Relaxed potential energy surface scans of 1,6-methano[10]annulene and its derivatives have been calculated using Hartree-Fock (HF), density functional (DFT), and second-order Moller-Plesset perturbation theory (MP2) in the pursuit of nonclassical structures corresponding to an extremely long C-1-C-6 bond (similar to 1.8 Angstrom). Substituents affect the relative stabilities between the aromatic and the bisnorcaradine forms, but their effects on the minima positions are moderate. We attribute the absence of a static C-C bond length in the vicinity of 1.8 Angstrom to the well-defined inherent minima of cyclopropane in its singlet state (-1.5 Angstrom) and trimethylene in its triplet state (similar to 2.6 Angstrom), which serve as the basis of our fragment analysis. The 1,6 bonding in these molecules is associated with a shallow potential well, in agreement with the Woodward-Hoffmann rules rather than to the existence of a static intermediate structure with a very long C-C bond. These results are in qualitative agreement with recent temperature-dependent C-13 NMR experiments of Dorn et al. The trends in the C-1-C-6 bridgehead bonding are well-reproduced by the correlated calculations and to a lesser extent even by the HF calculations. However, simple electron donation/withdrawal arguments fail for this series. Due to the similarity in the delocalization energy of 1,6-methano[10]annulenes and disubstituted methanobuckyballs, predictions are made concerning the structural preferences for some disubstituted methanofullerenes and -fulleroids. In contrast to general expectations open [6,6] methanofullerenes may exist. Major differences between methano[10]annulenes and methanofullerenes are derived from the constraints concerning the bookfolding angle that are strong in the latter and moderate in the former.