Here, ω av eg is the thermal average of the energy gap operator and Ĥg and Ĥe denote the nuclear Hamiltonians in the electronic ground-and excited state respectively. While Eqn. 3 is exact for a two-level system within the Condon approximation, no closed form expressions for G ∞ (t) exist except in model systems with simplified potential energy surfaces. Thus in practice, to get a suitable closed-form expression for realistic systems, the infinite order cumulant expansion is truncated at finite order. We denote the approximate response function due to an mth order cumulant expansion, which in turn can be represented by the mth order approximation of the line shape function, as