The analytical sum-over-states equations derived in the appendix are applicable in the case that the states and energies of the molecule are calculated by exactly diagonalizing some Hamiltonian H(R) describing the system in the molecule-fixed frame (which does not necessarily need to be the exact ab initio electronic Hamiltonian). Recall that this Hamiltonian is orientation-dependent because B mol 0 (R) is orientation-dependent. Possible choices for this Hamiltonian are for example the ab initio quasidegenerate perturbation theory (QDPT) effective Hamiltonian based on CASSCF/NEVPT2 nonrelativistic/scalar-relativistic wavefunctions, the ligand field theory (LFT) effective Hamiltonian, or various kinds of spin Hamiltonians. For quantum-chemical wavefunction parametrizations that are not based on the exact diagonalization of some Hamiltonian, one would need to derive specific analytical formulae for the analytical derivatives of the free energy, which probably would involve the solution of wavefunction response equations instead of an explicit summation over field-free excited states.