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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

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, SASPRO2

Relativistic effects are known to alter the chemical bonds and spectroscopic properties of heavy-element compounds. In this work, we introduce the concept of spin-orbit (SO) electronegativity of a heavy atom, as reflected by an SO-induced change in the interatomic distance between the heavy atom (HA) and a neighboring light atom (LA). We provide a transparent interpretation of these SO effects by using the concept of spin-orbit electron deformation density (SO-EDD). Spin-orbit coupling at the HA induces rearrangement of the electron density for the scalar-relativistically optimized geometry that, in turn, exerts a new force on the LA. The resulting expansion or contraction of the HA-LA bond depends on the nature and electron configuration of the HA. In addition, we quantify the change in atomic electronegativity induced by SO coupling for a series of hydrides, thereby complementing the SO-EDD picture. The trends in the SO-induced electronegativity and the HA-LA bond length across the periodic table of elements are demonstrated and interpreted, and also linked, intuitively, with the SO-induced NMR shielding at the LA.

Four-component relativistic treatments of the electron paramagnetic resonance g-tensor have so far been based on a common gauge origin and a restricted kinetically balanced basis. The results of such calculations are prone to exhibit a dependence on the choice of the gauge origin for the vector potential associated with uniform magnetic field and a related dependence on the basis set quality. In this work, this gauge problem is addressed by a distributed-origin scheme based on the London atomic orbitals, also called gauge-including atomic orbitals (GIAOs), which have proven to be a practical approach for calculations of other magnetic properties. Furthermore, in the four-component relativistic domain, it has previously been shown that a restricted magnetically balanced (RMB) basis for the small component of the four-component wavefunctions is necessary for achieving robust convergence with regard to the basis set size. We present the implementation of a four-component density functional theory (DFT) method for calculating the g-tensor, incorporating both the GIAOs and RMB basis and based on the Dirac–Coulomb Hamiltonian. The approach utilizes the state-of-the-art noncollinear Kramers-unrestricted DFT methodology to achieve rotationally invariant results and inclusion of spin-polarization effects in the calculation. We also show that the gauge dependence of the results obtained is connected to the nonvanishing integral of the current density in a finite basis, explain why the results of cluster calculations exhibit surprisingly low gauge dependence, and demonstrate that the gauge problem disappears for systems with certain point-group symmetries.

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.

Nuclear magnetic resonance (NMR) spectroscopy of paramagnetic molecules provides detailed information about their molecular and electron-spin structure. The paramagnetic NMR spectrum is a very rich source of information about the hyperfine interaction between the atomic nuclei and the unpaired electron density. The Fermi-contact contribution to ligand hyperfine NMR shifts is particularly informative about the nature of the metal-ligand bonding and the structural arrangements of the ligands coordinated to the metal center. In this account, we provide a detailed experimental and theoretical NMR study of compounds of Cr(III) and Cu(II) coordinated with substituted acetylacetonate (acac) ligands in the solid state. For the first time, we report the experimental observation of extremely paramagnetically deshielded 13C NMR resonances for these compounds in the range of 900-1200 ppm. We demonstrate an excellent agreement between the experimental NMR shifts and those calculated using relativistic density-functional theory. Crystal packing is shown to significantly influence the NMR shifts in the solid state, as demonstrated by theoretical calculations of various supramolecular clusters. The resonances are assigned to individual atoms in octahedral Cr(acac)3 and square-planar Cu(acac)2 compounds and interpreted by different electron configurations and magnetizations at the central metal atoms resulting in different spin delocalizations and polarizations of the ligand atoms. Further, effects of substituents on the 13C NMR resonance of the ipso carbon atom reaching almost 700 ppm for Cr(acac)3 compounds are interpreted based on the analysis of Fermi-contact hyperfine contributions.

International audience; We revise formal and numerical aspects of collinear and non-collinear density functional theories in the context of a two-component self-consistent treatment of spin–orbit coupling. Theoretical and numerical analyses of the non-collinear approaches confirm their ability to yield the proper collinear limit and provide rotational invariance of the total energy for functionals in the local-density or generalized-gradient approximations (GGAs). Calculations on simple molecules corroborate the formal considerations and highlight the importance of an effective screening algorithm to provide the sufficient level of numerical stability required for a rotationally invariant implementation of non-collinear GGA functionals. The illustrative calculations provide a first numerical comparison of both previously proposed non-collinear formulations for GGA functionals. The proposed screening procedure allows us to effectively deal with points of small magnetization, which would otherwise be problematic for the evaluation of the exchange–correlation energy and/or potential for non-collinear GGA functionals. Both previously suggested formulations for the non-collinear GGA are confirmed to be adequate for total energy calculations, provided that the screening is achieved on a sufficiently fine grid. All methods are implemented in the Crystal program.

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.

