A simple molecular orbital picture of RIXS distilled from many-body damped response theory
Ab initio calculations of resonant inelastic X-ray scattering (RIXS) rely on the damped response theory, which prevents the divergence of response solutions in the resonant regime. Within the damped response theory formalism, RIXS moments are expressed as sum over all electronic states of the system (SOS expressions). By invoking resonance arguments, these expressions can be reduced to a few terms, an approximation commonly exploited for interpretation of the computed cross sections. We present an alternative approach: a rigorous formalism for deriving a simple molecular orbital picture of the RIXS process from the many-body calculations using damped response theory. In practical implementations, the SOS expressions of RIXS moments are recast in terms of matrix elements between the zero-order wave functions and first-order frequency-dependent response wave functions of the initial and final states, such that the RIXS moments can be evaluated using complex response one-particle transition density matrices (1PTDMs). Visualization of these 1PTDMs connects the RIXS process with the changes in electronic density. We demonstrate that the real and imaginary components of the response 1PTDMs can be interpreted as contributions of the undamped off-resonance and damped near-resonance SOS terms, respectively. By analyzing these 1PTDMs in terms of natural transition orbitals, we derive a rigorous, black-box mapping of the RIXS process into a molecular orbital picture. We illustrate the utility of the new tool by analyzing RIXS transitions in the OH radical, benzene, para-nitroaniline, and 4-amino-4'-nitrostilbene. These examples highlight the significance of both near-resonance and off-resonance channels.