Exchange and correlation energy of an inhomogeneous electron gas

A convenient expression is derived for the coefficient, B_xc(n), which determines the first gradient corrections to the exchange and correlation energy of an inhomogeneous electron gas. The result is exact to all orders in $\text{e}$² and is expressed in terms of the single particle progagator. A method of approximation, which is exact at high density, is given for the explicit evaluation of B_xc. Numerical results are given for B_xc in the metallic density range.     

Kinetic energy of an inhomogeneous electron gas

It is well known that the kinetic energy of a system of N noninteracting particles in an external field V(r) in the nondegenerate ground state is a universal functional of the particle density (r) [1]. However, the explicit form of this functional is defined only for a certain class of functions (r). In particular, in the case of an almost constant or a slowly varying density we obtain the wellknown Thomas-Fermi-Weizsäcker-Kirzhnits functional [1, 2]. In [3] the kinetic energy functional of an electron in an atom is obtained in the WKB approximation. The kinetic energy of electrons with quantum numbers n andl is represented as the sum of two terms. The first term is written in the form of the density of the electrons with the given quantum numbers times some orthogonalized pseudopotential, which takes into account the orthogonality of their wave functions with respect to the core (its form is discussed below). The second term is the intrinsic kinetic energy of the electrons. The introduction of an orthogonalized pseudopotential is very convenient for the calculation of atomic properties [4, 5]. It is therefore of great interest to extend the results of [3] to the case of an electron gas in a metal and to obtain an expression for its orthogonalized crystalline pseudopotential. The solution of these problems is the aim of the present paper.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 117–120, July, 1977.     

Anomaly of the ground state energy of an electron gas

Based on a two point Padéapproximation, the ground state energy, pressure and compressibility of an electron gas are examined.     

The intrinsical character of the electronic correlation in an electron gas

By introducing the phase transformation of electron operators, we map the equation of motion of an one-particle Green's function into that of a non-interacting one-particle Green's function where the electrons are moving in a time-depending scalar potential and pure gauge fields for a D-dimensional electron gas, and we demonstrate that the electronic correlation strength strongly depends upon the excitation energy spectrum and collective excitation modes of electrons. It naturally explains that the electronic correlation strength is strong in the one dimension, while it is weak in the three dimensions.     

Using the spin-resolved electronic direct correlation function to estimate the correlation energy of the spin-polarized uniform electron gas

We report a simple ansatz that includes spin-polarization in two different models for the exchange-correlation hole. Both models were originally conceived for the non-polarized uniform electron gas. One of them is based on the electronic direct correlation function, a novel approach to build the long-range behavior of the exchange-correlation hole. This ansatz is shown to work quite well considering the limitations of the original models. Interestingly, the hole based on the direct correlation function provides better results in general. This suggests that it is better to model the electronic direct correlation function than it is to model the hole directly.     

Analytic theory of correlation energy and spin polarization in the 2D electron gas

We present an analytic theory of the pair distribution function and the ground-state energy in a two-dimensional (2D) electron gas with an arbitrary degree of spin polarization. Our approach involves the solution of a zero-energy scattering Schrödinger equation with an effective potential which includes a Fermi term from exchange and kinetic energy and a Bose-like term from Jastrow-Feenberg correlations. The form of the latter is assessed from an analysis of data on a 2D gas of charged bosons. We obtain excellent agreement with data from quantum Monte Carlo studies of the 2D electron gas. In particular, our results for the correlation energy show a quantum phase transition occurring at coupling strength r_s≈24 from the paramagnetic to the fully spin-polarized fluid.     

Short-range correlation in electron gas

Short-range correlation between electrons with antiparallel spins is considered. Electron-electron ladder interactions are shown to be important for the short range correlation in the metallic and lower densities of electrons.     

The surface energy of an electron gas in model crystals

The surface energy of an electron gas in a crystal is considered. The results obtained for a quadratic spectrum are generalized to an arbitrary energy spectrum in certain crystal models. The surface energy of an electron gas with a quadratic spectrum is found for a sample with a rough boundary when the height of irregularities is small compared with the electron wavelength.     

