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Orbital functionals in density-matrix- and current-density-functional theory

Abstract

Density-Functional Theory (DFT), although widely used and very successful in the calculation of several observables, fails to correctly describe strongly correlated materials. In the first part of this work we, therefore, introduce reduced-densitymatrix- functional theory (RDMFT) which is one possible way to treat electron correlation beyond DFT. Within this theory the one-body reduced density matrix (1- RDM) is used as the basic variable. Our main interest is the calculation of the fundamental gap which proves very problematic within DFT. In order to calculate the fundamental gap we generalize RDMFT to fractional particle numbers M by describing the system as an ensemble of an N and an N+1 particle system (with N{<=}M{<=}N+1). For each fixed particle number, M, the total energy is minimized with respect to the natural orbitals and their occupation numbers. This leads to the total energy as a function of M. The derivative of this function with respect to the particle number has a discontinuity at integer particle number which is identical to the gap. In addition, we investigate the necessary and sufficient conditions for the 1- RDM of a system with fractional particle number to be N-representable. Numerical results are presented for alkali atoms, small molecules, and  More>>
Authors:
Publication Date:
May 15, 2006
Product Type:
Thesis/Dissertation
Report Number:
INIS-DE-0141
Resource Relation:
Other Information: TH: Diss.
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; FUNCTIONALS; DENSITY MATRIX; CURRENT DENSITY; ELECTRON CORRELATION; ATOMS; MOLECULES; OCCUPATION NUMBER; MAGNETIC FIELDS; SPIN; MAGNETIZATION; ELECTRON DENSITY; ELECTRON GAS; ENERGY LEVELS; DENSITY FUNCTIONAL METHOD; ENERGY GAP; MANY-BODY PROBLEM; QUANTUM MECHANICS; ELECTRONIC STRUCTURE; POTENTIALS; QUANTUM DOTS; ALKALI METALS
OSTI ID:
20840991
Research Organizations:
Freie Univ. Berlin (Germany). Fachbereich Physik
Country of Origin:
Germany
Language:
English
Other Identifying Numbers:
TRN: DE07F2982
Availability:
INIS; Commercial reproduction prohibited; OSTI as DE20840991
Submitting Site:
DEN
Size:
107 pages
Announcement Date:
May 07, 2007

Citation Formats

Helbig, N. Orbital functionals in density-matrix- and current-density-functional theory. Germany: N. p., 2006. Web.
Helbig, N. Orbital functionals in density-matrix- and current-density-functional theory. Germany.
Helbig, N. 2006. "Orbital functionals in density-matrix- and current-density-functional theory." Germany.
@misc{etde_20840991,
title = {Orbital functionals in density-matrix- and current-density-functional theory}
author = {Helbig, N}
abstractNote = {Density-Functional Theory (DFT), although widely used and very successful in the calculation of several observables, fails to correctly describe strongly correlated materials. In the first part of this work we, therefore, introduce reduced-densitymatrix- functional theory (RDMFT) which is one possible way to treat electron correlation beyond DFT. Within this theory the one-body reduced density matrix (1- RDM) is used as the basic variable. Our main interest is the calculation of the fundamental gap which proves very problematic within DFT. In order to calculate the fundamental gap we generalize RDMFT to fractional particle numbers M by describing the system as an ensemble of an N and an N+1 particle system (with N{<=}M{<=}N+1). For each fixed particle number, M, the total energy is minimized with respect to the natural orbitals and their occupation numbers. This leads to the total energy as a function of M. The derivative of this function with respect to the particle number has a discontinuity at integer particle number which is identical to the gap. In addition, we investigate the necessary and sufficient conditions for the 1- RDM of a system with fractional particle number to be N-representable. Numerical results are presented for alkali atoms, small molecules, and periodic systems. Another problem within DFT is the description of non-relativistic many-electron systems in the presence of magnetic fields. It requires the paramagnetic current density and the spin magnetization to be used as basic variables besides the electron density. However, electron-gas-based functionals of current-spin-density-functional Theory (CSDFT) exhibit derivative discontinuities as a function of the magnetic field whenever a new Landau level is occupied, which makes them difficult to use in practice. Since the appearance of Landau levels is, intrinsically, an orbital effect it is appealing to use orbital-dependent functionals. We have developed a CSDFT version of the optimized effective potential (OEP) method which allows for the use of explicitly orbital-dependent functionals in the context of CSDFT. We present the derivation of corresponding equations and show results for a quantum dot in external magnetic fields in the second part of this thesis. (orig.)}
place = {Germany}
year = {2006}
month = {May}
}