Quasiclassical Trajectory Study of the CH 3 + + HD f CH 2 D + + H 2 Reaction † Kurt M. Christoffel, ‡ Zhong Jin, | Bastiaan J. Braams, § and Joel M. Bowman* Cherry L. Emerson Center for Scientific Computation and Department of Chemistry, 1521 Dickey DriVe, Emory UniVersity, Atlanta, Georgia 30322 ReceiVed: December 19, 2006; In Final Form: February 1, 2007 A full dimensional ab initio potential energy surface for the CH 5 + system based on coupled cluster electronic structure calculations and capable of describing the dissociation of methonium ion into methyl cation and molecular hydrogen (J. Phys. Chem. A 2006, 110, 1569) is used in quasiclassical trajectory calculations of the reaction CH 3 + + HD f CH 2 D + + H 2 for low collision energies of relevance to astrochemistry. Cross sections for the exchange are obtained at several relative translational energies and a fit to the energy dependence of the cross sections is used to obtain the rate constant at temperatures between 10 and 50 K. The calculated rate constant at 10 K agrees well with the previously reported experimental value. Internal energy distributions of the products are presented and discussed in the context of zero-point energy “noncompliance”. 1. Introduction Deuterated molecular hydrogen, HD, is the primary reservoir of deuterium in the dark, dense clouds of the interstellar medium (ISM). At the temperature of the ISM (approximately 10 K) the reactions of significance are exothermic and without any substantial activation barrier, primarily ion-molecule reactions. Three molecular ions in dark, dense interstellar clouds, H 3 + , CH 3 + and C 2 H 2 + , are known to exchange deuterium with HD. The exothermicity of these exchange reactions arises from zero- point energy differences between reactants and products. Since the reverse reactions are endothermic (and hence very slow) these exchange processes can produce deuterated ion (e.g., CH 2 D + ): normal ion (e.g., CH 3 + ) ratios that are orders of magnitude greater than the cosmic D:H ratio. 1,2 Rate constants (at approximately 10 K) for all three of these primary ion- molecule deuterium exchange reactions have been recently determined in a 22-pole ion trap apparatus. 3-5 In recent years within the chemical community there has been renewed interest in the methonium ion, CH 5 + . Almost since its discovery 6 in 1952, the issue of whether or not CH 5 + , a species exhibiting an unusual 3-center-2-electron bond, has a “struc- ture” has been a topic of speculation and (until recently largely theoretical) research. 7 This challenge motivated the pioneering density functional theory direct-dynamics studies of CH 5 + by Marx and Parrinello 8-10 that supported a fluxional nature for CH 5 + . In 1999 the high-resolution infrared spectrum of CH 5 + in the C-H stretching region (2770-3150 cm -1 ) was first reported by Oka and co-workers 11 and even now largely defies assignment and interpretation due to the large-amplitude motions and hydrogen scrambling. Both a low-resolution laser-induced reaction (LIR) spectrum of CH 5 + at 110 K (over the spectral range of 540-3250 cm -1 ) 12,13 and a high-resolution direct absorption spectrum of jet-cooled CH 5 + (over the spectral range of 2825-3050 cm -1 ) 14 have been very recently reported and analyzed. The development and refinement of a full dimensional potential energy surface (PES) in this lab has facilitated detailed dynamical studies of the CH 5 + system. 15-18 The earlier versions of this surface 15-17 were limited to energies well below the CH 3 + + H 2 dissociation threshold and were based on functional fitting of MP2 level electronic structure calculations. These surfaces were adequate for our earlier studies of bound CH 5 + dynamics and for diffusion Monte Carlo characterization of the quantum ground state. The latest version of our CH 5 + potential is based on higher quality CCSD(T)/aug-cc-pVTZ ab initio energies, has been extended to energies above the CH 3 + + H 2 threshold and incorporates established potentials to describe long-range in- teractions. 18 We use this surface here and the quasiclassical trajectory (QCT) method to study the dynamics of the astro- chemically significant CH 3 + + HD exchange reaction. The remainder of this paper is organized as follows. In section 2, we provide a description of the potential energy surface, the implementation of the QCT method for determining reaction cross sections and the method used to determine the rate constant for the CH 3 + + HD exchange in the temperature range 10-50 K. Our results are presented and discussed in section 3. In section 4, we summarize the important results and conclusions of our work. 2. Computational Details 2.1. Potential Energy Surface. Initial work in our lab toward development of a full-dimensional global potential energy surface for the CH 5 + system began late in 2002. The first reported version of the surface was based on Møller-Plesset perturbation theory (MP2) 19 level electronic structure calcula- tions using the correlation consistent polarization triple- (cc- pVTZ) basis set of Dunning. 20 These MP2/cc-pVTZ ab initio energies at 4096 unique geometries generated by direct dynamics trajectories at energies up to 8000 cm -1 above the CH 5 + global minimum were fit to a functional form that ensures the full permutational symmetry of the system. 15 Subsequently ad- ditional MP2/cc-pVTZ results generated on grids in normal coordinates and a new functional fit were used to obtain a potential energy surface reliable up to 13 000 cm -1 above the CH 5 + global minimum. 17 The geometries used in these potentials were focused in the region of the CH 5 + configuration space around the CH 5 + global † Part of the special issue “M. C. Lin Festschrift”. * Corresponding author. E-mail: jmbowma@emory.edu. ‡ Permanent address: Department of Chemistry, Augustana College, Rock Island, IL, 61201. § Present address: Department of Mathematics and Computer Science, Emory University, 400 Dowman Drive, Atlanta, GA, 30322. | Present address: Supercomputing Center of Computer Network Infor- mation Center, Chinese Academy of Sciences, Beijing, P. R. China. 6658 J. Phys. Chem. A 2007, 111, 6658-6664 10.1021/jp068722l CCC: $37.00 © 2007 American Chemical Society Published on Web 03/13/2007