Cumulant expansion for fast estimate of non-Condon effects in vibronic transition profiles

When existing, cumulants can provide valuable information about a given distribution and can in principle be used to either fully reconstruct or approximate the parent distribution function. A previously reported cumulant expansion approach for Franck–Condon profiles [Faraday Discuss., 150, 363 (2011)] is extended to describe also the profiles of vibronic transitions that are weakly allowed or forbidden in the Franck–Condon approximation (non-Condon profiles). In the harmonic approximation the cumulants of the vibronic profile can be evaluated analytically and numerically with a coherent state-based generating function that accounts for the Duschinsky effect. As illustration, the one-photon 1 (1)A(g) → 1 (1)B(2u) UV absorption profile of benzene in the electric dipole and (linear) Herzberg–Teller approximation is presented herein for zero Kelvin and finite temperatures.