Curvature dependent reactivity  of fullerenes and nanotubes are quantified via ab-initio total energy pseudo-potential density functional simulations. Both fullerenes and nanotubes are considered as promising materials for nano-mechanical and nano-electronic applications. Many of the possible applications, however, may require the functionalization through mechano-chemical means. The curvature dependence is expressed through pyramidalization of carbon atoms, and more pyramadalization means increasing S-character and charge density in the pyramid. The changes in the total energy are separated into the competing strain energy and reaction energy terms that are quantified as functions of the degree of pyramadalization. The strain energy terms follow a universal quadratic behavior and reaction energies are related to strain energies through simple analytic functions. The universal expressions and resulting quatifications will be discussed and explained through H atoms' reactivity with C60 fullerene, (10,0) nanotube, and graphene sheet. Reactivity of H and P atoms within a fullerene (endo-fullerenes) will be discussed in the context of possible applications of endo-fullerenes in quantum computation and nanoelectronic applications.
D. Srivastava, D. W. Brenner, J. D. Schall, K. D. Ausman, M. Yu and R. S. Ruoff, J. Phys. Chem. Vol 103, 4330 (1999).
See for example M. C. Payne et. al. Reviews of Modern Physics, Vol 64, 1045 (1992).