  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 (excited) state
considerably alter the quantitative interpretation of the spectral 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 by substituted in this case, though we find that accurate
quantitative results rely on knowledge of the excited-state potential energy
surface, though this typically is not known.
