Product Angular Distribution for the H + CD 4 f HD + CD 3 Reaction C. Rangel, J. Sanso ´ n, J. C. Corchado, and J. Espinosa-Garcia* Departamento de Quı ´mica Fı ´sica, UniVersidad de Extremadura, 06071 Badajoz, Spain G. Nyman* Department of Chemistry, Physical Chemistry, Go ¨teborg UniVersity, Sweden ReceiVed: May 29, 2006; In Final Form: July 19, 2006 Using an analytical potential energy surface previously developed by our group, namely PES-2002, we analyzed the gas-phase reaction between a hydrogen atom and perdeuterated methane. We studied the effect of quasiclassical trajectory (QCT) and reduced dimensionality quantum-scattering (QM) calculations, with their respective limitations, on CD 3 product angular distributions in the collision energy range 16.1-46.1 kcal‚mol -1 . It was found that at low collision energy, 16.1 kcal‚mol -1 , both the QCT and QM calculations yielded forward scattered CD 3 products, i.e., a rebound mechanism. However, at high energies only the QM calculations on the PES-2002 surface reproduced the angular scattering found experimentally. 1. Introduction The reaction of methane with hydrogen is the prototype of polyatomic reactions and has been widely studied both theoreti- cally and experimentally with two objectives: first, in itself, to obtain accurate kinetics and dynamics information and, second, as a test to probe the efficiency and accuracy of new experi- mental techniques and theoretical results (see ref 1 and refer- ences therein). Experimentally, state-to-state dynamics studies are difficult to perform at low energies for the title reaction, because the H atoms, which are produced in a photolysis process, are hot. Furthermore, the cross section is small, even for the case of high collision energies. For example, the reaction cross section is only 0.14 ( 0.03 Å 2 at 34.6 kcal‚mol -1 (ref 2). Thus, experimental studies of the product angular distributions 3-6 have been scarce, recent, and focused on the high-energy region. Only recently, Camden et al. 5 reported the first study of the state-to-state dynamics differential cross section at high energies (45.0 kcal‚mol -1 ) for the H + CD 4 gas-phase reaction. They found that the CD 3 products are sideways/backward scattered with respect to the incident H, suggesting a stripping mechanism. Later, this same laboratory 3,4 reported new experimental studies, also at high energy (27.8 kcal‚mol -1 ), finding the same experimental behavior. To explain the experimental product scattering distribution, these authors 3,4 performed quasiclassical trajectory (QCT) calculations on different potential energy surfaces (PES): (1) a DFT surface at the B3LYP/6-31G(d,p) level; (2) an analytic PES developed by our group, 1 named PES- 2002; and (3) two semiempirical surfaces, MSINDO and reparametrized MSINDO. They found that while the DFT surface reproduces the experimental behavior at high energies, the QCT calculations based on the PES-2002 surface give CD 3 products strongly forward scattered, suggesting a rebound mechanism, in strong contrast with the experimental evidence. In 2002, our group developed an analytical potential energy surface (PES-2002) to describe the H + CH 4 reaction and its isotopic analogues. 1 The PES is wholly symmetric with respect to the permutation of the four hydrogen atoms of methane and was calibrated to reproduce thermal rate constants, i.e., for low collision energies, using canonical variational statistical theory with semiclassical multidimensional tunneling (CVT/MT). From a kinetics point of view, it reproduces the behavior of the experimental measurements of thermal rate constants and kinetic isotope effects. Moreover, recently Zhao et al. 7 applied the quantum instanton approximation for thermal rate constants to this reaction using our PES-2002, finding good agreement with available experimental data over the wide temperature range 200-2000 K and concluded that this result lends support to the accuracy of the present potential energy surface. From a dynamics point of view, the PES-2002 surface qualitatively predicts that excitation of the CH 4 symmetric stretching and “umbrella” bend modes might be expected to enhance the forward rates, while only the CH 3 “umbrella” bend mode can appear vibrationally excited. This qualitative prediction agrees with other quantum scattering calculations. 8-10 We emphasize that the PES-2002 surface was calibrated to reproduce thermal rate constants, i.e., low energies, and its ability to reproduce dynamical features was neither sought nor tested. Given that the H atom is very difficult to obtain in thermal conditions, hot H atoms were used in the experiment and QCT calculations. 3-5 Thus, collision energies in the range 16.1-46.1 kcal‚mol -1 were used, as compared to the barrier height of 12.9 kcal‚mol -1 obtained with the PES-2002 surface. A priori, these experimental and previous theoretical calculations were performed at energies much higher than those taken into account during the calibration of the PES. As our analytical surface was fitted to reproduce thermal conditions, any calcula- tion based on this PES using these high energies would involve extrapolation to untested regions of the PES. Therefore, agree- ment between experiment and accurate theoretical calculations on PES-2002 would represent a predictive character of the PES. In general, when comparing theoretical and experimental dynamics results (in this case the product scattering distribu- tions), many factors are involved. First, of course, the quality and accuracy of the experimental data and, from the theoretical * Corresponding author. E-mail: joaquin@unex.es (J.E.-G.), nyman@ chem.gu.se (G.N.). 10715 J. Phys. Chem. A 2006, 110, 10715-10719 10.1021/jp063298+ CCC: $33.50 © 2006 American Chemical Society Published on Web 08/26/2006