Relativistic Electronic Structure Research Articles

Theoretical Predictions of Properties and Chemical Behavior of Superheavy Elements

Fully relativistic electronic structure calculations have been performed for gas phase and aqueous phase compounds of elements 104 through 108. Based on these calculations, volatility and complex formation, as well as trends in these properties, have been predicted. The transactinide compounds were shown to exhibit properties very similar to those of the lighter homologs in the respective chemical groups. Some deviations from the observed trends were established.

Relativistic one-electron approach to the effect of pressure on the magnetism ofEuCo2P2

Nonrelativistic and four-component relativistic electronic structure calculations with the discrete variational method within density functional theory were performed for embedded clusters representing the layered compound ${\mathrm{EuCo}}_{2}{\mathrm{P}}_{2},$ with ${\mathrm{ThCr}}_{2}{\mathrm{Si}}_{2}$-type structure. A relativistic one-electron model based on Kramers degeneracy was devised to describe the observed changes in the magnetism of this compound induced by applied pressure, which include the collapse of the Eu moment and the formation of Co moments. The ${}^{151}\mathrm{Eu}$ M\ossbauer isomer shift calculated with relativistic wave functions agrees well with experiment; however, the ${\mathrm{Eu}}^{2+}{\ensuremath{-}\mathrm{E}\mathrm{u}}^{3+}$ valence change previously proposed is not predicted.

Fully relativistic calculations of the effect of pressure on the magnetism of EuCo 2P 2

Self-consistent moment-polarized four-component relativistic electronic structure calculations were performed for embedded clusters representing the layered compound EuCo 2P 2 of ThCr 2Si 2-type structure, with lattice parameters a and c corresponding to ambient pressure and to pressure equal to 3.5 GPa. The relativistic discrete variational method in density functional theory was employed. It was found that the Eu sublattice moments, which order antiferromagnetically at ambient pressure, are supressed at high pressures; inversely, magnetism appears in the Co layer. However, only a small change with pressure in the charge of Eu, from +2.0 to +2.2, was derived from the calculations.

First principles calculations of the magnetic profiles of the Fe-V multilayers

The dependence of the magnetic moments of the Fe-V multilayers with respect to the thickness of the Fe region is investigated using first principles spin-polarized and fully relativistic electronic structure calculations, based upon the Full-Potential-Linearized-Muffin-Tin-Orbital (FP-LMTO) method.

The generalized active space concept for the relativistic treatment of electron correlation. I. Kramers-restricted two-component configuration interaction

As a prelude to a series of presentations dealing with the treatment of electron correlation and special relativity, we present the theoretical background and the implementation of a new two-component relativistic configuration interaction program. It is based on the method of generalized active spaces which has been extended from a nonrelativistic implementation to make use of two-component Hamiltonians and time reversal and double point group symmetry at both the spinor and Slater determinant level. We demonstrate how the great computational effort arising from such a general approach—the treatment of spin–orbit interaction and electron correlation in a fully variational framework—can be markedly reduced by the use of the aforementioned symmetries. Evidence for the performance of the program is given through a number of calculations on light systems with a significant spin–orbit splitting in low-lying electronic states and the well-known problem case thallium, which often serves as a rigorous test system in relativistic electronic structure calculations.

Temperature-dependent electronicstructure, spin-resolved photoemission, and magnetic dichroism ofultrathin ferromagnetic films: Co/Cu(001)

The temperature dependences of the electronic structure,spin-resolved photoemission, and magnetic linear dichroism of theprototypical system 2 ML Co on Cu(001) (ML stands for monolayer(s))are presented in a detailed theoretical study. Relativistic ab initio electronic structure calculations were carried out withinthe framework of multiple-scattering theory; the spin-resolvedphotoemission was calculated within the one-step model. Thetemperature dependence was taken into account within the disorderedlocal moment picture.The spectral features show a distinct dispersion and broadening withtemperature, in particular those derived from quantum-well states inthe Co film. These findings can be traced back to the layer- andspin-resolved Bloch spectral function. Further, Co-derived maximain the photoemission intensities behave significantly differently withtemperature to Cu-derived ones. The spin-resolved photoemissionintensities compare well with experimental data and with theoreticaldata obtained within the fluctuating local moment picture. Magneticlinear dichroism in spin-resolved photoemission is discussed interms of asymmetries which are related to the spin polarizations.