We present a detailed theory, implementation, and a benchmark study of a linear damped response time-dependent density functional theory (TDDFT) based on the relativistic four-component (4c) Dirac–Kohn–Sham formalism using the restricted kinetic balance condition for the small-component basis and a noncollinear exchange–correlation kernel. The damped response equations are solved by means of a multifrequency iterative subspace solver utilizing decomposition of the equations according to Hermitian and time-reversal symmetry. This partitioning leads to robust convergence, and the detailed algorithm of the solver for relativistic multicomponent wavefunctions is also presented. The solutions are then used to calculate the linear electric- and magnetic-dipole responses of molecular systems to an electric perturbation, leading to frequency-dependent dipole polarizabilities, electronic absorption, circular dichroism (ECD), and optical rotatory dispersion (ORD) spectra. The methodology has been implemented in the relativistic spectroscopy DFT program ReSpect, and its performance was assessed on a model series of dimethylchalcogeniranes, C4H8X (X = O, S, Se, Te, Po, Lv), and on larger transition metal complexes that had been studied experimentally, [M(phen)3]3+ (M = Fe, Ru, Os). These are the first 4c damped linear response TDDFT calculations of ECD and ORD presented in the literature.We present a detailed theory, implementation, and a benchmark study of a linear damped response time-dependent density functional theory (TDDFT) based on the relativistic four-component (4c) Dirac–Kohn–Sham formalism using the restricted kinetic balance condition for the small-component basis and a noncollinear exchange–correlation kernel. The damped response equations are solved by means of a multifrequency iterative subspace solver utilizing decomposition of the equations according to Hermitian and time-reversal symmetry. This partitioning leads to robust convergence, and the detailed algorithm of the solver for relativistic multicomponent wavefunctions is also presented. The solutions are then used to calculate the linear electric- and magnetic-dipole responses of molecular systems to an electric perturbation, leading to frequency-dependent dipole polarizabilities, electronic absorption, circular dichroism (ECD), and optical rotatory dispersion (ORD) spectra. The methodology has been implemented in the...

The performance of relativistic density functional theory (DFT) methods has been investigated for the calculation of the recently measured hyperfine coupling constants of hexafluorido complexes [ReF6 ] 2- and [IrF6 ] 2- . Three relativistic methods were employed at the DFT level of theory: the 2-component zeroth-order regular approximation (ZORA) method, in which the spin–orbit coupling was treated either variationally (EV ZORA) or as a perturbation (LR ZORA), and the 4-component Dirac–Kohn–Sham (DKS) method. The dependence of the results on the basis set and the choice of exchange-correlation functional was studied. Furthermore, the effect of varying the amount of Hartree–Fock exchange in the hybrid functionals was investigated. The LR ZORA and DKS methods combined with DFT led to very similar deviations (about 20%) from the experimental values for the coupling constant of complex [ReF6 ] 2- by using hybrid functionals. However, none of the methods were able to reproduce the large anisotropy of the hyperfine coupling tensor of complex [ReF6 ] 2- . For [IrF6 ] 2- , the EV ZORA and DKS methods reproduced the experimental tensor components with deviations of &10 and &5% for the hybrid functionals, whereas the LR ZORA method predicted the coupling constant to be around one order of magnitude too large owing to the combination of large spin–orbit coupling and very low excitation energies.

We report a combined experimental-theoretical study on the 31P NMR chemical shift for a number of trans-platinum(ii) complexes. Validity and reliability of the 31P NMR chemical shift calculations are examined by comparing with the experimental data. A successful computational protocol for the accurate prediction of the 31P NMR chemical shifts was established for trans-[PtCl2(dma)PPh3] (dma = dimethylamine) complexes. The reliability of the computed values is shown to be critically dependent on the level of relativistic effects (two-component vs. four component), choice of density functionals, dynamical averaging, and solvation effects. Snapshots obtained from ab initio molecular dynamics simulations were used to identify those solvent molecules which show the largest interactions with the platinum complex, through inspection by using the non-covalent interaction program. We observe satisfactory accuracy from the full four-component matrix Dirac-Kohn-Sham method (mDKS) based on the Dirac-Coulomb Hamiltonian, in conjunction with the KT2 density functional, and dynamical averaging with explicit solvent molecules.

We report a combined experimental-theoretical study on the 31P NMR chemical shift for a number of trans-platinum(ii) complexes. Validity and reliability of the 31P NMR chemical shift calculations are examined by comparing with the experimental data. A successful computational protocol for the accurate prediction of the 31P NMR chemical shifts was established for trans-[PtCl2(dma)PPh3] (dma = dimethylamine) complexes. The reliability of the computed values is shown to be critically dependent on the level of relativistic effects (two-component vs. four component), choice of density functionals, dynamical averaging, and solvation effects. Snapshots obtained from ab initio molecular dynamics simulations were used to identify those solvent molecules which show the largest interactions with the platinum complex, through inspection by using the non-covalent interaction program. We observe satisfactory accuracy from the full four-component matrix Dirac-Kohn-Sham method (mDKS) based on the Dirac-Coulomb Hamiltonian, in conjunction with the KT2 density functional, and dynamical averaging with explicit solvent molecules.

