Localized orbitals for arbitrary molecular wave functions

Localized orbitals are defined for arbitrary wave functions for atoms or molecules with even or odd numbers of electrons by making a particular non-orthogonal transformation among the natural orbitals which preserves the diagonal nature of the electron density. Different definitions of localized orbitals are obtained by relating them to different approximate forms for the wave function. The equilateral triangle configuration of H-3(+) is treated as an example.