Direct Dynamics Trajectory Study of Vibrational Effects: Can Polanyi Rules Be Generalized to a Polyatomic System? Jianbo Liu, † Kihyung Song, ‡ William L. Hase, § and Scott L. Anderson* ,† Department of Chemistry, UniVersity of Utah, Salt Lake City, Utah 84112; Department of Chemistry, Korea National UniVersity of Education, Chongwon, Chungbuk 363791, Korea; and Department of Chemistry and Biochemistry, Texas Tech UniVersity, Lubbock, Texas 79409 Received March 9, 2004; E-mail: anderson@chem.utah.edu Polanyi et al. 1 developed successful rules to predict the impor- tance of reactant vibration and collision energy (E col ) in driving reactions over barriers for triatomic A + BC systems; i.e., vibration should be relatively ineffective compared to E col for barriers early along the reaction coordinate, and the reverse is true for systems with late barriers. Reactions of polyatomic species are complicated, with many degrees of freedom and multiple reaction pathways, raising the question of whether some sort of analogous rules are possible. We recently reported an experimental study of a hydrogen abstraction (HA) reaction: 2 H 2 CO + + CD 4 f H 2 COD + + CD 3 . The reaction is exoergic by 0.18 eV with no activation barriers in excess of reactant energy. Nonetheless, the reaction efficiency is quite low (∼10%), unusual for ion-molecule reactions involving simple atom transfer. Reactivity is strongly enhanced by excitation of methane distortion vibrations (ν 4 and ν 2 ) but mode-specifically inhibited by different H 2 CO + vibrations, even at high E col . Observa- tion of mode-specific effects is consistent with ab initio results, indicating that the transition state (TS) on the minimum energy path is reactant-like, 2 such that the system still remembers its initial state at the TS. From a Polanyi rule perspective, however, a reactant- like TS would be regarded as “early”, and thus substantial enhancement from CD 4 vibrations would not be anticipated. Here we report a direct dynamics trajectory study of the effects of CD 4 distortion vibrations on this reaction that, for the first time, shows how vibrational effects originate in the reaction of small polyatomic species and how they relate to barrier location. Trajectories were calculated using VENUS99 3 and GAUSSIAN01. 4 The MP2/6-31G* level of theory was used because of methods fast enough for use in trajectories, it best fits benchmark calculations at the QCISD(T)/cc-pVDZ level. Figure 1 shows a representative reactive trajectory, where rCD is the separation of the abstracted D atom from the methane carbon atom, etc.. At the E col studied (1.5 eV), trajectories are direct with a single turning point in the relative motion of the center-of-masses of reactants and products. As shown in the Supporting Information, the trajectories accurately reproduce both integral and differential cross sections for the reaction. To explore the origins of the vibrational effects, we focus on correlations between reactivity and various trajectory parameters, sampled at the turning point of the inter-reactant separation (Figure 1). The turning point occurs within a few femtoseconds of the point of maximum potential energy. Another point of interest is the “HA point”, defined here as the point from which rCD of the CD 4 bond is being broken, increases monotonically (labeled “HA” in Figure 1). The HA point occurs ∼15 fs after the turning point; i.e., the actual CD bond breaking event occurs as the reactants rebound. In this sense, the HA point is “late” from the perspective of Polanyi rules. Low reaction efficiency suggests a dynamical bottleneck along the reaction path, and the vibrational effects presumably reflect behavior at the bottleneck. In Figure 2, the dependence of the bottleneck on reactant orientation is shown as a map of reaction probability for ground-state CD 4 , versus orientation at the turning point. Reaction probability is calculated as the fraction of trajectories leading to reaction for each range of two orientation parameters found to be critical. The two parameters are the angle between the CO bond and the abstracted D atom (R D-O-C ) and the dihedral angle that the D atom makes with respect to the H 2 CO + equilibrium plane (Φ plane ). Positive and negative Φ plane correspond to approach to the convex and concave faces of the vibrating H 2 CO + , respectively. Note that maximum reaction probability (∼0.6) is for the CD 4 approach with the D atom in the H 2 CO + plane, with R D-O-C near 110°. The Φ plane asymmetry implies that approach to the convex face of H 2 CO + is slightly favored, presumably because of less steric interference. Because E col is too high for significant orientation steering during reactant approach, the narrow range of † University of Utah. ‡ Korea National University of Education. § Texas Tech University. Figure 1. A representative plot of hydrogen abstraction trajectories. (a) The variation of rCD, rOD, and center-of-mass reactant distance during trajectory and (b) the variation of potential energy during trajectory. Figure 2. Dependence of reaction probability on angles RD-O-C and Φplane. The contour map is plotted for the ground state only. Published on Web 06/19/2004 8602 9 J. AM. CHEM. SOC. 2004, 126, 8602-8603 10.1021/ja048635b CCC: $27.50 © 2004 American Chemical Society