Reprinted with permission from Bora PL, Novotny J, Ruud K, Komorovsky S, Marek R. Electron-Spin Structure and Metal-Ligand Bonding in Open-Shell Systems from Relativistic EPR and NMR: A Case Study of Square-Planar Iridium Catalysts. Journal of Chemical Theory and Computation. 2019;15(1):201-214. Copyright © 2018 American Chemical Society Electron and nuclear magnetic resonance spectroscopies are indispensable and powerful methods for investigating the molecular and electronic structures of open-shell systems. We demonstrate that the NMR and EPR parameters are extremely sensitive quantitative probes for the electronic spin density around heavy-metal atoms and the metal–ligand bonding. Using relativistic density-functional theory, we have analyzed the relation between the spin density and the EPR and NMR parameters in paramagnetic iridium(II/IV) complexes with a PNP pincer ligand. As the magnetic-response parameters for compounds containing 5d transition metal(s) are heavily affected by spin–orbit coupling, relativistic effects must be included in the calculations. We have used a recent implementation of the fully relativistic Dirac−Kohn–Sham (DKS) method employing the hybrid PBE0 functional and an implicit solvent model to calculate EPR parameters and hyperfine NMR shifts. The modulation of the metal–ligand bond by the trans substituent (−Cl or ≡N) and the electronic spin structure around the central metal atom and ligands are shown to be reflected in the “long-range” through-bond Fermi-contact (FC) contributions to the ligand 13C and 1H hyperfine couplings. Interestingly, the hyperfine coupling constant of the ligand atom L (AL) bonded directly to the iridium center changes its sign because of the dominating role of the paramagnetic spin–orbit (PSO) term. Furthermore, the electronic g-shift and the PSO contribution to the ligand AL are shown to invert their signs when nitrogen is substituted for chlorine, reflecting the different formal metal oxidation states and the change in metal–ligand bond character. A full understanding of the substituent effects is provided by using chemical bond concepts in combination with a molecular-orbital (MO) theory analysis of the second-order perturbation theory expression for the EPR parameters. Our findings are easily transferable to other systems containing d-block elements and beyond. Relativistic DFT calculations of magnetic-resonance parameters are expected to frequently assist in future experimental observations and the characterization of hitherto unknown unstable or exotic species.

With the increasing interest in compounds containing heavier elements, the experimental and theoretical community requires computationally efficient approaches capable of simultaneous non-perturbative treatment of relativistic, spin-polarization, and electron correlation effects. The ReSpect program has been designed with this goal in mind and developed to perform relativistic density functional theory (DFT) calculations on molecules and solids at the quasirelativistic two-component (X2C Hamiltonian) and fully relativistic four-component (Dirac–Coulomb Hamiltonian) level of theory, including the effects of spin polarization in open-shell systems at the Kramers-unrestricted self-consistent field level. Through efficient algorithms exploiting time-reversal symmetry, biquaternion algebra, and the locality of atom-centered Gaussian-type orbitals, a significant reduction of the methodological complexity and computational cost has been achieved. This article summarizes the essential theoretical and technical advances made in the program, supplemented by example calculations. ReSpect allows molecules with >100 atoms to be efficiently handled at the four-component level of theory on standard central processing unit-based commodity clusters, at computational costs that rarely exceed a factor of 10 when compared to the non-relativistic realm. In addition to the prediction of band structures in solids, ReSpect offers a growing list of molecular spectroscopic parameters that range from electron paramagnetic resonance parameters (g-tensor, A-tensor, and zero-field splitting), via (p)NMR chemical shifts and nuclear spin–spin couplings, to various linear response properties using either conventional or damped-response time-dependent DFT (TDDFT): excitation energies, frequency-dependent polarizabilities, and natural chiroptical properties (electronic circular dichroism and optical rotatory dispersion). In addition, relativistic real-time TDDFT electron dynamics is another unique feature of the program. Documentation, including user manuals and tutorials, is available at the program’s website http://www.respectprogram.org.

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in The Journal of Chemical Physics, 151(18), 184111 and may be found at https://doi.org/10.1063/1.5121713. We present a formulation of relativistic linear response time-dependent density functional theory for the calculation of electronic excitation energies in the framework of the four-component Dirac-Coulomb Hamiltonian. This approach is based on the noncollinear ansatz originally developed by Scalmani and Frisch [J. Chem. Theory Comput. 8, 2193 (2012)] and improves upon the past treatment of the limit cases in which the spin density approaches zero. As a result of these improvements, the presented approach is capable of treating both closed- and open-shell reference states. Robust convergence of the Davidson-Olsen eigenproblem algorithm for open-shell reference states was achieved through the use of a solver which considers both left and right eigenvectors. The applicability of the present methodology on both closed- and open-shell reference states is demonstrated on calculations of low-lying excitation energies for Group 3 atomic systems (Sc3+–Ac3+) with nondegenerate ground states, as well as for Group 11 atomic systems (Cu–Rg) and octahedral actinide complexes (PaCl2−6, UCl−6, and NpF6) with effective doublet ground states.

The links between the molecular structure and nuclear magnetic resonance (NMR) parameters of paramagnetic transition-metal complexes are still relatively unexplored. This applies particularly to the contact term of the hyperfine contribution to the NMR chemical shift. We report combining experimental NMR with relativistic density functional theory (DFT) to study a series of Ru(III) complexes with 2-substituted β-diketones. A series of complexes with systematically varied substituents was synthesized and analyzed using 1H and 13C NMR spectroscopy. The NMR spectra recorded at several temperatures were used to construct Curie plots and estimate the temperature-independent (orbital) and temperature-dependent (hyperfine) contributions to the NMR shift. Relativistic DFT calculations of electron paramagnetic resonance and NMR parameters were performed to interpret the experimental observations. The effects of individual factors such as basis set, density functional, exact-exchange admixture, and relativity are a...

The importance of relativistic effects on the NMR parameters in heavy-atom (HA) compounds, particularly the SO-HALA (Spin–Orbit Heavy Atom on the Light Atom) effect on NMR chemical shifts, has been known for about 40 years. Yet, a general correlation between the electronic structure and SO-HALA effect has been missing. By analyzing 1H NMR chemical shifts of the sixth-period hydrides (Cs–At), we discovered general electronic-structure principles and mechanisms that dictate the size and sign of the SO-HALA NMR chemical shifts. In brief, partially occupied HA valence shells induce relativistic shielding at the light atom (LA) nuclei, while empty HA valence shells induce relativistic deshielding. In particular, the LA nucleus is relativistically shielded in 5d2–5d8 and 6p4 HA hydrides and deshielded in 4f0, 5d0, 6s0, and 6p0 HA hydrides. This general and intuitive concept explains periodic trends in the 1H NMR chemical shifts along the sixth-period hydrides (Cs–At) studied in this work. We present substantial...

