Improving the Accuracy of Machine-Learning-Based Exchange Correlation Functionals for Predicting Electronic Properties

The accuracy and efficiency of the density functional theory heavily depend on the exchange-correlation (XC) functional. Machine learning (ML) method can help to address the dilemma of accuracy versus efficiency in the XC functional approximation. For example, the Deep Kohn-Sham (DeePKS) method uplifts the accuracy of a base XC functional by employing a computationally efficient neural-network-based correction term, which is trained against a higher-level XC functional. However, the current DeePKS model is solely trained on energy and atomic forces, resulting in unsatisfactory performance in electronic properties like energy bands. In this study, we add the Hamiltonian matrix, as well as its eigenvalues and eigenvectors, into the loss function of the DeePKS model, and carry out tests in molecular systems like water clusters. The accuracy of the aforementioned electronic properties is largely improved, with satisfactory accuracy on energy and atomic forces. The model also shows considerable scalability from water cluster to bulk water.