Classical perturbation theory of good action-angle variables. Applications to semiclassical eigenvalues and to collisional energy transfer in polyatomic molecules

It is shown that the second-order semiclassical and quantum eigenvalues are identical within an additive constant for a model of two coupled oscillators. Numerous applications to semiclassical eigenvalues for different cubic and quartic force field problems show that the second-order theory typically accounts for all but 5% of the anharmonic contribution to the total energy, while third-order perturbation theory is always equal to or better than second order in accuracy, predicting eigenvalues for the (000) and (100) states of CO2 within 0.0001 eV of the exact semiclassical values. The applications to collisional energy transfer using classical trajectory methods consider a linear model of Kr + CO2(001). Agreement of moments of the final symmetric and asymmetric stretch good actions obtained using second-order perturbation theory with the analogous exact semiclassical results is generally to better than 15%, although some more serious errors are encountered at low collision energies when the errors in determining these moments become comparable to the moments themselves. The accuracy of perturbation theory in determining energy transfer information is, however, generally acceptable. 2 figures, 9 tables