Elsevier

Chemical Physics Letters

Volume 118, Issue 2, 19 July 1985, Pages 115-119
Chemical Physics Letters

Accurate semiclassical electronic structure from dimensional singularities

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Abstract

A novel semiclassical approach to electronic structure has recently been developed by using 1/D as an expansion parameter, where D is the dimensionality of space. The first few terms of the series have been determined for two-electron atoms, but give poor numerical results for the energy at D = 3. By taking advantage of some exact properties of the energy as a function of D, we are able to evaluate the major contribution from singularities at D = 1. This improves estimates from the first few terms by three orders of magnitude at D = 3. From the singularity analysis we are also able to show that the correlation energy is nearly linear as a function of 1/D, in accord with numerical calculation.

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