Comparison of approximations in density functional theory calculations: Energetics and structure of binary oxides

• Published in: Physical review. B 2017-09, Vol.96 (9), Article 094102
• Main Authors: Hinuma, Yoyo, Hayashi, Hiroyuki, Kumagai, Yu, Tanaka, Isao, Oba, Fumiyasu
• Format: Article
• Language: English
• Subjects: Aluminum oxide; Approximation; Bismuth oxides; Bismuth trioxide; Crystal structure; Density functional theory; Enthalpy; First principles; Gallium oxides; Hafnium oxide; Indium oxides; Lanthanum oxides; Lattice parameters; Lead oxides; Materials information; Materials selection; Mathematical analysis; Matrix algebra; Matrix methods; Molybdenum oxides; Outliers (statistics); Silicon dioxide; Solid phases; Transition pressure
• ISSN: 2469-9950; 2469-9969
• DOI: 10.1103/PhysRevB.96.094102

High-throughput first-principles calculations based on density functional theory (DFT) are a powerful tool in data-oriented materials research. The choice of approximation to the exchange-correlation functional is crucial as it strongly affects the accuracy of DFT calculations. This study compares performance of seven approximations, six of which are based on Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) with and without Hubbard U and van der Waals corrections (PBE, PBE+U, PBED3, PBED3+U, PBEsol, and PBEsol+U), and the strongly constrained and appropriately normed (SCAN) meta-GGA on the energetics and crystal structure of elementary substances and binary oxides. For the latter, only those with closed-shell electronic structures are considered, examples of which include Cu2O, Ag2O, MgO, ZnO, CdO, SnO, PbO, Al2O3, Ga2O3, In2O3, La2O3, Bi2O3, SiO2, SnO2, PbO2, TiO2, ZrO2, HfO2, V2O5, Nb2O5, Ta2O5, MoO3, and WO3. Prototype crystal structures are selected from the Inorganic Crystal Structure Database (ICSD) and cation substitution is used to make a set of existing and hypothetical oxides. Two indices are proposed to quantify the extent of lattice and internal coordinate relaxation during a calculation. The former is based on the second invariant and determinant of the transformation matrix of basis vectors from before relaxation to after relaxation, and the latter is derived from shifts of internal coordinates of atoms in the unit cell. PBED3, PBEsol, and SCAN reproduce experimental lattice parameters of elementary substances and oxides well with few outliers. Notably, PBEsol and SCAN predict the lattice parameters of low dimensional structures comparably well with PBED3, even though these two functionals do not explicitly treat van der Waals interactions. SCAN gives formation enthalpies and Gibbs free energies closest to experimental data, with mean errors (MEs) of 0.01 and −0.04 eV, respectively, and root-mean-square errors (RMSEs) are both 0.07 eV. In contrast, all GGAs including those with Hubbard U and van der Waals corrections give 0.1 to 0.2 eV MEs and at least 0.11 eV RMSEs. Phonon contributions of solid phases to the formation enthalpies and Gibbs free energies are estimated to be small at less than ∼0.1 eV/atom within the quasiharmonic approximation. The same crystal structure appears as the lowest energy polymorph with different approximations in most of the investigated binary oxides. However, there are some systems where the