Spin-orbit Contributions Research Articles

Computational study of the ground state properties of iodine and polyiodide ions

A computational study on iodine, iodide and polyiodide is carried out using different density functional methods and basis sets. All electron basis sets with hybrid and generalized-gradient approximation (GGA) functionals overestimate the bond distance and underestimate the vibrational frequency and formation energy of the iodine molecule. The local density approximation functionals with an effective core potential (ECP) basis set results in a very good bond distance but overestimates the vibrational frequency and formation energy. Hybrid functionals with ECPs give relatively good values for bond distance and vibrational frequency but hugely underestimate the formation energy. Only GGA functionals with ECP estimate all three parameters very well. The structural and vibrational properties and energetics (electron affinity and formation energy) of I, I−, I2, I2− and I3− are in good agreement with the corresponding experimental values for PW91 and ECP calculations. However, the basis set with diffuse function (along with polarized function) can describe the iodide and polyiodide better. The spin–orbit contribution needs to be included for a correct description of the energetics.

Relativistic two-component calculations of electronic g-tensor for oxo-molybdenum(V) and oxo-tungsten(V) complexes: The important role of higher-order spin-orbit contributions

In an effort towards the reliable calculation of EPR parameters of molybdenum and tungsten enzyme active sites, the effect of higher-order spin-orbit effects and of exchange–correlation functional on the electronic g-tensors of small [MVOCl5]2− and medium-sized [MVO(bdt)2]− (bdt=benzene-1,2-dithiolate), [MVOCl3(bpy)] (bpy=bipyridine) complexes (M=Mo or W) has been evaluated. Comparison of one-component calculations with perturbational treatment of spin-orbit coupling and two-component non-collinear spin density functional calculations indicate the substantial importance of higher-order spin-orbit effects, in particular for the tungsten species. Pseudopotential calculations tend to underestimate the spin-orbit effects compared to all-electron calculations based on the Douglas–Kroll–Hess Hamiltonian. Hybrid functionals with somewhat enhanced exact-exchange admixture tend to provide better agreement with experiment than pure gradient-corrected functionals.

Prediction of 207Pb NMR parameters for the solid ionic lead(II) halides using the relativistic ZORA-DFT formalism: Comparison with the lead-containing molecular systems

Density functional calculations of 207Pb NMR shielding in PbX 2 (X=F, Br, Cl and I) anionic fragments suggest that in solid PbX 2, the observed variation of chemical shift with halide is dominated by the paramagnetic contribution to the chemical shielding, with a lesser effect by the spin–orbit contribution. The calculations include relativistic effects at the level of the zero-order regular approximation (ZORA). The present observation contrasts with previous calculations for the molecular system, PbX 4, in which the spin–orbit contribution has been shown to be the major factor in the variation of the NMR chemical shift.

INVESTIGATIONS ON THE LOCAL STRUCTURE AND THE EPR PARAMETERS FORCu2+-DOPEDGaN

The local structure and the EPR parameters (g factors and the hyperfine structure constants) for Cu2+in GaN are theoretically studied from the perturbation formulas of these parameters for a 3d9ion in trigonally distorted tetrahedra. In these formulas, the ligand orbital and spin-orbit coupling contributions are taken into account from the cluster approach, in view of the strong covalency effect of the system. Based on the studies, the impurity Cu2+is found not to occupy exactly the host Ga3+site but to suffer a slight displacement (≈ 0.004 Å ) towards the ligand triangle along C3axis due to charge and size mismatching substitution. The theoretical EPR parameters show good agreement with the experimental data. The validity of the impurity displacement is also discussed.

Pressure effects on the spin–orbit interactions in low-dimensional quantum well systems

Donor binding energies and spin–orbit interactions (SOIs) are estimated in GaAs–Ga 1− x Al x As quantum well and quantum dot systems. The effect of the conduction band non-parabolicity on these energies is also estimated. In all the cases investigated, the maximum contribution by the non-parabolicity effect is about 5% for narrow well dimensions. It is also seen that the SOI is one order higher in a quantum dot system as compared to a quantum well case. In both cases, the spin–orbit splitting is four orders smaller than the donor binding energies. We observe that the Rashba and Dresslhaus SOIs are about the same order as the conventional spin–orbit contributions. We have also investigated the effect of pressure on the SOI energies and find appreciable enhancement in the quantum well case.

