Spin-orbit Relativistic Effects Research Articles

Designer spin-orbit superlattices: symmetry-protected Dirac cones and spin Berry curvature in two-dimensional van der Waals metamaterials

The emergence of strong relativistic spin-orbit effects in low-dimensional systems provides a rich opportunity for exploring unconventional states of matter. Here, we present a route to realise tunable relativistic band structures based on the lateral patterning of proximity-induced spin-orbit coupling. The concept is illustrated on a patterned graphene–transition metal dichalcogenide heterostructure, where the spatially periodic spin-orbit coupling induces a rich mini-band structure featuring massless and massive Dirac bands carrying large spin Berry curvature. The envisaged systems support robust and gate-tunable spin Hall responses driven by the quantum geometry of mini-bands, which can be tailored through metasurface fabrication methods and twisting effects. These findings open pathways to two-dimensional quantum material design and low-power spintronic applications.

Actinyl Electronic Structure Probed by XAS: The Role of Many-Body Effects.

A detailed analysis of the wave functions for the M5 to 5f excitations in the linear actinyls, UO22+, NpO22+, and PuO22+, and the theoretical X-ray absorption spectra obtained with these wave functions in comparison with experimental M5-edge high-resolution X-ray absorption near-edge structure (HR-XANES) spectra is presented. The wave functions include full treatment of scalar and spin-orbit relativistic effects through the use of a Dirac-Coulomb Hamiltonian; many-body effects are included in determining the wave functions. The character of the excited states and of the active spaces to describe the wave functions for these states are investigated and analyzed. It is shown that the excited states cannot, in general, be described with a single configuration but have an essential multiconfiguration character. The characterization of the properties of the excited states and the X-ray absorption spectra was achieved through the use of novel methods.

Can simple 'molecular' corrections outperform projector augmented-wave density functional theory in the prediction of 35 Cl electric field gradient tensor parameters for chlorine-containing crystalline systems?

Many-body expansion (MBE) fragment approaches have been applied to accurately compute nuclear magnetic resonance (NMR) parameters in crystalline systems. Recent examples demonstrate that electric field gradient (EFG) tensor parameters can be accurately calculated for 14 N and 17 O. A key additional development is the simple molecular correction (SMC) approach, which uses two one-body fragment (i.e., isolated molecule) calculations to adjust NMR parameter values established using 'benchmark' projector augmented-wave (PAW) density functional theory (DFT) values. Here, we apply a SMC using the hybrid PBE0 exchange-correlation (XC) functional to see if this can improve the accuracy of calculated 35 Cl EFG tensor parameters. We selected eight organic and two inorganic crystal structures and considered 15 chlorine sites. We find that this SMC improves the accuracy of computed values for both the 35 Cl quadrupolar coupling constant (CQ ) and the asymmetry parameter ( ) by approximately 30% compared with benchmark PAW DFT values. We also assessed a SMC that offers local improvements not only in terms of the quality of the XC functional but simultaneously in the quality of the description of relativistic effects via the inclusion of spin-orbit effects. As the inorganic systems considered contain heavy atoms bonded to the chlorine atoms, we find further improvements in the accuracy of calculated 35 Cl EFG tensor parameters when both a hybrid functional and spin-orbit effects are included in the SMC. On the contrary, for chlorine-containing organics, the inclusion of spin-orbit relativistic effects using a SMC does not improve the accuracy of computed 35 Cl EFG tensor parameters.

