541.572.7+546.26 Chemical activity of fullerene molecules is associated with a partially radical character of these molecules caused by the presence of effectively unpaired electrons (EUE). Values of the total number of N D and partial distribution N D of EUE over the atoms in a singlet state of molecules 60 and 70 have been calculated. "Chemical portraits" of molecules are presented, and N D values are proposed to be used as indicators for chemical activity of atoms and to predict thereby the position of favorable atom-atom contacts in addition reactions with participation of these molecules. Bases of "computational synthesis" procedures for fullerene 60 derivatives are exemplified by initial phases of its fluorination. Keywords: quantum chemistry, chemical activity, fullerene 60 and 70 , computational synthesis.Present ideas of chemical activity of fullerenes, mostly of 60 molecule, come to two basic statements. The first is that fullerene behaves like an electron-deficient polyalkene [1, 2], and not like an electron-enriched aromatic molecule as was originally supposed [3]. Rigid localization of double bonds in the molecule, confidently shown experimentally, is explained [1,2] by the presence of pentagon molecules in the structure precluding -electrons from conjugation. However, the electronic mechanism by which the pentagon structures localize double bonds remains entirely obscure.The second statement concerns selectivity of the chemical activity of molecules. The opinions on this point have divided. Some researchers incline to that the molecule has 30 equivalent reaction centers (by the number of double bonds) due to which most chemical reactions are not selective [2]. It is, however, difficult to reconcile this statement with the presence of primary derivatives of 60 , hydrides and halides, mostly of a specific stoichiometric composition, for example, 60 H 36 , C 60 Hal 24 , C 60 Hal 36 , C 60 Hal 48 [4,5]. Moreover, in obtaining the metallofullerenes, it has been established from the very beginning [1,6] that transition metals are forming an octahedron surrounding for the internal 60 nucleus. Thus the idea of atom-local selectivity (regioselectivity) of the molecule has appeared. The extension of this approach to organic derivatives of fullerene has led to a model suggested by Wudle [2,7] the core of which is a structural factor -pyracyclene fragment responsible for each elementary act of addition. In the author's opinion [2], localization of molecule the chemical activity within the fragment is caused by its pentagons. The presence of six such fragments in the structure of the 60 molecule made it possible to explain the formation of organic pseudo-octahedron covalent derivatives, fullerene stars with added products of different complexity [8].Attempts to give the quantum chemical (QC) description of 60 derivatives have been made repeatedly (see, for example, detailed works [9-11] and references therein). These computations, however, were aimed not so much at understanding the nature of the molecule c...