Calculation of the energy levels of excited vibrational states of the HD16O molecule by summing divergent series of the Rayleigh-Schrödinger perturbation theory. The shift of zero-order levels

Abstract

The Rayleigh-Schrodinger perturbation theory is applied to calculation of the energy levels of excited vibrational states of the HD16O molecule. The model of coupled anharmonic oscillators is considered, with the anharmonic part of potential energy being taken into account as the perturbation. The calculations are carried out for the vibrational states that correspond to three-to seven-fold vibrational excitations. Since the perturbation series diverge in the case of strong resonance interactions and their approximations by the Pade and Pade-Hermite methods do not yield sufficiently correct results, a calculation technique is applied that allows the zero-order approximation to be modified. The zero-order Hamiltonian is modified by shifting the vibrational frequencies, which decreases the mixing of states. The new Rayleigh-Schrodinger series can be summed using the quadratic Pade-Hermite approximation method.