Approximate ansatz for the expansion of the spherically averaged wave function in terms of interelectronic separation <tex>$r_{12}$</tex> for the Hookean atom, atomic ions, and the <tex>$H_{2}$</tex> moleculeApproximate ansatz for the expansion of the spherically averaged wave function in terms of interelectronic separation <tex>$r_{12}$</tex> for the Hookean atom, atomic ions, and the <tex>$H_{2}$</tex> molecule
Faculty of Sciences. Physics

Department of Physics

article

2003New York, N.Y., 2003

Mathematics

Physics

Chemistry

International journal of quantum chemistry. - New York, N.Y.

95(2003):1, p. 21-29

0020-7608

000185157200002

E

English (eng)

University of Antwerp

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 + (1)/(2)r(12))exp(-(1)/(8)r(12)(2)). 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 greater than or equal to 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. (C) 2003 Wiley Periodicals, Inc. Int J Quantum Chem 95: 21-29, 2003.

https://repository.uantwerpen.be/docman/irua/04165e/5872.pdf

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