The electron correlation cusp View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1996-12

AUTHORS

Harry F. King

ABSTRACT

The Kais function is an exact solution of the Schrödinger equation for a pair of electrons trapped in a parabolic potential well with r12−1 electron-electron interaction. Partial wave analysis (PWA) of the Kais function yields EL = E + C1(L + \-C−12)−3 + O(L−5) where E is the exact energy and EL the energy of a renormalized finite sum of partial waves omitting all waves with angular momentum ℓ > L. Slight rearrangement of an earlier result by Hill shows that the corresponding full CI energy differs from EL only by terms of order O(L−5) with FCI values of C1 and \-C−12 identical to PWA values. The dimensionless \-C2 parameter is weakly dependent upon the size of the physical system. Its value is 0.788 for the Kais function, and 0.893 for the less diffuse helium atom, and approaches \-C2→ 1 in the limit of an infinitely compact charge distribution. The ℓth energy increment satisfies an approximate virial theorem which becomes exact in the high ℓ limit. This analysis, formulated to facilitate use of the Maple system for symbolic computing, lays the mathematical ground work for subsequent studies of the electron correlation cusp problem. The direction of future papers in this series is outlined. More... »

PAGES

345-381

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf00186448

DOI

http://dx.doi.org/10.1007/bf00186448

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1042199047


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46 schema:description The Kais function is an exact solution of the Schrödinger equation for a pair of electrons trapped in a parabolic potential well with r12−1 electron-electron interaction. Partial wave analysis (PWA) of the Kais function yields EL = E + C1(L + \-C−12)−3 + O(L−5) where E is the exact energy and EL the energy of a renormalized finite sum of partial waves omitting all waves with angular momentum ℓ > L. Slight rearrangement of an earlier result by Hill shows that the corresponding full CI energy differs from EL only by terms of order O(L−5) with FCI values of C1 and \-C−12 identical to PWA values. The dimensionless \-C2 parameter is weakly dependent upon the size of the physical system. Its value is 0.788 for the Kais function, and 0.893 for the less diffuse helium atom, and approaches \-C2→ 1 in the limit of an infinitely compact charge distribution. The ℓth energy increment satisfies an approximate virial theorem which becomes exact in the high ℓ limit. This analysis, formulated to facilitate use of the Maple system for symbolic computing, lays the mathematical ground work for subsequent studies of the electron correlation cusp problem. The direction of future papers in this series is outlined.
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