A semi-local kinetic energy density functional (KEDF) was constructed based on machine learning (ML). The present scheme adopts electron densities and their gradients up to third-order as the explanatory variables for ML and the Kohn-Sham (KS) kinetic energy density as the response variable in atoms and molecules. Numerical assessments of the present scheme were performed in atomic and molecular systems, including first- and second-period elements. The results of 37 conventional KEDFs with explicit formulae were also compared with those of the ML KEDF with an implicit formula. The inclusion of the higher order gradients reduces the deviation of the total kinetic energies from the KS calculations in a stepwise manner. Furthermore, our scheme with the third-order gradient resulted in the closest kinetic energies to the KS calculations out of the presented functionals.
A quantum chemical reaction prediction (QC-RP) method based on machine learning was developed to predict chemical products from given reactants. The descriptors contain atomic information in reactants such as charge, molecular structure, and atomic/molecular orbitals obtained by the quantum chemical calculations. The QC-RP method involves two procedures, namely, learning and prediction. The learning procedure constructs screening and ranking classifiers using 1625 polar and 95 radical reactions in a textbook of organic chemistry. In the prediction procedure, the screening classifier distinguishes reactive and unreactive atoms and the ranking one provides reactive atom pairs in ranking order. Numerical assessments confirmed the high accuracies both of the screening and ranking classifiers in the prediction procedures. Furthermore, an analysis on the classifiers unveiled important descriptors for the prediction.
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