Exact Exchange Method Research Articles

Development and implementation of the exact exchange method for semiconductors using a localized basis set

One of the major deficiencies of density functional theory is presented in the approximation of the exchange energy term. An important advance in solving this problem has been the development of orbital-dependent exchange functionals. The exact exchange method is one of the best defined releases of such functionals. Up to now it has been applied in solid systems only using a plane wave representation basis set. In this paper we present a development and implementation of the exact exchange formalism for solid semiconductors using a basis set of localized numerical functions. The implementation of the exact exchange scheme has been carried out in the SIESTA code, as a new path to get the exchange part in the Kohn–Sham energy and potential. This program is an ab initio periodic fully self-consistent density functional code which uses norm-conserving non-local pseudopotentials. Linear combination of confined numerical pseudoatomic orbitals have been used to represent the Kohn–Sham orbitals. The calculation results of the electronic properties of several semiconductor systems using different qualities of the basis set are compared with experimental results and presented in this paper.

Exact-exchange density functional theory for quasi-two-dimensional electron gases

A simple exact-exchange density-functional method for a quasi-two-dimensional electron gas with variable density is presented. An analytical expression for the exact-exchange potential with only one occupied subband is provided, without approximations. When more subbands are occupied the exact-exchange potential is obtained numerically. The theory shows that, in contradiction with LDA, the exact-exchange potential exhibits discontinuities and the system suffers a zero-temperature first-order transition each time a subband is occupied. Results suggesting that the translational symmetry might be spontaneously broken at zero temperature are presented. An extension of the theory to finite temperatures allows to describe a drop in the intersubband spacing in good quantitative agreement with recent experiments.

Development of the exact exchange scheme using a basis set framework

AbstractA combination of the exact exchange (EXX) scheme for the approximation of the exchange term within the density functional theory is presented. For this task we have developed it and implemented in the atom code program. As will be discussed in this article, the use of this approach has the advantages of using a simple, but efficient, calculation numerical code and the refinement of the EXX method for the exchange part within the Khon–Sham formalism. We present the development of the EXX theory within an atomic scheme for energy calculations. Results for several atomic systems are presented. We found a remarkable improvement in the energies of all the systems studied compared with the local density approximation and generalized gradient approximation approaches. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2003

Structures, thermochemistry, and electron affinities of the germanium fluorides, GeFn/GeFn−(n=1–5)

Four different density functional methods have been employed to study the molecular structures, electron affinities, and first dissociation energies of the GeFn/GeFn−(n=1–5) molecules. The three types of electron affinities reported in this work are the adiabatic electron affinity (EAad), the vertical electron affinity (EAvert), and the vertical detachment energy (VDE). The first Ge–F dissociation energies De(Fn−1Ge–F), De(Fn−1Ge−–F), and De(Fn−1Ge–F−) of the GeFn/GeFn− species are also reported. The basis set used in this work is of double-ζ plus polarization quality with additional s- and p-type diffuse functions, labeled as DZP++. Among the four density functionals used in this work, the BHLYP (which includes 50% exact exchange) method determines the molecular structures in best agreement with experiment, while other methods generally overestimated bond lengths. The theoretical Ge–F bond distances for the GeFn−(n=1–4) anions are predicted about 0.1 Å longer than their corresponding neutral counterparts. No significantly bound minimum was found for the neutral GeF5 molecule, while a D3h structure was confirmed to be a genuine minimum for ionic GeF5−. Based on the precise experimental result of EAad(GeF), the adiabatic electron affinities obtained at the DZP++ BHLYP level of theory are again most reliable, with the BLYP method being next. The DZP++ BHLYP adiabatic electron affinities are 1.02, 0.85, 3.72, and 1.46 eV for GeF, GeF2, GeF3, and GeF4, respectively. The vertical detachment energy of GeF5− is predicted to be very large. The substantial value (1.46 eV) of the EA for GeF4 is especially interesting, in that the valence isoelectronic species SiF4 does not bind an electron. A number of experimental electron affinities and experimental thermochemical quantities appear to be error.

Theory of hyperfine fields of iron

The hyperfine fields of Fe, Ni, Co, and their alloys are calculated by use of nonlocal methods which allow us to go beyond the local density approximation (LDA) of the density functional theory. Two different methods, both belonging to the optimized effective potential method are proposed: the first one is the RPA applied to the Kohn-Sham orbitals, and the second one is the combination of the exact-exchange method for the core states and the LDA for the valence states. Both approaches give much improved description for the hyperfine fields of the magnetic transition metals. Especially for iron, the theory, for the first time, succeeded in predicting reasonable values for the Fermi contact hyperfine fields: -329 kG by the RPA and -394 kG by the combined approach.

Inclusion of electron correlation for the target wave function in low- to intermediate-energy e-N2 scattering.

In a recent calculation, an exact exchange method was developed for use in the partial-differential-equation approach to electron-molecule scattering and was applied to e-N2 scattering in the fixed-nuclei approximation with an adiabatic polarization potential at low energies (0-10 eV). Integrated elastic cross sections were calculated and found to be lower than experiment at energies both below and above the Pi(g) resonance. It was speculated at that time that improved experimental agreement could be obtained if a correlated target representation were used in place of the uncorrelated one. The present paper implements this suggestion and demonstrates the improved agreement. These calculations are also extended to higher energies (0-30 eV) so asd to include the Sigma(u) resonance. Some discrepancies among the experiments and between experiment and the various calculations at very low energy are noted.

A comparison of self-interaction-corrected local correlation energy functionals

A new selfinteraction-corrected local correlation energy functional is constructed to conform with the exact limiting behaviour in both one-electron systems and N-electron systems (N to infinity ) with slowly varying densities. It is combined with an exact treatment of exchange to selfconsistently calculate correlation energies, ionisation potentials, electron affinities, spin and number densities and diamagnetic susceptibilities for a number of atoms and ions. The results are compared with those from the Stoll-Pavlidou-Preuss (SPP) and the Perdew-Zunger (PZ) selfinteraction corrected forms as well as the Kohn-Sham (KS) form. For most of the above properties the new form is either as good as or better than the others. The authors conclude that for physical quantities that can be expressed as differences of energies or differences of spin up/down densities the exact exchange plus local correlation method is a viable and much simpler alternative to large configuration-interaction calculations for atoms and ions, especially for those with N>or=15.