Reaction surface Hamiltonian for the dynamics of reactions in polyatomic systems

Abstract

The reaction path description of chemical reactions has difficulty if there are regions where the reaction path is sharply curved, as is typically the case, e.g., in light atom (e.g., H,D) transfer reactions. It is shown here how this can be overcome by introducing two reaction coordinate-like degrees of freedom, i.e., two coordinates, r1 and r2, that are allowed to undergo arbitrarily large amplitude motion (LAM). Rather than a reaction path and a reaction coordinate measuring distance along it, the picture is now that of a reaction surface with two reaction-like coordinates (r1,r2) which specify position on the surface. The reaction surface is defined by minimizing the potential energy of the polyatomic system for fixed values of r1 and r2, and an algorithm for using ab initio quantum chemistry methods to do this is described. The remaining (3N−8) internal degrees of freedom are characterized as local harmonic motion orthogonal to the reaction surface; these local normal modes are defined by diagonalizing an appropriately projected force constant matrix. The classical (and quantum) reaction surface Hamiltonian is then derived, i.e., the Hamiltonian for which the dynamical variables are the two reaction-like coordinates (r1,r2) and the (3N−8) local normal mode coordinates (plus the usual three Euler angles for overall rotation), and their conjugate momenta. A zeroth order dynamical model is also described which has the form of a collinear-like atom–diatom reaction, i.e., a system with two degrees of freedom—in an effective 2D potential. This effective potential consists of the actual potential energy on the 2D reaction surface, the vibrationally adiabatic energy of the (3N−8) local normal modes, and the rotational energy of the complete polyatomic system, the latter two quantities being functions of the coordinates (r1,r2) on the reaction surface.