Combined Configuration-Interaction—Hylleraas-Type Wave-Function Study of the Ground State of the Beryllium Atom

Abstract

A method is proposed for the accurate determination of atomic wave functions and energies by the explicit introduction of interelectronic coordinates into a configuration-interaction wave function. This is accomplished by choosing the configurations in the wave function to be antisymmetrized projected products of one-electron functions with powers of interelectronic coordinates. A 107-configuration wave function for the ground state of the beryllium atom was constructed from a basis set consisting of $s$ and $p$ Slater-type orbitals and powers of interelectronic coordinates: ${r}_{\mathrm{ij}}^{v} (v.=0,1,2)$. The energy obtained from this wave function ($E=\ensuremath{-}14.66654$ a.u.) is an upper bound to the "exact" nonrelativistic energy of this state and it is believed to be within 0.0002a. u. of the "exact" value. The advantages that the present method offers for extending accurate Hylleraas-method calculations to atomic systems with $N>3$ are discussed.