Determination of spin‐orbit coupling contributions in the framework of density functional theory

We present a noniterative method to calculate spin-orbit coupling by means of a theoretical approach that provides the use of the full Breit-Pauli operator. This method was applied to compute one and two-electron spin-orbit coupling contributions between singlet and triplet, and doublet and doublet states, respectively. These states have been represented by monodeterminantal wave functions and optimized using the PW91 gradient-corrected exchange-correlation functional and the hybrid B3LYP one. They have been supplied by the conventional density functional theory packages, and thus coupled by our spin-orbit coupling code. Different size basis sets have been employed and the obtained results have been compared with the corresponding ones provided by some of the already existing methods and with the experimental data. They have been found to be in good quantitative agreement.

Evolution of the protonsdstates in neutron-rich Ca isotopes

We analyze the evolution with increasing isospin asymmetry of the proton single-particle states $2s1/2$ and $1d3/2$ in Ca isotopes, using nonrelativistic and relativistic mean-field approaches. Both models give similar trends and it is shown that this evolution is sensitive to the neutron shell structure, the two states becoming more or less close depending on the neutron orbitals that are filled. In the regions where the states get closer some parametrizations lead to an inversion between them. This inversion occurs near $^{48}\mathrm{Ca}$ as well as very far from stability where the two states systematically cross each other if the drip line predicted in the model is located far enough. We study in detail the modification of the two single-particle energies by using the equivalent potential in the Schroedinger-like Skyrme-Hartree-Fock equations. The role played by central, kinetic, and spin-orbit contributions is discussed. We finally show that the effect of a tensor component in the effective interaction considerably favors the inversion of the two proton states in $^{48}\mathrm{Ca}$.

Baryon Regge trajectories in the light of the [formula omitted] expansion

We analyze Regge trajectories in terms of the 1/Nc expansion of QCD. Neglecting spin–orbit contributions to the large Nc baryon mass operator, we consider the evolution of the spin-flavor singlet component of the masses with respect to the angular momentum. We find two distinct and remarkably linear Regge trajectories for symmetric and for mixed symmetric spin-flavor multiplets.

Density Functional Study of EPR Parameters and Spin-Density Distribution of Azurin and Other Blue Copper Proteins

Modern density functional methods have been used to study spin-density distribution, g tensors, as well as Cu and ligand hyperfine tensors for azurin models, for two more blue copper proteins plastocyanin and stellacyanin, and for small model complexes. The aim was to establish a consistent computational protocol that provides a realistic description of the EPR parameters as probes of the spin-density distribution between metal and coordinated ligands in copper proteins. In agreement with earlier conclusions for plastocyanin, hybrid functionals with appreciable exact-exchange admixtures, roughly around 50%, provide the best overall agreement with all parameters. Then the bulk of the spin density is almost equally shared by the copper atom and the sulfur atom of the equatorial cysteine ligand, and the best values are obtained for copper, histidine nitrogen, and cysteine beta-proton hyperfine couplings, as well as for g(parallel). Spin-orbit effects on the EPR parameters may be appreciable and have to be treated carefully to obtain agreement with experiment. Most notably, spin-orbit effects on the (65)Cu hyperfine coupling tensors in blue copper sites are unusually large compared to more regularly coordinated Cu(II) complexes with similar spin density on copper. In addition to the often emphasized high covalency of the Cu-S(Cys) bond, the characteristically small A(parallel) component of blue copper proteins is shown to derive to a large part from a near-cancellation between negative first-order (Fermi contact and dipolar) and unusually large positive second-order (spin-orbital) contributions. The large spin-orbit effects relate to the distorted tetrahedral structures. Square planar dithiolene complexes with similar spin density on copper exhibit much more negative A(parallel) values, as the cancellation between nonrelativistic and spin-orbit contributions is less complete. Calculations on a selenocysteine-substituted variant of azurin have provided further insight into the relations between bonding and EPR parameters.

GRAVITATIONAL WAVEFORMS FOR FINITE MASS BINARIES

One of the promising sources of gravitational radiation is a binary system composed of compact stars. It is an important question of how the rotation of the bodies and the eccentricity of the orbit affect the detectable signal. Here we present a method to evaluate the gravitational wave polarization states for inspiralling compact binaries with comparable mass. We consider eccentric orbits and the spin-orbit contribution in the case of one spinning object up to 1.5 post-Newtonian order. For circular orbits our results are in agreement with existing calculations.