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article, Konecny, L., Kadek, M., Komorovsky, S., Ruud, K. & Repisky, M. (2018). Resolution-of-identity accelerated relativistic two- and four-component electron dynamics approach to chiroptical spectroscopies. Journal of Chemical Physics, 149, 204104, appeared in Journal of Chemical Physics and may be found at https://doi.org/10.1063/1.5051032. We present an implementation and application of electron dynamics based on real-time time-dependent density functional theory (RT-TDDFT) and relativistic 2-component X2C and 4-component Dirac–Coulomb (4c) Hamiltonians to the calculation of electron circular dichroism and optical rotatory dispersion spectra. In addition, the resolution-of-identity approximation for the Coulomb term (RI-J) is introduced into RT-TDDFT and formulated entirely in terms of complex quaternion algebra. The proposed methodology was assessed on the dimethylchalcogenirane series, C4H8X (X = O, S, Se, Te, Po, Lv), and the spectra obtained by non-relativistic and relativistic methods start to disagree for Se and Te, while dramatic differences are observed for Po and Lv. The X2C approach, even in its simplest one-particle form, reproduces the reference 4c results surprisingly well across the entire series while offering an 8-fold speed-up of the simulations. An overall acceleration of RT-TDDFT by means of X2C and RI-J increases with system size and approaches a factor of almost 25 when compared to the full 4c treatment, without compromising the accuracy of the final spectra. These results suggest that one-particle X2C electron dynamics with RI-J acceleration is an attractive method for the calculation of chiroptical spectra in the valence region.

NMR spectroscopy is an indispensable tool in characterizing molecular systems, including transition-metal complexes. However, paramagnetic transition-metal complexes such as those with ruthenium in the +3 oxidation state are troublemakers because their unpaired electrons induce a fast nuclear spin relaxation that significantly broadens their NMR resonances. We recently demonstrated that the electronic and spin structures of paramagnetic Ru(III) systems can be characterized in unprecedented details by combining experimental NMR results with relativistic density-functional theory ( Novotny et al. J. Am. Chem. Soc. 2016 , 138 , 8432 ). In this study we focus on paramagnetic analogs of NAMI with the general structure [3-R-pyH]+trans-[RuIIICl4(DMSO)(3-R-py)]-, where 3-R-py stands for a 3-substituted pyridine. The experimental NMR data are interpreted in terms of the contributions of hyperfine (HF) NMR shielding and the distribution of spin density calculated using relativistic DFT. The DFT computational methodology is evaluated, and the effects of substituents, environment, and relativity on the hyperfine shielding are discussed. Particular attention is paid to the analysis of the fundamental Fermi-contact (FC), spin-dipole (SD), and paramagnetic spin-orbit (PSO) terms that contribute to the hyperfine 1H and 13C NMR shifts of the individual atoms in the pyridine ligands and the spin-polarization effects in the ligand system that are linked to the character of the metal-ligand bond. The individual HF shielding terms are systematically discussed as they relate to the traditional, but somewhat mixed, contact and pseudocontact NMR contributions used extensively by experimental spectroscopists in biomolecular NMR and the development of PARACEST magnetic-resonance contrast agents.

The performance of relativistic density functional theory (DFT) methods has been investigated for the calculation of the recently measured hyperfine coupling constants of hexafluorido complexes [ReF6]2− and [IrF6]2−. Three relativistic methods were employed at the DFT level of theory: the 2‐component zeroth‐order regular approximation (ZORA) method, in which the spin–orbit coupling was treated either variationally (EV ZORA) or as a perturbation (LR ZORA), and the 4‐component Dirac–Kohn–Sham (DKS) method. The dependence of the results on the basis set and the choice of exchange‐correlation functional was studied. Furthermore, the effect of varying the amount of Hartree–Fock exchange in the hybrid functionals was investigated. The LR ZORA and DKS methods combined with DFT led to very similar deviations (about 20 %) from the experimental values for the coupling constant of complex [ReF6]2− by using hybrid functionals. However, none of the methods were able to reproduce the large anisotropy of the hyperfine coupling tensor of complex [ReF6]2−. For [IrF6]2−, the EV ZORA and DKS methods reproduced the experimental tensor components with deviations of ≈10 and ≈5 % for the hybrid functionals, whereas the LR ZORA method predicted the coupling constant to be around one order of magnitude too large owing to the combination of large spin–orbit coupling and very low excitation energies.

This work has received support from the Research Council of Norway through a Centre of Excellence Grant (Grant No. 179568/V30) and project grants (Grant No. 214095, 177558) and the European Research Council starting grant (Grant No. 279619). The work has also received support from the Norwegian Supercomputing program NOTUR (Grant No. NN4654K).

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.

