where H and L are the configuration interaction coefficients with indicies corresponding to virtual and occupied molecular orbitals, and K mn is a vibrational factor associated with the product of the Franck-Condon factors and the matrix elements of the electronic-nuclear components and the vibrational wavefunctions of initial and final states. The electronic-nuclear matrix element can be expanded as a linear combination between basis functions of the molecular orbital expansion, allowing for truncation of important matrix elements as opposed to for the entire system. Their previous work showed that for the lower excited states transitions are typically mediated by -H-type normal modes, and is therefore reminiscent of the approximation previously made by Plotnikov (Equation ). Using Equation , Valiev and co-workers yielded rate constants in good agreement compared to using a more complete configuration space and incorporating additional effects (Tables and). The S 2 → S 1 internal conversion rate constant was found to be much smaller compared to a more complete calculations, which they rationalised to be evidence of anti-kasha fluorescence. It was concludes that by using this simplified method for estimation of the overall non-adiabatic coupling that difficulties should be expected when treating FIG. . Visualisation of the linearly expanded configuration space methodology developed in Ref 44. For some arbitrary system, computation of a high dimensional phase space, shown here as a Calabi-Yau surface, can be shifted from an exponential to a polynomial problem by searching for configuration vectors where the sum of all elements of that vector equals n. The deep green segment signifies the section of the CS for which n solves a Lagrangian multiplier, while the light green segments illustrate the rates for all other values of n ± x. In principle, integration of the curve equals the rate constant for the system. Calabi-Yau surface is adapted from Ref. deuterated systems, or of course systems with minimal hydrogen bonds, since the full configuration space is simplified to assume all transition participating modes are found only in hydrogen bond-type normal modes.