Integration of the Decoherence Function. To accurately compute the integral in Eq. 2 we employed the trapezoidal rule with a frequency step of 0.6 cm -1 . Recognizing the integrand as even, we extended the integration to both negative and positive frequencies. This approach effectively limited the error in solvent reorganization energy to below 0.1% and in total vibrational reorganization energy to under 0.001%.