Using the DFT PBE0 quantum-chemical method, we have determined the spin populations and the free valences of atoms in (i) 3,4-dimethylenefuran; (ii) exciplex 3,4-dimethylenefuran center dot O-2; (iii) phthalocyaninates PcCu and PcCo; (iv) cations Pc+Cu, Pc+Co, and Pc+Ni; (v) dication [PcAlOAlPc](2+); and (vi) two excited triplet diketones: fulleroid-type C-58(CO)(2) and cyclododeca-3,4,9,10-tetraene-1,7-dione. Free valences determine atomic contributions to the doubled variance of the many-electron spin. Unlike spin populations, they are insensitive to the choice of the component of a quasi-degenerate spin state of a chemical compound and account for the regioselectivity of the radical addition to 3,4-dimethylenefuran and the photochemical stability of Pc-containing nanosystems. In a triplet state of (CH12O2)-H-12, the spin density and the free valence are localized on a single carbonyl group, whereas, in a triplet state of C-58(CO)(2), they are delocalized.