Jacob W. Toney, Ayleen Y. Farnood, Samir Darouich and Heather J. Kulik (2026)
Highlighted by Jan Jensen
This paper caught my attention for two reasons. First, Morgan fingerprints cannot distinguish stereoisomers of transition-metal complexes, such as cisplatin and transplatin or fac and mer octahedral complexes, despite their potentially very different properties. Second, I often find that Morgan fingerprints tend to assign low similarities to small molecules that I would consider chemically quite similar. A compact fingerprint that incorporates geometry therefore sounds very useful.
The authors construct four matrices from atomic identities and interatomic distances, with entries representing approximate electrostatic, bonding, steric, and dispersion interactions. Each matrix is converted into a graph Laplacian, and 16 selected eigenvalues from each are combined into a fingerprint containing just 64 numbers. Molecular similarity is then calculated from the Euclidean distance between these fingerprints. The method requires neither bond assignment nor molecular alignment, and no training is involved.
The resulting fingerprints distinguish cis/trans and fac/mer isomers, as well as square-planar and tetrahedral coordination geometries. They also distinguish chair and twisted-boat cyclohexane while correctly identifying these as more similar than cyclohexane and piperidine. These examples are encouraging, although distinguishing two structures is only the first requirement: the more interesting question is whether the resulting distances reflect useful chemical similarity. Also, because the fingerprints depend only on interatomic distances, they cannot distinguish mirror-image enantiomers.
Figure 4 in the paper provides a more demanding test. Each molecule’s property is estimated by averaging the values for its five nearest neighbours in fingerprint space. For the small organic molecules in QM9, spectral fingerprints perform especially well for atomisation energies and polarisabilities, but, surprisingly, is tied with Morgan fingerprint for dipole moments and HOMO-LUMO gaps.
What surprised me even more is that Morgan fingerprints outperform the spectral fingerprints for both dipole moments and HOMO–LUMO gaps of the transition-metal complexes. You might expect the explicit geometry information to be particularly valuable here. One complication is that Morgan fingerprints are evaluated only for the roughly 73% of complexes that RDKit can parse, whereas spectral fingerprints work for the entire dataset. Nevertheless, the result is a useful reminder that greater structural resolution does not automatically produce more useful property neighbourhoods.
The computational cost is also impressive: the authors report generating fingerprints for 2.7 million protein-fragment structures in about three minutes, once coordinates are available. The code is available as SpectralScore. This approach might thus also be a cheaper alternatives to the shape-similarity algorithms used in drug discovery.
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