State-selected dynamics of the complex-forming bimolecular reaction Cl−+CH3Cl′→ClCH3+Cl′−: A four-dimensional quantum scattering study
Authors: Hennig Carsten , Schmatz Stefan 
Published: June 2004

Time-independent quantum scattering calculations have been carried out on the Walden inversion SN2 reaction Cl−+CH3Cl′(v1,v2,v3)→ClCH3(v1′,v2′,v3′)+Cl′−. The two C–Cl stretching modes (quantum numbers v3 and v3′) and the totally symmetric internal modes of the methyl group (C–H stretching vibration, v1 and v1′, and inversion bending vibration, v2 and v2′) are treated explicitly. A four-dimensional coupled cluster potential energy surface is employed. The scattering problem is formulated in hyperspherical coordinates using the exact Hamiltonian and exploiting the full symmetry of the problem. Converged state-selected reaction probabilities and product distributions have been calculated up to 6100 cm−1 above the vibrational ground state of CH3Cl, i.e., up to initial vibrational excitation (2,0,0). In order to extract all scattering resonances, the energetic grid was chosen to be very fine, partly down to a resolution of 10−12 cm−1. Up to 2500 cm−1 translational energy, initial excitation of the umbrella bending vibration, (0,1,0), is more efficient for reaction than exciting the C–Cl stretching mode, (0,0,1). The combined excitation of both vibrations results in a synergic effect, i.e., a considerably higher reaction probability than expected from the sum of both independent excitations, even higher than (0,0,2) up to 1500 cm−1 translational energy. Product distributions show that the umbrella mode is strongly coupled to the C–Cl stretching mode and cannot be treated as a spectator mode. The reaction probability rises almost linearly with increasing initial excitation of the umbrella bending mode. The effect with respect to the C–Cl stretch is five times larger for more than two quanta in this mode, and in agreement with previous work saturation is found. Exciting the high-frequency C–H stretching mode, (1,0,0), yields a large increase for small energies [more than two orders of magnitude larger than (0,0,0)], while for translational energies higher than 2000 cm−1, it becomes a pure spectator mode. For combined initial excitations including the symmetric C–H stretch, the spectator character of the latter is even more pronounced. However, up to more than 1500 cm−1 translational energy, the C–H vibration does not behave adiabatically during the course of reaction, because only 20% of the initial energy is found in the same mode of the product molecule. The distribution of resonance widths and peak heights is discussed, and it is found that individual resonances pertinent to intermediate complexes Cl−⋯CH3Cl show product distributions independent of the initial vibrational state of the reactant molecule. The relatively high reactivity, of resonance states with respect to excitation of any mode, found in previous work is confirmed in the present calculations. However, reactivity of intermediate states and reactivity with respect to initial vibrational excitation have to be distinguished. There is a strong mixing between the vibrational states reflected in numerous avoided crossings of the hyperspherical adiabatic curves.