Space partitioning in multiple scattering techniques. I. Hydrogen molecular ion and hydrogen molecule

The use of multiple scattering techniques combined with a statistical exchange potential for the description of the electronic structure of atoms, molecules, and solids depends strongly on the geometry (muffin tin, overlapping spheres, or cellular potentials) and on the form of the electron gas exchange. In this work we compare only the effects of using different geometries. For that purpose we have done calculations on the hydrogen molecular ion and Hartree‐type calculations on the hydrogen molecule so that no exchange effects are involved. To avoid arbitrariness in the choice of the sphere sizes we propose a nonempirical criterion that consists of using the set of radii that will minimize the charge in the interstitial region of the molecule or cluster. Some arguments are given to justify this criterion, and to clarify the differences between cellular, overlapping spheres, and muffin‐tin geometries. It is found that the cellular geometry gives a very good description around the equilibrium internuclear distance. However, for most systems of interest, exchange will be present. Thus, we have done, for comparison, the calculation on H 2 using X αβ statistical exchange. It is shown through this calculation that some of the correlation energy may be obtained by redefining the molecular orbitals in terms of non‐paired‐spins spatial orbitals, this formulation being required to obtain the correct free‐atom limit.