Derivation of the linear relationship between SWCNTs functionalization energies and sidewall curvature

A simple linear relationship between the functionalization reaction energies for the exohedral monovalent addition on the surface of an ideal, infinitely long, single-walled carbon nanotube (SWCNT) and the reciprocal SWCNT radius has been derived employing the hard?Csoft acid basis principle and the tight binding model. The slope of the derived linear relationship is a function of the effective number of valence electrons involved in the functionalization reaction. The intercept of the derived linear relationship, equal to the reaction energies on a planar graphite surface, is a function of the electrophilicity of the monovalent addend and of the condensed Fukui function of its reacting atom. The theoretical predictions of this simple formula are coherent with the computational density functional theory data reported in the literature.