Quasiclassical Trajectory Studies of State to State Collisional Energy Transfer in Polyatomic Molecules

Abstract

This chapter presents a detailed analysis of the quasiclassical trajectory method as applied to the calculation of state resolved collisional energy transfer cross sections and rate constants in polyatomic molecule collision systems. It begins (Sect.3.1) with a brief review of previous applications of this type. These applications show that a major difficulty with describing polyatomic molecule collisions using classical methods arises in the specification of initial and final molecular semiclassical eigenstates. Both anharmonic and Coriolis coupling effects cause the molecular Hamiltonian to be nonseparable, and often the calculated energy transfer rates and pathways can be significantly in error if these nonseparable effects are not included in the trajectory initial and final conditions. The proper way to define semiclassical eigenstates, via good action-angle variables, requires a difficult solution to the molecular Hamilton-Jacobi equation. Section 3.2 describes several ways to determine semiclassical eigenstates based on approximate partitionings of the vibration-rotation Hamiltonian (to simplify Coriolis effects) and a perturbation theory solution to the Hamilton-Jacobi equation for the good action-angle variables governing vibrational motions. Section 3.3 discusses the application of these methods for describing molecular internal states to trajectory studies of collisional energy transfer, focusing specifically on the transformations between cartesian and good variables and vica versa. Section 3.4 presents the results of an application of the methods of Sects.3.2,3 to collisional excitation in the He + SO2 system.