Expansion of the unrestricted determinant in the basis of paired orbitals

An analysis of spin mixture contained in the unrestricted determinant using Löwdin–Amos-Hall paired orbitals (POs) is developed. The space of POs is divided into subspaces of completely, partially and non-overlapping orbitals. Spin contamination is shown to be associated with the ‘active’ space of 2k partially overlapping POs with k being in practice fairly small number. In the basis of POs the unrestricted determinant is expanded in a linear combination of restricted determinants describing ‘basis’ configurations contained 0,1, … ,k pairs of spatially separated α and β spins.