Vibrational quasi-degenerate perturbation theory: applications to fermi resonance in CO₂, H₂CO, and C₆H₆

A quasi-degenerate perturbation method with vibrational self-consistent field (VSCF) reference wavefunction is developed. It simultaneously accounts for strong anharmonic mode–mode coupling among a few states (static correlation) by a configuration interaction theory and for weak coupling with a vast number of the other states (dynamic correlation) by a perturbation theory. A general formula is derived based on the van Vleck perturbation theory. An algorithm that selects a compact set of the most important VSCF configurations which contribute to the static correlation is proposed and a scheme to limit the number of configurations considered for dynamic correlation is also implemented. This method reproduces the vibrational frequencies of CO₂ and H₂CO that are subject to the strongest anharmonic mode–mode coupling within 10 cm⁻¹ of vibrational configuration interaction results in a computational expense reduced by a factor of one to two orders of magnitude. The method also reproduces the infrared absorption of C₆H₆ in the CH stretching (ν₁₂) frequency region, in which combination tones ν₁₃ν₁₆ and ν₂ν₁₃ν₁₈ appear on account of an intensity borrowing from ν₁₂via the anharmonic coupling.