Accurate Relativistic Real-Time Time-Dependent Density Functional Theory for Valence and Core Attosecond Transient Absorption Spectroscopy

First principles theoretical modeling of out-of-equilibrium processes observed in attosecond pump-probe transient absorption spectroscopy (TAS) triggering pure electron dynamics remains a challenging task, especially for heavy elements and/or core excitations containing fingerprints of scalar and spin-orbit relativistic effects. To address this, we formulate a methodology for simulating TAS within the relativistic real-time, time-dependent density functional theory (RT-TDDFT) framework, for both the valence and core energy regimes. Especially for TAS, full four-component (4c) RT simulations are feasible but computationally demanding. Therefore, in addition to the 4c approach, we also introduce the atomic mean-field exact two-component (amfX2C) Hamiltonian accounting for one- and two-electron picture-change corrections within RT-TDDFT. amfX2C preserves the accuracy of the parent 4c method at a fraction of its computational cost. Finally, we apply the methodology to study valence and near-L2,3-edge TAS processes of experimentally relevant systems and provide additional physical insights using relativistic nonequilibrium 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 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.

Relativistic Effects from Heavy Main Group p-Elements on the NMR Chemical Shifts of Light Atoms: From Pioneering Studies to Recent Advances

This review represents a compendium of computational studies of relativistic effects on the NMR chemical shifts of light nuclei caused by the presence of heavy main group p-block elements in molecules. The narration starts from a brief discussion of the relativistic theories and quantum chemical methods for the calculation of NMR chemical shifts at the relativistic level of the electronic theory. The main part of the review contains a survey on the relativistic calculations of NMR shielding constants of the most popular NMR-active light nuclei such as 1H, 13C, 19F, 29Si, 15N, and 31P of compounds containing heavy p-elements. A special focus is placed on the relativistic effects initiated by the 16th and 17th group elements. Different factors governing the behavior of the relativistic effects on the chemical shifts of light atoms are discussed. In particular, the stereochemistry of the relativistic “heavy atom on the light atom” effect and the influence of the spin–orbit relativistic effects on the vibrational contributions to the shielding constants of light nuclei are considered.

Chemical shift tensors as probes of chalcogen bonds: solid-state NMR study of telluradiazole-XCN− (X = O, S, Se) salt cocrystals

We report experimental 125Te magic-angle spinning solid-state nuclear magnetic resonance (MAS NMR) measurements of the tellurium chemical shift (CS) tensors in three [K(18-crown-6)]+ 3,4-dicyano-1,2,5-telluradiazole-XCN− (X = O, S, Se) salt cocrystals featuring chalcogen bonds. These data are compared to those for pure 3,4-dicyano-1,2,5-telluradiazole (1). A reduction in the span of the 125Te CS tensor is consistently noted in the salt cocrystals compared to pure 1. Isotopically 15N-labelled [K(18-crown-6)]+[1-OC15N]−, which features a chalcogen bond between Te and the cyanate nitrogen atom, is synthesized using KOC15N, and the nitrogen CS tensors are measured for both samples via 15N slow MAS NMR spectroscopy. Possible dynamic disorder of the cyanate ions in KOCN is ruled out. Two crystallographically distinct nitrogen sites are resolved for the salt cocrystal. Upon formation of [K(18-crown-6)]+[1-OC15N]−, the 15N isotropic CS and CS tensor span both decrease relative to the values for pure KOC15N, and the axial symmetry of this tensor is lost. These findings are supplemented with a series of density functional theory calculations of magnetic shielding tensors using cluster models or periodic boundary conditions. Inclusion of spin–orbit relativistic effects in the calculation of tellurium shielding tensors is particularly important in achieving agreement with experiment.

Partial charge transfer and absence of induced magnetization in EuS(111)/Bi2Se3 heterostructures

Heterostructures made from topological and magnetic insulators promise to form excellent platforms for new electronic and spintronic functionalities mediated by interfacial effects. We report the results of a first-principles density functional theory study of the geometric, electronic structure, and magnetic properties of EuS(111)/Bi$_2$Se$_3$ interface, including van der Waals and relativistic spin-orbit effects. In contrast to previous theoretical studies, we find no appreciable magnetic anisotropy in such a heterostructure. We also do not see additional induced magnetization at the interface or the magnetic proximity effect on the topological states. This is due to the localized nature of Eu moments, and because of a partial charge transfer of $\sim$0.5 electron from Eu to Se. The formation of the surface dipole shifts the Dirac cone about 0.4~eV below the chemical potential, and the associated electrostatic screening moves the topological state from the first to the second quintuple layer of Bi$_2$Se$_3$.

