Implementation of the SCAN Exchange-Correlation Functional with Numerical Atomic Orbitals

Abstract: Kohn-Sham density functional theory (DFT) is nowadays widely used for electronic structure theory simulations, and the accuracy and efficiency of DFT rely on approximations of the exchange-correlation functional. By inclusion of the kinetic energy density $\tau$, the meta-generalized-gradient approximation (meta-GGA) family of functionals achieves better accuracy and flexibility while retaining the efficiency of semi-local functionals. The SCAN meta-GGA functional has been proven to yield accurate results for solid and molecular systems. We implement meta-GGA functionals with both numerical atomic orbitals and plane wave basis in the ABACUS package. Apart from the exchange-correlation potential, we also discuss the evaluation of force and stress. To validate our implementation, we perform finite-difference tests and convergence tests with the SCAN meta-GGA functional. We further test water hexamers, weakly interacting molecules of the S22 dataset, as well as 13 semiconductors. The results show satisfactory agreements with previous calculations and available experimental values.