Characterizing the sensitivity of bonds to the curvature of carbon nanotubes

Jyotirmoy Deba, Debolina Paula, Utpal Sarkara* and Paul W Ayersb*
a Department of Physics, Assam University, Silchar-788011, India

b Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada

Email: a* utpalchemiitkgp[at]yahoo.com; b* ayers[at]mcmaster.ca

A systematic study has been performed to investigate the effect of curvature on bonding and various electronic properties of carbon nanotubes (CNT) using density functional theory. To understand the nature of the interaction between atoms in the nanotube, the Wiberg bond index, natural bond order analysis, and topological electron density analysis have been performed. The Wiberg Bond Index (WBI) reflects that all selected bonds are purely covalent character, a result that is confirmed by the negative values of 𝛻2ρ(rc) and H(rc) at the bond critical points (BCPs) of all the bonds we studied. As the diameter of the nanotube decreases and its curvature increases, the covalency (bond order) decreases, a conclusion that is supported by the increase of the bond lengths and also the decrease of the electron density and the energy density along the bond paths as the curvature increases. This is confirmed by the shortening of the bonds in the CNTs and a natural bond order analysis. Interestingly, perpendicular bonds are show greater higher-double-bond character than the parallel bonds. This may be because the effect of truncating the CNT (the boundary effects) are least significant when one considers bonds that are perpendicular to the boundary. The bond order of the C7-C15 and C3-C11 bonds decreases noticeably with increasing curvature, which is consistent with the decreasing accumulation of electron density along the bond path (BP) for these systems. To shed light into orbital contribution in bond formation and the most effective interaction between donor bonding orbital and acceptor antibonding orbital, analysis of natural bond orbitals is carried out. NBO analysis indicates that, for most of the systems we consider, the π - π* interaction between donor orbital C7-C15 and acceptor orbital C5-C6 or C13-C14 is significant, and has a higher stabilization energy than other interactions. Among the considered nanotubes, chemical reactivity parameters indicate that hardness increases and electrophilicity decreases with the increase of tube diameter, i.e. stability of nanotubes increases with the increase of diameter or decrease of curvature of the nanotube.

References:

1. J. Deb, D. Paul, U. Sarkar, Paul W. Ayers, Journal of Molecular Modeling (2018) 24:249.