Adiabatic treatments of vibrational dynamics in low-energy electron-molecule scattering

Accurate calculations of vibrational excitation cross sections for low-energy electron-molecule collisions require theoretical treatment of dynamical effects due to the vibrational kinetic energy operator. As alternatives to solving the integrodifferential equations that describe coupled electronic and vibrational motion, adiabatic methods, which parametrize the internuclear geometry, offer practical and conceptual simplifications. Here we investigate two such methods: the energy-modified adiabatic phase matrix method, which retains the vibrational kinetic energy in the fixed-nuclei scattering matrix and approximates the continuum energy, and the first-order non-degenerate adiabatic approximation, which evaluates fixed-nuclei scattering matrices off the energy-momentum shell in order to ensure strict conservation of energy. The present implementation of these methods is improved over previous versions. They are assessed against benchmark results from converged vibrational close-coupling calculations. Specifically, we compare integral and differential 0 --> 1 and 0 --> 2 cross sections for e-H-2 scattering at energies from their respective thresholds to 10 eV.