Physics-Based Molecular Fingerprints from Spectral Graph Theory Provide Efficient Geometry-Aware Measures of Chemical Similarity

2026-08-05

AI Summary

This work addresses the limitations of conventional molecular fingerprints, which are predominantly based on two-dimensional structures and thus fail to distinguish stereoisomers and conformers, while existing three-dimensional approaches often suffer from high computational cost or heavy data dependence. The authors propose a physics-inspired 3D molecular fingerprint that represents a molecule as a fully connected 3D graph, where edge weights encode heuristic physical interactions. By performing eigendecomposition on the graph Laplacian matrix, the method yields a fixed-length descriptor invariant to both atomic permutations and E(3) transformations. This approach uniquely integrates spectral graph theory with physically motivated 3D graph representations, achieving state-of-the-art performance across multiple chemical datasets. It offers strong interpretability, geometric awareness, and low computational complexity, making it well-suited for efficient large-scale chemical space screening and applicability domain analysis.

Abstract

Molecular representations are essential for the evaluation of molecular similarity and the development of structure-property relationships. Despite the known importance of 3D structure to determine chemical and physical properties, the most widely used molecular fingerprints encode only two-dimensional connectivity. Such representations fail to distinguish similar but distinct stereoisomers and conformers. Alternative 3D methods are typically defined pairwise, making their application to large chemical spaces prohibitive, while deep learning embeddings are expressive but uninterpretable and limited by their training data diversity. Here, we introduce novel physics-inspired molecular fingerprints based on principles from spectral graph theory. We represent molecules as a complete graph in 3D space, with edge weights encoding heuristic physical interactions. Eigenvalue decomposition of the resulting graph Laplacian matrix results in a computationally efficient fixed-length chemical fingerprint that encodes 3D structure while obeying necessary physical symmetries of permutation and E(3) invariance. Spectral fingerprints differentiate between unique molecular structures with identical 2D connectivity, overcoming a limitation of 2D descriptors, while maintaining the low computational cost needed for efficient screening of vast chemical spaces. We evaluate our fingerprints with community detection algorithms and observe strong performance against representative baselines across datasets from organic, inorganic, biological, reticular, and reaction chemistry. Nearest-neighbor property estimation and applicability domain analyses reveal the utility of our molecular representation in machine learning and cheminformatics. We anticipate that spectral fingerprints will serve as generalizable, interpretable, and efficient measures of chemical similarity that incorporate 3D information at minimal cost.

Problem

• molecular fingerprints
• 3D molecular representation
• chemical similarity
• stereoisomers
• conformers

Innovation

• spectral graph theory
• 3D molecular fingerprints
• E(3) invariance
• geometry-aware similarity
• graph Laplacian