Implementation of the meta-GGA exchange-correlation functional in numerical atomic orbital basis: With systematic testing on SCAN, rSCAN, and r(2)SCAN functionals

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 including the kinetic energy density t, the meta-generalized-gradient approximation (meta-GGA) family of functionals achieves better accuracy and flexibility while retaining the efficiency of semi-local functionals. For example, the strongly constrained and appropriately normed (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 bases 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, rSCAN, and r(2)SCAN meta-GGA functionals. We further test water hexamers, weakly interacting molecules from the S22 dataset, as well as 13 semiconductors using the three functionals. The results show satisfactory agreement with previous calculations and available experimental values.

Automated summary

Kohn-Sham density functional theory (DFT) is widely used for electronic structure simulations, and meta-GGA functionals improve accuracy and flexibility while maintaining efficiency. The ABACUS package implements meta-GGA functionals with both numerical atomic orbitals and plane wave bases. Validation tests and calculations using SCAN, rSCAN, and r(2)SCAN functionals show satisfactory agreement with previous results and experimental values for various systems.