Departamento de Química Física, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apdo. 644 E48080 Bilbao, Spain.
J Phys Chem A. 2010 Feb 18;114(6):2344-9. doi: 10.1021/jp9090848.
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.
本文报告了二阶约化密度矩阵的累积矩阵的某些元素与自旋密度矩阵的元素之间的关系的推导。 该关系对于通过划分 N 电子系统的自旋期望值<S(2)>来确定局部自旋非常有用。 该过程仅通过单电子矩阵元素（自旋密度矩阵的元素）表示单中心和双中心贡献。 我们报告了在三重态和双态中选择的分子和自由基的原子轨道 Hilbert 空间中的局部自旋的数值确定。
