Overlap populations, bond orders and valences for 'fuzzy' atoms

Proper definitions are proposed to calculate interatomic overlap populations, bond order (multiplicity) indices and actual atomic valences from the results of ab initio quantum chemical calculations, in terms of 'fuzzy' atoms, i.e., such divisions of the three-dimensional physical space into atomic regions in which the regions assigned to the individual atoms have no sharp boundaries but exhibit a continuous transition from one to another. The results of test calculations are in agreement with the classical chemical notions, exhibit unexpectedly small basis sensitivity and do not depend too much on the selection of the weight function defining the actual division of the space into 'fuzzy' atomic regions. The scheme is applicable on both SCF and correlated levels of theory. A free program is available.