Can One Hear the Shape of a Molecule (from its Coulomb Matrix Eigenvalues)?

Area of Science:

• Computational chemistry
• Cheminformatics
• Molecular modeling

Background:

• Coulomb matrix eigenvalues (CMEs) are established 3D molecular representations.
• CMEs have applications in predicting molecular properties and aiding computational searches.
• Understanding CME properties is crucial for interpreting molecular structure and similarity.

Purpose of the Study:

• To establish the properties of the CME representation and its link to molecular structure.
• To assess the ability of CMEs to preserve chemical intuition regarding isomer and conformer similarity.
• To evaluate CME's effectiveness in distinguishing constitutional isomers, especially for larger molecules.

Main Methods:

• Utilizing the Gershgorin circle theorem to analyze CME properties.
• Analyzing a dataset of 309,000 conformational samples of acyclic alkanes (CnH2n) from methane to undecane.
• Applying supervised and unsupervised machine-learning algorithms to classify isomers based on CME data.

Main Results:

• The Gershgorin circle theorem provides a theoretical basis for CME properties and their relation to molecular structure.
• CMEs demonstrate a degree of success in preserving chemical intuition about molecular similarity.
• Machine learning models show a misclassification rate below 1% for distinguishing constitutional isomers, even as molecular size increases.

Conclusions:

• CME analysis, supported by the Gershgorin circle theorem, offers insights into molecular structure and similarity.
• CMEs are valuable for differentiating isomers, although perfect discrimination becomes challenging for larger acyclic alkanes.
• The study validates CMEs as a robust descriptor for molecular structure in computational chemistry, with practical implications for isomer identification.