Francesca Tavazza

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.

Elongation and breaking mechanisms of gold nanowires under a wide range of tensile conditions

Semistatic density functional theory is used to explore the evolution of [1 1 0] and [1 1 1] gold nanowires during tensile deformation under a wide range of conditions, including different tensile axes (along high- and low-symmetry directions), nanowire shapes, and effective strain rates. Large structural changes are observed during the elongation. The analysis of such low-energy intermediate configurations provides quantitative information about the underlying energy landscape that cannot be obtained through experiments or more approximate modeling methods, and four stable intermediate atomic structures are identified. A rich diversity of deformation pathways is uncovered that converge to only two final local configurations with reproducible breaking strengths, in agreement with experimental results. Such a high reproducibility in the breaking force makes gold nanowires excellent candidates as intrinsic force standards at the nanolevel.

Dislocation nucleation during nanoindentation of aluminum

Through multiscale simulations, we explore the influence of both smooth and atomically rough indenter tips on the nucleation of dislocations during nanoindentation of single-crystal aluminum. We model the long-range strain with finite element analysis using anisotropic linear elasticity. We then model a region near the indenter atomistically and perform molecular dynamics with an embedded atom method interatomic potential. We find that smooth indenters nucleate dislocations below the surface but rough indenters can nucleate dislocations both at the surface and below. Increasing temperature from 0 to 300 K creates prenucleation defects in the region of high stress and decreases the critical depth.

Stability hierarchy of the pseudomorphic FeSi2 phases: α, γ, and defected CsCl

We present a total‐energy stability diagram of FeSi2 phases which explains the recent experimental findings of pseudomorphic epitaxy on Si(111), depending on film thickness and growth conditions. In particular, our tight binding calculations point out that the appearance of the fluorite structure (γ) at very low coverages can only be attributed to a binding energy with the silicon substrate sizeably larger than tetragonal (α) and CsCl‐defected phases.

Al2O3 as a suitable substrate and a dielectric layer for n-layer MoS2

Sapphire (α-Al2O3) is a common substrate for the growth of single- to few-layer MoS2 films, and amorphous aluminium oxide serves as a high-κ dielectric gate oxide for MoS2 based transistors. Using density-functional theory calculations with a van der Waals functional, we investigate the structural, energetic, and electronic properties of n-layer MoS2 (n = 1and 3) on the α-Al2O3 (0001) surface. Our results show that the sapphire stabilizes single-layer and tri-layer MoS2, while having a negligible effect on the structure, band gap, and electron effective masses of MoS2. This combination of a strong energetic stabilization and weak perturbation of the electronic properties shows that α-Al2O3 can serve as an ideal substrate for depositing ultra-thin MoS2 layers and can also serve as a passivation or gate-oxide layer for MoS2 based devices.

Implications of the choice of interatomic potential on calculated planar faults and surface properties in nickel

With the increasing use of molecular simulation to understand deformation mechanisms in transition metals, it is important to assess how well the simulations reproduce physical behavior both near equilibrium and under more extreme conditions. In particular, it is important to examine whether simulations predict unusual deformation paths that are competitive with those experimentally observed. In this work we compare generalized planar fault energy landscapes and surface energies for various interatomic potentials with those from density functional theory calculations to examine how well these more complicated planar faults and surface energies are captured and whether any deformations are energetically competitive with the {111}⟨112⟩ slip observed in FCC crystals. To do this we examine not just the (111) fault orientation, but also the (100), (110), (210), (211), (311), and (331) orientations to test behavior outside of the fitting range of the interatomic potentials. We find that the shape of the (111)[11 ] stacking fault energy curve varies significantly with potential, with the ratio of unstable to stable stacking fault energies ranging from 1.22 to 14.07, and some deformation paths for non-(111) orientations give activation barriers less than 50% higher than the unstable stacking fault energies. These are important considerations when choosing an interatomic potential for deformation simulations.

