A wave function correction-based approach to the identification of resonances for vibrational perturbation theory

An approach for identifying resonances in vibrational perturbation theory calculations is introduced. This approach makes use of the corrections to the wave functions that are obtained from non-degenerate perturbation theory calculations to identify spaces of states that must be treated with degenerate perturbation theory. Pairs of states are considered to be in resonance if the magnitude of expansion coefficients in the corrections to the wave functions in the non-degenerate perturbation theory calculation is greater than a specified threshold, χ^max. This approach is applied to calculations of the vibrational spectra of CH₄, H₂CO, HNO₃, and cc-HOONO. The question of how the identified resonances depend on the value of χ^max and how the choice of the resonance spaces affects the calculated vibrational spectrum is further explored for H₂CO. The approach is also compared to the Martin test [J. M. L. Martin et al., J. Chem. Phys. 103, 2589-2602 (1995)] for calculations of the vibrational spectra of H₂CO and cc-HOONO.