Some spin and spin-free aspects of coulomb correlation in molecules
A spin component analysis of the cumulant (irreducible) density matrices is provided. In particular, the spin-up spin-down cumulant density matrix, π, is considered as the most general definition of the Coulomb-hole density matrix. The local atomic cumulants produced from π, turn out to be the most important components of the atomic charge and spin correlators. These spin-up spin-down components, vanishing in the restricted Hartree–Fock model, reflect directly an effect of the Coulomb correlation on the generalized Wiberg bond order indices and Penney–Dirac bond orders. A spin-free algorithm for computing spin correlators and related local spins is proposed. The algorithm is implemented numerically at full configuration interaction (FCI) and simple coupled-cluster (CC) levels. The presented analysis is exemplified by some FCI and CC doubles computations on small hydrides and typical carbenes and cumulenes. © 2012 Wiley Periodicals, Inc.