Relationships between cumulant and Spin-Density Matrices: Application to the decomposition of Spin

Abstract

This paper reports the derivation of a relationship between some elements of the cumulant matrix of the second-order reduced density matrix and the elements of the spin-density matrix. This relationship turns out to be very useful to determine local spins through the partitioning of the spin expectation value 〈S2〉 of an N-electron system. The procedure enables expression of both one- and two-center contributions only in terms of one-electron matrix elements, the elements of the spin-density matrix. We report numerical determinations of local spins in the Hilbert space of atomic orbitais in selected molecules and radicals in triplet and doublet states. © 2010 American Chemical Society.