Periodic Molecular Arrangements from Space Groups

TL;DR

This paper presents a systematic method for determining all possible periodic molecular arrangements with specific space group symmetries in 2D and 3D, providing tables of generators to aid the process.

Contribution

It introduces a comprehensive technique based on prior work to find all periodic arrangements matching a space group's symmetry, with practical tables of generators included.

Findings

Method successfully finds all arrangements with given symmetry.

Tables of generators simplify the construction process.

Applicable to both 2D and 3D molecular arrangements.

Abstract

We demonstrate, using examples from $2$ and $3$-dimensions, a systematic method of finding all possible periodic arrangements of a given molecule or molecules such that the arrangements have the symmetry of a given space group. The technique is based on work by Rabson {\it et.\ al.\}. We give tables of generators which facilitate such work.