Helicity energy of a straight single-wall carbon nanotube

The energy of a straight single-wall carbon nanotube (SWNT) with different helicity is proposed by making continuum limit of the curvature elastic energy of a single-layer curved graphite carbon. We find that the zigzag is the only stable state with the lowest energy for the fixed diameter tubule. Our helicity energy formula agrees well with the energy of the zigzag configuration and armchair configuration SWNT’s calculated by quantum molecular dynamics numerical simulation.