On the density matrix of effectively unpaired electrons

This Letter describes the relationships between the density of effectively unpaired electrons and other tools as the cumulant of the second-order reduced density matrix and the statistical population analysis. A topological population analysis, based on the atoms in molecules (AIM) theory, is incorporated in to the framework of the density of effectively unpaired electrons. Numerical determinations are carried out within this analysis in several systems and the results are compared with those of a more traditional Mulliken approach.