Analytical Surface for the Reaction with No Saddle-Point NH 3 + F f NH 2 + FH. Application of Variational Transition State Theory Joaquı ´n Espinosa-Garcı ´a* and Jose ´ C. Corchado Departamento de Quı ´mica Fı ´sica, UniVersidad de Extremadura, 06071 Badajoz, Spain ReceiVed: January 16, 1997; In Final Form: March 21, 1997 X The title reaction and its deuterated analogue (ND 3 + F f ND 2 + FD) were studied by means of an analytical expression for their potential energy surface. The analytical form is the one previously used for the similar NH 3 + H f NH 2 + H 2 reaction. As calibration criteria, we used the reactant and product experimental properties and the theoretically calculated properties of a hydrogen-bonded complex linking NH 2 and FH. Using this potential energy surface, we analyzed the effects of the reaction path curvature (translation- vibration coupling) in order to explain the low vibrational excitation observed for the FH product, as a result of the compensation between the effects of the reaction path curvature and the randomization of the energy favored by the deep hydrogen-bonded well. Variational transition state theory was used to calculate the rate constants for the title reaction and the kinetic isotope effects over the temperature range 100-500 K, finding that anharmonic effects are very important: they lower the rate constants by a factor of about 200 and make the agreement between our theoretical values and the experimental estimates reasonable. Finally, our results were compared with those obtained by means of the simple Gorin model that yields values very close to the experimental measurements. Introduction The title reaction is difficult to study experimentally, because it is a fast reaction followed by the extremely fast secondary atom/radical reaction F + NH 2 f FH + NH, which is hard to eliminate by conventional experimental techniques. The title reaction has been widely studied by several experimental techniques, 1-9 and it yields a cold (noninverted) vibrational distribution of the FH product, although discrepancies have been found in the past, probably due to the experimental difficulties. Sloan et al. 6,8,9 have suggested that this cold, noninverted vibrational distribution could be caused by a strongly hydrogen- bonded FH‚‚‚NH 2 complex in the exit channel, which causes a randomization of the reaction exoergicity among all available product degrees of freedom. This behavior has been found in similar atom/radical reactions, such as 10 F + HO f FH + O and 11 F + HCO f FH + CO, which present a deep well in the exit channel corresponding to a strongly bound intermediate. The rate constants also present large discrepancies with values ranging from 10 -10 to 10 -12 cm 3 molecule -1 s -1 at room temperature, 7,12-14 although few studies have been made. The extensive experimental literature on this reaction contrasts with the paucity of theoretical studies, of which, to the best of our knowledge, there have been only two reported. In the first, Leroy et al. 15 studied the reaction using the ab initio UHF/6- 31G level, with energy properties computed at the configuration interaction level. In the second, Goddard et al., 8 using high- level ab initio calculations (up to 6-311G** CISD) found a hydrogen-bonded complex, FH‚‚‚NH 2 , in the exit channel which is 8.1 kcal mol -1 more stable than the products. They suggested that this strong interaction will lead to fast internal vibrational relaxation of the exoergicity of the reaction, yielding a cold, noninverted, FH vibrational distribution. These theoretical works only studied the reactants, products, and complex properties, and the computational efforts to locate a saddle point were unsuccessful. Moreover, neither the reaction path nor the theoretical rate constants were calculated. The deuterated analogue reaction, ND 3 + F f ND 2 + F, has not been theoretically studied at all, and the few experi- mental measurements present contradictory results. 4,5,7,9 Thus, while Wategaonkar and Setser 7 found an inverted FD vibrational distribution, Donaldson et al. 5 found a hot (but noninverted) distribution, although these authors recognized a problem with their ND 3 data because the ND 3 + F distribution is partly contaminated by a contribution from the secondary ND 2 + F reaction, which produces an inverted FD distribution. These practically barrierless hydrogen abstraction reactions are an exciting challenge for theoretical calculations, and since there is experimental interest in them, we have carried out a broad theoretical study of the reaction path to try to explain the product (FH/FD) vibrational distribution and to determine their rate constants using variational transition state theory . Methods and Calculation Details 1. Calibration of the Analytical Potential Energy Surface Function. The first step in our calculation was to obtain an analytical expression for the potential energy surface (PES) of this reaction. Since the complete construction of an analytical PES for a polyatomic reaction is an arduous task, we used the same methodology employed in previous work for developing analytical PES’s for polyatomic reactions, 16,17 based on modify- ing the analytical PES proposed for a similar reaction. We therefore changed some parameters of our recently proposed analytical PES for the NH 3 + H f NH 2 + H 2 reaction. 18 We changed the parameters related to the geometric, energy and vibrational properties of the reactants and products, so that the exothermicity, geometries, and vibrational frequencies agreed reasonably well with the available experimental values. 19 The results of this fit are listed in Table 1. In previous work, 16-18 the following step was to refit some parameters in order to reproduce the characteristics of an ab * Author to whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, May 15, 1997. 7336 J. Phys. Chem. A 1997, 101, 7336-7344 S1089-5639(97)00234-X CCC: $14.00 © 1997 American Chemical Society