The dynamical basis set

A new Cartesian basis set is defined that is suitable for the representation of molecular vibration-rotation bound states. The Cartesian basis functions are superpositions of semiclassical states generated through the use of classical trajectories that conform to the intrinsic dynamics of the molecule. Although semiclassical input is employed, the method becomes ab initio through the standard matrix diagonalization variational method. Special attention is given to classical-quantum correspondences for angular momentum. In particular, it is shown that the use of semiclassical information preferentially leads to angular momentum eigenstates with magnetic quantum number ‖M‖ equal to the total angular momentum J. The present method offers a reliable technique for representing highly excited vibrational-rotational states where perturbation techniques are no longer applicable.