A Scalar Relativistic Full-Potential LCAO Method

Abstract

We present a new scalar relativistic formulation for the full-potential linear-combinationof-atomic-orbitals method based on the density-functional theory. Three approximations are introduced to overcome computational difficulty. The first is to consider only the large component of the four-component spinor, neglecting the small component. The second is to neglect the energy dependence in the Hamiltonian reduced for the large component. The third is to replace the material-dependent potential with the atomic potential in relativistic corrections. After the three approximations, we identify the mass-velocity and Darwin terms and also the spin-orbit coupling, where the latter is to be omitted according to the definition of the scalar relativistic formulation. The computational effort of the present method is reduced considerably in comparison with that of the fully relativistic method, being almost the same as that of the nonrelativistic method. We apply the present method within the local-density approximation to several diatomic molecules with heavy elements, crystalline Au, and crystalline InSb. The results are improved considerably in comparison with the nonrelativistic results. The calculated structural properties are in good agreement with the fully relativistic results and also with the experimental results. The calculated electronic properties are also improved considerably in comparison with the nonrelativistic results and are also in good agreement with the fully relativistic results except for the effect due to the spin-orbit coupling.KEYWORDS: scalar relativistic calculations, full-potential calculations, LCAO method, density-functional theory, band calculations, structure optimizations 1 §1. IntroductionThe structural and electronic properties of materials with heavy elements are strongly affected by relativistic effects. Core electrons experience strong nuclear field and, consequently, the spatial extent of the core-electron orbitals is contracted substantially. As a result, the efficient screening of nuclear charge is caused by the core electrons, inducing the expansion of valence-electron orbitals, especially of d and f orbitals. 1) This effect, which is known as the indirect relativistic effect, strongly affects the structural properties as well as the electronic properties.2) The mass-velocity and Darwin terms are responsible for the indirect relativistic effect. Furthermore, of another importance is the spin-orbit coupling. For example, the splitting due to the spin-orbit coupling in the conduction and valence bands in crystals with heavy elements sometimes has the same order of magnitude as the crystal-field splitting.The strategy which treats the mass-velocity and Darwin terms but neglects the spin-orbit coupling is known as the scalar relativistic method. The method has a practical advantage that the computational effort is reduced considerably in comparison with the fully relativistic method, which considers not only the mass-velocity and Darwin terms but also the spin-orbit coupling. So far...

First-Principles Study of Spin–Orbit Interactions in Bismuth Iron Garnet

“…The used exchange-correlation potential is the Perdue-Zunger parametrization 9) of the results of the numerical study by Ceperley and Alder. 10) To distinguish the effect of spin-orbit coupling, two types of relativistic calculations are carried out; one is the fully relativistic full potential LCAO (FFLCAO) calculations 11) and the other is the scalar relativistic full potential LCAO (SFLCAO) calculations, 12) where the former includes all the relativistic effects while the latter includes relativistic effects except the spin-orbit coupling. In the FFLCAO calculations, we solve the Dirac-Kohn-Sham equations directly by adopting the atomic orbitals of four component Dirac spinors with positive energy as basis functions.…”

All-electron fully relativistic Kohn-Sham theory for solids based on the Dirac-Coulomb Hamiltonian and Gaussian-type functions

“…This analysis shows that in order to build 4c complex matrices for the Coulomb and exchange-correlation operators, it is sufficient to evaluate integrals in Eqs. (66) for five components of the overlap distribution -one for the LL sector, and four for the SS sector. The k-space matrix is then obtained by computing the Fourier series of these five components [Eq.…”

“…An alternate strategy to the use of plane waves, is to expand the KS orbitals in a set of local functions. Such full-potential methods employing numerical orbitals have been extended to include scalar relativistic corrections [66,67], as well as four-component (4c) SOC [68][69][70][71]. Alternatively, basis functions can be constructed by placing analytic Slater-type orbitals (STOs) or Gaussian-type orbitals (GTOs) on atomic centers.…”

“…two-component (2c) techniques using STOs were implemented by Philipsen et al [72,73] and Zhao et al [74] Relativistic calculations on solids with GTOs were reported with scalar-relativistic corrections [75,76], as well as approximate 2c schemes solving Pauli-type equations [77,78], or approaches based on the Douglass-Kroll-Hess Hamiltonian [79,80]. While calculations that include scalar-relativistic corrections on solids are common [66,67,75,76], extending nonrelativistic implementations by SOC poses severe methodological challenges due to the appearance of multicomponent spinor structure of the wave functions as well as the need to use complex algebra.…”

First-Principles Study of Effects of Boron on Magnetic Anisotropy in MgO/CoFe(B)/X (X = Ru, Ta) Systems

“…We carried out all-electron calculations using the scalar relativistic full-potential linearcombination-of-atomic-orbitals (SFLCAO) method for structure optimization and the fully 1/6 relativistic full-potential linear-combination-of-atomic-orbitals (FFLCAO) method for calculating magnetic anisotropy energy (MAE); [4][5][6] the SFLCAO and FFLCAO methods are both based on the density functional theory. We adopted the local spin density approximation (LSDA) using the Perdew-Wang parameterization of the Ceperley-Alder results as the exchange-correlation energy functional.…”