Spin resolved electron number distribution functions: How spins couple in real space

The probabilities of finding arbitrary partitions of the N(alpha)m(s)=12 and N(beta)m(s)=-12 electrons of a molecule into m arbitrary regions that exhaust the physical space are developed and computed, both for atomic and electron localization function basins, in a number of test systems. These spin resolved electron number distribution functions provide access to the coarse-grained distribution of spins in space even for singlet states, a nontrivial result. It is found that atoms within molecules partially retain their in vacuo preferences for certain spin configurations. This may lead to long range spin coupling among basins. An aufbaulike rule favoring spin coupling, particularly for Hartree-Fock wave functions, has also been found.