The role of various factors (structure, solvent, and relativistic treatment) was evaluated for square-planar 4d and 5d transition-metal complexes. The DFT method for calculating the structures was calibrated using a cluster approach and compared to X-ray geometries, with the PBE0 functional (def2-TZVPP basis set) providing the best results, followed closely by the hybrid TPSSH and the MN12SX functionals. Calculations of the NMR chemical shifts using the two-component (2c, Zeroth-Order Regular Approximation as implemented in the ADF package) and four-component (4c, Dirac-Coulomb as implemented in the ReSpect code) relativistic approaches were performed to analyze and demonstrate the importance of solvent corrections (2c) as well as a proper treatment of relativistic effects (4c). The importance of increased exact-exchange admixture in the functional (here PBE0) for reproducing the experimental data using the current implementation of the 2c approach is partly rationalized as a compensation for the missing exchange-correlation response kernel. The kernel contribution was identified to be about 15-20% of the spin-orbit-induced NMR chemical shift, DdSO, which roughly corresponds to an increase in DdSO introduced by the artificially increased exact-exchange admixture in the functional. Finally, the role of individual effects (geometry, solvent, relativity) in the NMR chemical shift is discussed in selected complexes. Although a fully relativistic DFT approach is still awaiting the implementation of GIAOs for hybrid functionals and an implicit solvent model, it nevertheless provides reliable NMR chemical shift data at an affordable computational cost. It is expected to outperform the 2c approach, in particular for the calculation of NMR parameters in heavy-element compounds., Czech Science Foundation [15-09381S, 14-03564S]; European Regional Development Fund [CZ.1.05/1.1.00/02.0068]; Research Council of Norway through a Centre of Excellence [179568, 214095, 177558]; Czech-Norway mobility grant from Norway Funds [NF-CZ07-MOP-3-245-2015]; program Center CERIT Scientific Cloud, part of the Operational Program Research and Development for Innovations [CZ.1.05/3.2.00/08.0144]

The relationship between cis-trans isomerism and anticancer activity has been mainly addressed for square-planar metal complexes, in particular, for platinum(ii), e.g., cis- and trans-[PtCl2(NH3)2], and a number of related compounds, of which, however, only cis-counterparts are in clinical use today. For octahedral metal complexes, this effect of geometrical isomerism on anticancer activity has not been investigated systematically, mainly because the relevant isomers are still unavailable. An example of such an octahedral complex is trans-[RuCl4(Hind)2]-, which is in clinical trials now as its indazolium (KP1019) or sodium salt (NKP1339), but the corresponding cis-isomers remain inaccessible. We report the synthesis of Na[cis-OsIIICl4(κN2-1H-ind)2]·(Na[1]) suggesting a route to the cis-isomer of NKP1339. The procedure involves heating (H2ind)[OsIVCl5(κN1-2H-ind)] in a high boiling point organic solvent resulting in an Anderson rearrangement with the formation of cis-[OsIVCl4(κN2-1H-ind)2] ([1]) in high yield. The transformation is accompanied by an indazole coordination mode switch from κN1 to κN2 and stabilization of the 1H-indazole tautomer. Fully reversible spectroelectrochemical reduction of [1] in acetonitrile at 0.46 V vs. NHE is accompanied by a change in electronic absorption bands indicating the formation of cis-[OsIIICl4(κN2-1H-ind)2]- ([1]-). Chemical reduction of [1] in methanol with NaBH4 followed by addition of nBu4NCl afforded the osmium(iii) complex nBu4N[cis-OsIIICl4(κN2-1H-ind)2] (nBu4N[1]). A metathesis reaction of nBu4N[1] with an ion exchange resin led to the isolation of the water-soluble salt Na[1]. The X-ray diffraction crystal structure of [1]·Me2CO was determined and compared with that of trans-[OsIVCl4(κN2-1H-ind)2]·2Me2SO (2·2Me2SO), also prepared in this work. EPR spectroscopy was performed on the OsIII complexes and the results were analyzed by ligand-field and quantum chemical theories. We furthermore assayed effects of [1] and Na[1] on cell viability and proliferation in comparison with trans-[OsIVCl4(κN1-2H-ind)2] [3] and cisplatin and found a strong reduction of cell viability at concentrations between 30 and 300 μM in different cancer cell lines (HT29, H446, 4T1 and HEK293). HT-29 cells are less sensitive to cisplatin than 4T1 cells, but more sensitive to [1] and Na[1], as shown by decreased proliferation and viability as well as an increased late apoptotic/necrotic cell population.

Relativistic effects significantly affect various spectroscopic properties of compounds containing heavy elements. Particularly in Nuclear Magnetic Resonance (NMR) spectroscopy, the heavy atoms strongly influence the NMR shielding constants of neighboring light atoms. In this account we analyze paramagnetic contributions to NMR shielding constants and their modulation by relativistic spin-orbit effects in a series of transition-metal complexes of Pt(II), Au(I), Au(III), and Hg(II). We show how the paramagnetic NMR shielding and spin-orbit effects relate to the character of the metal-ligand (M-L) bond. A correlation between the (back)-donation character of the M-L bond in d10 Au(I) complexes and the propagation of the spin-orbit (SO) effects from M to L through the M-L bond influencing the ligand NMR shielding via the Fermi-contact mechanism is found and rationalized by using third-order perturbation theory. The SO effects on the ligand NMR shielding are demonstrated to be driven by both the electronic structure of M and the nature of the trans ligand, sharing the σ-bonding metal orbital with the NMR spectator atom L. The deshielding paramagnetic contribution is linked to the σ-type M-L bonding orbitals, which are notably affected by the trans ligand. The SO deshielding role of σ-type orbitals is enhanced in d10 Hg(II) complexes with the Hg 6p atomic orbital involved in the M-L bonding. In contrast, in d8 Pt(II) complexes, occupied π-type orbitals play a dominant role in the SO-altered magnetic couplings due to the accessibility of vacant antibonding σ-type MOs in formally open 5d-shell (d8). This results in a significant SO shielding at the light atom. The energy- and composition-modulation of σ- vs π-type orbitals by spin-orbit coupling is rationalized and supported by visualizing the SO-induced changes in the electron density around the metal and light atoms (spin-orbit electron deformation density, SO-EDD). © 2017 American Chemical Society., Czech Science Foundation [16-05961S, 15-09381S]; Ministry of Education, Youth and Sports of the Czech Republic [LQ1601, LO1504]; multilateral cooperation project [8X17009]; SASPRO Program [1563/03/02]; European Union; Slovak Academy of Sciences; Grant Agency of the Ministry of Education of the Slovak Republic; Slovak Academy of Sciences VEGA [2/0116/17]; Research Council of Norway [179568]; Norwegian supercomputing program NOTUR [NN4654K]

