Z-1/2 expansion of the unrestricted Hartree-Fock equations for the ground state of lithium

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Abstract
The unrestricted Hartree-Fock equations are discussed for a wave function of the form det║aα, bβ, cα║+ det║bα, aβ, cα║. This is an eigenfunction of S2. The 1s-orbital functions a and b are expanded in powers of Z-1/2, while the 2s-orbital function c contains only powers of Z-1. These are evaluated to first order, from which the energy is obtained to third order. It is found that the second-order energy coefficient is a substantial improvement on that obtained from a single-determinantal wave function. The rate of convergence of the energy series is improved by means of scaling, so that the energy is expanded in powers of Z-s. For large values of Z the other spin eigenfunction involving a, b and c should be included in the wave function.