X-ray absorption spectroscopy (XAS) has gained popularity in recent years as it probes matter with high spatial and elemental sensitivities. However, the theoretical modeling of XAS is a challenging task since XAS spectra feature a fine structure due to scalar (SC) and spin-orbit (SO) relativistic effects, in particular near L and M absorption edges. While full four-component (4c) calculations of XAS are nowadays feasible, there is still interest in developing approximate relativistic methods that enable XAS calculations at the two-component (2c) level while maintaining the accuracy of the parent 4c approach. In this article we present theoretical and numerical insights into two simple yet accurate 2c approaches based on an (extended) atomic mean-field exact two-component Hamiltonian framework, (e)amfX2C, for the calculation of XAS using linear eigenvalue and damped response time-dependent density functional theory (TDDFT). In contrast to the commonly used one-electron X2C (1eX2C) Hamiltonian, both amfX2C and eamfX2C account for the SC and SO two-electron and exchange-correlation picture-change (PC) effects that arise from the X2C transformation. As we demonstrate on L- and M-edge XAS spectra of transition metal and actinide compounds, the absence of PC corrections in the 1eX2C approximation results in a substantial overestimation of SO splittings, whereas (e)amfX2C Hamiltonians reproduce all essential spectral features such as shape, position, and SO splitting of the 4c references in excellent agreement, while offering significant computational savings. Therefore, the (e)amfX2C PC correction models presented here constitute reliable relativistic 2c quantum-chemical approaches for modeling XAS.

Center for Free Electron Laser Science Max Planck Institute for the Structure and Dynamics of Matter Luruper Chaussee 149 22761Hamburg Germany

Centre of Polymer Systems University Institute Tomas Bata University in Zlín CZ 76001Zlín Czech Republic

Department of Physical and Theoretical Chemistry Faculty of Natural Sciences Comenius University Ilkovicova 6 SK 84215Bratislava Slovakia

Hylleraas Centre for Quantum Molecular Sciences Department of Chemistry UiT The Arctic University of Norway N 9037Tromsø Norway

Institute of Inorganic Chemistry Slovak Academy of Sciences Dúbravská cesta 9 SK 84536Bratislava Slovakia

Norwegian Defence Research Establishment P O Box 25 2027Kjeller Norway

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