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Computation 2016, 4(3), 30; doi:10.3390/computation4030030

Electron Correlations in Local Effective Potential Theory

1
The Graduate School of the City University of New York, New York, NY 10016, USA
2
Department of Physics, Ningbo University, Ningbo 315211, China
*
Author to whom correspondence should be addressed.
Academic Editors: Karlheinz Schwarz and Agnes Nagy
Received: 22 June 2016 / Revised: 8 August 2016 / Accepted: 10 August 2016 / Published: 16 August 2016
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Abstract

Local effective potential theory, both stationary-state and time-dependent, constitutes the mapping from a system of electrons in an external field to one of the noninteracting fermions possessing the same basic variable such as the density, thereby enabling the determination of the energy and other properties of the electronic system. This paper is a description via Quantal Density Functional Theory (QDFT) of the electron correlations that must be accounted for in such a mapping. It is proved through QDFT that independent of the form of external field, (a) it is possible to map to a model system possessing all the basic variables; and that (b) with the requirement that the model fermions are subject to the same external fields, the only correlations that must be considered are those due to the Pauli exclusion principle, Coulomb repulsion, and Correlation–Kinetic effects. The cases of both a static and time-dependent electromagnetic field, for which the basic variables are the density and physical current density, are considered. The examples of solely an external electrostatic or time-dependent electric field constitute special cases. An efficacious unification in terms of electron correlations, independent of the type of external field, is thereby achieved. The mapping is explicated for the example of a quantum dot in a magnetostatic field, and for a quantum dot in a magnetostatic and time-dependent electric field. View Full-Text
Keywords: electron correlations; local effective potential theory in electromagnetic fields; quantal density functional theory; Kohn-Sham density functional theory; Runge-Gross density functional theory electron correlations; local effective potential theory in electromagnetic fields; quantal density functional theory; Kohn-Sham density functional theory; Runge-Gross density functional theory
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Sahni, V.; Pan, X.-Y.; Yang, T. Electron Correlations in Local Effective Potential Theory. Computation 2016, 4, 30.

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