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

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

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

This review provides a perspective on the use of orbital-dependent functionals, which is currently considered one of the most promising avenues in modern density-functional theory. The focus here is on four major themes: the motivation for orbital-dependent functionals in terms of limitations of semilocal functionals; the optimized effective potential as a rigorous approach to incorporating orbital-dependent functionals within the Kohn-Sham framework; the rationale behind and advantages and limitations of four popular classes of orbital-dependent functionals; and the use of orbital-dependent functionals for predicting excited-state properties. For each of these issues, both formal and practical aspects are assessed.

Orbital-dependent density functionals: Theory and applications

By the Hellmann-Feynman theorem, the density n(r) of many electrons in the presence of external potential v(r) obeys the relationships F${d}^{3}$r n(r)\ensuremath{\nabla}v(r)=0 and F${d}^{3}$r n(r)r\ifmmode\times\else\texttimes\fi{}\ensuremath{\nabla}v(r)=0. By the virial theorem, the interacting kinetic and electron-electron repulsion expectation values obey 2T[n]+${V}_{\mathrm{ee}}$[n]=-F${d}^{3}$r n(r)r\ensuremath{\cdot}\ensuremath{\nabla}[\ensuremath{\delta}T/\ensuremath{\delta}n(r)+\ensuremath{\delta}${V}_{\mathrm{ee}}$/\ensuremath{\delta}n(r)]. The exchange energy functional ${E}_{x}$[n] and potential ${v}_{x}$([n];r)\ensuremath{\equiv}\ensuremath{\delta}${E}_{x}$/\ensuremath{\delta}n(r) must satisfy ${E}_{x}$[n]+F${d}^{3}$r n(r)r\ensuremath{\cdot}\ensuremath{\nabla}${v}_{x}$([n];r)=0, while the correlation energy and potential must satisfy ${E}_{c}$[n]+F${d}^{3}$r n(r)r\ensuremath{\cdot}\ensuremath{\nabla}${v}_{c}$([n];r)0. Somewhat counterintuitively, it is not true that T[${n}_{\ensuremath{\gamma}}$]=${\ensuremath{\gamma}}^{2}$T[n] and ${V}_{\mathrm{ee}}$[${n}_{\ensuremath{\gamma}}$]=\ensuremath{\gamma}${V}_{\mathrm{ee}}$[n], where ${n}_{\ensuremath{\gamma}}$(r)\ensuremath{\equiv}${\ensuremath{\gamma}}^{3}$n(\ensuremath{\gamma}r) is a scaled density with scale factor \ensuremath{\gamma}\ensuremath{\ne}1. In fact, it is impossible to partition the exact Hohenberg-Kohn functional into a piece that scales as ${\ensuremath{\gamma}}^{2}$ and a piece that scales as \ensuremath{\gamma}, even if complete freedom with the partitioning is allowed. Instead there are universal scaling inequalities.For instance, T[${n}_{\ensuremath{\gamma}}$]+${V}_{\mathrm{ee}}$[${n}_{\ensuremath{\gamma}}$]${\ensuremath{\gamma}}^{2}$T[n]+ \ensuremath{\gamma}${V}_{\mathrm{ee}}$[n] and T[${n}_{\ensuremath{\gamma}}$]+\ensuremath{\gamma}${V}_{\mathrm{ee}}$[${n}_{\ensuremath{\gamma}}$]g${\ensuremath{\gamma}}^{2}$(T[n ]+${V}_{\mathrm{ee}}$[n]), and consequent inequalities involving ${E}_{c}$[n]. All the above virial and scaling requisites are universal in that they are independent of external potential and they must hold for arbitrary proper n. In addition, for the ground-state energy (E) and n of any atom or molecule at its equilibrium nuclear configuration, there is the inequality E-${T}_{s}$[n], where ${T}_{s}$ is the noninteracting kinetic energy. In the closed-shell tight-binding limit, the correlation potential obeys F${d}^{3}$r n(r)r\ensuremath{\cdot}\ensuremath{\nabla}${v}_{c}$([n];r)=0, and so cannot be a monotonic function of r for an atom in this limit.Further, (\ensuremath{\partial}/\ensuremath{\partial}\ensuremath{\gamma})${E}_{c}$[${n}_{\ensuremath{\gamma}}$]${\ensuremath{\Vert}}_{\ensuremath{\gamma}=1}$=E $_{c}$[n]+${T}_{c}$[n]=-F${d}^{3}$r n(r)r\ensuremath{\cdot}\ensuremath{\nabla}${v}_{c}$([n];r), which implies that the exact ${E}_{c}$ should be fairly insensitive to scaling. With the help of the ionization-potential theorem, it is argued that the exact ${v}_{c}$([n];r) in an atom often has a positive part. Common approximations to the correlation potential are examined for their effects upon the highest occupied Kohn-Sham orbital energy and the density moment 〈${r}^{2}$〉, and these effects are found to be related. Further improvements needed in the approximate correlation potentials are relatively large, but not nearly so large as those recently suggested for the atoms Ne, Ar, Kr, and Xe: The discrepancy between theoretical values of 〈${r}^{2}$〉 from Hartree-Fock or configuration-interaction calculations, and experimental values from measured diamagnetic susceptibilities, is tentatively resolved in favor of theory.

