where Z p is the partition function, ω is the energy gap in the frequency domain, and Tr [ρ ic (t, T )] is the trace of the thermal vibrational correlation function. Full analytical derivations of the correlation function can be found in Refs. . Reimers reported on solutions for calculating Duschinsky rotations and vector displacements, required for the correlation function. It is worth highlighting that sometimes Equation 19 is cast with the partition function and density absorbed into the coupling term. One of the most well known implementations of this methodology is the Momap software package , which be believe to be one of the only licensed software packages which can calculate internal conversion. Calculations on azulene for example yield a rate 2.3 × 10 10 s -1 for the S 1 → S 0 pathway, comparing very well to experiment. Further calculations by Veys & Escudero on multiple azulene derivatives found various rates on the order of 10 11 s -1 for the S 1 → S 0 transition, and 10 9 s -1 for the S 2 → S 1 transition. Importantly, the correlate well with experimental observations. We do note that to our knowledge, Momap does not yet account for Herzberg-Teller contributions to the vibronic coupling.