Interactions in concentric carbon nanotubes: The radius vs the chirality angle contributions

In multiwall carbon nanotubes in general, and in double wall carbon nanotubes, DWCNTs, in particular, the guest-host interactions depend primarily on the difference of the nanotubes radii, Delta r. The chirality angle mismatch of the two tubes, Delta theta, also matters since it determines the pattern of pi-stacking interactions that ultimately is responsible for the shift of graphite layers into the so-called A-B structure. Here we calculate the minimum energy structures of 198 DWCNTs and construct two functions of Delta r and Delta theta that fit the calculated data. Cross terms exists between Delta r and Delta theta. The shape of the functions is rationalized in simple physical terms and can be used to construct minimum energy multiwall nanotubes.