Conformational Pruning via the Permutation Invariant Root-Mean-Square Deviation of Atomic Positions

The Cartesian root-mean-square deviation (RMSD) of atomic
coordinates
is fundamental for comparing three-dimensional molecular structures,
particularly in identifying and classifying molecular conformations.
Since molecular properties are determined by the molecular conformation,
pruning duplicates via a structural similarity metric like the RMSD
will reduce redundant calculations and hence directly impact the cost
of automated workflows in computational chemistry. However, the traditional
RMSD metric struggles when dealing with local symmetry in molecules
and atom permutation, often leading to inflated errors and computational
inefficiency. This work addresses these challenges by providing clear
definitions of structural similarity within conformational ensembles
and developing an efficient divide-and-conquer algorithm for their
distinction. The proposed permutation invariant RMSD (iRMSD) approach
efficiently overcomes challenges associated with symmetric molecules
and multiple rotamers by incorporating a procedure that assigns canonical
atom identities and optimizes the atom-to-atom assignment process.
This procedure leads to significant reductions in computational complexity,
making the method highly suitable for rapid, large-scale conformational
analysis and automated property prediction workflows, both by effective
pruning of duplicate conformations and by enabling cross-methodology
ensemble comparison.