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Title
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Force-balance and differential equation for the ground-state electron density in atoms and molecules
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Author
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Abstract
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| Holas and March (1995) established a force-balance equation from the many-electron Schrodinger equation. Here, we propose this as a basis for the construction of a (usually approximate) differential equation for the ground-state electron density. By way of example we present the simple case of two-electron systems with different external potentials bur with weak electron-electron Coulomb repulsion lambda e(2)/r(12). In this case first-order Rayleigh-Schrodinger (RS) perturbation theory of the ground-state wave function is known to lead to a compact expression for the first-order density matrix gamma(r, r') in terms of its diagonal density rho(r) and the density corresponding to lambda = 0. This result allows the force-balance equation to be written as a third-order linear, differential homogeneous equation for the ground-state electron density rho(r). The example of the two-electron Hookean atom is treated: For this case one can also transcend the first-order RS perturbation theory and get exact results for discrete choices of force constants (external potential). (C) 2000 John Wiley & Sons, Inc. |
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Language
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English
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Source (journal)
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International journal of quantum chemistry. - New York, N.Y., 1967, currens
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Publication
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New York, N.Y.
:
Wiley
,
2000
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ISSN
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0020-7608
[print]
1097-461X
[online]
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Volume/pages
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77
:4
(2000)
, p. 716-720
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ISI
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000085977200004
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Full text (Publisher's DOI)
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Full text (publisher's version - intranet only)
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