Hellmann-Feynman, virial, and scaling requisites for the exact universal density functionals. Shape of the correlation potential and diamagnetic susceptibility for atoms

The series Lecture Notes in Chemistry (LNC), reports new developments in chemistry and molecular science quickly and informally, but with a high quality and the explicit aim to summarize and communicate current knowledge for teaching and training purposes. Books published in this series are conceived as bridging material between advanced graduate textbooks and the forefront of research. They will serve the following purposes:  • provide an accessible introduction to the field to postgraduate students and nonspecialist researchers from related areas, • provide a source of advanced teaching material for specialized seminars, courses and schools, and • be readily accessible in print and online. The series covers all established fields of chemistry such as analytical chemistry, organic chemistry, inorganic chemistry, physical chemistry including electrochemistry, theoretical and computational chemistry, industrial chemistry, and catalysis. It is also a particularly suitable forum for volumes addressing the interfaces of chemistry with other disciplines, such as biology, medicine, physics, engineering, materials science including polymer and nanoscience, or earth and environmental science.  Both authored and edited volumes will be considered for publication. Edited volumes should however consist of a very limited number of contributions only. Proceedings will not be considered for LNC.  The year 2010 marks the relaunch of LNC.

Lecture notes in Chemistry

The extra-electron binding energies of the ground-state monatomic negative ions with $Zl86$ are calculated using the self-interaction correction (SIC) to the local spin-density approximation (LSD) for exchange and correlation. The results agree reasonably with experiment, and the errors reflect the familiar "interconfigurational energy error" common to LSD and SIC. Some of the rare earths, e.g., Ce and possibly Gd, are predicted to form stable negative ions. In addition we have the following: (1) Relativistic (other than spin-orbit) contributions to the electron affinities are included and discussed. In Au the relativistic effects boost the calculated affinity from 1.5 to 2.5 eV. (2) The doubly negative ions ${\mathrm{O}}^{2\ensuremath{-}}$ and ${\mathrm{Te}}^{2\ensuremath{-}}$ are predicted to have no stable ground state. (3) Electron affinities are calculated for a few excited atomic states. (4) The calculated ground-state densities $n(r)$ of all the neutral atoms and negative ions are monotonically decreasing functions of $r$. (5) Corrections to the random-phase-approximation electron-gas correlation energy are shown to cancel out of SIC calculations for atoms.

Calculated electron affinities of the elements

The large relative error of the local density approximation for the transverse-photon-electron or Breit energy in atoms and solids is shown to arise from spurious self-interaction of the 1s electrons. Orbital self-interaction correction dramatically reduces this error. On the other hand, the large relative error of the local density approximation for the Breit contribution to the 2s electron removal energy is almost unchanged by self-interaction correction.

https://iopscience.iop.org/article/10.1088/0022-3719/15/26/004/pdf

Lee A. Cole

Papers

Calculated electron affinities of the elements

On the local density approximation for Breit interaction

On “theory and method for accelerating the convergence of self-consistent electronic structure calculations”