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 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. © 2023 The Authors. Published by American Chemical Society.2/0135/21; NN4654K; Ministerstvo Školství, Mládeže a Tělovýchovy, MŠMT: RP/CPS/2022/007; Agentúra na Podporu Výskumu a Vývoja, APVV: APVV-19-0516, APVV-21-0497; Norges Forskningsråd: 262695, 314814, 315822; Horizon 2020: 945478, SASPRO

Accurate X-ray absorption spectra near L- and M-edges from relativistic four-component damped response time-dependent density functional theory

The simulation of X-ray absorption spectra requires both scalar and spin-orbit (SO) relativistic effects to be taken into account, particularly near L- and M-edges where the SO splitting of core p and d orbitals dominates. Four-component Dirac-Coulomb Hamiltonian-based linear damped response time-dependent density functional theory (4c-DR-TDDFT) calculates spectra directly for a selected frequency region while including the relativistic effects variationally, making the method well suited for X-ray applications. In this work, we show that accurate X-ray absorption spectra near L-2,L-3- and M-4,M-5-edges of closed-shell transition metal and actinide compounds with different central atoms, ligands, and oxidation states can be obtained by means of 4c-DR-TDDFT. While the main absorption lines do not change noticeably with the basis set and geometry, the exchange-correlation functional has a strong influence with hybrid functionals performing the best. The energy shift compared to the experiment is shown to depend linearly on the amount of Hartee-Fock exchange with the optimal value being 60% for spectral regions above 1000 eV, providing relative errors below 0.2% and 2% for edge energies and SO splittings, respectively. Finally, the methodology calibrated in this work is used to reproduce the experimental L-2,L-3-edge X-ray absorption spectra of [RuCl2(DMSO)(2)(Im)(2)] and [WCl4(PMePh2)(2)], and resolve the broad bands into separated lines, allowing an interpretation based on ligand field theory and double point groups. These results support 4c-DR-TDDFT as a reliable method for calculating and analyzing X-ray absorption spectra of chemically interesting systems, advance the accuracy of state-of-the art relativistic DFT approaches, and provide a reference for benchmarking more approximate techniques.Research Council of NorwayResearch Council of Norway [315822, 252569]; Ministry of Education, Youth and Sports of the Czech Republic -DKRVO [RP/CPS/2020/006]; Slovak Grant Agency VEGAVedecka grantova agentura MSVVaS SR a SAV (VEGA) [2/0135/21, APVV-19-0516]; Slovak Grant Agency APVVSlovak Research and Development Agency [2/0135/21, APVV-19-0516]; UNINETT Sigma2, the National Infrastructure for High Performance Computing and Data Storage in Norway [NN4654K]; Ministry of Education, Youth and Sports of the Czech Republic through the e-INFRA CZ [90140]RP/CPS/2020/006; NN4654K, Sigma2; Ministerstvo Školství, Mládeže a Tělovýchovy, MŠMT: 90140; Norges Forskningsråd: 252569, 315822; Vedecká Grantová Agentúra MŠVVaŠ SR a SAV, VEGA: 2/0135/21, APVV-19-051

Relativistic heavy-neighbor-atom effects on NMR shifts: Concepts and trends across the periodic table

Chemical shifts present crucial information about an NMR spectrum. They show the influence of the chemical environment on the nuclei being probed. Relativistic effects caused by the presence of an atom of a heavy element in a compound can appreciably, even drastically, alter the NMR shifts of the nearby nuclei. A fundamental understanding of such relativistic effects on NMR shifts is important in many branches of chemical and physical science. This review provides a comprehensive overview of the tools, concepts, and periodic trends pertaining to the shielding effects by a neighboring heavy atom in diamagnetic systems, with particular emphasis on the "spin-orbit heavy-atom effect on the light-atom"NMR shift (SO-HALA effect). The analyses and tools described in this review provide guidelines to help NMR spectroscopists and computational chemists estimate the ranges of the NMR shifts for an unknown compound, identify intermediates in catalytic and other processes, analyze conformational aspects and intermolecular interactions, and predict trends in series of compounds throughout the Periodic Table. The present review provides a current snapshot of this important subfield of NMR spectroscopy and a basis and framework for including future findings in the field. © 2020 American Chemical Society.Czech Science FoundationGrant Agency of the Czech Republic [18-05421S]; Ministry of Education, Youth, and Sports of the Czech RepublicMinistry of Education, Youth & Sports - Czech Republic [LQ1601, LO1504, LTAUSA19148]; Grant Agency of the Masaryk University [MUNI/E/1335/2019]; Slovak Grant Agency VEGAVedecka grantova agentura MSVVaS SR a SAV (VEGA) [2/0116/17, APVV-15-0726]; Slovak Grant Agency APVVSlovak Research and Development Agency [2/0116/17, APVV-15-0726]; Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence StrategyGerman Research Foundation (DFG) [EXC 2008/1-390540038]; DFG collaborative research centerGerman Research Foundation (DFG) [CRC1349, 387284271]; CESNET [LM2015042]; CERIT Scientific Cloud [LM2015085]; IT4Innovations National Supercomputing Center [LM2015070

Four-Component Relativistic Density Functional Theory Calculations of EPR g- and Hyperfine-Coupling Tensors Using Hybrid Functionals: Validation on Transition-Metal Complexes with Large Tensor Anisotropies and Higher-Order Spin-Orbit Effects

The four-component matrix Dirac-Kohn-Sham (mDKS) implementation of EPR g- and hyperfine A-tensor calculations within a restricted kinetic balance framework in the ReSpect code has been extended to hybrid functionals. The methodology is validated for an extended set of small 4d1 and 5d1 [MEXn] q systems, and for a series of larger Ir(II) and Pt(III) d7 complexes (S=1/2) with particularly large g-tensor anisotropies. Different density functionals (PBE, BP86, B3LYP-xHF, PBE0-xHF) with variable exact-exchange admixture x (ranging from 0% to 50%) have been evaluated, and the influence of structure and basis set has been examined. Notably, hybrid functionals with exact-exchange admixture of about 40% provide the best agreement with experiment and clearly outperform the generalized-gradient approximation (GGA) functionals, in particular for the hyperfine couplings. Comparison with computations at the one-component second-order perturbational level within the DouglasKroll-Hess framework (1c-DKH), and a scaling of the speed of light at the four-component mDKS level, provide insight into the importance of higher-order relativistic effects for both properties. In the more extreme cases of some iridium(II) and platinum(III) complexes, the widely used leading-order perturbational treatment of SO effects in EPR calculations fails to reproduce not only the magnitude but also the sign of certain g-shift components (with the contribution of higher-order SO effects amounting to several hundreds of ppt in 5d complexes). The four-component hybrid mDKS calculations perform very well, giving overall good agreement with the experimental data