  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.
