Since the adsorption edges are representations of the local symmetry of a pair of sites, they can also be used for the enumeration of paired molecule configurations. In this way, each of the unique tilts of an OH molecule can be enumerated. Similarly, when an adsorbate has multiple adjoined atoms which bond to the surface, these bidentate adsorption cases can also be exhaustively enumerated. For bidentate adsorption, the resulting connectivity matrix will be unique for each possible structure. However, for tilted molecules, additional information is needed for unique identification, such as dihedral angles or the index of an adsorption edge.