Self-consistent solution of Kohn-Sham equations for infinitely extended systems with inhomogeneous electron gas

Journal Article · Wed Jul 15 00:00:00 EDT 2009 · Journal of Experimental and Theoretical Physics

DOI:https://doi.org/10.1134/S1063776109070188· OSTI ID:21457162

Posvyanskii, D. V., E-mail: [e-mail]; Shul'man, A. Ya., E-mail: ash@cplire.r ^[1]

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1. Russian Academy of Sciences, Kotel'nikov Institute of Radio Engineering and Electronics (Russian Federation)

The density functional approach in the Kohn-Sham approximation is widely used to study properties of many-electron systems. Due to the nonlinearity of the Kohn-Sham equations, the general self-consistence searching method involves iterations with alternate solving of the Poisson and Schroedinger equations. One of problems of such an approach is that the charge distribution renewed by means of the solution of the Schroedinger equation does not conform to boundary conditions of the Poisson equation for the Coulomb potential. The resulting instability or even divergence of iterations manifests itself most appreciably in the case of infinitely extended systems. The known attempts to deal with this problem are reduced in fact to abandoning the original iterative method and replacing it with some approximate calculation scheme, which is usually semi-empirical and does not permit to evaluate the extent of deviation from the exact solution. In this work, we realize the iterative scheme of solving the Kohn-Sham equations for extended systems with inhomogeneous electron gas, which is based on eliminating the long-range character of Coulomb interaction as the cause of tight coupling between charge distribution and boundary conditions. The suggested algorithm is employed to calculate energy the spectrum, self-consistent potential, and electrostatic capacitance of the semi-infinite degenerate electron gas bounded by an infinitely high barrier, as well as the work function and surface energy of simple metals in the model with homogeneous distribution of positive background. The difference between self-consistent Hartree solutions and those taking into account the exchange-correlation interaction is analyzed. The comparison with the results previously published in the literature is carried out. The case study of the metal-semiconductor tunnel contact shows this method as applied to an infinitely extended system where the steady-state current can flow.

• OSTI ID: 21457162
• Journal Information: Journal of Experimental and Theoretical Physics, Vol. 109, Issue 1; Other Information: DOI: 10.1134/S1063776109070188; Copyright (c) 2009 Pleiades Publishing, Ltd.; ISSN 1063-7761
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
APPROXIMATIONS
BOUNDARY CONDITIONS
CAPACITANCE
CHARGE DISTRIBUTION
COMPARATIVE EVALUATIONS
CORRELATIONS
COULOMB FIELD
DENSITY FUNCTIONAL METHOD
ELECTRON GAS
ELECTRONS
EXACT SOLUTIONS
EXCHANGE INTERACTIONS
ITERATIVE METHODS
METALS
POISSON EQUATION
POTENTIALS
SCHROEDINGER EQUATION
SEMICONDUCTOR MATERIALS
SURFACE ENERGY
WORK FUNCTIONS
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
ELECTRIC FIELDS
ELECTRICAL PROPERTIES
ELEMENTARY PARTICLES
ELEMENTS
ENERGY
EQUATIONS
EVALUATION
FERMIONS
FREE ENERGY
FUNCTIONS
INTERACTIONS
LEPTONS
MATERIALS
MATHEMATICAL SOLUTIONS
PARTIAL DIFFERENTIAL EQUATIONS
PHYSICAL PROPERTIES
SURFACE PROPERTIES
THERMODYNAMIC PROPERTIES
VARIATIONAL METHODS
WAVE EQUATIONS