MPInterfaces: A Materials Project based Python tool for high-throughput computational screening of interfacial systems

Abstract A Materials Project based open-source Python tool, MPInterfaces, has been developed to automate the high-throughput computational screening and study of interfacial systems. The framework encompasses creation and manipulation of interface structures for solid/solid hetero-structures, solid/implicit solvents systems, nanoparticle/ligands systems; and the creation of simple system-agnostic workflows for in depth computational analysis using density-functional theory or empirical energy models. The package leverages existing open-source high-throughput tools and extends their capabilities towards the understanding of interfacial systems. We describe the various algorithms and methods implemented in the package. Using several test cases, we demonstrate how the package enables high-throughput computational screening of advanced materials, directly contributing to the Materials Genome Initiative (MGI), which aims to accelerate the discovery, development, and deployment of new materials.

The effect of internal impurities on the mechanical and conductance properties of gold nanowires during elongation

The conductance and mechanical properties of contaminated gold nanowires (NWs) were studied using first principle calculations. Nanowires containing internal impurities of H2O or O2 were elongated along two different directions. It was found that both impurities interact with the gold atoms and affect the properties of the NWs. From a mechanical viewpoint, the impurities increase the bond strength in their vicinity and, throughout the entire elongation, remain surrounded by gold atoms. The impurities do not migrate to the surface and never end up in the single atom chain. The NW fracture always occurs at an Au–Au bond, far from the impurity. Therefore, the impurities do not affect the fracture strength but do decrease the strain at fracture. A variety of conductance effects were observed depending on the type and location of the impurity, and the O2 has the most significant impact. The O2 reduces the conductance when it is close to the gold atoms in the main pathway. However, at the late stages of the elongation, both impurities are located far from the main pathway and have little influence on the conductance.

High-throughput Identification and Characterization of Two-dimensional Materials using Density functional theory

We introduce a simple criterion to identify two-dimensional (2D) materials based on the comparison between experimental lattice constants and lattice constants mainly obtained from Materials-Project (MP) density functional theory (DFT) calculation repository. Specifically, if the relative difference between the two lattice constants for a specific material is greater than or equal to 5%, we predict them to be good candidates for 2D materials. We have predicted at least 1356 such 2D materials. For all the systems satisfying our criterion, we manually create single layer systems and calculate their energetics, structural, electronic, and elastic properties for both the bulk and the single layer cases. Currently the database consists of 1012 bulk and 430 single layer materials, of which 371 systems are common to bulk and single layer. The rest of calculations are underway. To validate our criterion, we calculated the exfoliation energy of the suggested layered materials, and we found that in 88.9% of the cases the currently accepted criterion for exfoliation was satisfied. Also, using molybdenum telluride as a test case, we performed X-ray diffraction and Raman scattering experiments to benchmark our calculations and understand their applicability and limitations. The data is publicly available at the website http://www.ctcms.nist.gov/~knc6/JVASP.html.

Facilitating the selection and creation of accurate interatomic potentials with robust tools and characterization

The Materials Genome Initiative seeks to significantly decrease the cost and time of development and integration of new materials. Within the domain of atomistic simulations, several roadblocks stand in the way of reaching this goal. While the NIST Interatomic Potentials Repository hosts numerous interatomic potentials (force fields), researchers cannot immediately determine the best choice(s) for their use case. Researchers developing new potentials, specifically those in restricted environments, lack a comprehensive portfolio of efficient tools capable of calculating and archiving the properties of their potentials. This paper elucidates one solution to these problems, which uses Python-based scripts that are suitable for rapid property evaluation and human knowledge transfer. Calculation results are visible on the repository website, which reduces the time required to select an interatomic potential for a specific use case. Furthermore, property evaluation scripts are being integrated with modern platforms to improve discoverability and access of materials property data. To demonstrate these scripts and features, we will discuss the automation of stacking fault energy calculations and their application to additional elements. While the calculation methodology was developed previously, we are using it here as a case study in simulation automation and property calculations. We demonstrate how the use of Python scripts allows for rapid calculation in a more easily managed way where the calculations can be modified, and the results presented in user-friendly and concise ways. Additionally, the methods can be incorporated into other efforts, such as openKIM.