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We explore the generalization to the helical case of the classical Ewald method, the harbinger of all modern self-consistent treatments of waves in crystals, including ab initio electronic structure methods. Ewald-like formulas that do not rely on a unit cell with translational symmetry prove to be numerically tractable and able to provide the crucial component needed for coupling objective molecular dynamics with the self-consistent charge density-functional based tight-binding treatment of the inter-atomic interactions. The robustness of the method in addressing complex hetero-nuclear nano- and bio-systems is demonstrated with illustrative simulations on a helical boron nitride nanotube, a screw dislocated zinc oxide nanowire, and an ideal DNA molecule

Ewald summation on a helix: A route to self-consistent charge density-functional based tight-binding objective molecular dynamics