We design a density-functional-theory (DFT) exchange-correlation functional that enables an accurate treatment of systems with electronic surfaces. Surface-specific approximations for both exchange and correlation energies are developed. A subsystem functional approach is then used: an interpolation index combines the surface functional with a functional for interior regions. When the local density approximation is used in the interior, the result is a straightforward functional for use in self-consistent DFT. The functional is validated for two metals (Al, Pt) and one semiconductor (Si) by calculations of (i) established bulk properties (lattice constants and bulk moduli) and (ii) a property where surface effects exist (the vacancy formation energy). Good and coherent results indicate that this functional may serve well as a universal first choice for solid-state systems and that yet improved functionals can be constructed by this approach.

Elpasolite is the predominant quaternary crystal structure (${\mathrm{AlNaK}}_2{\mathrm{F}}_6$ prototype) reported in the Inorganic Crystal Structure Database. We develop a machine learning model to calculate density functional theory quality formation energies of all $\sim 2\times {10}^6$ pristine $AB{C}_2{D}_6$ elpasolite crystals that can be made up from main-group elements (up to bismuth). Our model’s accuracy can be improved systematically, reaching a mean absolute error of $0.1\mathrm{eV}/\mathrm{atom}$ for a training set consisting of $10\times {10}^3$ crystals. Important bonding trends are revealed: fluoride is best suited to fit the coordination of the $D$ site, which lowers the formation energy whereas the opposite is found for carbon. The bonding contribution of the elements $A$ and $B$ is very small on average. Low formation energies result from $A$ and $B$ being late elements from group II, $C$ being a late (group I) element, and $D$ being fluoride. Out of $2\times {10}^6$ crystals, 90 unique structures are predicted to be on the convex hull—among which is ${\mathrm{NFAl}}_2{\mathrm{Ca}}_6$, with a peculiar stoichiometry and a negative atomic oxidation state for Al.

We compare the accuracy of conventional semilocal density functional theory (DFT), the DFT+U method, and the Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional for structural parameters, redox reaction energies, and formation energies of transition metal compounds. Conventional DFT functionals significantly underestimate redox potentials for these compounds. Zhou et al. [Phys. Rev. B 70, 235121 (2004)] addressed this issue with DFT+U and a linear-response scheme for calculating U values. We show that the Li intercalation potentials of prominent Li-ion intercalation battery materials, such as the layered LixMO2 (M=Co and Ni), LixTiS2; olivine LixMPO4 (M=Mn, Fe, Co, and Ni); and spinel-like LixMn2O4, LixTi2O4, are also well reproduced by HSE06, due to the self-interaction error correction from the partial inclusion of Hartree-Fock exchange. For formation energies, HSE06 performs well for transition metal compounds, which typically are not well reproduced by conventional DFT functionals but does not significantly improve the results of nontransition metal oxides. Hence, we find that hybrid functionals provide a good alternative to DFT+U for transition metal applications when the large extra computational effort is compensated by the benefits of (i) avoiding species-specific adjustable parameters and (ii) a more universal treatment of the self-interaction error that is not exclusive to specific atomic orbital projections on selected ions.

We show that the AM05 functional [Armiento and Mattsson, Phys. Rev. B 72, 085108 (2005)] has the same excellent performance for solids as the hybrid density functionals tested in Paier et al. [J. Chem. Phys. 124, 154709 (2006); 125, 249901 (2006)]. This confirms the original finding that AM05 performs exceptionally well for solids and surfaces. Hartree–Fock hybrid calculations are typically an order of magnitude slower than local or semilocal density functionals such as AM05, which is of a regular semilocal generalized gradient approximation form. The performance of AM05 is on average found to be superior to selecting the best of local density approximation and PBE for each solid. By comparing data from several different electronic-structure codes, we have determined that the numerical errors in this study are equal to or smaller than the corresponding experimental uncertainties.

Two of the most popular generalized gradient approximations used in the applications of the density functional theory, PW91 and PBE, are generally regarded as essentially equivalent. They produce similar numerical results for many simple properties, such as lattice constants, bulk moduli, and atomization energies. We examine more complex properties of systems with electronic surface regions, with the specific application of the monovacancy formation energies of Pt and Al. A surprisingly large and consistent discrepancy between PBE and PW91 results is obtained. This shows that despite similarities found between some simple material properties, PBE and PW91 are not equivalent. The differences obtained for the monovacancy formation energies are related to differences in surface intrinsic errors which are substantiated using the idealized, well-controlled, jellium surface model. In view of the differences obtained with the PW91 and PBE functionals we develop separate surface intrinsic error corrections for these and revisit some earlier results.