Here, the subscripts g and e denote the electronic groundand excited state respectively, ρ g is the ground state density matrix of nuclear degrees of freedom, and the trace is carried out over all nuclear degrees of freedom. In practice, Eqn. 2 is impossible to evaluate for realistic condensed-phase systems, and suitable approximations have to be found. In the cumulant scheme, the linear response function is defined as an infinite expansion with respect to cumulants of the energy gap fluctuation operator. Under the Condon approximation, the electronic transition dipole moment is independent of nuclear degrees of freedom, and we can write: