Density functional theory method for twisted geometries with application to torsional deformations in group-IV nanotubes

•Real-space formulation and implementation of Kohn-Sham Density Functional Theory suited to twisted geometries.•Uses higher order finite difference discretization in helical coordinates.•Employs cyclic and helical symmetries.•Accurate, efficient and systematically convergent numerical technique.•Extensive simulations involving electro-mechanical properties of Group IV nanotubes are presented.