First, Eqn. 5 requires the exact nuclear wavefunctions ν e j , {ν g i } to be known and the wavefunction overlap ν e j |ν g i to be easily evaluated for all i,j. In practice, this means that the full PESs of the molecule in the condensed phase have to be approximated through a model Hamiltonian. The most popular choice, invoked in the Franck-Condon (FC) method, is to approximate the PESs as harmonic around their respective minima. Second, evaluating Eqn. 5 directly, for example by parameterizing a GBOM (see Appendix A 1), means that the condensed phase environment can often only be accounted for approximately in the resulting spectrum, either through collective representations of the solvent environment through a PCM, or by invoking a timescale separation between solute and solvent degrees of freedom. These shortcomings render a direct evaluation of the spectral decomposition expression potentially impractical in condensed phase systems, especially for systems with strong solute-solvent interactions and chromophores with low frequency anharmonic modes ill described by a harmonic model PES.