Mechanically interlocked molecules (rotaxanes and catenanes) have already revolutionized molecular electronics and have the promise of a similar impact in other areas of nanotechnology, ranging from nanoactuators to in vivo drug nanocarriers. However, it would be most useful to have quantitative criteria for predicting structures, binding, and excitation energies for use in designing molecules with mechanical bonds. We assess here the use of density functional theory (DFT) to a noncovalently bound complex and find that no density functional is fully satisfactory. However, we find that the new M06-suite of density functionals, which include attractive medium-range interactions, leads to dramatic improvements in the structures (error of 0.04 angstrom in the interplanar distances for M06-L compared to 0.42 angstrom for B3LYP) and excitation energies (within 0.08 eV for TD-M06-HF without empirical correction compared to 2.2 eV error for TD-B3LYP). However, M06 predicts the complex to be too strongly bound by 22.6 kcal mol(-1) (B3LYP leads to too weak a bond by 29 kcal mol(-1)), while current empirical FF DREIDING is too weakly bound by only 15 kcal mol(-1).