Treatment of Fermi resonance effects on transition moments in vibrational perturbation theory

Abstract

An algebraic expression for the vibrational transition moment of fundamental transitions within the context of second-order vibrational perturbation theory (VPT2) has been modified to account for cases in which the fundamental interacts through a Fermi resonance with close-lying two-quantum levels. This procedure is applied to the formaldehyde molecule, and it is shown that explicit treatment of the 5₁ ≈ 2₁6₁ ≈ 3₁₆₁ resonance is necessary to give intensities of the ν₅ transitions that agree qualitatively with that seen experimentally. In addition, use of the Almlöf–Taylor atomic natural orbital basis sets results in an extremely close correspondence between predicted and observed level positions; the largest difference found for the 23 one- and two-quantum transitions for which experimental assignments have been made is 15 cm⁻¹. This is a remarkable result, especially when one considers that seven of these levels are involved in relatively strong resonances.

Keywords:

• Fermi resonance effects
• Transition moments
• Vibrational perturbation theory

Acknowledgement

This work was supported by the Robert A. Welch Foundation under grant F-1283.