Gaussian Expansion of Hydrogen-Atom Wavefunctions

The 1s, 2s, 2p, and the four equivalent 3d hydrogen-atom wavefunctions were expanded as linear combinations of functions of the form, exp ( —ar2), without the use of spherical harmonic functions to give angular dependence. The Gaussian functions were located at different points in space in order to give the proper orbital symmetry. Expansion parameters were determined by a variational calculation of the hydrogen-atom energy. Energy errors are 0.2, 0.45, 0.25, and 0.9%, respectively, for the 1s, 2s, 2p, and 3d functions. It is suggested that the approximations are sufficiently accurate to find use in molecular-energy calculations, particularly since integrals involving several centers are more readily evaluated in terms of Gaussian rather than exponential radial functions.