Efficient interpolation of molecular properties across chemical compound space with low-dimensional descriptors

Abstract: We demonstrate accurate data-starved models of molecular properties for interpolation in chemical compound spaces with low-dimensional descriptors. Our starting point is based on three-dimensional, universal, physical descriptors derived from the properties of the distributions of the eigenvalues of Coulomb matrices. To account for the shape and composition of molecules, we combine these descriptors with six-dimensional features informed by the Gershgorin circle theorem. We use the nine-dimensional descriptors thus obtained for Gaussian process regression based on kernels with variable functional form, leading to extremely efficient, low-dimensional interpolation models. The resulting models trained with 100 molecules are able to predict the product of entropy and temperature ($S \times T$) and zero point vibrational energy (ZPVE) with the absolute error under 1 kcal mol$^{-1}$ for $> 78$ \% and under 1.3 kcal mol$^{-1}$ for $> 92$ \% of molecules in the test data. The test data comprises 20,000 molecules with complexity varying from three atoms to 29 atoms and the ranges of $S \times T$ and ZPVE covering 36 kcal mol$^{-1}$ and 161 kcal mol$^{-1}$, respectively. We also illustrate that the descriptors based on the Gershgorin circle theorem yield more accurate models of molecular entropy than those based on graph neural networks that explicitly account for the atomic connectivity of molecules.