Correlation Energies and Angular Components of the Wave Functions of the Ground States ofH−, He i, and Li ii

With a view to examining the effects of configuration interaction in the ground state of the three simple atomic systems, ${\mathrm{H}}^{-}$, He i, and Li ii, a three-parameter variational function involving a symmetrized exponential in the nuclear distances and a linear factor in the interelectron distance has been obtained for He i and Li ii. These functions together with the one of the same type already in existence for ${\mathrm{H}}^{-}$ have been expanded in series of Legendre functions of the cosine of the angle between the two radius vectors. The coefficients in these expansions are functions of the nuclear distances of the two electrons. The various component functions are presented, together with the coefficients with which they enter the expansions, and their contributions to the total energies. A discussion is given of the method of estimating the magnitude of the total correlation, or configuration interaction, energy and its radial, angular, and mixed parts. A table is given of the values of the correlation energy and its various parts for ${\mathrm{H}}^{-}$, He i, and Li ii.