Coherent potential theory for interacting bands: Phonons and excitons in substitutionally disordered molecular crystals

A coherent potential approximation (CPA) theory for disordered molecular solids with interacting bands is reported here. This theory has a wide range of applications. Various examples of interacting bands can be cited, such as electronic states coupled via vibronic or spin‐orbit couplings, vibrational states with degeneracies in the gas phase or coupled by Fermi resonance, triplet magnetic sublevels coupled via exciton interactions, and phonons in general. The theory is developed using the self‐consistent condition with a single‐site and single‐band approximation. In particular, two approaches are adopted. In the first approach, a self‐energy is assigned for each subband. In the second approach, a common self‐energy is assumed for all the subbands. The two different approaches require different inputs to the theory. In one case, the entire dispersion relations of the pure system are called for; in the other, only the partial density‐of‐states functions for each degree of freedom are needed. It is also shown that in the limit of infinite dilution, the formalism reduces to the proper single‐impurity levels within the single‐band approximation