. The reason for the difference is the inclusion of the values of k2, from Fontijn’sIs experiments. These values are larger than Sutherland and Michael’s values. In view of this difference, the uncertainty in our quoted thermochemical values is probably 2 kJ mol-’. Reaction 3. Parameters fitted to the data for reaction 3 are presented in the first line of Table V. According to these results, the reaction is about 5 kJ mol-I endothermic at 0 K. This contrasts with the accepted view that this reaction is thermoneutral.@ This discrepancy has previously been discussed by Kerr and Parsonage74 and by S h a ~ .It ~could ~ be caused by an error in the thermochemistry, in k3for in k3,. The thermochemistry of CH3 has been confirmed by several t e c h n i q ~ e s . ’ - ~The ~ * values ~ ~ of k3fhave been obtained with good reproducibility. The results for the reverse reaction are more scattered, both within experimental studies and between studies. In some cases, the concentrations of H atoms were estimated from rates of reference reactions that are not well-known. In other cases, H atoms may also react with the product, CH3, and it is difficult to know what stoichiometric coefficient to apply. Further experimental work on this reaction is recommended. A referee has asked about possible correlation between the parameters, Le., the sensitivity of one to variations in the other three. We have tested this by fixing one parameter at a value 1 standard deviation greater than its fitted value and observing changes in the fitted values of the others. Increasing E f - E, increased the other parameters by 0.1-0.2 standard deviation. Increasing one of the other parameters, e.g., wB,increased Ef E, by 0.1 standard deviation and decreased the others by about 0.8 standard deviation. Thus, the transition-state parameters, Ef, wB,and P,are strongly correlated to each other but weakly correlated to the thermodynamic quantity Ef - E,. The quoted standard deviations do incorporate uncertainties caused by these correlations. In the third line of Table V are the results of the ab initio calculations of W a l ~ hincorporating ,~~ configuration interaction. These calculations predict the reaction to be substantially exothermic, in contradiction to all experimental results. This low ab initio zero-point energy for the products is reflected in a lower energy at the barrier top as well. The geometric mean of the five lowest vibrational frequencies is in good agreement with the value inferred from experiment, especially considering the 10% uncertainty in quantum mechanical results. The quoted value of T* is for a bare potential barrier without zero-point energy. In the next line of the table are parameters from the Raff semiempirical potential energy surface as modified by Steckler et aL6 This surface is strongly endothermic and hence unrealistic, but it is included in the table because it has been the subject of improved canonical variational transition-state-theory calculations employing the small-curvature semiclassical adiabatic ground-state (74) Kerr, J. A.; Parsonage, M. J. Evaluated Kineric Dura on Gas Phase Hydrogen Transfer Reacrions of Methyl Radicals; Butterworths: London, 1976. (75) Shaw, R. W. J. Phys. Chem. Ref Data 1978, 7, 1179. (76) Pacey, P. D.; Wimalasena, J. H. J. Phys. Chem. 1984, 88, 5657.
1424 The Journal of Physical Chemistry, Vol. 94, No. 4, 1990 TABLE VI: Parameters in Equation 6 for Reaction of CH, with HCI from Fits to Experimental Data
source expt (0.06) JANAF a b initio79
E, - E,, kJ mol-' -4.7 f 0.1
El, kJ mol-' 7.6 f 0.8
789 A 71
9.6
619
WE,
cm-'
P,K 11 1 f 60
-4.2
-5.0
(217)
tunneling approximation6 (ICVT/SCSAG). These sophisticated TST rate constants have been fitted by our simple model, with the moments of inertia and reactant and product frequencies adjusted to agree with this surface. The results appear in the following line. The fit to the 13 ICVT rate constants is excellent; the greatest residual corresponds to a difference in rate constants of 3'70. The endothermicities match within 0.25 kJ mol-'. The adiabatic barrier height (54.8 kJ mol-') for this surface agrees with the fitted value within 0.8 kJ mol-'. The characteristic tunneling temperature for the adiabatic barrier (327 K) agrees well with the fitted value. There is a difference of 275 cm-' between the fitted bending frequency and the harmonic mean value for the saddle point of the potential energy surface. Steckler et aL6 have shown that these frequencies increase steeply along the reaction coordinate from the saddle point to the location of the vibrationally adiabatic barrier top. Thus, the fitted parameters are closer to the properties of the vibrationally adiabatic barrier. A similar comparison for the more realistic 53 surface of Joseph et al.' appears in the final lines of Table V. This surface (described in the second to last line) has been adjusted until the ICVT/ SCSAG rate constants and isotope effects and the overall equilibrium constant were in reasonable agreement with experiment. The value of T* quoted is for a bare potential barrier. The reactant frequencies in our model have been changed to agree with the 53 surface. The four remaining parameters in the model have been fit by least squares to the 22 ICVT/SCSAG rate constants for this surface from ref 7 . The largest deviation between fitted and calculated rates was 11%. The fitted parameters in the last line are similar to the surface properties above them. Data on the forward reaction were previously fit to a TST expression with bending vibrational frequencies taken from ab initio calculations and the moments of inertia allowed to vary.* The effective barrier height was found to be 67 f 2 kJ mol-' and T*, 485 f 32 K . Heat capacities of activation from fits to eq 9 range between 17 and 41 J K-I mol-1.2~2437s Reaction 4 . Parameters obtained by fitting our model to the selected data for this reaction are given in the first line of Table VI.
