New theoretical developments and applciations of non-Condon Fermi's golden rule rates for nonradiative decay of electronic excited states

Great advances have been made during the past two decades in direct calculation of quantum transitions in complex molecular environments and intricate quantum dynamical processes. As yet, for a large class of systems, transitions can be characterized by rates combined with appropriate master equations. For the calculation of rates, Fermi’s golden rule (FGR) has been widely and successfully used for various molecular systems. However, in its applications to complex molecular systems, there remain various open issues that require further theoretical development. One of such issues is the non-Condon effect due to the depenedence of nonadiabatc derivative coupling on momenta and positions. This work addresses general theoretical issues in addressing the non-Condon effects and presents a new compact rate expression that allows semiquantitative determination of rates within well defined quasiadiabatic approximations. Application of the new rate expression to nonradiative decay of azulene clrafies long standing issues concerning its anti-Kasha mechanism.