By breaking the spin symmetry in the relativistic domain, a powerful tool in physical sciences was lost. In this work, we examine an alternative of spin symmetry for systems described by the many-electron Dirac-Coulomb Hamiltonian. We show that the square of many-electron operator $\mathcal{K}_+$, defined as a sum of individual single-electron time-reversal (TR) operators, is a linear Hermitian operator which commutes with the Dirac-Coulomb Hamiltonian in a finite Fock subspace. In contrast to the square of a standard unitary many-electron TR operator $\mathcal{K}$, the $\mathcal{K}^2_+$ has a rich eigenspectrum having potential to substitute spin symmetry in the relativistic domain. We demonstrate that $\mathcal{K}_+$ is connected to $\mathcal{K}$ through an exponential mapping, in the same way as spin operators are mapped to the spin rotational group. Consequently, we call $\mathcal{K}_+$ the generator of the many-electron TR symmetry. By diagonalizing the operator $\mathcal{K}^2_+$ in the basis of Kramers-restricted Slater determinants, we introduce the relativistic variant of configuration state functions (CSF), denoted as Kramers CSF. A new quantum number associated with $\mathcal{K}^2_+$ has potential to be used in many areas, for instance, (a) to design effective spin Hamiltonians for electron spin resonance spectroscopy of heavy-element containing systems; (b) to increase efficiency of methods for the solution of many-electron problems in relativistic computational chemistry and physics; (c) to define Kramers contamination in unrestricted density functional and Hartree--Fock theory as a relativistic analog of the spin contamination in the nonrelativistic domain., Comment: 15 pages, published in Phys. Rev. A, one FORTRAN program; Changes: minor text formatting, add supplemental material as Appendix I, add comparison with three open-shell electrons to Sec. VII last paragraph

The Liouville-von Neumann equation based on the four-component matrix Dirac-Kohn-Sham Hamiltonian is transformed to a quasirelativistic exact two-component (X2C) form and then used to solve the time evolution of the electronic states only. By this means, a significant acceleration by a factor of 7 or more has been achieved. The transformation of the original four-component equation of motion is formulated entirely in matrix algebra, following closely the X2C decoupling procedure of Ilias and Saue [ J. Chem. Phys. 2007 , 126 , 064102 ] proposed earlier for a static (time-independent) case. In a dynamic (time-dependent) regime, however, an adiabatic approximation must in addition be introduced in order to preserve the block-diagonal form of the time-dependent Dirac-Fock operator during the time evolution. The resulting X2C Liouville-von Neumann electron dynamics (X2C-LvNED) is easy to implement as it does not require an explicit form of the picture-change transformed operators responsible for the (higher-order) relativistic corrections and/or interactions with external fields. To illustrate the accuracy and performance of the method, numerical results and computational timings for nonlinear optical properties are presented. All of the time domain X2C-LvNED results show excellent agreement with the reference four-component calculations as well as with the results obtained from frequency domain response theory.

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.

Source:DOI: 10.1021/jacs.6b02749 Ruthenium-based compounds are potential candidates for use as anticancer metallodrugs. The central ruthenium atom can be in the oxidation state +2 (e.g., RAPTA, RAED) or +3 (e.g., NAMI, KP). In this study we focus on paramagnetic NAMI analogs of a general structure [4-R-pyH]+ trans-[RuIIICl4(DMSO)(4-R-py)]−, where 4-R-py stands for a 4-substituted pyridine. As paramagnetic systems are generally considered difficult to characterize in detail by NMR spectroscopy, we performed a systematic structural and methodological NMR study of complexes containing variously substituted pyridines. The effect of the paramagnetic nature of these complexes on the 1H and 13C NMR chemical shifts was systematically investigated by temperature-dependent NMR experiments and density-functional theory (DFT) calculations. To understand the electronic factors influencing the orbital (δorb, temperature-independent) and paramagnetic (δpara, temperature-dependent) contributions to the total NMR chemical shifts, a relativistic twocomponent DFT approach was used. The paramagnetic contributions to the 13C NMR chemical shifts are correlated with the distribution of spin density in the ligand moiety and the 13C isotropic hyperfine coupling constants, Aiso (13C), for the individual carbon atoms. To analyze the mechanism of spin distribution in the ligand, the contributions of molecular spin−orbitals (MSOs) to the hyperfine coupling constants and the spatial distribution of the z-component of the spin density in the MSOs calculated at the relativistic four-component DFT level are discussed and rationalized. The significant effects of the substituent and the solvent on δpara, particularly the contact contribution, are demonstrated. This work should contribute to further understanding of the link between the electronic structure and the NMR chemical shifts in open-shell systems, including the ruthenium-based metallodrugs investigated in this account.

