Non-orthogonal orbitals in intermediate valency

In a previous paper (ibid., vol.9, p.1417 (1976)) it was suggested that intermediate valence in SmS might be regarded as due to configuration mixing at each Sm site, one configuration having a 4f electron excited into a less localised orbital constructed of 5d-6s Wannier orbitals on adjacent sites. This idea is followed in more detail, in a model system which has two types of localised orbitals, tightly bound s-orbitals and less localised S-orbitals. The S-orbitals are combined to form chi orbitals which are more extended and which are non-orthogonal. It is shown that the complication which might then be anticipated is manageable and that the use of non-orthogonal orbitals leads to a better description of the ground state of a model intermediate valence system than has yet been obtained by any other method. The method is essentially based on the variational principle. It is shown that a particular choice leads to a standard result, and a better choice leads to a lower mean energy. The method can probably be applied to a number of related problems.