Maximal Orthogonal Orbitals

Abstract

A set of orthogonal orbitals has been constructed from a given set of nonorthogonal orbitals so that the projection of the configuration in which each nonorthogonal orbital is singly occupied upon the configuration in which each corresponding orthonormal orbital is singly occupied has maximum amplitude. These orthogonal functions are referred to as maximal orthogonal orbitals. If, instead of maximizing the probability of the corresponding configuration in the $v\text{'}\mathrm{s}$, one maximizes the magnitude of the sum of the projections of each $u$ on its corresponding orthogonal orbital, then Löwdin's set of orthogonal functions is the solution. Löwdin's functions differ from the maximal orthogonal orbitals only in third and higher order terms in the overlap matrix.