Machine learning for non-additive intermolecular potentials: quantum chemistry to first-principles predictions

Abstract

Via a generally applicable method, we interpolate ab initio calculations of intermolecular interactions and produce successful first-principles predictions.

Accurate Prediction of Three-Body Intermolecular Interactions via Electron Deformation Density-Based Machine Learning

“…This emphasizes the need for careful selection of appropriate training data such that the training set contains a wide range of possible values. Our observations reflect those of Graham and Wheatley and Shiranirad et al, who both noted the importance of the training set composition and the need to sample the three-body PES adequately to achieve acceptable predictive performance while keeping the number of training points to a minimum. We investigate the appropriate selection of training data points further in section .…”

“…Even though the data set was split in a stratified manner (i.e., covering the range of all possible interaction energy values) into training and testing points, panels a and b of Figure show the very poor correlation between true and predicted test Δ E (3) and E int values, respectively. Many studies using ML to predict both total ,, and interaction energies , have noted the importance of selecting relevant configurations via active or sequential learning to achieve accurate test predictions. When fitting ML models to potential energy surfaces, the selected configurations are typically those that encompass the most thermodynamically relevant geometries and also those configurations that are “distinct” from each other (as measured by the distance between descriptors in kernel space, or using some other distance metric). − In this study, we fit interaction energies for diverse trimers containing different molecule types.…”

“…To choose an appropriate training set from our reference three-body interaction energies, we used sequential learning, , which is a type of active learning that starts with a minimal training set and progressively moves points from the test to training set. Starting with a training set containing the 5 highest-energy reference points, at each iteration a GPR model is trained using 5-fold cross validation to select the hyperparameters which minimize the cross-validated (CV) RMSE.…”

“…These steps are repeated until a sufficiently small (<0.5 kcal mol –1 ) RMSE is obtained. Graham and Wheatley found that using sequential learning to construct the training data set was essential to obtain an acceptably small RMSE from a minimal number of reference points: when using a different method for training data selection, the RMSE was approximately 10 times larger compared to that from sequential learning with the same number of training points. As shown below, we similarly observed a large difference in test RMSE when comparing models trained via sequential learning versus randomly splitting the data set into training and test portions.…”

“…Bose et al also looked at water clusters up to decamers, using support vector regression (SVR) to predict two- and three-body interaction terms. Most recently, Graham and Wheatley used GPR to interpolate between three-body nonadditive interaction data in the potential energy surface (PES) of CO 2 and Ar mixtures. For certain geometries on the PES, an empirical power-law form was used to describe the long-range behavior.…”