where δU (t) = U (t) -ωeg is the energy gap fluctuation, and the angular brackets with the subscript "cl" indicate a classical equilibrium ensemble average. The harmonic QCF is known to be exact for the TCF of an operator that linearly depends on the harmonic vibrational coordinates, which also makes the truncation of the cumulant expansion at second order exact. The spectral density measures the coupling strength between the electronic excitation and nuclear motions. Another property that quantitatively measures the coupling between the electronic transition and nuclear motion is the reorganization energy, which is related to spectral density as