Distribution of effectively unpaired electrons

The density of effectively unpaired electrons employed recently by the authors [J. Am. Chem. Soc. 122 (2000) 186] is identical with the distribution D(r) of `oddʹ electrons proposed much earlier by Takatsuka, Fueno, and Yamaguchi [Theor. Chim. Acta 48 (1978) 175]. The function D(r|r′) is also implicitly present in several definitions of the free valence index. Basic properties of D(r|r′) are reviewed and a number of new results are reported. The distribution D(r) is advocated as a rigorous criterion of the radical character in molecules of any spin. Numerical examples deal with the dissociation of N2 and O2 molecules.