Resonant inelastic X-ray scattering: How well does LR-TDDFT perform?

Erik Vitols^1,2*, Vinícius Vaz da Cruz³, Thomas Fransson⁴, Iulia Emilia Brumboiu¹

¹Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Torun, Torun, Poland
²Division of Theoretical Chemistry and Biology, KTH Royal Institute of Technology, Stockholm, Sweden
³Helmholtz-Zentrum Berlin für Materialien und Energie, Institute for Methods and Instrumentation for Synchrotron Radiation Research, Berlin, Germany
⁴Independent researcher, Independent, Stockholm, Sweden

* Presenter:Erik Vitols, email:evitols@kth.se

Resonant inelastic X-ray scattering (RIXS) stands as one of the most information-rich spectroscopic techniques, uniquely capable of probing excited states through their dependence on momentum, energy, and polarization. As a second-order process, RIXS is not subject to the same selection rules as that of one-photon spectroscopies and can reveal dipole-forbidden states. RIXS also inherits the site- and element-specificity of X-ray spectroscopies. Recent advances—particularly through high brilliance X-ray sources—have reignited interest in RIXS, a technique that requires intense beams. [1] However, the inherent difficulty in interpreting RIXS signals underscores the critical need for both accurate and efficient spectral calculations to aid interpretation. While hierarchical methods such as the algebraic diagrammatic construction (ADC) scheme for the polarization propagator have shown promise for calculating RIXS spectra, [2] these methods are computationally costly. To enable efficient RIXS calculations, we have evaluated and benchmarked the performance of linear response time-dependent DFT (LR-TDDFT) approaches on a set of small molecules. With ADC at the ADC(2)-x/ADC(3/2) levels of theory as reference, two LR-TDDFT approaches have been investigated: (i) the restricted-subspace approximation [3], which selects only those occupied/virtual orbitals relevant to the targeted core- and valence-excited manifolds, and (ii) the two-shot approach [4], where the core- and valence-excited states are calculated separately. In this work, we benchmark a range of xc functionals—including hybrid, range-separated, and tailored range-separated variants—to establish a foundation for obtaining RIXS cross-sections at the LR-TDDFT level. Our LR-TDDFT approaches agree closely with the ADC(2)-x/ADC(3/2) reference, and we demonstrate applicability by computing the C₆₀ RIXS spectrum at the first core resonance, which shows excellent agreement with experiment. Our benchmark helps computational approaches keep pace with experimental advances and provides a framework for reliable predictions, paving the way for routine applications of LR-TDDFT in RIXS studies.

[1] de Groot et al., Nature Reviews Methods Primers 4.1 (2024): 45.
[2] Rehn et al., Journal of Chemical Theory and Computation 13.11 (2017): 5552-5559.
[3] Vaz da Cruz et al., Physical Chemistry Chemical Physics 23.3 (2021): 1835-1848.
[4] Nascimento et al., Journal of Chemical Theory and Computation 17.5 (2021): 3031-3038.

Keywords: RIXS, TDDFT, ADC