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 for 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 suit- able for rapid, large-scale conformational analysis and automated property prediction workflows, both by effective pruning of duplicate conformations and enabling cross-methodology ensemble comparison.