Thermophysical properties of low-density neon gas from highly accurate first-principles calculations and dielectric-constant gas thermometry measurements.

New interatomic potential energy and interaction-induced polarizability curves for two ground-state neon atoms were developed and used to predict the second density, acoustic, and dielectric virial coefficients and the dilute gas shear viscosity and thermal conductivity of neon at temperatures up to 5000 K. The potential energy curve is based on supermolecular coupled-cluster (CC) calculations at very high levels up to CC with single, double, triple, quadruple, and perturbative pentuple excitations [CCSDTQ(P)]. Scalar and spin-orbit relativistic effects, the diagonal Born-Oppenheimer correction, and retardation of the dispersion interactions were taken into account. The interaction-induced polarizability curve, which in this work is only needed for the calculation of the second dielectric virial coefficient, is based on supermolecular calculations at levels up to CCSDT and includes a correction for scalar relativistic effects. In addition to these first-principles calculations, highly accurate dielectric-constant gas thermometry (DCGT) datasets measured at temperatures from 24.5 to 200 K were analyzed to obtain the difference between the second density and dielectric virial coefficients with previously unattained accuracy. The agreement of the DCGT values with the ones resulting from the first-principles calculations is, despite some small systematic deviations, very satisfactory. Apart from this combination of two virial coefficients, the calculated thermophysical property values of this work are significantly more accurate than any available experimental data.

State-of-the-Art Quantum Chemistry Meets Variable Reaction Coordinate Transition State Theory to Solve the Puzzling Case of the H2S + Cl System.

The atmospheric reaction of H2S with Cl has been reinvestigated to check if, as previously suggested, only explicit dynamical computations can lead to an accurate evaluation of the reaction rate because of strong recrossing effects and the breakdown of the variational extension of transition state theory. For this reason, the corresponding potential energy surface has been thoroughly investigated, thus leading to an accurate characterization of all stationary points, whose energetics has been computed at the state of the art. To this end, coupled-cluster theory including up to quadruple excitations has been employed, together with the extrapolation to the complete basis set limit and also incorporating core–valence correlation, spin–orbit, and scalar relativistic effects as well as diagonal Born–Oppenheimer corrections. This highly accurate composite scheme has also been paralleled by less expensive yet promising computational approaches. Moving to kinetics, variational transition state theory and its variable reaction coordinate extension for barrierless steps have been exploited, thus obtaining a reaction rate constant (8.16 × 10–11 cm3 molecule–1 s–1 at 300 K and 1 atm) in remarkable agreement with the experimental counterpart. Therefore, contrary to previous claims, there is no need to invoke any failure of the transition state theory, provided that sufficiently accurate quantum-chemical computations are performed. The investigation of the puzzling case of the H2S + Cl system allowed us to present a robust approach for disclosing the thermochemistry and kinetics of reactions of atmospheric and astrophysical interest.

Anion Photoelectron Spectroscopy and Theoretical Study of HAuCN and [HAuCN]-: Spin-Orbit Coupling and Low-Lying Excited States.

We report a study of the electronic structures and chemical bonding of gaseous [HAuCN]- and the corresponding neutral molecule using photoelectron spectroscopy and relativistic quantum chemistry calculations. The electron affinity of the neutral HAuCN is reported to be 4.75 eV for the first time. The low-lying excited states of neutral molecule are observed and assigned according to the calculations utilizing a sophisticated electron correlation method incorporating both the scalar and spin-orbit relativistic effects. Our theoretical calculations suggest the geometry will be distorted from linear structure to the bent during the process of detaching one electron from the anion. Various chemical bonding analyses based on theoretical calculations have been performed for the titled complexes, and the apparent covalent natures of interactions between gold and the studied ligands have been verified.

