Descriptions of local spins in the three-dimensional physical space

This report describes the partitioning of the expectation value of the spin-squared operator < S ^ 2 > corresponding to an N-electron system in the three-dimensional physical space, according to the Bader and fuzzy atom approaches. Numerical determinations performed in selected open-shell systems at Hartree–Fock and density functional theory levels confirm the reliability of the local spins obtained. A comparison between these results and their counterpart ones arising from the partitioning in the Hilbert space is analyzed in detail.