From Feynman proof of Maxwell equations to noncommutative quantum mechanics

In 1990, Dyson published a proof due to Feynman of the Maxwell equations assuming only the commutation relations between position and velocity. With this minimal assumption, Feynman never supposed the existence of Hamiltonian or Lagrangian formalism. In the present communication, we review the study of a relativistic particle using "Feynman brackets." We show that Poincaré's magnetic angular momentum and Dirac magnetic monopole are the consequences of the structure of the Lorentz Lie algebra defined by the Feynman's brackets. Then, we extend these ideas to the dual momentum space by considering noncommutative quantum mechanics. In this context, we show that the noncommutativity of the coordinates is responsible for a new effect called the spin Hall effect. We also show its relation with the Berry phase notion. As a practical application, we found an unusual spin-orbit contribution of a nonrelativistic particle that could be experimentally tested. Another practical application is the Berry phase effect on the propagation of light in inhomogeneous media.

The pure rotational spectrum of CrCN (X 6 Σ +): an unexpected geometry and unusual spin interactions

The pure rotational spectrum of CrCN (X 6Σ+) has been recorded in the frequency range 250–520 GHz using direct-absorption techniques. This is the first spectroscopic investigation of the CrCN radical. This species was synthesized by reacting Cr vapour with (CN)2. Spectra were obtained for the main isotopic species, the 53Cr and 13C isotopologues, and the heavy atom stretch and several quanta of the bending vibration. The molecule was found to have a linear cyanide geometry and a 6Σ+ ground state. Rotational, fine structure, and l-type doubling constants have been determined. The spin–spin parametre λ was found to be small–a likely result of competing second-order spin–orbit contributions from excited 4Σ−, 4Π, and 6Π states. However, λ increased significantly in the bending mode, which may be caused by a reduction of the 6Σ+−4Π interaction strength due to spin–orbit vibronic coupling. In contrast, the value of γ, arising from interactions with a nearby 6Πstate, was independent of v 2. The CrCN bond lengths were determined to be r Cr–C = 2.019 Å and r C–N = 1.148 Å. Delocalization of the 3dπ electrons into the CN 2π* orbital, which is polarized towards the carbon atom, may account for the CrCN structure.

Spin–orbit effects in single electron quantum rings

We describe the effects of spin–orbit contribution in the presence of a uniform axial electric field on the electronic structure of single electron quantum rings in addition to the conventional Stark effect. The spin-split levels are obtained by considering the spatial asymmetries induced by the Rashba and the Dresselhaus spin–orbit interactions on the spinor states. The quantum-ring flat geometry allows us to study the spin-hybridization effects induced by spin–orbit coupling under a wide range of values of the axial electric field. The influence of the peculiar axial and perpendicular confinements in the structure on the spin orientation, the azimuthal component of the angular momentum and their coupling to the external fields is discussed in details for two materials.

Understanding the EPR Parameters of Glycine-Derived Radicals: The Case of N-Acetylglycyl in the N-Acetylglycine Single-Crystal Environment

As a step toward an in-depth understanding of the electron paramagnetic resonance parameters of glycyl radicals in proteins, the hyperfine tensors and, particularly, the g-tensor of N-acetylglcyl in the environment of a single crystal of N-acetylglycine have been studied by systematic state-of-the-art quantum chemical calculations on various suitable model systems. The quantitative computation of the g-tensors for such glycyl-derived radicals is a veritable challenge, mainly because of the very small g-anisotropy combined with a nonsymmetrical, delocalized spin-density distribution and several atoms with comparable spin-orbit contributions to the g-tensors. The choice of gauge origin of the magnetic vector potential, and of approximate spin-orbit operators, both turn out to be more critical than found in previous studies of g-tensors for organic radicals. Environmental effects, included by supermolecular hydrogen-bonded models, were found to be moderate, because of a partial compensation between the influences from intramolecular and intermolecular hydrogen bonds. The largest effects on the g-tensor are caused by the conformation of the radical. The density functional theory methods employed systematically overestimate both the Delta gx and Delta gy components of the g-tensor. This is important for parallel investigations on the protein-glycyl radicals. The 1H alpha and 13C alpha hyperfine couplings depend only slightly on the supermolecular model chosen and appear less sensitive probes of detailed structure and environment.

