Basis functions for electronic structure calculations on spheres

Abstract

We introduce a new basis function (the spherical gaussian) for electronic structure calculations on spheres of any dimension $D$. We find \alert{general} expressions for the one- and two-electron integrals and propose an efficient computational algorithm incorporating the Cauchy-Schwarz bound. Using numerical calculations for the $D=2$ case, we show that spherical gaussians are more efficient than spherical harmonics when the electrons are strongly localized.

11 pages, 1 figure, accepted for publication in the Journal of Chemical Physics

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• Uniform electron gases: III. Low-density gases on three-dimensional spheres
• Homogeneous electron gas in arbitrary dimensions