The relationship between calculated and experimental electronic transition energies

Abstract

Most theoretical calculations of molecular electronic structure are performed with fixed nuclear coordinates, assuming the Born—Oppenheimer approximation. Generally, the equilibrium nuclear coordinates for the ground state are employed. Calculated electronic transition energies, E vert c, are vertical transitions from the classical minimum in the ground-state potential surface to that point on the excited-state surface with the same nuclear positions. A problem arises because experimental absorption spectra do not conveniently yield this quantity. Most often the experimental band maximum has been equated with E vert c. Occasionally one finds comparisons with adiabatic or zero—zero energies and the theoretical values. This paper summarizes the relationship between E vert c and experimental spectra. Within the Crude Born—Oppenheimer framework and to first order in vibronic coupling a rigorous procedure for determining E vert c from an experimental spectrum is presented. The zeroeth and first moments of an absorption band unambiguously fix the energy of the vertical Franck—Condon transition. This may be extended to include the Herzberg—Teller correction. Finally, it is pointed out that, in addition, the vibrational zero-point reorganizational energy must be admitted. The magnitude of the various energy corrections can amount to uncertainties on the order of ± 1000 cm −1. It is important to recognize this fact when comparing experimental spectroscopic energies with those from accurate crystal field and ab initio calculations.