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Many nanostructures today are low-dimensional and flimsy, and therefore geteasily distorted. Distortion-induced symmetry-breaking makes conventional,translation-periodic simulations invalid, which has triggered developments fornew methods. Revised periodic boundary conditions (RPBC) is a simple methodthat enables simulations of complex material distortions, either classically orquantum-mechanically. The mathematical details of this easy-to-implementapproach, however, have not been discussed before. Therefore, in this paper wesummarize the underlying theory, present the practical details of RPBC,especially related to a non-orthogonal tight-binding formulation, discussselected features, electrostatics in particular, and suggest some examples ofusage. We hope this article to give more insight to RPBC, to help and inspirenew software implementations capable of exploring the physics and chemistry ofdistorted nanomaterials.

Revised Periodic Boundary Conditions: Fundamentals, Electrostatics, and the Tight-Binding Approximation