Long-range forces between C nanotubes and between C cages: Some polarizability bounds and scaling approximations yielding interaction energies at intermediate separations

Recent work of Schröder and Hyldgaard leads us to propose for the interaction energy per unit length ϕ(d, R) between two parallel C nanotubes of equal radii R at distance d, the approximate scaling property ϕ(d, R) = f(R)d−5I(R/d) where I is known. The function f(R) is expected to be model dependent. Contact is then made with the classic study of Girifalco et al. In addition, some results are presented for interaction energy between 'almost spherical' C cages. Specifically considered are (i) the HOMO-LUMO gap and (ii) bounds on polarizabilities.