Since it is assumed that a particular chemical environment can match multiple SMARTS in a hierarchy, it is important to establish how the SMARTS patterns are ordered and traversed. This is especially important for force field design since each node in the hierarchy contains different physical parameters. The SMARTS patterns, viewed as sets and subsets, require an ordering of the hierarchy to ensure consistent, deterministic labeling. Here, it is important to define exactly how subset membership is established since the SMARTS can be arbitrary graphs. Specializing a general pattern with one