Improved Simple Analytical Wave Functions for Atoms

Approximate wave functions for the ground states of He, Be, Ne, and Na+ are constructed which are antisymmetrized products of single Slater orbitals of nonintegral principal quantum numbers, ns,ns′,np, and variable orbital exponents, ζs,ζs′,ζp. Best values for the several parameters n and ζ are determined by the variational method, and the corresponding energies are computed. Significant improvements over the usual integral-n approximations are found; for Na+ there is obtained an energy — 161.44 a.u., compared with the integral-n result — 160.94 a.u. and the Hartree-Fock value — 161.88 a.u. The ground states of the two-electron ions H— through NaX are similarly treated, and the diamagnetic susceptibilities of He, Be, Ne, and Na+ are computed theoretically and compared with observed and other theoretical values.