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

Many nanostructures today are low-dimensional and flimsy, and therefore get easily distorted. Distortion-induced symmetry-breaking makes conventional, translation-periodic simulations invalid, which has triggered developments for new methods. Revised periodic boundary conditions (RPBC) is a simple method that enables simulations of complex material distortions, either classically or quantum-mechanically. The mathematical details of this easy-to-implement approach, however, have not been discussed before. Therefore, in this paper we summarize the underlying theory, present the practical details of RPBC, especially related to a non-orthogonal tight-binding formulation, discuss selected features, electrostatics in particular, and suggest some examples of usage. We hope this article to give more insight to RPBC, to help and inspire new software implementations capable of exploring the physics and chemistry of distorted nanomaterials.