Assessing the performance of exchange-correlation functionals on lattice constants of binary solids at room temperature within the quasiharmonic approximation

The exchange-correlation functional is at the core of density functional theory (DFT) and determines the accuracy of DFT in describing the interactions among electrons/ions in solids and molecules. The strongly constrained and appropriately normed functional (SCAN) and its derivatives, regularized SCAN (rSCAN) and regularized-restored SCAN (r2SCAN), are particularly promising due to their remarkable overall accuracy in the description of various properties while retaining a high computational efficiency as compared to hybrid functionals. However, an exhaustive assessment on the performance of these functionals in predicting the finite-temperature lattice constant of solids is still lacking. Here, we systematically study the room-temperature lattice constants of 60 cubic binary compounds within the quasiharmonic approximation using SCAN, rSCAN, r2SCAN, local density approximation (LDA), and two common generalized gradient approximation (GGA) functionals, Perdew-Burke-Ernzerhof (PBE) and revised PBE for solid and surface (PBEsol). We found that SCAN exhibits numerical instabilities in free energy calculations, manifested by the presence of spurious imaginary frequencies in phonon dispersion relationships and poor fitting in Murnaghan's equation of state of Helmholtz free energy for 30 compounds. The revised SCAN functionals show much better numerical stabilities and reduce the number of the compounds with numerical issues to 22 and 9 for rSCAN and r2SCAN, respectively. The mean relative absolute errors (MRAE) of the calculated lattice constants at room temperature for the remaining 30 binary compounds are 0.92%, 1.10%, 0.32%, 0.51%, 0.58%, and 0.67% for LDA, PBE, PBEsol, SCAN, rSCAN, and r2SCAN, respectively. Furthermore, we found that the SCAN functional incorrectly predicts unstable phonon modes for a few compounds at their equilibrium volumes, which indicates the existence of a new ground state structure with lower energy than the cubic structure at 0 K, disagreeing with experiments. Our results provide a useful guide in choosing suitable functionals in describing anharmonic phonons and shed light on second-order force constant calculations that may help to develop more accurate exchange-correlation functionals for solids.