Benchmarking DFT Approximations for studying Apatites

Despite the growing interest in apatites, available experimental studies on their properties are limited in scope. Researchers, therefore, are increasingly resorting to predictions using the density functional theory (DFT). However, large deviations can be seen between DFT based estimates and experimental results, presumably due to approximations made in DFT models. We undertake a comprehensive benchmarking exercise involving sixteen exchange-correlation (XC) functionals (including dispersion corrections), five pseudopotentials (PPs), and two basis sets to unravel their best combination for studying apatites. The comparison involves lattice parameters, elastic constants, bulk modulus, and band gap of three specific apatites -- hydroxyapatite, fluorapatite and chlorapatite. We show, quite reassuringly, a weak sensitivity of the properties to the choice of PP and the basis. The XC approximation and/or the inclusion of the dispersion corrections has significant influence on the accuracy of predicted properties. The underlying reasons behind different XC functionals providing different properties are identified. Our recommendation is to use dispersion corrections in XC functionals for studying apatites but with some caution. Overall, the optB86b-vdW functional provides the best accuracy when compared to the available experimental results.