Use of Pseudopotentials in Atomic-Structure Calculations

Abstract

Taking the general point of view that the ideas of pseudopotential analysis can be usefully applied to the removal of orthogonality constraints in a wide class of problems, we describe a generalization of the method of pseudopotentials which is applicable to many‐electron systems. The generalized pseudopotential derived herein reduces to the phillips–Kleinman pseudopotential under the one‐electron Hartree–Fock approximation, and a study of its structure helps to clarify some of the properties of one‐electron pseudopotentials. The generalized formalism is then applied to ions with one valence electron, such as Be⁺ and Mg⁺, where it suggests a simple model potential which gives a good description of the Rydberg spectra of these ions. The relationship of the pseudopotential to the model potential is discussed. The theory is then applied to atoms with two valence electrons, such as Be and Mg, and it is shown how the use of one‐electron pseudopotentials or model potentials can simplify, for example, the “exact pair” equations describing the motion of the valence‐electron pair in the Hartree–Fock sea and permit the removal of orthogonality constraints on the pair wavefunction. Good results are obtained in calculations of the valence‐pair energy of Be and Mg. Further approximations are discussed which allow calculation of the valence‐pair energy when the core orbitals are not known. The approximate methods are applied to Be, Mg, and Sr with good results.