The fitted exothermicity at 0 K agrees well with the accepted value from the JANAF tables.60 Thus, in this case, the heat of formation of CH3 is confirmed. However, if we had included the early data from steady-state photolysis experiments on reaction 4f and excluded the recent VLPR and mass spectrometric experiments, we would have found the reaction to be thermoneutral. This result would have been in line with our fit for reaction 3. There have not been any ab initio calculations on this but semiempirical calculations have been performed using the bond energy bond order (BEBO) This method gives a barrier height 2.4 kJ mol-' greater than we find. It was not possible to find all the bending frequencies by the BEBO method, so some were adjusted to agree with experimental rates. The harmonic means of the six lowest frequency vibrations in the transition states were 624 and 762 cm-' in ref 44 and 77, respectively. These are similar to our fitted value. A fit of eq 9 to data for the reverse reaction gives a heat capacity of activation of 18 J K-' mol-'.44 (77) Whytock, D. A,: Lee, J. H.; Michael, J. V.: Payne. W. A,; Stief, L. J . J . Chem. Phys. 1977, 66, 2690. (78) Since this article was submitted a study of reaction 18 at 1200 K has appeared (Bott, J. F.; Cohen, N . Inr. J . Chem. K i m . 1989, 21, 485). (79) Since this article was submitted ab initio calculations have been reported (Truong, T. N.; Truhlar, D. G.; Baldridge, K. K.; Gordon, M. S.: Steckler, R. J . Chem. Phys. 1989, 90, 7137). Results are in the last line of Table VI.
Furue and Pacey V. Conclusions
In this section, we will summarize the results and attempt to draw some general conclusions. We begin by examining the fits of our model to the results of more sophisticated VTST calculations. The more sophisticated calculations are not necessarily correct, but the treatment of tunneling is superior to our own. The question is whether our one-dimensional tunneling model can successfully mimic a multidimensional effect. First, we observe that the fits in Tables 111 and V were good, with SRMSR between 0.008 and 0.03. Second, the values of El - E, reproduce those of the original surface within 0.25 kJ mol-'. Such differences may be the result of rounding errors and small differences in the treatment of vibration and rotation in reactants and products. Values of EEagree with the original vibrationally adiabatic barrier heights within 0.8 kJ mol-'. The surface with the largest difference has a rather sharp barrier: so these differences may be a reflection of the individualistic shapes of the barriers. Here, we recall that we found a larger difference in E f in a fits6 to the results of even more sophisticated quantum dynamical calculations. It is more difficult to make comparisons for the effective bending frequency, wB,because we have used a single frequency to represent several frequencies. It appears that the fitted frequency agrees with the geometric mean frequency at the vibrationally adiabatic barrier top within about 10%. We would expect that the characteristic tunneling temperature would be related to the curvature of the top of the vibrationally adiabatic barrier. There are only two cases (the VA barrier in Table I11 and the MR surface in Table V) where the latter quantity is available. Here, the fitted values of T* agree with the values calculated from the barrier top within 6%. Because of the tendency for quantal particles to cut the corner between reactant and product valleys, we had not anticipated that the agreement would be this good. In summary, values of E f and E, from our fits correspond to the vibrationally adiabatic barrier heights in ICVT calculations with multidimensional tunneling corrections; values of T* and wB agree reasonably well with the curvature and geometric mean bending term value at the vibrationally adiabatic barrier top. With respect to the fits to experimental data, the most striking conclusion is the sensitivity of values of El - E, to systematic errors in the rate constants. This is most dramatic for reaction 3, where there is a discrepancy in k3for k3rat low temperatures. We note a tendency in a number of studies to perform experiments at many temperatures but, at