Statistical theory of electron densities at nonzero temperatures

1992 ◽  
Vol 70 (2) ◽  
pp. 478-481 ◽  
Author(s):  
Gary G. Hoffman ◽  
Robert A. Harris ◽  
Lawrence R. Pratt
Keyword(s):  
Statistical Theory ◽  
Electron Density ◽  
Ground State ◽  
Finite Temperature ◽  
Density Functional ◽  
Plasma Chemistry ◽  
Plasma Simulation ◽  
Fermi Theory ◽  
Electron Densities ◽  
Thomas Fermi

This paper derives the finite temperature optimized Thomas–Fermi theory applicable to the electronic structure of atoms, molecules, and ions under conditions where both the bulk electron density and the electron temperature are substantial. The derivation provides a simple rule for transcribing the finite temperature case from the previous ground-state statistical electron-density functional theories. Keywords: plasma simulation, plasma chemistry, statistical theory of electron densities, Thomas–Fermi theory, optimized Thomas–Fermi theory.

Statistical theory of electron densities: multiple scattering perturbation theory

1991 ◽  
Vol 435 (1894) ◽  
pp. 245-255 ◽  
Keyword(s):  
Perturbation Theory ◽  
Multiple Scattering ◽  
Electron Density ◽  
Energy Scale ◽  
Zero Order ◽  
Fermi Theory ◽  
Electron Densities ◽  
Thomas Fermi ◽  
Order Contribution ◽  
Explicit Formulae

A multiple scattering perturbation theory for electron densities, originally discussed by N. H. March and A. M. Murray, is derived in a new way. The new derivation does not depend on special choices for the origin of the energy scale. Therefore, it clarifies the point that the result of the perturbation calculation, the electron density, should be independent of the energy origin chosen for the purposes of the calculation even though the individual terms of the series do depend on that choice. This point is not evident in the previous derivations. Appreciation of this point permits adoption of an origin of the energy scale which varies with position without any change in form of the perturbation expansion. This extends the original theory beyond the significant limitation that the zero-order result is the uniform density of the free-electron gas. In particular, the energy origin can be chosen so that the zero-order contribution reproduces any physical model electron density. The theory then gives successive corrections and allows investigation of the usefulness of physical models by an analysis of the low-order corrections. These ideas permit a compact new derivation of the Thomas–Fermi theory, a derivation which also produces explicit formulae for corrections of all orders. An especially useful choice for the energy origin yields the optimized Thomas–Fermi theory as the zero-order contribution. Therefore, new results of this development are explicit formulae for the corrections to that simple theory.

Is it Reasonable to Obtain Information on the Polarizability and Hyperpolarizability Only from the Electron Density?

2018 ◽  
Vol 71 (4) ◽  
pp. 295 ◽  
Author(s):  
Dylan Jayatilaka ◽  
Kunal K. Jha ◽  
Parthapratim Munshi
Keyword(s):  
Density Matrix ◽  
Electron Density ◽  
Ground State ◽  
Density Functional ◽  
Particle Density ◽  
Density Matrices ◽  
Hartree Fock ◽  
Electron Density Matrix ◽  
Ground State Electron ◽  
Side Result

Formulae for the static electronic polarizability and hyperpolarizability are derived in terms of moments of the ground-state electron density matrix by applying the Unsöld approximation and a generalization of the Fermi-Amaldi approximation. The latter formula for the hyperpolarizability appears to be new. The formulae manifestly transform correctly under rotations, and they are observed to be essentially cumulant expressions. Consequently, they are additive over different regions. The properties of the formula are discussed in relation to others that have been proposed in order to clarify inconsistencies. The formulae are then tested against coupled-perturbed Hartree-Fock results for a set of 40 donor-π-acceptor systems. For the polarizability, the correlation is reasonable; therefore, electron density matrix moments from theory or experiment may be used to predict polarizabilities. By constrast, the results for the hyperpolarizabilities are poor, not even within one or two orders of magnitude. The formula for the two- and three-particle density matrices obtained as a side result in this work may be interesting for density functional theories.

The Electron Density in the Thomas-Fermi Theory

1973 ◽  
Vol 41 (7) ◽  
pp. 906-909 ◽  
Author(s):  
David R. Harrington
Keyword(s):  
Electron Density ◽  
Fermi Theory ◽  
Thomas Fermi

Variationally Determined Occupation "Numbers" in an Extended Thomas-Fermi Scheme

1984 ◽  
Vol 39 (10) ◽  
pp. 919-923
Author(s):  
A. M. K. Müller
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Step Function ◽  
Correlation Effects ◽  
Fermi Theory ◽  
Functional Theory ◽  
Thomas Fermi ◽  
Occupation Numbers ◽  
The Density Functional Theory ◽  
Future Work

Abstract Thomas-Fermi theory is generalized by the introduction of an occupation distribution function f(s). The ansatz f(s) = Ɵ (s1 - s) of the conventional TF theory is derived from a variational principle. The implications with respect to the density functional theory are discussed. Future work is intended to include interaction, leading to deviations from the step function, which will account for correlation effects.

Many-Electron Problem in Terms of the Density: From Thomas–Fermi to Modern Density-Functional Theory

2003 ◽  
Vol 02 (02) ◽  
pp. 301-322 ◽  
Author(s):  
Manoj K. Harbola ◽  
Arup Banerjee
Keyword(s):  
Density Functional Theory ◽  
Perturbation Theory ◽  
Electron Density ◽  
Current Density ◽  
Density Functional ◽  
Electron System ◽  
Time Dependent ◽  
Functional Theory ◽  
Thomas Fermi ◽  
Alkali Metal Clusters

In this paper we focus on the use of electron density and current-density as basic variables in describing a many-electron system. We start with a discussion of the seminal Thomas–Fermi theory and its extension by Bloch for time-dependent hamiltonians. We then present modern density-functional theory (for both time-independent and time-dependent hamiltonians) and approximations involved in implementing it. Also discussed is perturbation theory in terms of electron density and its use for calculating various response properties and related quantities. In particular, van der Waals coefficient C6 is calculated using density and current density in time-dependent perturbation theory. Throughout the paper, results for alkali-metal clusters are presented to demonstrate the strength of density-based theories.

Ground state of alloys by the method of the electron density functional

1978 ◽  
Vol 21 (11) ◽  
pp. 1416-1420
Author(s):  
V. M. Kuznetsov ◽  
S. A. Beznosyuk ◽  
Yu. A. Khon ◽  
V. P. Fadin
Keyword(s):  
Electron Density ◽  
Ground State ◽  
Density Functional
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