is the oscillator strength, ω if is the vertical excitation/de-excitation energy, β = 1 for absorption and β = 3 for emission, and µ if is the transition electric dipole moment between two electronic states of the dye with reference state nuclear configuration R i j obtained from an MD trajectory at temperature T . The frequency of the light is given by ω, and N snaps is the number of uncorrelated snapshots from either a ground or excited state MD trajectory. The Gaussian function, N , is centered at ω if with standard deviation s, a parameter that is often used to account for limited sampling. Some nuclear quantum effects on the optical spectra can be included through the MD sampling by employing a path integral formalism. However, the spectra generated from the nuclear ensemble approach lack vibronic features and, thus, generally are not the correct shape.