Structural and vibrational theoretical analysis of protonated formaldehyde in its $\tilde{X}^{1} A^{\prime}$ ground electronic state

Abstract

A structural and vibrational study of protonated formaldehyde (H₂COH⁺) in its ground electronic state, at the CCSD/cc-pVTZ theory level, is presented. The variation of the molecular structure with the torsion angle shows clear dependence of the H₂C wagging and COH angles. Anharmonic one- and two-dimensional vibrational models for two out-of-plane vibrational modes (H₂C torsion, and H₂C wagging) are constructed. Since H₂COH⁺ is classified under a G₄ non-rigid group, the vibrational Hamiltonians are factorized using the symmetry of the G₄ group and solved variationally. The one-dimensional results for torsion and wagging yield fundamental frequencies are 844.12 and 1,252.89 cm⁻¹, respectively. A two-dimensional COH angle + torsion model gives a torsion frequency of 762.32 cm⁻¹. Finally, a wagging + torsion model predicts frequencies of 931.93 and 1,255.82 cm⁻¹ for torsion and wagging, respectively. The variation of frequency values for torsion suggests an important coupling between this mode and the bending and wagging vibration modes.