each temperature, to examine only one experimental condition or perhaps a few conditions with small changes in concentrations, flow rates, etc. In such cases, one cannot be sure that quoted "rate constants" are indeed constant. It would be of more benefit to our purpose to have some studies performed at a single temperature but with all other experimental conditions varied by about 1 order of magnitude to demonstrate that there are no interfering processes. The standard deviations of El - E, are small, from 0.1 to 0.6 kJ mol-'. This reflects the precision of modern kinetic techniques and indicates the potential of kinetics to provide valuable thermochemical information, if systematic errors can be eliminated. The present method provides smaller standard deviations for E r - E, than previous methods of analyzing kinetic data. For example, Arrhenius activation energies usually have substantial uncertainties (unless the Arrhenius plot is very linear and very extensive). When activation energies are subtracted to find AH, the uncertainties accumulate. As we saw in our discussion of reaction 3 and Table V, errors in the predominantly kinetic pado not induce significant errors in Er rameters, E,, wB,and P, - E,. Our absolute values of Ef- E , are in agreement with accepted values for three of the four reactions. We recommend the value of E , - E, from spectroscopy60 for reaction 1 and the present value for reaction 2 and we recommend further work on reactions 3 and 4. The other parameters inferred from experiment are also subject to possible systematic errors in the data. The only competing
J. Phys. Chem. 1990, 94, 1425-1431
1425
must be available for the reverse reaction. The method can be directly applied to other reactions that meet the above criteria. Where transfer of a hydrogen atom is not involved, the tunneling factor and Tc should be deleted. Where one of the moments of inertia or a reactant or product frequency is unknown, it could then replace Tc as the fourth parameter. If the range of the data is limited, T* or wB could be fixed at a theoretical value. The range and precision of the experimental data will determine the number and reliability of the parameters determined. The method simultaneously tests the accuracy of the kinetic and equilibrium data, the validity of the TST model, and the reliability of parameters obtained from thermochemical tables and ab initio calculations. In the present test, reasonable values have been obtained for 15 of the 16 parameters.
method of determining these quantities is a b initio calculation. The present method gave more accurate values of Ef - E , than ab initio calculations. By analogy, we argue that the present values of Ef and E, are also more accurate. In any case, values of Ef and E, from a b initio calculations agree with the present results within 10 kJ mol-'; values of w B agree within 10%. Values of Tc for vibrationally adiabatic barriers are not available from ab initio calculations. Values of wBare similar for all four reactions. Ef - E,, Ef, and Tc change dramatically from reaction 1 to 2 but change little from reaction 2 to 3. This reflects the strong polarity of the O H bond and the weak polarities of the N H and C H bonds. Barrier heights and T* are sharply lower for reaction 4; the former effect has been attributed to the polarizability of CLS2 We have applied a new least-squares method to determine four parameters for each of four activation barriers. In its present form, the method works for hydrogen atom transfer reactions. Moments of inertia of reactants, products, and transition state and frequencies of the variable vibrational modes in reactants and products are required as input. Rate constants for the reaction must have been measured over a wide temperature range and a rate constant or equilibrium constant at one temperature or more
Acknowledgment. We thank the Natural Sciences and Engineering Research Council of Canada for financial support and A. Fontijn, R. M. Marshall, M. J. Pilling, and D. G. Truhlar for valuable correspondence. Registry No. O H , 3352-57-6; H2, 1333-74-0; CH,, 2229-07-4; HCI, 7647-01-0; H , 12385-13-6; H,O, 7732-18-5; NH3, 7664-41-7; CH,, 7482-8; CI, 22537-15-1.
