Note on the role of vibrational modes in molecular electronic transitions

A simple application of a readily available quantum chemistry program (AMPAC) permits an illuminating presentation of the role of vibrational modes in electronic transitions. A direct comparison of modal surfaces for different electronic states of the same molecule can be made by using a perspective plot of the Duschinsky matrix for the transition with mode indices or eigenvalue sequence, as the planar axes. The sum of squares of the off-diagonal elements of the Duschinsky matrix can be used to give a measure of the difference between vibrational modes of the initial and final states. Calculations indicate that, in biacetyl, the triplet state is closer vibrationally to the anion ground state than either the singlet or the neutral ground state, while in glyoxal the ground state neutral has greater vibrational similarity to the anion ground state. The measure also indicates little change in vibrational modes upon intersystem crossing in formaldehyde.