A classical path/forced rotor theory of state-to-state rotational energy transfer

Abstract

The problem of rotational energy transfer (RET) is examined from a point of view intermediate between the current approaches based on empirical models or numerical solution of the coupled scattering equations. A semiclassical perspective is taken in which a classically described collision with an atom exerts a time dependent torque on the rotor and the resulting forced rotor dynamics is addressed quantum mechanically. By treating the anharmonicity in the rotational energy levels as a perturbation, a simple approximate expression is found for the inelastic transition probability. It reveals a marked difference between the distribution of final rotational states incurred from an individual collision trajectory as compared to trajectory averaged measures of RET, such as cross sections. The theory is applied to the scattering of Li2(A 1Σ+u) by Ne, Ar, Xe;Na2(A 1Σ+u) by He and Ne; N+2(X 2Σ+g) by He, and CN(X 2Σ+) by He. Its predictions compare well with those from a fully quantum mechanical description of rigid rotor scattering and with experiment. The insight into the energy transfer dynamics gained from the semiclassical approach is used to examine the assumptions underlying empirical models of rotational energy transfer.