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Springer eBooks

An Introduction to Density Functional Theory from the Perspective of the Independent-Particle Model and Its Corrections

Eugene S. Kryachko, Eduardo V. Ludeña

Published Jan 1, 1990• 1 citation
Publisher
DOI
10.1007/978-94-009-1970-9_4

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Foundations of Density Functional Theory

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Occupation numbers of natural orbitals capture the physics of strong electron correlations in momentum space. A natural orbital density functional theory based on the antisymmetrized geminal product provides these occupation numbers and the corresponding electron momentum density. A practical implementation of this theory approximates the natural orbitals by the Kohn–Sham orbitals and uses a mean-field approach to estimate pairing amplitudes leading to corrections for the independent particle model. The method is applied to weakly doped La2CuO4.
Abstract The doubly differential cross-section for weak inelastic scattering of waves or particles by manybody systems is derived in Born approximation and expressed in terms of the dynamic structure factor according to van Hove. The application of this very general scheme to scattering of neutrons, x-rays and high-energy electrons is discussed briefly. The dynamic structure factor, which is the space and time Fourier transform of the density-density correlation function, is a property of the many-body system independent of the external probe and carries information on the excitation spectrum of the system. The relation of the electronic structure factor to the density-density response function defined in linear-response theory is shown using the fluctuation-dissipation theorem. This is important for calculations, since the response function can be calculated approximately from the independent-particle response function in self-consistent field approximations, such as the random-phase approximation or the local-density approximation of the density functional theory. Since the density-density response function also determines the dielectric function, the dynamic structure can be expressed by the dielectric function.