Ultrafast computation of exact symmetry-corrected RMSD of conformers

Accurate quantification of molecular structural similarity through root mean square deviation (RMSD) is essential for protein-ligand docking validation, conformational analysis, and molecular dynamics simulations, yet current methods face a critical trade-off: polynomial-time algorithms sacrifice chemical correctness by ignoring molecular connectivity, while graph isomorphism approaches exhibit prohibitive computational costs for symmetric molecules.This limitation prevents routine exact symmetry correction in applications where distinguishing genuine conformational differences from atom labeling artifacts is essential, such as evaluating docking poses and pruning conformational ensembles.This work introduces the Hierarchical Neighborhood of Atoms (HNA) partitioning, a recursive classification of chemically equivalent atoms that enables fast computation of exact symmetry-corrected RMSD.Hierarchical decomposition reduces search complexity from the product of branch combinations to their sum, achieving computation time reductions of several orders of magnitude compared to existing topology-preserving methods.Comprehensive benchmarks on large molecular databases demonstrate mean execution times in the millisecond range across molecules ranging from small compounds to proteins, with complete success on all calculations without failures or timeouts.In contrast to linear assignment approaches that produce high rates of topologically invalid mappings, this algorithm ensures chemically correct atom correspondences, enabling practical exact symmetry correction across the full spectrum of molecular complexity relevant to drug discovery and biomolecular structure prediction.