Compact representation of helium wave functions in perimetric and hyperspherical coordinates

A basis set representation which includes an explicit treatment of the Fock expansion in hyperspherical coordinates, was used for variational calculations of the ground-state energy of helium. The Fock functions provided the exact analytic structure of the true wave function when two electrons coalesced near the nucleus. The modified Gauss-Laguerre quadrature allowed an accurate numerical evaluation of integrals containing logarithms of the hyperradius. The results demonstrate that the convergence rate of a nearly orthogonal basis set, such as the triple product of Laguerre polynomials in perimetric coordinates, may be improved through the addition of a few specially designed basis functions.