Each FS structure is subjected to the DECAF classification. If this signals one or more new equivalence group(s), i.e. atom(s) with atomic environments that differ in the embedded low-dimensional space by more than the employed finite MSC bandwidth, then this yields corresponding new entries in the to-do list of local atomic environments. These entries now contain the identified atom with a distinctly new environment as highlighted atom and the FS structure as the total atomic configuration of the system. This way, the progressively performed TS searches crunch through the to-do list entries and -if indicated -generate new entries with novel atomic environments. The new entries are sorted in order of increasing energy of the stored atomic configuration of the system, and if several entries concern new equivalence groups that fall within their mutual MSC bandwidth, then only the lowest energy entry is retained. This thus prioritizes the search on lower-energy system states, while simultaneously minimizing TS search redundancy as searches centered on more than one representative atom of each equivalence group (aka local atomic environment) are never performed.