Semiclassical determination of eigenvalues in nonbending ozone

Abstract

The authors have determined all the vibrational eigenvalues below 16,000 cm/sup -1/ for a two-mode ozone potential, using the surface of section semiclassical method combined with interpolation to integer quantum numbers; with this approach more than 80 eigenvalues were determined from only 21 arbitrary classical trajectories. The ozone potential surface is represented by a 20 x 20 grid of points obtained at the 6-31G* level with electron correlation included via a fourth-order Moeller-Plesset perturbation calculation. The forces needed to integrate the classical equations of motion are found by using a two-dimensional spline fit to the potential points. Classical trajectories are then generated; each gives tow surfaces of section from which classical actions and noninteger quantum numbers are extracted. A two-dimensional interpolation of the energy surface expressed as a function of these quantum numbers then rapidly locates the eigenvalues. These semiclassical eigenvalues generally agree with variationally determined quantum eigenvalues to within a few wavenumbers, for the first five states of each parity; this agreement holds even for states with eigenvalues corresponding to trajectories located in a classical resonance region.