Improved scheme to solve the atomic Schrödinger equation in hyperspherical coordinates

An improved scheme to accelerate the convergence in the calculations of N-electron atoms, which is based on the exact method we proposed before in hyperspherical coordinates, is presented. The factors influencing the rate of convergence in both parts of expansions in wave function with the hyperspherical harmonics (HHs) of hyperangles and the generalized Laguerre polynomials (GLPs) of hyperradius were investigated. A reselected asymptotic term was introduced by including more structural features in it to accelerate the convergence in the expansion part with the HHs, and a transformation of the hyperradius was used to keep the convergence going properly in the expansion part with the GLPs. Calculations with this scheme for the helium atom were given and compared with some other ones. More accurate results were obtained by considering a simple cusp parameter. © 1996 John Wiley & Sons, Inc.