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Phys. Rev. A 30, 2745–2748 (1984)

Exact differential equation for the density and ionization energy of a many-particle system

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Mel Levy
Institute for Theoretical Physics, University of California, Santa Barbara, California 93106 and Chemistry Department and Quantum Theory Group, Tulane University, New Orleans, Louisiana 70118

John P. Perdew
Institute for Theoretical Physics, University of California, Santa Barbara, California 93106 and Physics Department and Quantum Theory Group, Tulane University, New Orleans, Louisiana 70118

Viraht Sahni
Institute for Theoretical Physics, University of California, Santa Barbara, California 93106 and Physics Department, Brooklyn College of the City University of New York, Brooklyn, New York 11210

Received 11 August 1983; revised 23 July 1984; published in the issue dated November 1984

The ground-state density n of a many-electron system obeys a Schrödinger-like differential equation for n1/2(r⃗), which may be solved by standard Kohn-Sham programs. The exact local effective (nonexternal) potential, veff(r⃗), is displayed explicitly in terms of wave-function expectation values, from which veff(r⃗)>~0 for all r⃗. A derivation for n as |r⃗|→∞ implies that this new effective potential tends asymptotically to zero, as does the exact Kohn-Sham potential, with the highest occupied eigenvalue as the exact ionization energy. A new exact expression is also presented for the exchange-correlation hole density ρxc(r⃗, r⃗′) about an electron at r⃗, as |r⃗|→∞.

© 1984 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevA.30.2745
DOI:
10.1103/PhysRevA.30.2745
PACS:
 
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