Variational calculations with a hyperspherical basis on atomic helium

We have recently formulated an expansion of the N electron wavefunction in an appropriate set of harmonics on the 3 N-dimensional hypersphere. Angular correlation appears in the usual way, while radial correlation appears as a generalized angular correlation. Calculations on¹S helium have been performed to explore the convergence of this expansion. Energies for various angular approximations have been compared with Bunge's angular limits and show a fractional error <3.5× 10^–4. A theoretical contraction procedure is shown to usefully reduce basis size without forfeiting accuracy.Supported in part by a research grant to the Johns Hopkins University from the National Science Foundation.