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Exchange and correlation in density functional theory of atoms and molecules

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Density Functional Theory I

Part of the book series: Topics in Current Chemistry ((TOPCURRCHEM,volume 180))

Abstract

The exchange and correlation energies and potentials, occurring in various density functional theory approaches and schemes are reviewed and their definitions compared. The ways of their determination and their long-range properties are discussed. General expressions for the exchange and correlation energy and the long-range asymptotic form of the exchange potential are obtained for mixed-state systems. Line-integral expressions for the exchange and correlation potentials, valid both for pure-state and mixed-state systems are derived. Approximation to the electrostatic-plus-exchange energy and corresponding potential for arbitrary mixed-state systems and approximation to the correlation energy and potential for a specific class of mixed-state systems are proposed. They are expressible in terms of any approximate functional of the density for the exchange energy and correlation energy, respectively, known for pure-state systems.

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Abbreviations

DFT:

density functional theory

DM:

density matrix

DS:

Dirac-Slater

GS:

ground-state

HF:

Hartree-Fock

HK:

Hohenberg-Kohn

KS:

Kohn-Sham

OP:

optimized potential

QM:

quantum mechanical

SCS:

spin compensated system

TFD:

Thomas-Fermi-Dirac

app:

approximate

c:

correlation

D:

determinantal

ee:

electron-electron (interaction)

eff:

effective

ens:

ensemble

es:

electrostatic

ext:

external

ferro:

ferromagnetic

ncl:

non-classical

para:

paramagnetic

s:

single-particle (noninteracting)

x:

exchange

xc:

exchange-correlation

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Author information

Authors and Affiliations

  1. Institute of Physical Chemistry of the Polish Academy of Sciences, 44/52 Kasprzaka, PL-01-224, Warsaw, Poland

    A. Holas

  2. Inorganic Chemistry Laboratory, University of Oxford, South Parks Road, OX1 3QR, Oxford, England

    N. H. March

Authors
  1. A. Holas
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  2. N. H. March
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Editor information

R. F. Nalewajski

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© 1996 Springer-Verlag

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Holas, A., March, N.H. (1996). Exchange and correlation in density functional theory of atoms and molecules. In: Nalewajski, R.F. (eds) Density Functional Theory I. Topics in Current Chemistry, vol 180. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61091-X_3

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  • DOI: https://doi.org/10.1007/3-540-61091-X_3

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61091-5

  • Online ISBN: 978-3-540-49945-9

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