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On the relationship between the electron‐pair distribution function and the correlation energy of an atom
Author(s) -
Ugalde J. M.,
Boyd Russell J.
Publication year - 1986
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560290102
Subject(s) - atom (system on chip) , radial distribution function , physics , electronic correlation , correlation , atomic physics , energy (signal processing) , correlation function (quantum field theory) , virial theorem , total correlation , helium atom , distribution (mathematics) , ground state , function (biology) , electron , quantum mechanics , helium , mathematics , molecular dynamics , geometry , evolutionary biology , galaxy , computer science , dielectric , biology , embedded system , mathematical analysis
The pair distribution function h ( r 12 ; r 1 , γ) and the virial theorem are used to derive a general expression for the local contributions to the total correlation energy of an atom. A direct link between correlation effects and the correlation energy is obtained by use of G ( r 1 , γ) and Γ( r 1 , y ). The former is the probability associated with a given choice of r 1 and γ, while the latter describes the local contribution to the correlation energy. Explicit calculations for the ground state of helium indicate that the angular dependence of the local contribution to the correlation energy is essentially independent of r 1 , whereas the local correlation energy shows a strong r 1 dependence. The maximum contribution to the correlation energy occurs at intermediate values of γ where there is close agreement between the Hartree–Fock and exact densities.