Quadrupole and hexadecapole couplings for127IinLi127I

The quadrupole and hexadecapole coupling constants for ${}^{127}\mathrm{I}$ in LiI were determined from relativistic Dirac-Fock electronic structure and self-consistent nuclear structure calculations. While the calculated quadrupole coupling constant agrees with the experimental value, the predicted hexadecapole coupling constant ranges between +6 and +20 mHz, which is of opposite sign and about three orders of magnitude smaller than the value deduced from recent high resolution radio-frequency molecular beam measurements [J. Cederberg, D. Olson, A. Nelson, D. Laine, P. Zimmer, M. Welge, M. Feig, T. H\"oft, and N. London, J. Chem. Phys. 110, 2431 (1999)].

Approximate relativistic electronic structure methods based on the quaternion modified Dirac equation

New implementations of the Lévy–Leblond, zeroth-order regular approach (ZORA) and spin-free Dirac equation are presented within the framework of the four-component relativistic program system DIRAC. This implementation allows systematic incorporation of relativistic effects at different levels of theory and corresponding computational cost. One of the possibilities of the new code is to neglect the effect of spin–orbit coupling in the orbital optimization process and introduce it in a later stage of the calculation. This method is shown to be unstable despite the boundedness of the spin–orbit operator itself. © 2000 American Institute of Physics.

Relativistic electronic structure calculations with positive-energy and negative-energy orbitals

We give an overview of a new approach to the theory and practice of relativistic electronic structure calculations. The self-consistent field (SCF) approaches and the no-pair formulation are seen as particular cases of a rigorous general framework in which both positive-energy and negative-energy orbitals are incorporated on an equal footing from the outset. Starting from any reasonable relativistic Hamiltonian, we construct its complete representation H in an antisymmetrized N-particle basis made by a fixed set of orbitals. Since H is not bounded from below, a direct variational approach is doubtful. It is shown that the N eigenvalues of H split into two sets: the lowest N − correspond to a mathematically well-defined problem, but upon optimization of the orbital basis in every case they fall towards minus infinity (this is not the variational collapse, which refers to another problem). The remaining N + eigenvalues are upper bounds to the eigenvalues of the no-pair Hamiltonian, and acquire physical meaning upon energy-optimization through a variational principle. After optimization, they represent bonafide bound states approximating the ground state, the first-excited state, and so on. Convergence towards definite eigenvalues, as the size of the orbital basis is increased, is not necessarily from above, as in the variational nonrelativistic case, but may be from below or show an oscillatory behaviour. The solution of the SCF equations for model wavefunctions with vanishing singly-excited configuration interaction (CI) coefficients are shown to be identical with the eigenfunctions of the singly-excited CI representation of H with eigenvalue N −+1, thus justifying the standard SCF approach. Also, distinct from traditional SCF, higher excited states can be readily calculated in our formulation, and for any combination of open shells. A variety of atomic calculations illustrating the features and scope of our approach are presented. The corresponding documented computer programs are freely available.

Relativistic electronic structure and Fermi surface of URu 2Si 2 in antiferromagnetic state

A self-consistent calculation of electronic band structure for antiferromagnetically ordered URu 2Si 2 is performed using an all-electron fully relativistic spin-polarized LAPW method with exchange-correlation potentials in a local density approximation. The obtained magnetic moment at the uranium site shows a tiny value of 0.09 μ B due to cancellation between the spin and the orbital moment. It explains the small value of 0.04 μ B observed by neutron-scattering measurement. The Fermi surfaces are figured out from the band structure, and origins of the frequency-branches measured by de Haas–van Alphen effect are revealed.

Theoretical analysis of parity-violating energy differences between the enantiomers of chiral molecules

Fully relativistic four-component electronic structure ab initio calculations including neutral current corrections are reported for a number of small chiral molecules that are of interest in the experimental search for differences in the vibrational spectra of the two enantiomers of handed molecules. The largest vibrational energy differences, of the order 0.2 Hz, are found in chiral methane derivatives which include an iodine substituent. The vibrational energy differences in CHBrClF are 7 and 2 mHz for the carbon-chlorine and carbon-fluorine stretching modes, respectively, which are 3 to 4 orders of magnitude smaller than the precision reported in recent experiments.

