Michiel J. van Setten

Reproducibility in density functional theory calculations of solids

A comparison of DFT methods Density functional theory (DFT) is now routinely used for simulating material properties. Many software packages are available, which makes it challenging to know which are the best to use for a specific calculation. Lejaeghere et al. compared the calculated values for the equation of states for 71 elemental crystals from 15 different widely used DFT codes employing 40 different potentials (see the Perspective by Skylaris). Although there were variations in the calculated values, most recent codes and methods converged toward a single value, with errors comparable to those of experiment. Science, this issue p. 10.1126/science.aad3000; see also p. 1394 A survey of recent density functional theory methods shows a convergence to more accurate property calculations. [Also see Perspective by Skylaris] INTRODUCTION The reproducibility of results is one of the underlying principles of science. An observation can only be accepted by the scientific community when it can be confirmed by independent studies. However, reproducibility does not come easily. Recent works have painfully exposed cases where previous conclusions were not upheld. The scrutiny of the scientific community has also turned to research involving computer programs, finding that reproducibility depends more strongly on implementation than commonly thought. These problems are especially relevant for property predictions of crystals and molecules, which hinge on precise computer implementations of the governing equation of quantum physics. RATIONALE This work focuses on density functional theory (DFT), a particularly popular quantum method for both academic and industrial applications. More than 15,000 DFT papers are published each year, and DFT is now increasingly used in an automated fashion to build large databases or apply multiscale techniques with limited human supervision. Therefore, the reproducibility of DFT results underlies the scientific credibility of a substantial fraction of current work in the natural and engineering sciences. A plethora of DFT computer codes are available, many of them differing considerably in their details of implementation, and each yielding a certain “precision” relative to other codes. How is one to decide for more than a few simple cases which code predicts the correct result, and which does not? We devised a procedure to assess the precision of DFT methods and used this to demonstrate reproducibility among many of the most widely used DFT codes. The essential part of this assessment is a pairwise comparison of a wide range of methods with respect to their predictions of the equations of state of the elemental crystals. This effort required the combined expertise of a large group of code developers and expert users. RESULTS We calculated equation-of-state data for four classes of DFT implementations, totaling 40 methods. Most codes agree very well, with pairwise differences that are comparable to those between different high-precision experiments. Even in the case of pseudization approaches, which largely depend on the atomic potentials used, a similar precision can be obtained as when using the full potential. The remaining deviations are due to subtle effects, such as specific numerical implementations or the treatment of relativistic terms. CONCLUSION Our work demonstrates that the precision of DFT implementations can be determined, even in the absence of one absolute reference code. Although this was not the case 5 to 10 years ago, most of the commonly used codes and methods are now found to predict essentially identical results. The established precision of DFT codes not only ensures the reproducibility of DFT predictions but also puts several past and future developments on a firmer footing. Any newly developed methodology can now be tested against the benchmark to verify whether it reaches the same level of precision. New DFT applications can be shown to have used a sufficiently precise method. Moreover, high-precision DFT calculations are essential for developing improvements to DFT methodology, such as new density functionals, which may further increase the predictive power of the simulations. Recent DFT methods yield reproducible results. Whereas older DFT implementations predict different values (red darts), codes have now evolved to mutual agreement (green darts). The scoreboard illustrates the good pairwise agreement of four classes of DFT implementations (horizontal direction) with all-electron results (vertical direction). Each number reflects the average difference between the equations of state for a given pair of methods, with the green-to-red color scheme showing the range from the best to the poorest agreement. The widespread popularity of density functional theory has given rise to an extensive range of dedicated codes for predicting molecular and crystalline properties. However, each code implements the formalism in a different way, raising questions about the reproducibility of such predictions. We report the results of a community-wide effort that compared 15 solid-state codes, using 40 different potentials or basis set types, to assess the quality of the Perdew-Burke-Ernzerhof equations of state for 71 elemental crystals. We conclude that predictions from recent codes and pseudopotentials agree very well, with pairwise differences that are comparable to those between different high-precision experiments. Older methods, however, have less precise agreement. Our benchmark provides a framework for users and developers to document the precision of new applications and methodological improvements.

Ab initiostudy ofMg(AlH4)2

Magnesium alanate Mg(AlH4)2 has recently raised interest as a potential material for hydrogen storage. We apply ab initio calculations to characterize structural, electronic and energetic properties of Mg(AlH4)2. Density functional theory calculations within the generalized gradient approximation (GGA) are used to optimize the geometry and obtain the electronic structure. The latter is also studied by quasi-particle calculations at the GW level. Mg(AlH4)2 is a large band gap insulator with a fundamental band gap of 6.5 eV. The hydrogen atoms are bonded in AlH4 complexes, whose states dominate both the valence and the conduction bands. On the basis of total energies, the formation enthalpy of Mg(AlH4)2 with respect to bulk magnesium, bulk aluminum and hydrogen gas is 0.17 eV/H2 (at T = 0). Including corrections due to the zero point vibrations of the hydrogen atoms this number decreases to 0.10 eV/H2. The enthalpy of the dehydrogenation reaction Mg(AlH4)2 -> MgH2 +2Al+3H2(g) is close to zero, which impairs the potential usefulness of magnesium alanate as a hydrogen storage material.

