Predicting molecular properties using adjacency matrix powers and atomic number sequences

Accurate prediction of physicochemical properties such as boiling points is central to virtual screening, process design, and regulatory assessment in cheminformatics. Here, we introduce a permutation-invariant molecular descriptor derived from powers of a weighted adjacency matrix-where edge weights encode bond types (single=1, double=2, triple=3, aromatic=1.5)-and a sorted atomic number sequence padded to a fixed length. The descriptor captures walk-based topological information while maintaining a compact, fixed-size representation for molecules up to 134 atoms. We benchmark its performance against five established representations (MACCS keys, Morgan fingerprints, Mordred descriptors, Coulomb matrix, Weisfeiler-Lehman graph kernels) using Support Vector Regression, Random Forest, Extreme Gradient Boosting (XGBoost), and a Directed Message-Passing Neural Network (D-MPNN via Chemprop).

On a diverse dataset of 5432 small organic compounds with experimentally measured boiling points, our descriptor paired with XGBoost achieved a 5-fold cross-validation mean absolute error of 18.52±0.34°C, root mean square error of 27.16±0.32°C, and $R^2$=0.898±0.002. While high-dimensional Mordred descriptors yielded the most accurate predictions (MAE=10.54±0.23°C, $R^2$=0.960±0.003), our descriptor presents a balanced alternative to simple fingerprints and more complex graph-based representations.

This study demonstrates that a computationally efficient, walk-based descriptor can achieve robust and interpretable performance in boiling-point regression tasks. Its low dimensionality and generalizability across models make it a promising tool for broader thermophysical property prediction and integration into graph-neural-network architectures.