This is an Accepted Manuscript of an article published by Taylor & Francis in Molecular Physics on 8 June 2016, available online: http://www.tandfonline.com/10.1080/00268976.2016.1191688. Approaches and programs for calculations of the EPR g-tensor in the framework of the two- and four-component methods are still very rare. There are three main reasons for this: the wider community's unawareness of the importance of second- and higher order spin–orbit effects on the g-tensor, the methodological problems associated with performing such calculations and the lack of understanding of these problems. This paper reports on the implementation of a method for calculation of the g-tensor in the framework of the relativistic unrestricted two- and four-component Hartree–Fock and density functional theory approaches based on the Kramers pair formalism. This implementation allows us to analyse problems which arise when the g-tensor is calculated via Kramers pairs in the unrestricted framework.

Source:http://dx.doi.org/10.1080/00268976.2016.1239846 The description of chemical phenomena in solution is as challenging as it is im- portant for the accurate calculation of molecular properties. Here, we present the implementation of the polarizable continuum model (PCM) in the four-component Dirac–Kohn–Sham density functional theory framework, o ↵ ering a cost-e ↵ ective way to concurrently model solvent and relativistic e ↵ ects. The implementation is based on the matrix representation of the Dirac–Coulomb Hamiltonian in the basis of restricted kinetically balanced Gaussian-type functions, exploiting a non-collinear Kramers unrestricted formalism implemented in the program ReSpect ,andthein- tegral equation formalism of the PCM (IEF-PCM) available through the standalone library PCMSolver . Calculations of EPR parameters ( g -tensors and hyperfine cou- pling A -tensors), as well as of the temperature-dependent contribution to paramag- netic NMR (pNMR) shifts, are presented to validate the model and to demonstrate the importance of taking both relativistic and solvent e ↵ ects into account for mag- netic properties. As shown for selected Ru and Os complexes, the solvent shifts may amount to as much as 25% of the gas-phase values for g -tensor components and even more for pNMR shifts in some extreme cases.

Copyright 2015 AIP Publishing. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in Journal of Chemical Physics 2015, 143 and may be found at http://dx.doi.org/10.1063/1.4934533 We present nuclear spin–rotation constants, absolute nuclear magnetic resonance (NMR) shielding constants, and shielding spans of all the nuclei in 175LuX and 197AuX (X = 19F, 35Cl, 79Br, 127I), calculated using coupled-cluster singles-and-doubles with a perturbative triples (CCSD(T)) correction theory, four-component relativistic density functional theory (relativistic DFT), and non-relativistic DFT. The total nuclear spin–rotation constants determined by adding the relativistic corrections obtained from DFT calculations to the CCSD(T) values are in general in agreement with available experimental data, indicating that the computational approach followed in this study allows us to predict reliable results for the unknown spin–rotation constants in these molecules. The total NMR absolute shielding constants are determined for all the nuclei following the same approach as that applied for the nuclear spin–rotation constants. In most of the molecules, relativistic effects significantly change the computed shielding constants, demonstrating that straightforward application of the non-relativistic formula relating the electronic contribution to the nuclear spin–rotation constants and the paramagnetic contribution to the shielding constants does not yield correct results. We also analyze the origin of the unusually large absolute shielding constant and its relativistic correction of gold in AuF compared to the other gold monohalides.

Published version. Source at http://doi.org/10.1039/c5cc05732a. Magnetically induced probability currents in molecules are studied in relativistic theory. Spin–orbit coupling (SOC) enhances the curvature and gives rise to a previously unobserved current cusp in AuH or small bulge-like distortions in HgH2 at the proton positions. The origin of this curvature is magnetically induced spin-density arising from SOC in the relativistic description.

We have calculated the (13) C NMR chemical shifts of a large ensemble of halogenated organic molecules (81 molecules for a total of 250 experimental (13) C NMR data at four different levels of theory), ranging from small rigid organic compounds, used to benchmark the performance of various levels of theory, to natural substances of marine origin with conformational degrees of freedom. Carbon atoms bonded to heavy halogen atoms, particularly bromine and iodine, are known to be rather challenging when it comes to the prediction of their chemical shifts by quantum methods, due to relativistic effects. In this paper, we have applied the state-of-the-art four-component relativistic density functional theory for the prediction of such NMR properties and compared the performance with two-component and nonrelativistic methods. Our results highlight the necessity to include relativistic corrections within a four-component description for the most accurate prediction of the NMR properties of halogenated organic substances.

Accepted manuscript version. Published version at http://doi.org/10.1021/acs.jctc.5b00276. We present an implementation of the nuclear spin–rotation (SR) constants based on the relativistic four-component Dirac–Coulomb Hamiltonian. This formalism has been implemented in the framework of the Hartree–Fock and Kohn–Sham theory, allowing assessment of both pure and hybrid exchange–correlation functionals. In the density-functional theory (DFT) implementation of the response equations, a noncollinear generalized gradient approximation (GGA) has been used. The present approach enforces a restricted kinetic balance condition for the small-component basis at the integral level, leading to very efficient calculations of the property. We apply the methodology to study relativistic effects on the spin–rotation constants by performing calculations on XHn (n = 1–4) for all elements X in the p-block of the periodic table and comparing the effects of relativity on the nuclear SR tensors to that observed for the nuclear magnetic shielding tensors. Correlation effects as described by the density-functional theory are shown to be significant for the spin–rotation constants, whereas the differences between the use of GGA and hybrid density functionals are much smaller. Our calculated relativistic spin–rotation constants at the DFT level of theory are only in fair agreement with available experimental data. It is shown that the scaling of the relativistic effects for the spin–rotation constants (varying between Z3.8 and Z4.5) is as strong as for the chemical shieldings but with a much smaller prefactor.

