Natural bond orbitals: Local sets showing minimal intra-pair correlations and minimal unpaired electron populations

Abstract

Adopting the 2nd order Density Matrix level, the usual Natural Bond Orbital (NBO) populations are explored accordingly: they are split into paired and unpaired (defined as “the simultaneous occurrence of an electron and a hole of opposite spins in an orbital”) populations. The Coulomb correlations and the unpaired electron populations are calculated explicitly, revealing new and unexplored features for NBO sets. It is shown that the ‘natural’ origin of these sets implies that the intra-pair correlations, and hence the unpaired electrons, are minimal in NBOs. The unpaired electron populations in valence NBOs provide a criterion for the quantal/classical, and hence for the active/inert behavior of bonds and molecules; this is tested in several well known prototypical systems. The interaction of two unpaired electrons between bonding and antibonding NBOs of two different bonds gives rise to a Heitler-London structure between the two bond regions; its weight (probability), and the included Coulomb and Fermi correlations are calculated in the basis of a spin-dependent formalism of generalized Density Matrices.