Δ-Machine Learning of Polarizability Tensors Using a Dipole Interaction Model

As a fundamental response property, the molecular polarizability is responsible for a wide variety of physical phenomena relevant for understanding light-matter and intermolecular interactions. Therefore, it is important to have accurate and efficient methods to calculate the polarizability tensor. In this work, we introduce a model that combines a polarizable dipole interaction model (PIM) with Δ-machine learning to predict polarizability tensors, which we refer to as Δ_PIM^CCSD. To describe the rotational symmetry, we adapt a unique reference geometry obtained by diagonalizing the PIM polarizability tensor. A major benefit is that only the diagonal elements of the polarizability tensor needs to be learned. The model was parameterized to the coupled cluster singles and doubles (CCSD) polarizabilities from the QM7b data set and was used to predict the polarizabilities for various systems, such as small molecules and molecules from the QM9 data set. We show that the Δ_PIM^CCSD is comparable in accuracy to density-functional theory with the B3LYP exchange correlation functional (DFT/B3LYP) at a lower cost for molecules with similar chemical composition as the QM7b data set. For the QM9 data set, this was also found, although only after correcting for the smaller basis set used for calculating the polarizabilities in this data set. For molecules smaller and chemically more diverse than the training set, we find that the model performs worse than DFT/B3LYP. Ultimately, our work suggests that larger and more chemically diverse data sets with polarizabilities obtained at a high level of theory are needed. Finally, our results suggest that the model can be improved by incorporating atom-specific polarizabilities into PIM to better account for local environments. In summary, the combination of PIM with Δ-machine learning provides a simple and promising approach for predicting polarizability tensors.