Nonequilibrium Fermi golden rule for electronic transitions through conical intersections

We consider photoinduced electronic transitions through conical intersections in large molecules. Starting from the linear vibronic model Hamiltonian and treating linear diabatic couplings within the second order cumulant expansion, we have developed a simple analytical expression for the time evolution of electronic populations at finite temperature. The derived expression can be seen as a nonequilibrium generalization of the Fermi golden rule due to a nonequilibrium character of the initial photoinduced nuclear distribution. All parameters in our model are obtained from electronic structure calculations followed by a diabatization procedure. The results of our model are found to agree well with those of quantum dynamics for a test set of systems: fulvene molecule, 2,6-bis(methylene) adamantyl cation, and its dimethyl derivative.