Half theory. II. The application of fractional spherical harmonics to chemical bonding

In this paper, we use fractional hydrogenic wave functions as trial functions in a variational calculation of the ground state energies of the H2+ ion and the He atom. We find improved estimates over those obtained using the standard integer angular momentum atomic trial states. We will see that a benefit of using these fractional functions is the generation of a directional charge distribution, which may serve to orient the atoms in chemical bonds.