ELECTRONIC STRUCTURES OF CRYSTALLINE AND AMORPHOUS SiO2

Spin correlations in an interacting electron liquid are studied in the high-frequency limit and in both two and three dimensions. The third-moment sum rule is evaluated and is used to derive exact limiting forms (at both long and short wavelengths) for the spin-antisymmetric local-field factor, limω→∞G-(q,ω). In two dimensions limω→∞G-(q,ω) is found to diverge as 1/q at long wavelengths, and the spin-antisymmetric exchange-correlation kernel of time-dependent spin density functional theory diverges as 1/q2 in both two and three dimensions. These signal a failure of the local-density approximation, one that can be redressed by alternative approaches.

Correlation effects and the high-frequency spin susceptibility of an electron liquid: Exact limits

The approximation method developed by Lobo et al. for classical distribution function is applied to the spin dependent Wigner distribution function in a quantum system. A quantum mechanical expression for generalized spin susceptibility of an interacting electron gas is derived. Self-consistent numerical calculations of magnetic structure factor and generalized spin susceptibility are carried out for an electron gas at metallic density of electrons. Spin dependent pair distribution function and static spin susceptibility are numerically calculated from the calculated magnetic structure factor. The results for the pair distribution function for antiparallel spins are found to be positive for the entire range of real metallic density of electrons.

Electron Correlations at Metallic Densities. III. Generalized Spin Susceptibility and Spin Correlation

A scheme which allows one to calculate the effect of the lattice on the density response function of an electron gas is considered. This is based upon summing an infinite subset of gradient terms in the density functional theory of the exchange and correlation energy of the electrons. The scheme contains both the local density approximation and the uniform gas limit as special cases. The effect of a single gradient correction term to the local density approximation is investigated, and it is shown that this effect can be significant.

Bloch wave effects in the density response function

As a step in the calculation of gradient terms to the exchange and correlation energy in the spin-density functional theory, the authors consider the perturbation expansion of this energy for a paramagnetic electron gas. It is shown that the two relevant kernels can be expressed exactly in terms of the density and magnetisation dependence of the pair functions for the inhomogeneous gas. A method based upon the fitting of the third frequency moments of the density and spin-density response functions is used to calculate the perturbation kernels for a range of electron density. It is shown that the correlation contribution to these kernels can be substantial.

The exchange and correlation energy of a spin-polarised electron gas

A nonlinear integral equation for the ground-state magnetic structure factor S ~ (k) of an electron liquid has been obtained by using a method originally due to Mihara and Puff. This equation is solved self-consistently to get the values of S ~ (k) which are used to estimate the pair correlation functions of electrons with parallel and antiparallel spins. The results obtained compare favorably with that of earlier sophisticated calculations.

Spin correlations in an electron liquid at metallic densities

Structure Factor of the Electron Liquid from the Moment Sum Rules

The effects of exchange and correlations on the diamagnetic susceptibility of an interacting electron gas are investigated using the double-time Green's-function method. The equation of motion of the appropriate Green's function is linearized using a moment-conserving decoupling approximation. The many-body corrections to the diamagnetic susceptibility at metallic densities are found to be small. The present expression reduces to the exact result in the high-density limit. Many of the results of earlier calculations also follow from our expression for the diamagnetic susceptibility.

H. B. Singh

Papers

Spin correlations in an electron liquid at metallic densities

Structure Factor of the Electron Liquid from the Moment Sum Rules

Diamagnetic susceptibility of an interacting electron gas

Spin susceptibility of simple metals

A sum rule for the transverse current correlation function in an electron liquid