Russian Chemical Bulletin, International Edition, Vol. 57, No. 12, pp. 2520—2525, December, 2008 2520 Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 12, pp. 2469—2474, December, 2008. 1066-5285/08/5712-2520 © 2008 Springer Science+Business Media, Inc. 1,3-Dipolar addition reactions to fullerenes: the role of the local curvature of carbon surface D. Sh. Sabirov, а,b S. L. Khursan, b and R. G. Bulgakov а a Institute of Petrochemistry and Catalysis, Russian Academy of Sciences 141 prosp. Oktyabrya, 450075 Ufa, Russian Federation. Fax: +7 (347) 284 2750. E-mail: sabirovdsh@bsu.bashedu.ru b Bashkir State University 32 ul. Zaki Validi, 450074 Ufa, Russian Federation. Fax: +7 (347) 223 6701 Structural peculiarities of fullerenes C 20 , C 24 , C 30 , C 36 , C 40 , C 60 , C 70 , and C 76 and their adducts with 1,3-dipolarophiles (ozone and diazomethane) were investigated by the DFT meth- od with the PBE functional. A correlation between the heats of 1,3-dipolar addition reactions and the carbon surface curvatures at reaction sites in the original fullerene molecules was found. Keywords: fullerenes, fullereno-1,2,3-trioxolanes, fullerenopyrazolines, pyramidalization angle, local surface curvature, bond order, methods of density functional theory. Various methods for functionalization of fullerenes C 60 and C 70 have been proposed since the discovery of fulle- renes. 1,2 Being electron-deficient polyenes in chemical na- ture, fullerenes are involved in radical, nucleophilic, and cycloaddition reactions. The [2+n]-cycloaddition reac- tions are particularly promising for the synthesis of novel fullerene derivatives. 2 Among them, an important position is occupied by the reactions of 1,3-dipolar addition of ozone and diazo compounds. A common feature of these reactions is the formation of unstable addition products (fullereno-1,2,3-trioxolane or fullerenopyrazoline), which determines the structure of the final reaction products. Also, the addition of ozone and diazomethane at the dou- ble bond is characterized by low activation energies. 3,4 The reaction with ozone is one of the first fullerene reactions proposed to synthesize oxygen-containing deriv- atives of fullerenes C 60 and C 70 . It involves the formation of unstable fullereno-1,2,3-trioxolane 5,6 whose transfor- mations lead to fullerene spheroids modified with epoxy 5,6 or carbonyl 5,7—9 functional groups. Incessant interest in the ozonolysis reactions of fullerenes C 60 and C 70 is due to the possibility of synthesis of water-soluble fullerene-based polyketons and polyethers. 9 The cycloaddition of diazo compounds to fullerene C 60 proceeds by a complex mechanism. 10 A concerted addi- tion of carbenes generated by thermolysis of the diazo com- pounds to the 6,6-bond leading to [6,6]closed structures competes with the 1,3-cycloaddition of the diazo com- pound to the fullerene followed by extrusion of nitrogen molecule from the pyrazoline intermediate resulting in the [5,6]open and [6,6]closed isomers. The reaction with di- azo compounds still remains the main synthetic route to the [5,6]open (fulleroid) structures. Unlike fullerenes C 60 and C 70 , the reactivities of the C 20 , 11 C 36 , 12 C 76 , 13 and other fullerenes synthesized more recently and less available as yet have been poorly studied so far. They can be evaluated experimentally and using modern quantum chemical methods, which offer great prospects for prediction of the chemical properties of dif- ferent compounds. The chemical properties of fullerenes and nanotubes are to a great extent depend on the carbon cage strain due to nonplanar arrangement of sp 2 -hybridized carbon at- oms. 1 It is convenient to estimate the deviation of a react- ing carbon atom from the plane passing through three neighboring carbon atoms of the fullerene cage using the pyramidalization angle, θ P , of the reaction center, which is defined as follows 14 : θ P = θ σπ – 90°, (1) where θ σπ is the angle between the directions of the σ- and π-bonds of the reaction center. For sp 2 -hybridization, the symmetry axis of the π-orbital is normal to the plane of three σ-bonds (θ σπ = 90°, θ P = 0°); for sp 3 -hybridization, one has θ P ~19°. The θ P values are mainly used to predict the nanotube reactivities. 15 There is lack of information on the studies of the effect of the carbon surface curvature on the fullerene reactivities in 1,3-dipolar addition reactions. In the present work, we investigated the dependence of the heats of the addition reactions of ozone and diazomethane (the simplest diazo compound) to fullerenes on the local curvature of the car-