Generalization of the Franck-Condon model for phonon excitations by resonant inelastic x-ray scattering

Resonant inelastic x-ray scattering (RIXS) is increasingly used to quantify vibronic interactions in materials. In the case of periodic systems, this is most often done through fitting experimental results to a parameterized but exact analytical solution of a simple Holstein Hamiltonian that consists of a single electronic level coupled linearly to a single Einstein vibrational mode. Working within this standard framework, we consider the impact of minor generalizations of this model, namely, introducing a second Einstein oscillator and allowing the curvature of the excited-state potential energy surface to differ from that of the ground-state potential energy surface. We find that dynamics occurring in the RIXS intermediate (electronically excited) state considerably alter the quantitative interpretation of the phonon features observed in the RIXS final state. This complicates the use of the single mode model when multiple phonon modes are active. Our generalized model may in principle be substituted in this case, though we find that accurate quantitative results rely on knowledge of the excited-state potential energy surface, which typically is not known.