Test set for materials science and engineering with user-friendly graphic 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 electronic-structure calculations is crucial to advanced method development, high-throughput computations, and data analyses. In this paper, we present a test set for computational materials science and engineering (MSE), that aims to provide 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 as representatives for the first- and second-row elements and their binaries with cubic crystal structures and various bonding characters. A strong effort is made to push the borders of numerical accuracy for cohesive properties as calculated using the local-density approximation (LDA), several generalized gradient approximations (GGAs), meta-GGAs and hybrids in \textit{all-electron} resolution, and the second-order Møller-Plesset perturbation theory (MP2) and the random-phase approximation (RPA) with frozen-core approximation based on \textit{all-electron} 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 \href{http://mse.fhi-berlin.mpg.de}{\texttt{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 post-processing error analysis.

arXiv comment18 pages, 7 figures

References in corpus (14)

• Climbing the Density Functional Ladder: Non-Empirical Meta-Generalized Gradient Approximation Designed for Molecules and Solids
• Van der Waals density functionals applied to solids
• Assessing the Performance of Recent Density Functionals for Bulk Solids
• Resolution-of-identity approach to Hartree-Fock, hybrid density functionals, RPA, MP2, and \textit{GW} with numeric atom-centered orbital basis functions
• Random-phase approximation and its applications in computational chemistry and materials science
• Error estimates for solid-state density-functional theory predictions: an overview by means of the ground-state elemental crystals
• Rungs 1 to 4 of DFT Jacob's ladder: extensive test on the lattice constant, bulk modulus, and cohesive energy of solids
• Beyond the Random Phase Approximation for the Electron Correlation Energy: The Importance of Single Excitations
• Density Functionals that Recognize Covalent, Metallic, and Weak Bonds
• A Full Configuration Interaction Perspective on the Homogeneous Electron Gas
• Exchange-Correlation Energy from Pairing Matrix Fluctuation and the Particle-Particle Random Phase Approximation
• Many-body quantum chemistry for the electron gas: convergent perturbative theories
• Coupled Cluster Channels in the Homogeneous Electron Gas
• Towards efficient orbital-dependent density functionals for weak and strong correlation

Cited by in corpus (6)

• Data-driven materials science: status, challenges and perspectives
• Coupled cluster theory in materials science
• All-electron periodic $G_0{W}_0$ implementation with numerical atomic orbital basis functions: algorithm and benchmarks
• Phase Stability of the Argon Crystal: A First-Principles Study Based on Random Phase Approximation plus Renormalized Single Excitation Corrections
• Finite-size Effects in periodic EOM-CCSD for Ionization Energies and Electron Affinities: Convergence Rate and Extrapolation to the Thermodynamic Limit
• Self-interaction corrected SCAN functional for molecules and solids in the numeric atom-center orbital framework