Relativistic heavy-atom effects on heavy-atom nuclear shieldings

The principal relativistic heavy-atom effects on the nuclear magnetic resonance (NMR) shielding tensor of the heavy atom itself (HAHA effects) are calculated using ab initio methods at the level of the Breit-Pauli Hamiltonian. This is the first systematic study of the main HAHA effects on nuclear shielding and chemical shift by perturbational relativistic approach. The dependence of the HAHA effects on the chemical environment of the heavy atom is investigated for the closed-shell X(2+), X(4+), XH(2), and XH(3) (-) (X=Si-Pb) as well as X(3+), XH(3), and XF(3) (X=P-Bi) systems. Fully relativistic Dirac-Hartree-Fock calculations are carried out for comparison. It is necessary in the Breit-Pauli approach to include the second-order magnetic-field-dependent spin-orbit (SO) shielding contribution as it is the larger SO term in XH(3) (-), XH(3), and XF(3), and is equally large in XH(2) as the conventional, third-order field-independent spin-orbit contribution. Considering the chemical shift, the third-order SO mechanism contributes two-thirds of the difference of approximately 1500 ppm between BiH(3) and BiF(3). The second-order SO mechanism and the numerically largest relativistic effect, which arises from the cross-term contribution of the Fermi contact hyperfine interaction and the relativistically modified spin-Zeeman interaction (FC/SZ-KE), are isotropic and practically independent of electron correlation effects as well as the chemical environment of the heavy atom. The third-order SO terms depend on these factors and contribute both to heavy-atom shielding anisotropy and NMR chemical shifts. While a qualitative picture of heavy-atom chemical shifts is already obtained at the nonrelativistic level of theory, reliable shifts may be expected after including the third-order SO contributions only, especially when calculations are carried out at correlated level. The FC/SZ-KE contribution to shielding is almost completely produced in the s orbitals of the heavy atom, with values diminishing with the principal quantum number. The relative contributions converge to universal fractions for the core and subvalence ns shells. The valence shell contribution is negligible, which explains the HAHA characteristics of the FC/SZ-KE term. Although the nonrelativistic theory gives correct chemical shift trends in present systems, the third-order SO-I terms are necessary for more reliable predictions. All of the presently considered relativistic corrections provide significant HAHA contributions to absolute shielding in heavy atoms.

Dzyaloshinsky-Moriya antisymmetric exchange coupling in cuprates: Oxygen effects

We revisit a problem of Dzyaloshinsky-Moriya antisymmetric exchange coupling for a single bond in cuprates specifying the local spin-orbital contributions to Dzyaloshinsky vector focusing on the oxygen term. The Dzyaloshinsky vector and respective weak ferromagnetic moment is shown to be a superposition of comparable and, sometimes, competing local Cu and O contributions. The intermediate oxygen $^{17}$O Knight shift is shown to be an effective tool to inspect the effects of Dzyaloshinsky-Moriya coupling in an external magnetic field. We predict the effect of $strong$ oxygen weak antiferromagnetism in edge-shared CuO$_2$ chains due to uncompensated oxygen Dzyaloshinsky vectors. Finally, we revisit the effects of symmetric spin anisotropy, in particular, those directly induced by Dzyaloshinsky-Moriya coupling.

Electronic Structure of Four-Coordinate C3v Nickel(II) Scorpionate Complexes: Investigation by High-Frequency and -Field Electron Paramagnetic Resonance and Electronic Absorption Spectroscopies

