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

The Rayleigh-Schrödinger perturbation theory is applied to calculation of the energy levels of excited vibrational states of the HD 16 O 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 Padé and Padé-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-Schrödinger series can be summed using the quadratic Padé-Hermite approximation method.