The exact density functional for the ground-state energy is strictly self-interaction-free (i.e., orbitals demonstrably do not self-interact), but many approximations to it, including the local-spin-density (LSD) approximation for exchange and correlation, are not. We present two related methods for the self-interaction correction (SIC) of any density functional for the energy; correction of the self-consistent one-electron potenial follows naturally from the variational principle. Both methods are sanctioned by the Hohenberg-Kohn theorem. Although the first method introduces an orbital-dependent single-particle potential, the second involves a local potential as in the Kohn-Sham scheme. We apply the first method to LSD and show that it properly conserves the number content of the exchange-correlation hole, while substantially improving the description of its shape. We apply this method to a number of physical problems, where the uncorrected LSD approach produces systematic errors. We find systematic improvements, qualitative as well as quantitative, from this simple correction. Benefits of SIC in atomic calculations include (i) improved values for the total energy and for the separate exchange and correlation pieces of it, (ii) accurate binding energies of negative ions, which are wrongly unstable in LSD, (iii) more accurate electron densities, (iv) orbital eigenvalues that closely approximate physical removal energies, including relaxation, and (v) correct longrange behavior of the potential and density. It appears that SIC can also remedy the LSD underestimate of the band gaps in insulators (as shown by numerical calculations for the rare-gas solids and CuCl), and the LSD overestimate of the cohesive energies of transition metals. The LSD spin splitting in atomic Ni and $s\ensuremath{-}d$ interconfigurational energies of transition elements are almost unchanged by SIC. We also discuss the admissibility of fractional occupation numbers, and present a parametrization of the electron-gas correlation energy at any density, based on the recent results of Ceperley and Alder.

Self-interaction correction to density-functional approximations for many-electron systems

A scheme that reduces the calculations of ground-state properties of systems of interacting particles exactly to the solution of single-particle Hartree-type equations has obvious advantages. It is not surprising, then, that the density functional formalism, which provides a way of doing this, has received much attention in the past two decades. The quality of the energy surfaces calculated using a simple local-density approximation for exchange and correlation exceeds by far the original expectations. In this work, the authors survey the formalism and some of its applications (in particular to atoms and small molecules) and discuss the reasons for the successes and failures of the local-density approximation and some of its modifications.

The density functional formalism, its applications and prospects

Calculations of ground-state and excited-state properties of materials have been one of the major goals of condensed matter physics. Ground-state properties of solids have been extensively investigated for several decades within the standard density functional theory. Excited-state properties, on the other hand, were relatively unexplored in ab initio calculations until a decade ago. The most suitable approach up to now for studying excited-state properties of extended systems is the Green function method. To calculate the Green function one requires the self-energy operator which is non-local and energy dependent. In this article we describe the GW approximation which has turned out to be a fruitful approximation to the self-energy. The Green function theory, numerical methods for carrying out the self-energy calculations, simplified schemes, and applications to various systems are described. Self-consistency issue and new developments beyond the GW approximation are also discussed as well as the success and shortcomings of the GW approximation.

https://iopscience.iop.org/article/10.1088/0034-4885/61/3/002/pdf

The GW method

I. Introduction and Scope 231A. Definitions of Atomic Electron Affinities 233B. Definitions of Molecular Electron Affinities 233II. Experimental Photoelectron Electron Affinities 235A. Historical Background 235B. The Photoeffect 236C. Experimental Methods 237D. Time-of-Flight Negative Ion PhotoelectronSpectroscopy239E. Some Thermochemical Uses of ElectronAffinities241F. Layout of Table 10: ExperimentalPhotoelectron Electron Affinities242III. Theoretical Determination of Electron Affinities 242A. Historical Background 2421. Theoretical Predictions of Atomic ElectronAffinities2422. Theoretical Predictions of MolecularElectron Affinities243B. Present Status of Theoretical Electron AffinityPredictions243C. Basis Sets and Theoretical Electron Affinities 244D. Density Functional Theory (DFT) andElectron Affinities245E. Layout of Tables 8 and 9: Theoretical DFTElectron Affinities247F. Details of Density Functional MethodsEmployed in Tables 8 and 9247IV. Discussion and Observations 248A. Statistical Analysis of DFT Results ThroughComparisons to Experiment and OtherTheoretical Methods248B. Theoretical EAs for Species with UnknownExperimental EAs251C. On the Applicability of DFT to Anions and theFuture of DFT EA Predictions251D. Specific Theoretical Successes 251E. Interesting Problems 2521. C

/pdf/atomic-and-molecular-electron-affinities-photoelectron-3x4vklpj6q.pdf

Atomic and molecular electron affinities: photoelectron experiments and theoretical computations.

Oxygen vacancies in transition metal and rare earth oxides: Current state of understanding and remaining challenges

Expressions for the kinetic energy $T$ (and incidentally also for the exchange energy ${E}_{x}$) of a ground-state inhomogeneous electron gas as a functional of the electron density $n(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$, and for $n(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ as a functional of the one-electron potential $V(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$, are readily generalized to the case of two unequal spin densities ${n}_{\ensuremath{\uparrow}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ and ${n}_{\ensuremath{\downarrow}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$. As an example the authors consider the expansions of $T$ up to fourth order in the gradients of $n$, and of $n$ up to fourth order in the gradients of $V$. These expansions are tested for the extreme case of one- and two-electron atoms. It is found that (i) The $n[V]$ expansion contains serious pathologies, while the $T[n]$ expansion leads to much more reasonable results when applied to either the exact density $n(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ or to an $n(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ obtained by minimization of the approximate total-energy functional $E[n]$. (ii) Good approximations to $E$ and $n(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ in one-electron atoms are obtained only when the complete spin polarization of a single electron is taken into account via $T[{n}_{\ensuremath{\uparrow}}, {n}_{\ensuremath{\downarrow}}]$. (iii) Within a variational calculation, the inclusion of second- and fourth-order gradient corrections to the zeroth-order (Thomas-Fermi) approximation for $T$ leads to systematic improvements in the analytic behavior of $n(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$ near the nucleus. The authors also compare the local-exchange approximation with the local-exchange-correlation approximation in one- and two-electron atoms, and find that correlation should not be neglected.

G. L. Oliver

Papers

Spin-density gradient expansion for the kinetic energy

A self-interaction corrected approach to many-electron systems: Beyond the local spin density approximation