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Approximate ansatz for the expansion of the spherically averaged wave function in terms of interelectronic separation r 12 for the Hookean atom, atomic ions, and the H 2 molecule
Author(s) -
Amovilli C.,
Nagy Á.,
March N. H.
Publication year - 2003
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.10705
Subject(s) - ansatz , wave function , electron , atom (system on chip) , ground state , physics , ion , atomic physics , function (biology) , quantum mechanics , chemistry , evolutionary biology , computer science , biology , embedded system
Abstract For the two‐electron Hookean atom, it is first emphasized that, for a specific force constant k = 1/4, the ground‐state wave function has a simple dependence on the interelectronic separation r 12 , namely, (1 + ½ r 12 )exp(−⅛ r 2 12 ). For this two‐electron model, therefore, the study of Rassolov and Chipman on the electron–electron cusp conditions on the spherically averaged wave function for the N electron atomic ions can be generalized to all orders in the interelectronic separation r 12 . This Hookean model has therefore been used to give some justification for an ansatz for the spherically averaged wave function in atomic ions with N electrons for N ≥ 2. Several approximate two‐electron wave functions satisfying the Rassolov and Chipman conditions were tested and found to give excellent results. Another ansatz has been tested numerically on the ground state of two‐electron atomic ions and the H 2 molecule. Finally, for the Hookean atom a partial differential equation that is essentially for the pair correlation density is given in the Appendix. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 95: 21–29, 2003