Properties of the simplest localized molecular orbitals: The P-LMOs

The columns of the LCAO density matrix, P, obtained in a standard Hartree-Fock or Kohn-Sham calculation, can be interpreted as coefficients of occupied localized molecular orbitals (LMOs). Requiring no extra calculations once P is available, they constitute the simplest possible set of occupied LMOs. They are nonorthogonal, moreover redundant, and are related to the usual projected atomic orbitals that emerge as the columns of matrix PS, where S is the overlap matrix of atomic orbitals. Both P-LMOs and PS-LMOs may serve as molecular orbitals even for procedures that determine P directly, i.e., avoiding the construction of molecular orbitals. To enhance localization, the LMOs resulting from the square root of P are also investigated. Properties of P-LMOs and P1/2-LMOs are discussed, and they are compared to PS-LMOs and to other well-known types of localized orbitals.