Source: doi: 10.1063/1.4972892 We report the Nuclear Magnetic Resonance (NMR) spin–spin coupling constants for diatomic alkali halides MX, where M = Li, Na, K, Rb, or Cs and X = F, Cl, Br, or I. The coupling constants are determined by supplementing the non-relativistic coupled-cluster singles-and-doubles (CCSD) values with relativistic corrections evaluated at the four-component density-functional theory (DFT) level. These corrections are calculated as the differences between relativistic and non-relativistic values determined using the PBE0 functional with 50% exact-exchange admixture. The total coupling constants obtained in this approach are in much better agreement with experiment than the standard relativistic DFT values with 25% exact-exchange, and are also noticeably better than the relativistic PBE0 results obtained with 50% exact-exchange. Further improvement is achieved by adding rovibrational corrections, estimated using literature data.

The spin-rotation and nuclear magnetic shielding constants are analysed for both nuclei in the HCl molecule. Nonrelativistic ab initio calculations at the CCSD(T) level of approximation show that it is essential to include relativistic effects to obtain spin-rotation constants consistent with accurate experimental data. Our best estimates for the spin-rotation constants of (1)H(35)Cl are CCl = -53.914 kHz and C(H) = 42.672 kHz (for the lowest rovibrational level). For the chlorine shielding constant, the ab initio value computed including the relativistic corrections, σ(Cl) = 976.202 ppm, provides a new absolute shielding scale; for hydrogen we find σ(H) = 31.403 ppm (both at 300 K). Combining the theoretical results with our new gas-phase NMR experimental data allows us to improve the accuracy of the magnetic dipole moments of both chlorine isotopes. For the hydrogen shielding constant, including relativistic effects yields better agreement between experimental and computed values.

Copyright 2015 AIP Publishing. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in Journal of Chemical Physics 2015, 142 and may be found at http://dx.doi.org/10.1063/1.4913639 In this work, we report on the development and implementation of a new scheme for efficient calculation of indirect nuclear spin-spin couplings in the framework of four-component matrix Dirac-Kohn-Sham approach termed matrix Dirac-Kohn-Sham restricted magnetic balance resolution of identity for J and K, which takes advantage of the previous restricted magnetic balance formalism and the density fitting approach for the rapid evaluation of density functional theory exchange-correlation response kernels. The new approach is aimed to speedup the bottleneck in the solution of the coupled perturbed equations: evaluation of the matrix elements of the kernel of the exchange-correlation potential. The performance of the new scheme has been tested on a representative set of indirect nuclear spin-spin couplings. The obtained results have been compared with the corresponding results of the reference method with traditional evaluation of the exchange-correlation kernel, i.e., without employing the fitted electron densities. Overall good agreement between both methods was observed, though the new approach tends to give values by about 4%-5% higher than the reference method. On the average, the solution of the coupled perturbed equations with the new scheme is about 8.5 times faster compared to the reference method.

Copyright 2015 AIP Publishing. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in Journal of Chemical Physics 2015, 142 and may be found at http://dx.doi.org/10.1063/1.4913634 We present an updated semi-experimental absolute shielding scale for the 17O and 33S nuclei. These new shielding scales are based on accurate rotational microwave data for the spin–rotation constants of H2 17O [Puzzarini et al., J. Chem. Phys. 131, 234304 (2009)], C17O [Cazzoli et al., Phys. Chem. Chem. Phys. 4, 3575 (2002)], and H2 33S [Helgaker et al., J. Chem. Phys. 139, 244308 (2013)] corrected both for vibrational and temperature effects estimated at the CCSD(T) level of theory as well as for the relativistic corrections to the relation between the spin–rotation constant and the absolute shielding constant. Our best estimate for the oxygen shielding constants of H2 17O is 328.4(3) ppm and for C17O −59.05(59) ppm. The relativistic correction for the sulfur shielding of H2 33S amounts to 3.3%, and the new sulfur shielding constant for this molecule is 742.9(4.6) ppm.

We demonstrate that the apparent disagreement between experimental determinations and four-component relativistic calculations of the absolute shielding constants of heavy nuclei is due to the breakdown of the commonly assumed relation between the electronic contribution to the nuclear spin-rotation constants and the paramagnetic contribution to the NMR shielding constants. We demonstrate that this breakdown has significant consequences for the absolute shielding constant of (119)Sn, leading to errors of about 1000 ppm. As a consequence, we expect that many absolute shielding constants of heavy nuclei will be in need of revision.

Relativistic effects are important for the accurate evaluation of the observables of nuclear magnetic resonance (NMR) spectroscopy, the nuclear magnetic shielding and the indirect spin–spin coupling tensors. Some of the most notable relativistic effects, in particular for light elements in the vicinity of heavy nuclei, are due to spin–orbit effects, an effect difficult to evaluate when starting from a non-relativistic wavefunction. Two- and four-component relativistic methods include spin–orbit effects variationally, and the recent improvements in the computational efficiency of these methods open new opportunities for accurate calculations of NMR parameters also for molecules with heavy elements. We here present an overview of the different approximations that have been introduced for calculating relativistic effects with two- and four-component methods and how these methods can be used to calculate the NMR parameters. We will also give some examples of systems that have been studied computationally with two- and four-component relativistic methods and discuss the importance of relativistic effects on the shielding and indirect spin–spin coupling constants.