Relativistic Density Functional Theory

Engel, E.; Dreizler, R. M.

doi:10.1007/978-3-642-14090-7_8

Cited by 16 publications

(9 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In relativistic KS-DFT, [96][97][98][99][100] the XC functional should in principle also include relativistic effects and should be formulated in terms of the four-current density. 101 The latter is the basic density variable in relativistic KS-DFT. A relativistic generalization of the local density approximation (RLDA) 98 has been proposed, as well as a semi-empirical gradient corrected variant (RGGA).…”

Section: Fully Relativistic Dirac Approachmentioning

confidence: 99%

“…A relativistic generalization of the local density approximation (RLDA) 98 has been proposed, as well as a semi-empirical gradient corrected variant (RGGA). 97,102 Common practice, however, is to use a non-relativistic XC functional in conjunction with the Dirac kinetic energy, 95,101 which is the procedure we follow in this work. We use here a 4c-DKS approach with nonrelativistic GGA and hybrid GGA functionals.…”

Section: Fully Relativistic Dirac Approachmentioning

confidence: 99%

See 1 more Smart Citation

Relativistic correction scheme for core-level binding energies from GW

Keller

Blüm

Rinke

et al. 2020

The Journal of Chemical Physics

View full text Add to dashboard Cite

We present a relativistic correction scheme to improve the accuracy of 1s core-level binding energies calculated from Green's function theory in the GW approximation, which does not add computational overhead. An element-specific corrective term is derived as the difference between the 1s eigenvalues obtained from the self-consistent solutions to the non-or scalar-relativistic Kohn-Sham equations and the four-component Dirac-Kohn-Sham equations for a free neutral atom. We examine the dependence of this corrective term on the molecular environment and on the amount of exact exchange in hybrid exchange-correlation functionals. This corrective term is then added as a perturbation to the quasiparticle energies from partially self-consistent and single-shot GW calculations. We show that this elementspecific relativistic correction, when applied to a previously reported benchmark set of 65 core-state excitations [J. Phys. Chem. Lett. 11, 1840], reduces the mean absolute error (MAE) with respect to experiment from 0.55 to 0.30 eV and eliminates the species dependence of the MAE, which otherwise increases with the atomic number. The relativistic corrections also reduce the species dependence for the optimal amount of exact exchange in the hybrid functional used as starting point for the single-shot G 0 W 0 calculations. Our correction scheme can be transferred to other methods, which we demonstrate for the Delta self-consistent field (∆SCF) approach based on density functional theory.

show abstract

Section: Fully Relativistic Dirac Approachmentioning

confidence: 99%

Section: Fully Relativistic Dirac Approachmentioning

confidence: 99%

Relativistic correction scheme for core-level binding energies from GW

Keller

Blüm

Rinke

et al. 2020

The Journal of Chemical Physics

View full text Add to dashboard Cite

show abstract

“…For more recent developments and investigations of relativistic density functional theory in atomic systems, see Ref. [244].…”

