  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.
