Deep learning functional relationship between electron density and exchange-correlation potential

Abstract

The Schrödinger equation is mainly basis of quantum mechanics methods to solve physical and chemical problems. Density-functional theory is one of the most popular methods, since it has high efficiency and reliable accuracy. Despite the success, there are still many problems in DFT continuing to haunt scientists, such as poor description of dissociation problem. To solve this problem, an exchange-correlation potential is set up by a fully-connected neural network. The near-precise exchange-correlation potential is obtained by a simple \texorpdfstring{$\Delta v_{\textrm{H}}(\mathbf{r})$~}~correction Kohn-Sham inversion method. The converged electron density generated by this method together with the near-precise potential build the dataset for training and validation. The fully-connected neural network is constructed and applied to the dataset to map the (quasi-) local electron density distribution to the potential at the center of the (quasi-) local region. The well-trained neural network model works as a term of exchange-correlation functional for additional self-consistent calculations. Five systems, including HF, H\textsubscript{2}O, CH\textsubscript{4}, HF/H\textsubscript{2}O/CH\textsubscript{4} and HF/H\textsubscript{2}O/NH\textsubscript{3}/CH\textsubscript{4}/C\textsubscript{2}HF, have been studied by using this fully-connected based neural network functional. The converged electron density and corresponding molecular properties are generated. The results of B3LYP and CCSD are also calculated for comparison and benchmark respectively. The accuracy of the fully-connected neural network based functional is confirmed by the better results than B3LYP ones. Another test on CH\textsubscript{3}OH molecule, which is out of the dataset, is used to test the transferability of the neural network functional. The fully-connected neural network functional works very well for equilibrium and non-equilibrium structures, especially solving the dissociation problem. Despite the success, there are still some shortcomings that need to be further considered. As knowledge and technology develops, the problems can be further resolved, that the neural network can act as a universal functional for various systems.