Anharmonic coupling of vibrational modes in atom–polyatomic collisions: A time-correlation function treatment

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Abstract
The role of molecular anharmonicity in hyperthermal collisions of atoms with polyatomic targets is investigated using a time-correlation function approach. By means of a cumulant expansion, the vibrational correlation is expressed in terms of displacement–displacement correlation functions, which are evaluated from the corresponding double-time Green functions; these in turn are obtained from their hierarchy of equations of motion. For a general intramolecular potential that contains anharmonic couplings between all the vibrational modes, the hierarchy is closed by means of a decoupling procedure that conserves the first few frequency moments of the spectral function. Consequently, the correlation functions can be evaluated analytically without need of internal state expansions, and they include the effects of anharmonic forces to infinite order. As examples, the targets CO2, N2O, and OCS are studied in detail, using spectroscopically derived vibrational potentials that contain quadratic through quartic terms; the roles of intra- and intermode anharmonic couplings are carefully considered. Differential cross sections for vibrational excitation calculated with the anharmonic potential are compared with those obtained from the harmonic model, for the systems Li+/CO2 and Li+/N2O at the collision energy E=4.72 eV. Results indicate that anharmonic forces make a small (15% to 25%) contribution to the vibrational energy transferred to these targets in hyperthermal collisions.