Main-group test set for materials science and engineering with user-friendly graphical tools for error analysis: systematic benchmark of the numerical and intrinsic errors in state-of-the-art electronic-structure approximations

Abstract

Understanding the applicability and limitations of electronic-structure methods needs careful and efficient comparison with accurate reference data. Knowledge of the quality and errors of electronicstructure calculations is crucial to advanced method development, high-throughput computations and data analyses. In this paper, we present a main-group test set for computational materials science and engineering (MSE), that provides accurate and easily accessible crystal properties for a hierarchy of exchange-correlation approximations, ranging from the well-established mean-field approximations to the state-of-the-art methods of many-body perturbation theory. We consider cohesive energy, lattice constant and bulk modulus of a set of materials that representatives for the firstand secondrow elements and their binaries with cubic crystal structures and various bonding characters. A strong effort is made to achieve high numerical accuracy for cohesive properties as calculated using the localdensity approximation (LDA), several generalized gradient approximations (GGAs), meta-GGAs and hybrids in all-electron resolution, and the second-order Møller-Plesset perturbation theory (MP2) and the random-phase approximation (RPA) both with frozen-core approximation based on allelectron Hartree-Fock, PBE and/or PBE0 references. This results in over 10 000 calculations, which record a comprehensive convergence test with respect to numerical parameters for a wide range of electronic-structure methods within the numerical atom-centered orbital framework. As an indispensable part of the MSE test set, a web site is established http://mse.fhi-berlin.mpg.de. This not only allows for easy access to all reference data but also provides user-friendly graphical tools for postprocessing error analysis.OPEN ACCESS RECEIVED dimensionality. In quantum chemistry for atoms and molecules, test sets with accurate reference values for various relevant chemical and physical properties have been since long established [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. These test sets play an instrumental role in the development of hierarchical electronic-structure approximations for both wavefunction theory (WFT) and density functional theory (DFT). In particular, they are needed for validating numerical implementations [16][17][18][19], investigating the basis set convergence [20][21][22][23][24], and benchmarking the intrinsic limitations of the various quantum-chemistry methods [1-6, 14, 15, 25-38]. For most existing test sets, the developers provide all essential information for each calculation, including molecular geometry, basis set, and/or code-specific numerical setting [39, 40].Condensed-matter physics and materials science is lacking behind, so far, with respect to comparable benchmark datasets. Two types of accurate reference data are crucial. One is essentially the exact values, obtained from either precise experiments or high-level theoretical calculations. They are prerequisite for an unbiased benchmark of the intrinsic errors associa...

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