H + CD 4 Abstraction Reaction Dynamics: Product Energy Partitioning ² Wenfang Hu, ‡ Gyo 1 rgy Lendvay, § Diego Troya, # George C. Schatz,* ,‡ Jon P. Camden, | Hans A. Bechtel, |,⊥ Davida J. A. Brown, | Marion R. Martin, | and Richard N. Zare | Department of Chemistry, Northwestern UniVersity, EVanston Illinois 60208-3113, Chemical Research Center, Hungarian Academy of Sciences, H-1525 Budapest, P.O. Box 17, Hungary, Department of Chemistry, Virginia Tech, 107 DaVidson Hall, Blacksburg, Virginia 24061-0212, and Department of Chemistry, Stanford UniVersity, Stanford, California 94305-5080 ReceiVed: September 5, 2005; In Final Form: NoVember 12, 2005 This paper presents experimental and theoretical studies of the product energy partitioning associated with the H + CD 4 (ν ) 0) f HD + CD 3 reaction for the collision energy range 0.5-3.0 eV. The theoretical results are based on quasiclassical trajectories from (1) first principles direct dynamics calculations (B3LYP/ 6-31G**), (2) an empirical surface developed by Espinosa-Garcı ´a [J. Chem. Phys. 2002, 116, 10664] (EG), and (3) two semiempirical surfaces (MSINDO and reparametrized MSINDO). We find that most of the energy appears in product translation at energies just above the reactive threshold; however, HD vibration and rotation become quite important at energies above 1 eV, each accounting for over 20% of the available energy above 1.5 eV, according to the B3LYP calculations. The barrier on the B3LYP surface, though being later than that on EG, predicts significantly higher HD vibrational excitation than EG. This deviation is contradictory to what would be expected on the basis of the Polanyi rules and derives from modest differences in the potential energy surfaces. The CD 3 internal energy is generally quite low, and we present detailed rotational state distributions which show that the CD 3 rotational distribution is largely independent of collision energy in the 0.75-1.95 eV range. The most populated rotational levels are N ) 5 and 6 on B3LYP, with most of that excitation being associated with motion about the C 2 axes, rather than C 3 axis, of the CD 3 product, in good agreement with the experimental results. Through our extensive studies in this and previous work concerning the scattering dynamics, we conclude that B3LYP/6-31G** provides the best available description of the overall dynamics for the title reaction at relatively high collision energies. I. Introduction The H + CH 4 reaction and its isotopic counterparts are benchmark systems for gas-phase polyatomic reactions. Com- posed of only five light atoms in addition to the carbon atom, the H + CH 4 reaction represents the simplest example of the H + alkane reactions that are important in hydrocarbon combus- tion. The hydrogen abstraction reaction path, H + CH 4 f H 2 + CH 3 , is nearly thermoneutral, ∆H(0 K) )-9.3 × 10 -4 eV, 1 and proceeds through a C 3V transition state that is 0.64 eV above the reactants according to CCSD(T) calculations (Table 1). Numerous experimental studies have addressed the kinetics of both the forward and reverse reactions, 2-4 but relatively few have provided insight concerning the state-to-state dynamics 5,6 due to the small reaction cross section. For instance at 1.5 eV collision energy, the absolute total cross section is only 0.14 ( 0.03 Å 2 . 5 Extensive theoretical efforts have contributed to the construc- tion of the potential energy surface (PES), 7-15 and calculations of the rate constants and reaction dynamics. 3,16-34 The dynamics techniques employed include quantum dynamics, classical and quasiclassical trajectory methods, direct dynamics, transition state theory, and variants of transition state theory. In 1995, Jordan and Gilbert 12 published a 4-fold symmetric PES (here- after referred to as JG) based on the functional forms of the Joseph et al. potential. 11 This surface was used in many reduced- dimensionality 20,22-24,28-30 and full-dimensionality 25,26 quantum dynamics calculations to determine thermal rate constants but was found to have important flaws. Espinosa-Garcı ´a then recalibrated this surface with updated kinetic and ab initio data and developed a surface (EG) that is totally symmetric with respect to the methane hydrogens. A quantum instanton ap- proximation calculation 34 utilizing the EG surface obtained rate constants in the 200-2000 K range in good agreement with experiment. After that, Manthe and co-workers 15 proposed a high level ab initio PES that yields rate constants of accuracy comparable to the available experiments. This surface, however, is not globally defined and thus cannot be used in state-resolved dynamics. Although recent interest has been in the development of various approximate and exact quantum mechanical (QM) scattering calculations, the quasiclassical trajectory (QCT) method still plays a central role in providing valuable dynamical information for polyatomic reactions. Nevertheless, the complete construction of a multidimensional PES for use in dynamical simulations is a demanding task, even for this simplest of six- atom reactions, as it requires high quality electronic structure calculations over a broad range of molecular configurations. In the present study, we emphasize the use of direct dynamics in ² Part of the special issue “Ju ¨rgen Troe Festschrift”. * To whom correspondence should be addressed. E-mail: schatz@ chem.northwestern.edu. ‡ Northwestern University. § Hungarian Academy of Sciences. # Virginia Tech. | Stanford University. ⊥ Present address: Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA 02139. 3017 J. Phys. Chem. A 2006, 110, 3017-3027 10.1021/jp055017o CCC: $33.50 © 2006 American Chemical Society Published on Web 12/16/2005