The density of effectively unpaired electrons employed recently by the authors [J. Am. Chem. Sec. 122 (2000) 186] is identical with the distribution D(r) of 'odd' 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 N-2 and O-2 molecules.