Section: Hohenberg-kohn and Kohn-sham Density Functional Theorymentioning

confidence: 99%

Towards an ab initio covariant density functional theory for nuclear structure

Shen

Liang

Long

et al. 2019

Progress in Particle and Nuclear Physics

102

View full text Add to dashboard Cite

Nuclear structure models built from phenomenological mean fields, the effective nucleon-nucleon interactions (or Lagrangians), and the realistic bare nucleon-nucleon interactions are reviewed. The success of covariant density functional theory (CDFT) to describe nuclear properties and its influence on Brueckner theory within the relativistic framework are focused upon. The challenges and ambiguities of predictions for unstable nuclei without data or for high-density nuclear matter, arising from relativistic density functionals, are discussed. The basic ideas in building an ab initio relativistic density functional for nuclear structure from ab initio calculations with realistic nucleon-nucleon interactions for both nuclear matter and finite nuclei are presented. The current status of fully self-consistent relativistic Brueckner-Hartree-Fock (RBHF) calculations for finite nuclei or neutron drops (ideal systems composed of a finite number of neutrons and confined within an external field) is reviewed. The guidance and perspectives towards an ab initio covariant density functional theory for nuclear structure derived from the RBHF results are provided. Summary and Perspectives 521. Introduction Brief introduction on nuclear theoryThe discoveries of radioactivity by Becquerel [1] and the Curies [2, 3] and the existence of a compact nucleus at the center of an atom by Rutherford et al. [4] opened the door of nuclear physics. During the hundred years of development in nuclear physics, there emerged several significant milestones, including the discovery of the neutron by Chadwick [5] which verified the composition of the nucleus as protons and neutrons, the meson-exchange theory for the strong interaction between nucleons by Yukawa [6], the independent-particle shell model of the nucleus by Goeppert-Mayer [7], Haxel, Jensen, and Suess [8], and the collective Hamiltonian for nuclear rotation and vibration by Rainwater [9], Bohr and Mottelson [10,11], etc.With the understanding of the composition of a nucleus as protons and neutrons [5] and the meson-exchange theory for the strong interaction between the nucleons [6], nuclear physicists hoped to describe the nucleus, a quantum many-body system, from the underlying nucleon-nucleon interaction. Euler, a student of Heisenberg, assumed the nuclear force as a two-body (2N) interaction with a Gaussian shape and calculated the infinite nuclear system, i.e., homogeneous nuclear matter, using second-order perturbation theory [12]. However, the strong repulsive core of the realistic nuclear force [13] prevents the application of perturbation theory.On the other hand, the nuclear structure model with a phenomenological mean field achieved great success. Goeppert-Mayer [7], Haxel, Jensen, and Suess [8] introduced a strong spin-orbit potential and proposed the nuclear independentparticle shell model that successfully explained the conventional magic numbers in nuclei. Rainwater [9], Bohr and Mottelson [10, 11] explored the nuclear deformation and proposed the nuclear collective mode...

show abstract

“…It is widely accepted that relativistic effect is important in the calculation of gold systems. − Theoretically, the relativistic effect can be calculated by performing four-component, two-component, and scalar relativistic (SC) calculations, which attempt to solve the Dirac−Hartree−Fock equation at various levels of approximation. According to Kullie et al, calculations including the two-component relativistic spinors, which account for the spin−orbit (SO) coupling effect, and using relativistic effective core potentials (RECPs) are very efficient, and the two-component relativistic spinor method is already implemented in the NWCHEM software package for the DFT methods. − It has also been pointed out by Rusakov et al that such techniques can accurately account for the relativistic effect but with acceptable cost.…”

Section: Introductionmentioning

confidence: 99%

Validation of Density Functional Methods for the Calculation of Small Gold Clusters

Shi

Fan

2010

J. Phys. Chem. A

View full text Add to dashboard Cite

The performance of various density functional theory methods on the geometries and energetics of Au(2), Au(3), Au(4), and Au(5) has been systematically evaluated. The results were compared with those from experiments or high-level wave function theory methods. In the present study, spin-orbit (SO) coupling was considered. It was found that SO coupling plays a very important role in the calculation of both the atomization energies and relative stability of the isomers of gold clusters. Functionals including SO coupling effect will overestimate the atomization energies of gold clusters compared with those just including the scalar relativistic (SC) effect. On the other hand, hybrid functionals will underestimate the atomization energies compared with those of the corresponding pure functionals. For the calculation of the relative stability of the different isomers, many functionals not including SO coupling will predict the wrong stability order. In addition, SO correction to the atomization energy of the cluster (ΔE(SO)) has a weak dependence on the choice of functional. A linear relationship was established between ΔE(SO) and the number of Au atoms and Au-Au bonds in the cluster. The relationship indicates that inclusion of SO coupling will favor the isomer with more Au-Au bonds. Among all of the functionals evaluated, the SO TPSSh method has the best overall performance, and SC M06-L also performs well, although it predicts that the two isomers of Au(3) are almost degenerate in energy.

show abstract

Relativistic Density Functional Theory

Cited by 16 publications

References 0 publications

Relativistic correction scheme for core-level binding energies from GW

Relativistic correction scheme for core-level binding energies from GW

Towards an ab initio covariant density functional theory for nuclear structure

Validation of Density Functional Methods for the Calculation of Small Gold Clusters

Contact Info

Product

Resources

About