Computational Nanomechanics of Quasi-one-dimensional Structures in a Symmetry-Adapted Tight Binding Framework

The success of many nanotechnologies depends on our ability to understand and control the mechanics of nano objects, such as nanotubes and nanobelts. Because of the numerous experimental difficulties encountered at this scale, simulation can emerge as a powerful predictive tool. For this, new multiscale simulation methods are needed in which a continuum model emerges from a precise, quantum mechanical description of the atomic scale. Because computing nanomechanical responses requires large systems, computationally affordable but less accurate classical atomistic treatments of the atomic scale are widely adopted and only multiscale classical atomistic-to-continuum bridging is achieved. As a first step towards achieving accurate multiscale models for nano objects, based on a quantum-mechanical description of chemical bonding, here we present an ingenious symmetry-adapted atomistic scheme that performs calculations under helical boundary conditions. The utility of the microscopic method is illustrated with examples discussing the nanomechanical response of carbon nanotubes and thermodynamical stability of silicon nanowires.