On the energy losses of slow ions in an interacting degenerate electron gas

Energy losses of slow ions with velocitiesv?v _F (v _F is the Fermi velocity) in an interacting degenerate electron gas are calculated on the basis of the dielectric theory of Singwi. It is shown that the local field effects taken into account in this theory lead to an increase of the energy losses as compared with the Lindhard stopping power by a factor which can reach a few tens of percent for some compressed ICF plasmas. Corresponding factors for simple metals are as much as 2–3 and are in agreement with experiment.     

Ground state correlation in the two-dimensional polarized electron gas

The ground state energy and radial distribution functions of the polarized two-dimensional electron gas with valley degeneracyn _v =1 and 2 are calculated using the hypernetted-chain approximation with the effective correlation factor method for Fermions. The paramagnetic susceptibility is calculated and compared with experiment in silicon inversion layers.     

Experimental investigation of nonlocality effects in the electron energy spectrum in an electronegative gas

The nonlocality of the electron energy distribution function (EEDF) in a dc discharge in oxygen is observed experimentally. A method is developed for measuring the isotropic part of the EEDF in a low-temperature plasma of electronegative gases. The radial dependence of the EEDF and the radial distributions of the electron density, the average electron energy, and the potential are determined. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 7, 511–516 (10 April 1996)     

On the Coulomb energy of a finite-temperature electron gas

We rederive the Coulomb expansion of the electron gas average energy at finite temperature, starting from scratch, i.e., using only the framework of the grand canonical ensemble and not the finite-T Green's function formalism. We recover the analytical expressions of the exchange and correlation energy in both the high-T and theT=0 limits. We explicitly show the origin of the crossover of the correlation energy leading term frome ⁴ lne ² at zero temperature toe ³ at finiteT. We also discuss the relative importance of exchange and correlation in both limits.     

Crystallization of an electron gas

The ground state energy of an electron gas that is evaluated by the method of Padé approximants shows a singularity which may be associated with the formation of the Wigner lattice. The energy curve in the vicinity of this singularity is examined, and the pressure and the correlation energy are evaluated. Permanent address: Department of Physics, State University of New York at Buffalo, N.Y., U.S.A.     

Rigorous evaluation of the ring diagram contribution to the ground state energy of an electron gas

The ground state energy and the correlation energy of an electron gas are evaluated rigorously without using the smallr _s expansion and the small momentum-transfer approximation in the ring diagram contribution and taking into consideration the first order and second order exchange graphs. The Fermi momentum is determined by solving the number density equation without using iteration and is compared with that obtained by iteration. The ground state energy is found to stay positive in contrast to the iterative solution which becomes negative beyond a certain value ofr _s .     

Dependence of structure factor and correlation energy on the width of electron wires

The structure factor and correlation energy of a quantum wire of thickness b ? a _B are studied in random phase approximation (RPA) and for the less investigated region r _s < 1. Using the single-loop approximation, analytical expressions of the structure factor are obtained. The exact expressions for the exchange energy are also derived for a cylindrical and harmonic wire. The correlation energy in RPA is found to be represented by ? _c (b, r _s ) = α(r _s )/b + β(r _s ) ln(b) + η(r _s ), for small b and high densities. For a pragmatic width of the wire, the correlation energy is in agreement with the quantum Monte Carlo simulation data.     

Non-local exchange correlation energy in quasi-two-dimensional electron layers

We introduce a simple, non-local approximation for the exchange-correlation energy of an inhomogeneous electron gas. This approximation is shown to be quantitatively accurate in several important limiting cases. The method is used to calculate the non-local exchange-correlation energy for density distributions representing quasi-two-dimensional electron layers. These energies are compared to the widely used three-dimensional local-density approximation and suggest that the latter approximation may contain errors on the order of 10–30% for layer profiles typical of real systems.