Time‐correlation function approach to molecular anharmonicity in hyperthermal atom‐molecule collisions

In hyperthermal atom‐molecule collisions, differential cross sections for vibrational and rotational excitation are related to correlation functions of the positions of the atoms that constitute the target. We present a new approach to the evaluation of the correlation functions that encompasses the effects of anharmonic vibrations of the polyatomic. By means of cumulant expansion techniques, the vibrational correlation function is expressed in terms of displacement—displacement correlation functions, which are obtained from the corresponding double‐time Green functions. The displacement‐displacement Green functions are evaluated by decoupling their hierarchy of equations of motion with a linearization procedure that includes anharmonic forces to infinite order. Results for cubic and quartic anharmonicities in N 2 , CO, and in the bending mode of CO 2 indicate that, at hyperthermal collision energies, anharmonic forces contribute less than 1% to the vibrational energy transferred to these targets.