Resonant Inelastic X-ray Scattering: How Well Does LR-TDDFT Perform?

Resonant inelastic X-ray scattering (RIXS) is one of the most information-rich spectroscopic techniques, uniquely capable of probing excited states through their dependence on momentum, energy, and polarization. However, the inherent difficulty in interpreting RIXS signals underlines the critical need for accurate and efficient spectral calculations to facilitate their understanding. While hierarchical wave function-based methods such as the algebraic diagrammatic construction (ADC) scheme for the polarization propagator have shown promising results in the calculation of RIXS spectra, they remain computationally demanding. To enable fast and efficient RIXS calculations, we evaluate the performance of linear-response time-dependent density functional theory (LR-TDDFT). Two LR-TDDFT approaches are investigated: the restricted-subspace approximation, which uses a subset of occupied and virtual orbitals to compute the valence-excited and selected core-excited states at the same time, and the two-shot LR-TDDFT approach, where the core- and valence-excited states are calculated independently. We benchmark a range of functionals─including global hybrid, range-separated, and tailored range-separated variants─on a set of small molecules using ADC as the reference. We find that all range-separated hybrids and most global hybrid functionals exhibit good agreement with the reference across all metrics. Furthermore, we demonstrate the applicability of LR-TDDFT by computing the RIXS spectrum of C