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On the determination of radial electron–electron distribution functions
Author(s) -
Benesch Robert
Publication year - 1972
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.560060114
Subject(s) - electron , physics , atomic physics , matrix (chemical analysis) , function (biology) , distribution (mathematics) , spin (aerodynamics) , electron density , distribution function , chemistry , quantum mechanics , mathematics , mathematical analysis , thermodynamics , chromatography , evolutionary biology , biology
The problem of evaluating the radial electron–electron distribution function P 0 ( r 12 ) from the spin‐free 2‐particle density matrix P (2) ( r 1 , r 2 I r' 1 , r' 2 ) is considered in detail. The analysis is first applied to 2‐electron S ‐type functions built from l 2 configurations. For the special case l = 0, the expression for P 0 ( r 12 ) reduces to the result obtained by Coulson and Neilson. For non‐spherically symmetric states of N ‐electron atoms, the angular integrations are handled by a procedure used by Calais and Löwdin in their evaluation of atomic integrals containing functions of r 12 . Consideration is also given to the evaluation of necessary radial integrals.