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 nonorthogonal tight-binding formulation, discuss selected features, electrostatics in particular, and suggest some examples of usage. We hope this article can give more insight into RPBC, and it will help and inspire new software implementations capable of exploring the physics and chemistry of distorted nanomaterials.