Showing papers on "Orbital-free density functional theory published in 1957"

Statistical Theory of Many-Electron Systems. General Considerations Pertaining to the Thomas-Fermi Theory

Abstract: The density matrix for a many-electron system has been examined with a view toward extending the statistical theory of Thomas and Fermi. The single-particle density matrix is expanded in terms of a power series in $\ensuremath{\hbar}$, according to a procedure developed here for operators consisting of a series of powers of the classical Hamiltonian, the zeroth-order terms corresponding to the Thomas-Fermi theory. Second-order terms in the expansion are identifiable in the expression for the energy: they correspond to exchange energy, the Weizs\"acker inhomogeneity correction for the kinetic energy and, possibly, correlation energy. Their presence follows from the expansion procedure, rather than from an a priori insertion into the theory.While the development here has been concerned mainly with the single-particle density function at the absolute zero of temperature, the procedure has been developed in sufficiently general terms to permit an evaluation to be made of the many-electron density matrix as a function of temperature.The results which have been obtained have been utilized to modify the theory of Fermi and Amaldi which has then been applied to the following atomic states: H ($^{2}S$), He ($^{1}S$), He ($^{3}S$), ${\mathrm{C}}^{++}$ ($^{1}S$), O ($^{1}S$). The disparity between the calculated energy for He ($^{3}S$) and the observed value is less than 6%, while for the remaining cases the disparity does not exceed 2.5%. The radial densities obtained correspond roughly to available quantum densities; they fail, however, to indicate any "shell-structure" nor to display the expected behavior for distances very close to, or very far from the atomic nucleus.