Projector augmented-wave and all-electron calculations across the periodic table: a comparison of structural and energetic properties

TL;DR

This study compares all-electron and PAW density-functional theory calculations across the periodic table, evaluating their agreement on structural and energetic properties to establish reliability and identify discrepancies.

Contribution

It provides a comprehensive reference database comparing all-electron and PAW methods for materials properties, highlighting their agreement and discrepancies across the periodic table.

Findings

PAW and all-electron calculations agree within a few meV/atom and a fraction of a percent.

Current electronic-structure methods are generally reliable but show discrepancies needing standardization.

The study underscores the importance of verification, validation, and reference data sets in computational materials science.

Abstract

We construct a reference database of materials properties calculated using density-functional theory in the local or generalized-gradient approximation, and an all-electron or a projector augmented-wave (PAW) formulation, for verification and validation of first-principles simulations. All-electron calculations use the full-potential linearised augmented-plane wave method, as implemented in the \texttt{Elk} open-source code, while PAW calculations use the datasets developed by some of us in the open-source \texttt{PSlibrary} repository and the \texttt{Quantum ESPRESSO} distribution. We first calculate lattice parameters, bulk moduli, and energy differences for alkaline metals, alkaline earths, and $3d$ and $4d$ transition metals in three ideal, reference phases (simple cubic, fcc, and bcc), representing a standardized crystalline monoatomic solid-state test. Then, as suggested by K. Lejaeghere {\it et al.}, [Critical Reviews in Solid State and Material Sciences 39, p 1 (2014)], we compare the equations of state for all elements, except lanthanides and actinides, in their experimental phase (or occasionally a simpler, closely related one). PAW and all-electron energy differences and structural parameters agree in most cases within a few meV/atom and a fraction of a percent, respectively. This level of agreement, comparable with the previous study, includes also other PAW and all-electron data from the electronic-structure codes \texttt{VASP} and \texttt{WIEN2K}, and underscores the overall reliability of current, state-of-the-art electronic-structure calculations. At the same time, discrepancies that arise even within the same formulation for simple, fundamental structural properties point to the urgent need of establishing standards for verification and validation, reference data sets, and careful refinements of the computational approaches used.