Unification of the matrix notation in molecular surface science

The matrix notation connecting the adsorbate lattice with the substrate is a suitable method to define periodic molecular overlayers on single crystalline surfaces. Despite the simplicity of this notation, there are different sets of rules in use, which are incomplete and allow ambiguous results. We suggest here a new consistent set of rules for unit cell selection and how to find in a uniform way a single matrix notation for equivalent structures. This is in particular important for meaningful database entries. Using examples from the literature, we show why existing rules fail to give unambiguous results and discuss in a tutorial manner how to apply the new rules.