Novel descriptors for the prediction of molecular properties

Abstract Molecular descriptors are fundamental to the fields of cheminformatics, drug discovery, and materials science, serving as quantitative representations of molecular structures that facilitate the prediction of various properties and activities. In this article, we introduce three matrix-based descriptors, <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mrow> <m:mi mathvariant="script">D</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo>,</m:mo> <m:msub> <m:mrow> <m:mi mathvariant="script">D</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msub> </m:math> {{\mathscr{D}}}_{1},{{\mathscr{D}}}_{2} , and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mrow> <m:mi mathvariant="script">D</m:mi> </m:mrow> <m:mrow> <m:mn>3</m:mn> </m:mrow> </m:msub> <m:mo>,</m:mo> </m:math> {{\mathscr{D}}}_{3}, engineered from distance and degree matrices of hydrogen-suppressed molecular graphs, aimed at capturing structural and topological information with minimal dimensionality. To validate their powers, we use two machine learning models, a graph neural network (GNN) and XGBoost, to predict two physicochemical properties, boiling points, and enthalpy of vaporization of alkanes. We observe that both the models remain successful in relating the molecules in terms of their describing vectors to their properties. A comprehensive cross-validation reveals that the proposed descriptors, particularly <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mrow> <m:mi mathvariant="script">D</m:mi> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msub> </m:math> {{\mathscr{D}}}_{2} and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mrow> <m:mi mathvariant="script">D</m:mi> </m:mrow> <m:mrow> <m:mn>3</m:mn> </m:mrow> </m:msub> </m:math> {{\mathscr{D}}}_{3} , consistently outperform the traditional matrix-based representations, the Coulomb matrix, and the signless Laplacian matrix. Notably, <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mrow> <m:mi mathvariant="script">D</m:mi> </m:mrow> <m:mrow> <m:mn>3</m:mn> </m:mrow> </m:msub> </m:math> {{\mathscr{D}}}_{3} , with only ten features, achieves comparable accuracy to the high-dimensional descriptors, reflecting excellent generalization and interpretability. The GNN model demonstrates enhanced performance stability and robustness to descriptor variance, while XGBoost provides complementary insights into descriptor importance and error behavior. Our findings underscore the utility of low-dimensional, structurally informed descriptors in driving accurate and scalable property prediction models and offer a versatile foundation for future quantitative structure–property relationship applications across diverse molecular domains.