Relativistic topological molecular descriptors of metal trihalides

A series of novel two-dimensional, metal trihalides MX3, have been explored recently because of their unusual Dirac half-metallicity, intriguing topological spintronic properties arising from both inherent magnetization and large relativistic spin-orbit coupling effects exhibited by these 2D metal halides. Moreover due to large spin-orbit coupling which results in unusual band gaps combined with their stopping power and higher Curie temperature, 2D materials such as BiI3 find important applications in room temperature radiation detectors. Hence the present work is devoted to relativistic topological characterization of two classes of 2D trihalides. We outline techniques for incorporation of relativistic parameters into topological expression through 2-component Wannier spinors obtained by localization methods. Mathematical expressions of several structurally based topological indices are proposed in terms of parameters that can be derived from relativistic quantum computations including spin-orbit coupling for the first time.

Prediction of Structures and Atomization Energies of Coinage Metals, (M)n, n < 20: Extrapolation of Normalized Clustering Energies to Predict the Cohesive Energy.

The geometries of the group 11 coinage metals (n = 2-20) were optimized to determine the lowest energy isomers for each cluster size, singlets for even numbers and doublets for odd numbers. For copper and silver, 2-D (planar) geometries were favored up to n = 6. For gold, 2D (planar) geometries were favored up to n = 13. Normalized clustering energies were plotted as a function of cluster size (n-1/3, for n = 4-20) with various DFT functionals and the CCSD(T)-F12b method and were extrapolated to predict the bulk cohesive energy. In the case of copper and silver, there is excellent agreement between the cohesive energies predicted at the CCSD(T)-F12b level of theory and the experimental values. For gold, the CCSD(T)-F12b values needed to be corrected for spin-orbit relativistic effects to obtain good agreement with experiment. Electronic properties including the HOMO-LUMO gaps for the even clusters and the spin densities for the odd clusters were calculated. The lowest gap is predicted to occur for n = 16 where the HOMO and LUMO are very similar in shape.

The Nature of Halogen Dependence of 103Rh NMR Chemical Shift in Complex Anions cis-[X1X2Rh(CO)2]− (X1, X2 = Cl, Br, I)

DFT calculations within the two-component quasirelativistic approach and further analysis of 103Rh NMR shielding (including the natural bond orbitals method) in a series of flat-square complex anions cis-[X1X2Rh(CO)2]− (X1, X2 = Cl, Br, I) are used to determine the role of relativistic spin-orbit effects in 103Rh NMR shielding in these systems. Electron delocalization observed in these complexes provides the possibility of relativistic spin-orbit effects but complicates the interpretation of 103Rh NMR shielding in terms of chemically meaningful fragments of electronic system (lone pairs, chemical bonds).

Carbon monoxide activation by atomic thorium: ground and excited state reaction pathways.

Multi-reference configuration interaction (MRCI) and single reference coupled cluster calculations are performed for the ThCO and OThC isomers. Scalar and spin-orbit relativistic effects are considered through a relativistic pseudopotential and the coupling of MRCI wavefunctions via the Breit-Pauli spin-orbit Hamiltonian. Optimized geometries, excitation energies, and vibrational frequencies are reported for both isomers. Full potential energy profiles are constructed for the Th+CO reaction and the conversion of the produced ThCO to OThC. Linear ThCO was found to be more stable than the highly ionic bent OThC system by about 4 kcal mol-1. The interconversion barrier is estimated to be around 30 kcal mol-1. Our results are in agreement with earlier experimental data for the two isomers. The lowest lying states of Th do not populate f-orbitals and resemble the electronic structure of Ti. Therefore, the ability of the two atoms to activate the C[triple bond, length as m-dash]O bond is compared. OTiC is found to be about 40 kcal mol-1 less stable than TiCO revealing the efficiency of Th and possibly other f-block elements to activate multiple chemical bonds as opposed to d-block metals.

