Development and assessment of the machine-learned electron correlation model

Abstract

We constructed a machine-learned electronic correlation model to develop a method for evaluating electronic correlation energy with high accuracy and low computational cost. This model is constructed using the correlation energy density at the complete basis-set (CBS) limit of coupled cluster theory as the objective variable. The grid-based energy density analysis and composite method to evaluate the correlation energy at the CBS limit, which were proposed in our group, were applied to obtain the objective variable. As the descriptor, density variables such as electron density and density gradient were used in the same way as correlation functionals in density functional theory (DFT). A multi-layer neural network was adopted as a machine learning method. Numerical assessments clarified that our correlation model is capable of reproducing the accurate electron correlation energy with a relatively small basis set. Furthermore, reaction energies of chemical reactions were calculated by combining with the CBS limit of the Hartree−Fock energy, resulting in the accuracy better than DFT calculations based on a large number of exchange-correlation functionals.