Semiclassical Theory for Low-Energy Molecular Collisions.H+-H2Vibrational Excitation

Abstract

A form of semiclassical theory for molecular inelastic or reactive scattering is developed. In such a theory we achieve a separation of the dynamics into two parts, elastic motion and inelastic or reactive motion, by the following procedure. The isotropic part of the intermolecular potential, $V_0$, is expanded in a Taylor series about the equilibrium internuclear geometries of the interacting molecules. This separates $V_0$ into a part which is not dependent on the internal coordinates of the molecules, for which only elastic scattering can occur, and a part which is dependent on the internal coordinates. This latter part, along with the unexpanded anisotropic parts of the intermolecular potential, can act as a "coupler" to produce inelastic or reactive scattering. The constant term in the expansion for $V_0$, is used as the potential in which the classical trajectory governing the elastic motion is calculated. This determines the "distance of closest approach" and, relative to the range of the couplers, defines an "energy of activation" or effective threshold, if relevant. The time-dependent Schrödinger equation is solved to produce inelastic or reactive probabilities. The theory is applied to ${\mathrm{H}}^{+}$ -${\mathrm{H}}_2$ vibrational excitation in the two- and three-state approximations for energies $15<E<\mathrm{}1000\mathrm{}$ eV. Discrepancies with the measurements of Herrero and Doering probably can be attributed to the omission of the electron-capture channel. The agreement with the 0 → 2 measured cross section above 200 eV is excellent.