Cooperative Behaviors in Carbene Additions through Local Modifications of Nanotube Surfaces

We investigate the cooperative behavior of two carbene additions to a (5,5) armchair single-walled carbon nanotube (SWNT) and find that in certain configurations, double additions are more stable than uncorrelated distant double additions by 7 to 24 kcal/mol. We also find certain configurations to be very unstable. We employ density functional theory (DFT) PW91 calculations using periodic boundary conditions and compare 20 different double-addition configurations. We trace the cooperative behavior to the power of the first addition to modify the geometry locally. We investigate both inner (endohedral) and outer (exohedral) additions and observe fundamental differences between these two. In the qualitative interpretations of the results, analogies to the valence tautomerization of 1,6-methano[10]annulene are helpful in establishing that when the carbene addition opens the CC bond in the nanotube (exohedral addition), then the number of π-electrons is unchanged, leading to less spatially extended perturbations of the nanotube. Endohedral carbene additions reduce the number of π-electrons, leading to a more pronounced and spatially more extended cooperative effect. We find that local quinonoid-like perturbations of the geometry extend over several rings near the endohedral perturbation. Such extended defects should play a role in the properties of substituted nanotubes and can be visualized using Clar diagrams.