[2+1] Additions of (n,0)(n=6−10) single-walled carbon nanotubes with di-vacancies based on defect curvature: A first-principles study

Binding energies ([Formula: see text], geometric and electronic structures for [[Formula: see text]](O/[[Formula: see text]]) additions of O atom on ([Formula: see text])([Formula: see text] − 10) single-walled carbon nanotubes with di-vacancies are studied using a GGA-PBE method, and defect curvature ([Formula: see text]) is used to predict reactivities of different C—C bonds at defect area. Calculated results show that the C—C bonds can be divided into two types: broken C—C bonds corresponding to adducts with a C—O—C configuration structure and unbroken C—C bonds corresponding to adducts with a closed-3MR structure. [Formula: see text] of O/[[Formula: see text]] additions for the adduct with the C—O—C configuration structure monotonously increases with the increase of [Formula: see text] in any ([Formula: see text],0)([Formula: see text]) tube and decreases with the increase of [Formula: see text] in ([Formula: see text],0)([Formula: see text], 7, 10) tubes. Besides the fact that [Formula: see text] value is mainly determined by the defect curvature, it is also affected by band gaps, bonding characteristic of C—C bonds in the highest occupied molecular orbital (HOMO) and geometric structures. The study would provide a theoretical basis for surface modifications of carbon nanotubes with atomic vacancy defects.