Positional isomerism, stability, and polarizability of C₂₀(CH₂)_n(n= 1–10), the cyclopropane adducts of the smallest fullerene: General formula for calculation of mean polarizability of fullerene derivatives C₂₀X_nY_mand C₆₀X_nY_mwith fixed (n+m) number of different addends

All regioisomers of fullerene adducts C20(CH2)n have been found and their stability and polarizability have been studied by the PBE/3ζ method. As in the case of the C60 and C70 adducts, mean polarizability of C20(CH2)n quadratically depends on the number of addends and demonstrates the depression, viz. negative deviation of polarizability from the linear additive scheme. Another, linear formula is proposed for calculating mean polarizability of the C20 and C60 fullerene adducts with mixed functionalization C20(CH2)nOm and C60(CH2)nOm and fixed number of addends. The obtained results will be further used to work out the algorithm for counting all possible C60Xn cycloadducts and searching a general formula for calculation of the C60XnYm polarizability with variable (n + m) number of addends.