Adiabatic analysis of distant perturbations

Abstract

The simplest form of Herzberg-Teller theory involves the vibronic coupling of a single mode between two energetically separated molecular states. An adiabatic analysis of this system is presented which incorporates the effect of the distant state without recourse to direct summation over distant energy levels. The theory is compared to exact numerical results for vibronic-coupling in propynal and formaldehyde. The adiabatic eigenvalues are exceptionally accurate, especially if proper radial Born-Oppenheimer terms are added to the adiabatic potential for the ground state. The quality of the resultant amplitudes associated with the distant state are adequate to represent any intensity borrowing effects in the molecular spectra to well within 5 per cent. The adiabatic theory is quite general and can be used with equal force to represent distant perturbations due to repulsive as well as attractive states, and without any commitment to linear vibronic coupling models.