A series of complexes of formula TpNiX, where Tp*- = hydrotris(3,5-dimethylpyrazole)borate and X = Cl, Br, I, has been characterized by electronic absorption spectroscopy in the visible and near-infrared (NIR) region and by high-frequency and -field electron paramagnetic resonance (HFEPR) spectroscopy. The crystal structure of TpNiCl has been previously reported; that for TpNiBr is given here: space group = Pmc2(1), a = 13.209(2) A, b = 8.082(2) A, c = 17.639(4) A, alpha = beta = gamma = 90 degrees , Z = 4. TpNiX contains a four-coordinate nickel(II) ion (3d8) with approximate C3v point group symmetry about the metal and a resulting S = 1 high-spin ground state. As a consequence of sizable zero-field splitting (zfs), TpNiX complexes are "EPR silent" with use of conventional EPR; however, HFEPR allows observation of multiple transitions. Analysis of the resonance field versus the frequency dependence of these transitions allows extraction of the full set of spin Hamiltonian parameters. The axial zfs parameter for TpNiX displays pronounced halogen contributions down the series: D = +3.93(2), -11.43(3), -22.81(1) cm(-1), for X = Cl, Br, I, respectively. The magnitude and change in sign of D observed for TpNiX reflects the increasing bromine and iodine spin-orbit contributions facilitated by strong covalent interactions with nickel(II). These spin Hamiltonian parameters are combined with estimates of 3d energy levels based on the visible-NIR spectra to yield ligand-field parameters for these complexes following the angular overlap model (AOM). This description of electronic structure and bonding in a pseudotetrahedral nickel(II) complex can enhance the understanding of similar sites in metalloproteins, both native nickel enzymes and nickel-substituted zinc enzymes.

Spin-orbit effects in GaAs quantum wells: Interplay between Rashba, Dresselhaus, and Zeeman interactions

The interplay between Rashba, Dresselhaus and Zeeman interactions in a quantum well submitted to an external magnetic field is studied by means of an accurate analytical solution of the Hamiltonian, including electron-electron interactions in a sum rule approach. This solution allows to discuss the influence of the spin-orbit coupling on some relevant quantities that have been measured in inelastic light scattering and electron-spin resonance experiments on quantum wells. In particular, we have evaluated the spin-orbit contribution to the spin splitting of the Landau levels and to the splitting of charge- and spin-density excitations. We also discuss how the spin-orbit effects change if the applied magnetic field is tilted with respect to the direction perpendicular to the quantum well.

The Basis Set Convergence of Spin-Spin Coupling Constants Calculated by Density Functional Methods.

The previously proposed polarization-consistent basis sets, optimized for density functional calculations, are evaluated for calculating indirect nuclear spin-spin coupling constants. The basis set limiting values can be obtained by performing a series of calculations with increasingly larger basis sets, but the convergence can be significantly improved by adding functions with large exponents. An accurate calculation of the Fermi-contact contribution requires the addition of tight s functions, while the paramagnetic spin-orbit contribution is sensitive to the presence of tight p functions. The spin-dipolar contribution requires the addition of p, d, and f functions. The optimal exponents for the tight functions can be obtained by optimizing the absolute sum of all contributions to the spin-spin coupling constant. On the basis of a series of test cases, we propose a standard set of tight s, p, d, and f functions to be added to the polarization-consistent basis sets. The resulting pcJ-n basis sets should be suitable for calculating spin-spin coupling constants with density functional methods.

Calculation of zero-field splitting parameters: Comparison of a two-component noncolinear spin-density-functional method and a one-component perturbational approach

Two different sets of approaches for the density-functional calculation of the spin-orbit contributions to zero-field splitting (ZFS) parameters of high-spin systems have been implemented within the same quantum chemistry code ReSpect and have been validated and compared for a series of model systems. The first approach includes spin-orbit coupling variationally in a two-component calculation, using either an all-electron Douglas-Kroll-Hess ansatz or two-component relativistic pseudopotentials. The ZFS parameters are computed directly from energy differences between different relativistic states. Additionally, an approximate second-order perturbation theory approach has been implemented, based on nonrelativistic or scalar relativistic wave functions. For a series of group 16 triplet diatomics and for the octet GdH3 molecules, two-component density functional calculations underestimate the zero-field splitting D systematically by a factor of 2. This may be rationalized readily by the incomplete description of states with absolute value MJ < J by a single-determinantal wave function built from two-component spinors. In the case of two 3d transition metal complexes and for GdH3, the results depend furthermore sensitively on exchange-correlation functional. Results of the alternative one-component approach agree strikingly with the two-component data for systems with small spin-orbit effects and start to deviate from them only for heavier systems with large spin-orbit effects. These results have fundamental implications for the achievable accuracy of one-component density-functional approaches used widely to compute ZFS parameters in the field of molecular magnetism. Possible refinements of both one-and two-component approaches are discussed.