Title
Force-balance and differential equation for the ground-state electron density in atoms and molecules
Author
Faculty/Department
Faculty of Sciences. Physics
Publication type
article
Publication
New York, N.Y. ,
Subject
Mathematics
Physics
Chemistry
Source (journal)
International journal of quantum chemistry. - New York, N.Y.
Volume/pages
77(2000) :4 , p. 716-720
ISSN
0020-7608
ISI
000085977200004
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
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.
E-info
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