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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-19-0516

An unambiguous assignment of coupling pathways plays an important role in the description and rationalization of NMR indirect spin-spin coupling constants (SSCCs). Unfortunately, the SSCC analysis and visualization tools currently available to quantum chemists are restricted to nonrelativistic theory. Here, we present the theoretical foundation for novel relativistic SSCC visualization techniques based on analysis of the SSCC densities and the first-order current densities induced by the nuclear magnetic dipole moments. Details of the implementation of these techniques in the ReSpect program package are discussed. Numerical assessments are performed on through-space SSCCs, and we choose as our examples the heavy-atom Se-Se, Se-Te, and Te-Te coupling constants in three similar molecules for which experimental data are available. SSCCs were calculated at the nonrelativistic, scalar relativistic, and four-component relativistic density functional levels of theory. Furthermore, with the aid of different visualization methods, we discuss the interpretation of the relativistic effects, which are sizable for Se-Se, very significant for Se-Te, and cannot be neglected for Te-Te couplings. A substantial improvement of the theoretical SSCC values is obtained by also considering the molecular properties of a second conformation.

Accepted manuscript version. Published version at http://doi.org/10.1021/ct501078d. We report the first implementation of real-time time-dependent density functional theory (RT-TDDFT) at the relativistic four-component level of theory. In contrast to the perturbative linear-response TDDFT approach (LR-TDDFT), the RT-TDDFT approach performs an explicit time propagation of the Dirac–Kohn–Sham density matrix, offering the possibility to simulate molecular spectroscopies involving strong electromagnetic fields while, at the same time, treating relativistic scalar and spin–orbit corrections variationally. The implementation is based on the matrix representation of the Dirac–Coulomb Hamiltonian in the basis of restricted kinetically balanced Gaussian-type functions, exploiting the noncollinear Kramers unrestricted formalism implemented in the program ReSpect. We also present an analytic form for the delta-type impulse commonly used in RT-TDDFT calculations, as well as a dipole-weighted transition matrix analysis, facilitating the interpretation of spectral transitions in terms of ground-state molecular orbitals. The possibilities offered by the methodology are illustrated by investigating vertical excitation energies and oscillator strengths for ground-state to excited-state transitions in the Group 12 atoms and in heavy-element hydrides. The accuracy of the method is assessed by comparing the excitation energies obtained with earlier relativistic linear response TDDFT results and available experimental data.

A four-component relativistic method for the calculation of NMR shielding constants of paramagnetic doublet systems has been developed and implemented in the ReSpect program package. The method uses a Kramer unrestricted noncollinear formulation of density functional theory (DFT), providing the best DFT framework for property calculations of open-shell species. The evaluation of paramagnetic nuclear magnetic resonance (pNMR) tensors reduces to the calculation of electronic g tensors, hyperfine coupling tensors, and NMR shielding tensors. For all properties, modern four-component formulations were adopted. The use of both restricted kinetically and magnetically balanced basis sets along with gauge-including atomic orbitals ensures rapid basis-set convergence. These approaches are exact in the framework of the Dirac-Coulomb Hamiltonian, thus providing useful reference data for more approximate methods. Benchmark calculations on Ru(III) complexes demonstrate good performance of the method in reproducing experimental data and also its applicability to chemically relevant medium-sized systems. Decomposition of the temperature-dependent part of the pNMR tensor into the traditional contact and pseudocontact terms is proposed.