Accurate Relativistic Real-Time TDDFT for Valence and Core Attosecond Transient Absorption Spectroscopy

Attosecond pump-probe transient absorption spectroscopy (TAS) has opened the possibility to study pure electron dynamics on its natural time scale. However, due to the out-of-equilibrium nature of the process, first-principle theoretical modelling remains a challenging task, specially for heavy elements and/or core excitations where relativistic corrections become imperative, as the spectra contain significant imprints of both scalar and spin-orbit relativistic effects. To alleviate this problem, we formulated a methodology for computing TAS spectrum within the relativistic real-time time-dependent density functional theory (RT-TDDFT) framework, for both the valence and core energy regime. Even though RT simulations using full four-component (4c) method are feasible, they are still computationally expensive, especially for TAS. Therefore, in addition to the 4c approach, we have introduced the atomic mean-field exact two-component (amfX2C) Hamiltonian for RT-TDDFT, which accounts for one- and two-electron picture-change corrections and preserves the accuracy of the parent 4c method but at a fraction of its computational cost. Finally, we apply the amfX2C approach to study valence and near L 2,3 -edge TAS processes of experimentally relevant systems, providing additional physical insights through the lens of non-equilibrium response theory

Exact two-component TDDFT with simple two-electron picture-change corrections: X-ray absorption spectra near L- and M-edges of four-component quality at two-component cost

X-ray absorption spectroscopy (XAS) has gained popularity in recent years as it probes matter with high spatial and elemental sensitivity. However, the theoretical modelling 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 overestimatation 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 modelling XAS