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 ND and its partial density NDA 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 NDA values and independently calculated free valence over atoms of χ60 (χ = C, Si) and C70 molecules makes it possible to consider the NDA maps as chemical portraits of the fullerenes. The NDA 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 NDA-based computational synthesis of the fullerene derivatives are illustrated for initial steps of C60 fluorination. © 2007 Wiley Periodicals, Inc.