Orbital Approximation to Spatial Eigenfunctions of the Many-Electron Hamiltonian

A new procedure is developed for calculating the best wavefunction for an N-electron atom in terms of N one-electron orbitals which are eigenfunctions of l2, lz and sz. This is a special case of a method for calculating the best wavefunction in terms of N orbitals unrestricted in angular momentum but restricted in spin component and is thus a partial generalization of Löwdin's EHF method. We calculate approximate spatial eigenfunctions of H using the function Φ[α,λ] = Dλλ[α] ∑ i = 1k δiPiφ, where φ is a product of N spatial orbitals and where the Pi are the k permutations out of which k linearly independent projections onto the Young tableau [α,λ] can be obtained. The method gives an improvement to each of Goddard's GI solutions in such a way that they all give the same energy when fully minimized, while only involving k−1 additional parameters. For Li atom there is only one additional parameter and calculations are performed using Goddard's GI and GF orbitals, obtaining small improvements in the energy. An energy of −7.4477076 a.u. is obtained.