Effects of Nodal Plane of Wave Function upon Photochemical Reactions of Organic Molecules Shin-ichi Nagaoka*.+and Umpei Nagashima Institute for Molecular Science, Okazaki 444, Japan (Received: April 18, 1989; I n Final Form: July 18, 1989)
Explanation similar to that given for intramolecular proton transfer in excited states [ J . Phys. Cfiem. 1988, 92, 1661 often applies equally well to other photochemical reactions of organic molecules. The reason for the reactions is understood by considering the nodal pattern of the wave function in the excited state. The nodal plane stabilizes the products.
important role in the dynamic process in the SI(") state.5 Qualitative features of the ab initio calculation results of OHBA are consistent with this explanatiom6 In the S2(")state, the closed conformer is preferentially stabilized. This prediction is consistent with the absence of proton transfer in the S,(*) state of OHBAe3s5 In this report, we show that explanation similar to that mentioned above often applies equally well to other photochemical reactions of organic molecules. Many photoreactions can be rationalized considering the nodal pattern of the wave function in the excited state.
Introduction Proper qualitative explanation for various photochemical reactions allows us to recognize their important features immediately and provides useful information on the reaction mechanisms. The photoreaction mechanism must include knowledge of the force responsible for converting structures. The nodal pattern of the wave function can become a strong candidate for the force. In previous papers,'" we reported intramolecular proton transfer in various electronic states of o-hydroxybenzaldehyde (OHBA). The reason for the intramolecular proton transfer is understood by considering the t-electron nodal pattern in the excited state (Figure In the La state of benzene, two t electrons are localized on the C, and C2 atoms owing to the nodal plane shown in Figure 1 By substitutions of C H O and O H groups for the H I and H, atoms, respectively, benzene results in the closed conformer of OHBA. If the intramolecular proton transfer to yield the enol tautomer takes place in the La state, the two electrons can be largely delocalized as the result of the formation of the Cl=Co and C2=02 bonds. The La state of the enol tautomer of OHBA thus becomes significantly lower in energy than that of benzene owing to the delocalization, and in OHBA the 'La and 'Lbstates result in the first excited '(t,r*)state (SI(")state) and the second excited '(t,t*) state (S2(")state), respectively (Figure 1). The nodal plane stabilizes the proton-transferred enol tautomer in the SI(*)state.g The deformation of the benzene skeleton plays an
(1) Nagaoka, S.; Hirota, N.; Sumitani, M.; Yoshihara, K. J. Am. Chem. SOC.1983, 105, 4220. (2) Nagaoka, S.;Hirota, N.; Sumitani, M.; Yoshihara, K.; LipczynskaKochany, E.; Iwamura, H. J. Am. Chem. Soc. 1984, 106, 6913. (3) Nagaoka, S.; Fujita, M.; Takemura, T.; Baba, H. Chem. Phys. Left. 1986, 123,489. (4) Nagaoka, S. J. Photochem. Photobiol. 1987, A40, 185. (5) Nagaoka, S.; Nagashima, U.; Ohta, N.; Fujita, M.; Takemura, T. J . Phys. Chem. 1988, 92, 166. (6) Nagaoka, S.; Nagashima, U. Chem. Phys. 1989, 136, 153. (7) Hoshimoto, E.; Nagaoka, S.;Yamauchi, S.; Hirota, N. Absfrucr of Papers, Annual Symposium on Molecular Structure, Tokyo, Japan, Oct. 1988; p 682. (8) Nagashima, U.; Nagaoka, S.; Katsumata, S., manuscript in preparation. (9) If this is the case, the dynamic process in the SI(")state is more properly called hydrogen t r a n ~ f e r . ' . ~As . ~ described previously,6 we cannot unambiguously determine whether or not the proton (or hydrogen atom) really transfers in the SI(.) state. In this paper, we use the term proton transfer according to custom.
I
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Present address and address for correspondence: Department of Chemistry, Faculty of Science, Ehime University, Matsuyama 790, Japan. 0 0 2 2 - 3 6 5 4 ,/ 9 0 /,2-0 9- 4 -
1425$02.50/0 I
0 1990 American Chemical Societv -
