Constituting a part of fullerenes odd electrons which are removed from the covalent bonding (Int J Quantum Chem, 2004, 100, 375), effectively unpaired electrons are posed by the singlet instability of the unrestricted Hartree-Fock SCF solution. The feature occurs to be of a particular importance leading to a quantitative description of atomically matched chemical susceptibility of the odd-electron molecular species via the relevant electron density on atoms. A correct determination of the total number of effectively unpaired electrons N-D and its partial density N-DA is well provided by the UHF solution. The calculation procedure and the obtained results reliability are justified for a set of diatomic molecules and ethylene. Practically full identity of the distribution of both N-DA values and independently calculated free valence over atoms of X-60 (X = C, Si) and C-70 molecules makes it possible to consider the N-DA maps as chemical portraits of the fullerenes. The N-DA value is offered to be a quantitative pointer of the atom chemical activity thus highlighting targets, which are the most favorable for addition reactions of any type. Basic grounds for a N-DA-based computational synthesis of the fullerene derivatives are illustrated for initial steps of C-60 fluorination. (c) 2007 Wiley Periodicals, Inc.