as can be seen by expanding the decoherence function Γ(t) in Eq. ( ) up to second order in time. contrasts the exact decoherence dynamics with this Gaussian form (dashed line). As shown, this simple estimate accurately captures the early time decay but does not capture possible recurrences and overestimates the overall decoherence by a factor of ∼ 2. Thus, such formulas are useful to understand the early stages of decoherence but exaggerate the decoherence rate for electrons in molecules. Nevertheless, to capture the electronic decoherence for molecules immersed in solvent and other condensed phase environments, Fig. underscores the utility of the simple Gaussian estimate as it captures the early-time decoherence dynamics correctly while avoiding explicitly solving the quantum dynamics. By contrast, computationally expensive efforts to capture the decoherence based on propagating the correlated quantum dynamics of electrons and nuclei at 0 K using Multi Configurational Time Dependent Hartree (MCTDH) are only relevant for early times where finite temperature effects due to solvent do not play a role. Figure shows that this early-time region of the decoherence can be accurately captured while avoiding propagating the quantum dynamics all together.