GW100: Benchmarking G0W0 for Molecular Systems.

We present the GW100 set. GW100 is a benchmark set of the ionization potentials and electron affinities of 100 molecules computed with the GW method using three independent GW codes and different GW methodologies. The quasi-particle energies of the highest-occupied molecular orbitals (HOMO) and lowest-unoccupied molecular orbitals (LUMO) are calculated for the GW100 set at the G0W0@PBE level using the software packages TURBOMOLE, FHI-aims, and BerkeleyGW. The use of these three codes allows for a quantitative comparison of the type of basis set (plane wave or local orbital) and handling of unoccupied states, the treatment of core and valence electrons (all electron or pseudopotentials), the treatment of the frequency dependence of the self-energy (full frequency or more approximate plasmon-pole models), and the algorithm for solving the quasi-particle equation. Primary results include reference values for future benchmarks, best practices for convergence within a particular approach, and average error bars for the most common approximations.

First principles modelling of magnesium titanium hydrides

Mixing Mg with Ti leads to a hydride Mg(x)Ti((1 - x))H(2) with markedly improved (de)hydrogenation properties for x ≤ 0.8, as compared to MgH(2). Optically thin films of Mg(x)Ti((1 - x))H(2) have a black appearance, which is remarkable for a hydride material. In this paper we study the structure and stability of Mg(x)Ti((1 - x))H(2), x = 0-1 by first-principles calculations at the level of density functional theory. We give evidence for a fluorite to rutile phase transition at a critical composition x(c) = 0.8-0.9, which correlates with the experimentally observed sharp decrease in (de)hydrogenation rates at this composition. The densities of states of Mg(x)Ti((1 - x))H(2) have a peak at the Fermi level, composed of Ti d states. Disorder in the positions of the Ti atoms easily destroys the metallic plasma, however, which suppresses the optical reflection. Interband transitions result in a featureless optical absorption over a large energy range, causing the black appearance of Mg(x)Ti((1 - x))H(2).

Benchmark of GW Approaches for the GW100 Test Set

For the recent GW100 test set of molecular ionization energies, we present a comprehensive assessment of different GW methodologies: fully self-consistent GW (scGW), quasiparticle self-consistent GW (qsGW), partially self-consistent GW0 (scGW0), perturbative GW (G0W0), and optimized G0W0 based on the minimization of the deviation from the straight-line error (DSLE-min GW). We compare our GW calculations to coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] reference data for GW100. We find scGW and qsGW ionization energies in excellent agreement with CCSD(T), with discrepancies typically smaller than 0.3 eV (scGW) and 0.2 eV (qsGW), respectively. For scGW0 and G0W0 the deviation from CCSD(T) is strongly dependent on the starting point. We further relate the discrepancy between the GW ionization energies and CCSD(T) to the deviation from straight line error (DSLE). In DSLE-minimized GW calculations, the DSLE is significantly reduced, yielding a systematic improvement in the description of the ionization energies.

Automation methodologies and large-scale validation for GW: Towards high-throughput GW calculations

The search for new materials, based on computational screening, relies on methods that accurately predict, in an automatic manner, total energy, atomic-scale geometries, and other fundamental characteristics of materials. Many technologically important material properties directly stem from the electronic structure of a material, but the usual workhorse for total energies, namely density-functional theory, is plagued by fundamental shortcomings and errors from approximate exchange-correlation functionals in its prediction of the electronic structure. At variance, the

GW100: A Plane Wave Perspective for Small Molecules

GW

First-principles study of paraelectric and ferroelectric CsH2PO4 including dispersion forces: Stability and related vibrational, dielectric, and elastic properties

method is currently the state-of-the-art {\em ab initio} approach for accurate electronic structure. It is mostly used to perturbatively correct density-functional theory results, but is however computationally demanding and also requires expert knowledge to give accurate results. Accordingly, it is not presently used in high-throughput screening: fully automatized algorithms for setting up the calculations and determining convergence are lacking. In this work we develop such a method and, as a first application, use it to validate the accuracy of

First-principles investigation of the structural, dynamical, and dielectric properties of kesterite, stannite, and PMCA phases of Cu2ZnSnS4

G_0W_0

High-throughput density-functional perturbation theory phonons for inorganic materials

using the PBE starting point, and the Godby-Needs plasmon pole model (