For a given LMO domain i, if the value of the DOI of LMO i with PAO µ is greater than a given tolerance T CUT DO (default 10 -2 for default settings, and 5 • 10 -3 for tight settings), µ is added to the PAO domain of i, and this process is repeated for all PAOs. The pair domain of pair ij is thus formed from the union of the PAO domain of i and the PAO domain of j. Analogously, the triplet domain for triplet ijk is the union of the PAOs in the domains of i, j, and k. A separate cutoff, T CUT DO TRIPLES , defaulting to 10 -2 , is used for triples since fewer PAOs are needed per LMO to form a adequate representation for triplets compared to pairs. PAO domains for quadruplet ijkl are formed cognately, with the cutoff T CUT DO QUADS defaulting to 10 -2 as well.