On the Origin of the Distinctly Different Reactivity of Ruthenium in [MO]+ /CH4 Systems (M=Fe, Ru, Os).

The thermal gas-phase reactions of [RuO]+ with methane have been explored by FT-ICR mass spectrometry and high-level quantum-chemical calculations. In contrast to the previously studied [FeO]+ /CH4 and [OsO]+ /CH4 couples, which undergo oxygen/hydrogen atom transfers and dehydrogenation, respectively, the [RuO]+ /CH4 system produces selectively [Ru(CH)2 ]+ and H2 O, albeit with much lower efficiency. Various mechanistic scenarios were uncovered, and the associated electronic origins were revealed by high-level quantum-chemical calculations. The reactivity differences observed for the [MO]+ /CH4 couples (M=Fe, Ru, Os) are due to the subtle interplay of the spin-orbit coupling efficiency, orbital overlap, and relativistic effects.

Spin-orbit effects on magnetically induced current densities in the M5- (M = N,P,As,Sb,Bi,Mc) clusters.

This study reports the spin-orbit effects on the aromaticity of the N5-, P5-, As5-, Sb5-, Bi5-, and Mc5- anionic clusters via the magnetically induced current-density method. All-electron density functional theory (DFT) calculations were carried out using the four-component Dirac-Coulomb (DC) hamiltonian, including scalar and spin-orbit relativistic effects. The magnetic index of aromaticity was calculated by numerical integration over the current flow between two atoms in the pentagonal ring. These values were compared to the spin-free values (spin-orbit coupling switched off), in order to assess the spin-orbit effect on aromaticity. It was found that in the heavy anions, Bi5- and Mc5-, there is a significant influence of the spin-orbit coupling. © 2018 Wiley Periodicals, Inc.

Linking the Character of the Metal–Ligand Bond to the Ligand NMR Shielding in Transition-Metal Complexes: NMR Contributions from Spin–Orbit Coupling

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).

State-of-the-art ab initio potential energy curve for the xenon atom pair and related spectroscopic and thermophysical properties.

A new ab initio interatomic potential energy curve for two ground-state xenon atoms is presented. It is based on supermolecular calculations at the coupled-cluster level with single, double, and perturbative triple excitations [CCSD(T)] employing basis sets up to sextuple-zeta quality, which were developed as part of this work. In addition, corrections were determined for higher coupled-cluster levels up to CCSDTQ as well as for scalar and spin-orbit relativistic effects at the CCSD(T) level. A physically motivated analytical function was fitted to the calculated interaction energies and used to compute the vibrational spectrum of the dimer, the second virial coefficient, and the dilute gas transport properties. The agreement with the best available experimental data for the investigated properties is excellent; the new potential function is superior not only to previous ab initio potentials but also to the most popular empirical ones.

A theoretical exploration of new species on the 1[H, Se, I] potential energy surface: Energetics, structures, IR spectra, and heats of formation

New molecular species HSeI, HISe, and SeI were investigated theoretically for the first time at a high level of theory, CCSD(T). Computations were carried out with the series of correlation consistent basis sets (aug-cc-pVnZ-PP) and the results extrapolated to the complete basis set limit. Accounting for core-valence correlation into the wavefunction, and of anharmonic effects on the vibrational frequencies were also explored, making the results of structural, energetic, and vibrational properties a very reliable source of data for these yet unknown species. HSeI, viewed as normal covalently bonded species, turned out to be more stable by 42.04kcalmol−1 than HISe. Bonding between I and Se in HISe can be rationalized as resulting from an electron pair donation from I to Se, the classical dative bond. These two species are separated by a barrier (ΔG#) of 52.35kcalmol−1. Corrections arising from spin-orbit and scalar relativistic effects were also considered in the evaluation of atomization energies. For SeI, we estimate ΔfH values of 36.87 and 35.16kcalmol−1 at 0K and 298.15K; for HSeI, we had 18.25 and 16.72kcalmol−1, respectively.