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

Traditional molecular fingerprints, such as Morgan fingerprints, are widely used in cheminformatics but are limited by their reliance on 2D connectivity. These methods fail to distinguish between stereoisomers and conformers, which often exhibit distinct chemical properties. While 3D-aware representations exist, they are frequently computationally expensive, require pairwise alignment, or lack interpretability. This study addresses these limitations by developing a spectral graph theory-based approach to generate 3D-aware, alignment-free, and efficient molecular fingerprints.

The researchers represent each molecule as a complete graph where vertices are atoms and edges are weighted by four heuristic physical interactions: electrostatics, bonding, sterics, and dispersion. By constructing a graph Laplacian for each interaction channel and performing eigenvalue decomposition, they generate a fixed-length fingerprint. This approach ensures the representation is invariant to atomic permutation and E(3) transformations (rotation and translation).

The spectral fingerprints successfully differentiate between molecular structures that share identical 2D connectivity but differ in 3D geometry, such as conformers and stereoisomers. The authors demonstrate that these fingerprints are computationally efficient, allowing for the rapid screening of large chemical datasets. When evaluated using community detection algorithms, the spectral fingerprints show strong performance across diverse chemical domains, including organic, inorganic, biological, reticular, and reaction chemistry. Furthermore, the study confirms the utility of these fingerprints in machine learning workflows, specifically for k-nearest-neighbor property estimation and applicability domain analysis, where they serve as a training-free, interpretable complement to deep learning models.

This work provides a robust, low-cost alternative to existing molecular representations. By incorporating 3D information without the prohibitive computational cost of alignment-based methods or the black-box nature of deep learning embeddings, these spectral fingerprints enable more accurate chemical similarity assessments. This is particularly valuable for high-throughput virtual screening and the development of structure-property relationships in complex chemical spaces where 3D structure is a primary determinant of function.