Abstract
The determination of the ground state energy and the ground state electron density distribution of a many-electron system in a fixed external potential is a problem of major importance in condensed matter physics. For a given Hamiltonian and for specified boundary conditions, it is possible in principle to obtain directly numerical solutions of the the Schrodinger equation. Even with current generations of computers, this is feasible in practice only for systems of rather small total electron number. Of course, a variety of alternative methods, such as self-consistent mean field theories, also exist. However, these are approximate.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
P. Hohenberg and W. Kohn, Phys. Rev. B. 136, 864 (1964).
W. Kohn and L.J. Sham, Phys. Rev. 140, A1133 (1965).
N.D. Mermin, Phys. Rev. 137, A1441 (1965).
W. Kohn and P. Vashishta, in Theory of the Inhomogeneous Electron Gas, edited by S. Lundqvist and N.H. March (Plenum, New York, 1983), p. 79.
D. Pines and P. Nozieres, The Theory of Quantum Liquids, (Benjamin, New York, 1966).
D.J.W. Geldart and M. Rasolt, in The Single Particle Density in Physics and Chem istry, edited by N.H. March and B.M. Deb (Academic, London, 1987), p. 151.
D.J.W. Geldart and M. Rasolt, in Strongly Correlated Electron Systems, edited by M.P. Das and D. Neilson (Nova Science Publishers, New York, 1992).
K.G. Wilson and J. Kogut, Phys. Reports. 12, 75 (1974).
S-K. Ma and K.A. Brueckner, Phys. Rev. 165, 18 (1968).
L.J. Sham, in Computational Methods in Band Theory, edited by P.J. Marcus, J.F. Janak, and A.R. Williams (Plenum, New York, 1971), p. 458.
D.J.W. Geldart and M. Rasolt, Report submitted to the National Research Council of Canada (1972).
L. Kleinman, Phys. Rev. B. 10, 2221 (1974).
D.J.W. Geldart. M. Rasolt, and CO. Ambladh, Sol. State Commun. 16, 243 (1975).
M. Rasolt and D.J.W. Geldart, Phys. Rev. Lett. 35, 1234 (1975).
D.J.W. Geldart and M. Rasolt, Phys. Rev. B. 13, 1477 (1976).
It may be convenient to consider the entire system to be confined within a very large container having inpenetrable walls if realistic equilibrium of vapour and condensed phases is important. In cases of immediate interest, the true vapour phase is not an essential feature and the relatively small volume occupied by the condensed phase is the more important thermodynamical variable. There are still subtleties associated with taking the thermodynamic limit, particularly when isolating surface and bulk effects, but the problems with vanishing density of particles can be controlled.
D.J.W. Geldart and R. Taylor, Can. J. Phys. 48, 155 (1970).
A.D. Becke, Phys. Rev. A. 38, 3098 (1988). References to other work aimed at providing generalizations of simple gradient expansions are also given in this work.
D.J.W. Geldart, E. Dunlap, M.L. Glasser, and M.R.A. Shegelski, Sol. State Commun. 88, 81 (1993).
E. Dunlap and D.J.W. Geldart, Can. J. Phys. 72, 1 (1994).
M.L. Glasser, D.J.W. Geldart, and E. Dunlap, Can. J. Phys. 72, 7 (1994).
M.R.A. Shegelski, D.J.W. Geldart, M.L. Glasser and D. Neilson, Can. J. Phys. 72, 14 (1994).
J.A. Chevary and S.H. Vosko, Phys. Rev. B. 42, 5320 (1990). This paper also contains references to earlier numerical work.
E. Engel and S.H. Vosko, Phys. Rev. B. 42, 4940 (1990).
F. Herman, J.P. Van Dyke, and I.B. Ortenburger, Phys. Rev. Lett. 22, 807 (1969).
A.M. Boring, Phys. Rev. B. 2, 1506 (1970).
A.D. Becke, J. Chem. Phys. 84, 4524 (1986).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media New York
About this chapter
Cite this chapter
Geldart, D.J.W. (1995). Energy Functionals: Gradient Expansions and Beyond. In: Gross, E.K.U., Dreizler, R.M. (eds) Density Functional Theory. NATO ASI Series, vol 337. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9975-0_3
Download citation
DOI: https://doi.org/10.1007/978-1-4757-9975-0_3
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4757-9977-4
Online ISBN: 978-1-4757-9975-0
eBook Packages: Springer Book Archive