Variational incorporation of negative-energy orbitals in relativistic electronic structure calculations

Significant effects of negative-energy orbitals in molecules with light atoms have recently been observed in calculations by perturbation theory from wave functions expressed in terms of positive-energy orbitals. We give a detailed discussion of how to incorporate, through a rigorous variational theorem, negative-energy orbitals in relativistic calculations of bound electronic states without any a priori knowledge of positive-energy orbitals, neither ad hoc potentials nor self-consistent-field (SCF) equations. The energy contribution of negative-energy orbitals, generally shown to be of positive sign, can be minimized by resorting to a minimax theorem or in other more practical ways, thus allowing large-scale configuration interaction (CI) with (+) orbitals obtained from correlated calculations, rather than from uncorrelated ones as in the conventional no-pair approach. General SCF equations are derived yielding positive-energy orbitals in the limit of the independent-particle model. The method is illustrated with relativistic CI calculations taken from the recent literature. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 80: 461–470, 2000

Numerical electronic structure calculations for atoms. II. Generalized variable transformation and relativistic calculations

The pairs of radial functions P-i and Q(i), which are part of the four-component single-particle spinors in the relativistic description of the electronic structure of bound states of atoms, are usually determined as solutions of eigenvalue problems. The latter constitute two-point boundary value problems which involve coupled pairs of first-order ordinary radial differential equations. To introduce a suitable notation, the theory involved in relativistic electronic structure calculations for atoms is briefly reviewed, including a general treatment of arbitrary transformations for the radial variable. Such variable transformations must be specified then, either explicitly (by a transformation function) or implicitly (by the solution method itself), for any actual calculation, though initially the variable transformation is almost completely independent of the numerical method to be applied. We consider suitable transformation functions out of which an actual choice can be made within wide limits. In our approach the resulting transformed radial differential equations are discretized then with finite-difference methods. Since the accuracy and efficiency of these methods is increased when a constant step size h between contiguous points tin the transformed variable) is used, it is only here where the careful choice of the variable transformation is important. The resulting system of linear equations is solved for the radial functions with standard linear algebra methods rather than shooting methods. The present work extends the general study of variable transformations, given recently for nonrelativistic electronic structure calculations in Part I, to the relativistic case, important results following from the present work are (i) a discretization scheme for first-order ordinary differential equations similar to the well-known standard Numerov scheme used within the nonrelativistic framework, (ii) a consistent numerical algorithm with an overall truncation error of order h(4), (iii) a method for handling effective potentials behaving singularly like r(-1) at the origin las encountered, e.s., when the atomic nucleus is represented by a pointlike charge density distribution), and, in connection with this last point, (iv) the avoidance of nonanalytic short-range behavior of the solutions to be obtained from the differential equations. (C) 2000 John Wiley & Sons, Inc.

Fully relativistic spin-polarized LMTO calculations of the magneto-optical Kerr effect ofdandfferromagnetic materials. I. Chromium spinel chalcogenides

CuCr{sub 2}Se{sub 4} is one of the few compounds that exhibits a magneto-optical (MO) Kerr angle of greater than one degree at room temperature. To better understand the origin of this effect, the MO properties of ferromagnetic CuCr{sub 2}X{sub 4} (X=S,thinspSe,thinspTe) spinel chalcogenides are evaluated using fully relativistic local-density electronic structure calculations. Treating the 3d electronic states within the standard band description, excellent agreement with the measured MO spectra is obtained. The calculations are analyzed to further elucidate aspects of the Kerr rotation. {copyright} {ital 1999} {ital The American Physical Society}

Fully relativistic spin-polarized LMTO calculations of the magneto-optical Kerr effect ofdandfferromagnetic materials. II. Neodymium chalcogenides

${\mathrm{CuCr}}_{2}{\mathrm{Se}}_{4}$ is one of the few compounds that exhibits a magneto-optical (MO) Kerr angle of greater than one degree at room temperature. To better understand the origin of this effect, the MO properties of ferromagnetic ${\mathrm{CuCr}}_{2}{X}_{4} (X=\mathrm{S},\mathrm{}\mathrm{S}\mathrm{e},\mathrm{}\mathrm{Te})$ spinel chalcogenides are evaluated using fully relativistic local-density electronic structure calculations. Treating the $3d$ electronic states within the standard band description, excellent agreement with the measured MO spectra is obtained. The calculations are analyzed to further elucidate aspects of the Kerr rotation.

