  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 spectral
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 $1 ^{1}\mathrm{A_{g}}\rightarrow1
^{1}\mathrm{B_{2u}}$ UV absorption spectrum of benzene in the electric dipole
and (linear) Herzberg-Teller approximation is presented herein for zero Kelvin
and finite temperatures.
