Efficient interpolation of molecular properties across chemical compound
  space with low-dimensional descriptors
Yun-Wen Mao Roman V. Krems
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.