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Spectroscopic techniques based on core-level excitations offer powerful tools for probing molecular and electronic structures with high spatial resolution. However, accurately calculating spectral features at the L or M edges is challenging due to the significant influence of spin–orbit and multiplet effects. While scalar-relativistic effects can be incorporated with minimal computational cost, accounting for spin–orbit interactions requires complex frameworks that can be computationally expensive. In this work, we develop a reduced-cost state-interaction approach for simulating near-edge soft x-ray absorption spectra of closed-shell transition metal complexes with relativistic effects incorporated using the ZORA-Kohn–Sham Hamiltonian. The computed spectra closely agree with those obtained with state-of-the-art approaches. This methodology provides a practical and cost-effective alternative to more rigorous two-component methods, making it particularly valuable for large-scale calculations and applications such as resonant inelastic x-ray scattering simulations, where capturing a large number of excited states is essential.
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This content will become publicly available on July 11, 2026
Computing L- and M-edge spectra using the DFT/CIS method with spin–orbit coupling
Modeling L-edge spectra at X-ray wavelengths requires consideration of spin–orbit splitting of the 2p orbitals. We introduce a low-cost tool to compute core-level spectra that combines a spin–orbit mean-field description of the Breit–Pauli Hamiltonian with nonrelativistic excited states computed using the semi-empirical density-functional theory configuration-interaction singles (DFT/CIS) method, within the state-interaction approach. Our version of DFT/CIS was introduced recently for K-edge spectra and includes a semi-empirical correction to the core orbital energies, significantly reducing ad hoc shifts that are typically required when time-dependent (TD-)DFT is applied to core-level excitations. In combination with the core/valence separation approximation and spin–orbit couplings, the DFT/CIS method affords semiquantitative L-edge spectra at CIS cost. Spin–orbit coupling has a qualitative effect on the spectra, as demonstrated for a variety of 3d transition metal systems and main-group compounds. The use of different active orbital spaces helps to facilitate spectral assignments. We find that spin–orbit splitting has a negligible effect on M-edge spectra for 3d transition metal species.
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- Award ID(s):
- 1955282
- PAR ID:
- 10627026
- Publisher / Repository:
- Royal Society of Chemistry
- Date Published:
- Journal Name:
- Physical Chemistry Chemical Physics
- Volume:
- 27
- Issue:
- 31
- ISSN:
- 1463-9076
- Page Range / eLocation ID:
- 16336 to 16353
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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