Relationships between Cumulant and Spin-Density Matrices: Application to the Decomposition of Spin

A. TORRE; D.R. ALCOBA; L. LAIN; R.C. BOCHICCHIO

JOURNAL OF PHYSICAL CHEMISTRY A

AMER CHEMICAL SOC

Lugar: New York; Año: 2010 vol. 114 p. 2344 - 2349

1089-5639

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 <S^2> 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 orbitals in selected molecules and radicals in triplet and doublet states.