The advantages of using such a methodology are that symmetrically identical structures are automatically grouped and the characteristic methods are relatively low in memory to store as you move to increasingly large number of structure produced. The characteristic vectors could further be reduced in size and the inherently O(N 2 ) structure comparison scaling could be made O(N ), where N is the number of structures, by employing local sensitivity hashing. We find this step to be unnecessary for our needs in this work but would be arbitrary to implement should we need to move to larger ensembles. It should be noted that this methodology, in its current implementation, is chemical species agnostic.