Relativistic electronic structure of an icosahedral Au 12Pd cluster

Multicenter symmetry-adapted angular momentum basis functions have been generated for the icosahedral double point group. These basis functions are used to obtain the Dirac molecular orbitals for the icosahedral Au 12Pd and Au 13 clusters via the self-consistent-field Dirac scattered wave method. The Au 12Pd cluster should be diamagnetic due to a singlet ground state, while the Au 13 cluster is paramagnetic. The calculated cluster electronegativities ( χ) for Au 12Pd and Au 13 are almost identical, being 7.62 and 7.68 eV, respectively. However, the calculated softness ( S) is equal to 4.0 eV −1 for Au 12Pd, and equal to 3.4 eV −1 for Au 13. These results indicate that Au 12Pd should be more reactive than Au 13.

Ab initioDirac-Hartree-Fock calculations of chemical properties andPT-odd effects in thallium fluoride

The theory of $\mathrm{PT}$-odd interactions relevant to existing experimental measurements of the hyperfine structure of TlF is reviewed. We outline a relativistic electronic structure theory based on single-particle four-component Dirac spinors, and implemented using methods borrowed from ab initio quantum chemistry. Numerical calculations are reported of the electronic structure of TlF, some of its chemical properties, and of its $\mathrm{PT}$-odd electronic matrix elements. From these results, and from published experimental data, we derive bounds on the value of the electric dipole moment of the proton, ${d}_{p},$ the tensor coupling constant ${C}_{T},$ and the Schiff moment of the ${}^{205}$Tl nucleus, $Q$, which are now the tightest available for these quantities. General issues regarding the calculation of the electronic structures of molecules containing heavy elements are also addressed.

Optimal decoupling of positive‐ and negative‐energy orbitals in relativistic electronic structure calculations beyond Hartree–Fock

Optimal decoupling of positive‐ and negative‐energy orbitals in relativistic electronic structure calculations beyond Hartree–Fock

Optimal decoupling of positive- and negative-energy orbitals in relativistic electronic structure calculations beyond Hartree-Fock

When the one-body part of the relativistic Hamiltonian H is a sum of one-electron Dirac Hamiltonians, relativistic configuration interaction (CI) calculations are carried out with an ad hoc basis of positive-energy orbitals, {uj+, j=1, 2,…,m} and, more recently, with the full bases of positive-energy and negative-energy orbitals, {uj+, uj−, j=1, 2,…,m}. The respective eigenproblems H+Ck+=Ek+Ck+, k=1, 2,…,(m), and HCk=EkCk; k=1, 2,…,(2m) are related through Ek+≤Ek+(2m−(m) [R. Jauregui et al., Phys. Rev. A 55, 1781 (1997)]. This inequality becomes an equality for the independent-particle Hartree–Fock model and some other simple multiconfiguration models, leading to an exact decoupling of positive-energy and negative-energy orbitals. Beyond Hartree–Fock, however, it is generally impossible to achieve an equality. By definition, optimal decoupling is obtained when the difference Ek+(2m)−(m)−Ek+ is a minimum, which amounts to maximize the energy Ek+ with respect to any set of m functions in the 2m-dimensional space {uj+, uj−, j=1, 2,…,m}. Straight maximization is a slowly convergent process. Fortunately, numerical calculations on high-Z atomic states show that optimally decoupled, or best positive-energy orbitals are given, to within 6 decimals in atomic units by the positive-energy natural orbitals of the full eigenfunction Ck+(2m)−(m). Best orbitals can accurately be obtained through CI-by-parts treatments for later use in large-scale relativistic CI, as illustrated with Ne ground-state calculations. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 70: 805–812, 1998

The use of Gaussian spinors in relativistic electronic structure calculations: the effect of the boundary of the finite nucleus of uniform proton charge distribution

The ground-state electronic energies of hydrogen-like ions are computed by solving the matrix Dirac equation in large basis sets of Gaussian spinors to compare the accuracy of the expansion method with that of Desclaux's finite-difference and Matsuoka's matching equation methods. The nuclei are approximated as spheres of uniform charge distribution. We examine in detail the quality of the computed spinors in the vicinity of the nuclear boundary where relativistic dynamics is also important.