Kevin F. Garrity

Pseudopotentials for high-throughput DFT calculations

The increasing use of high-throughput density-functional theory (DFT) calculations in the computational design and optimization of materials requires the availability of a comprehensive set of soft and transferable pseudopotentials. Here we present design criteria and testing results for a new open-source “GBRV” ultrasoft pseudopotential library that has been optimized for use in high-throughput DFT calculations. We benchmark the GBRV potentials, as well as two other pseudopotential sets available in the literature, to all-electron calculations in order to validate their accuracy. The results allow us to draw conclusions about the accuracy of modern pseudopotentials in a variety of chemical environments.

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.

Crystalline oxides on silicon.

This review outlines developments in the growth of crystalline oxides on the ubiquitous silicon semiconductor platform. The overall goal of this endeavor is the integration of multifunctional complex oxides with advanced semiconductor technology. Oxide epitaxy in materials systems achieved through conventional deposition techniques is described first, followed by a description of the science and technology of using atomic layer-by-layer deposition with molecular beam epitaxy (MBE) to systematically construct the oxide-silicon interface. An interdisciplinary approach involving MBE, advanced real-space structural characterization, and first-principles theory has led to a detailed understanding of the process by which the interface between crystalline oxides and silicon forms, the resulting structure of the interface, and the link between structure and functionality. Potential applications in electronics and photonics are also discussed.

Chemistry of ferroelectric surfaces.

It has been recognized since the 1950s that the polar and switchable nature of ferroelectric surfaces can potentially lead to polarization direction-dependent surface chemistry. Recent theoretical studies and advances in growing high quality epitaxial ferroelectric thin films have motivated a flurry of experimental studies aimed at creating surfaces with switchable adsorption and catalytic properties, as well as films whose polarization direction switches depending on the gas phase environment. This research news article briefly reviews the key findings of these studies. These include observations that the adsorption strengths, and in certain cases the activation energies for reactions, of polar molecules on the surfaces of ferroelectric materials are sensitive to the polarization direction. For bare ferroelectric surfaces, the magnitudes of these differences are not large, but are still comparable to the energy barrier required to switch the polarization of approximately 10 nm thick films. Highlights of a recent study where chemical switching of a thin film ferroelectric was demonstrated are presented. Attempts to use the ferroelectric polarization to influence the behavior of supported catalytic metals will also be described. It will be shown that the tendency of the metals to cluster into particles makes it difficult to alter the chemical properties of the metal surface, since it is separated from the ferroelectric by several layers of metal atoms. An alternate approach to increasing the reactivity of ferroelectric surfaces is suggested that involves modifying the surface with atoms that bind strongly to the surface and thus remain atomically dispersed.

Antiferroelectricity in thin-filmZrO2from first principles

Density functional calculations are performed to investigate the experimentally-reported field-induced phase transition in thin-film ZrO2 (J. Muller et al., Nano. Lett. 12, 4318). We find a small energy difference of ~ 1 meV/f.u. between the nonpolar tetragonal and polar orthorhombic structures, characteristic of antiferroelectricity. The requisite first-order transition between the two phases, which atypically for antiferroelectrics have a group-subgroup relation, results from coupling to other zone-boundary modes, as we show with a Landau-Devonshire model. Tetragonal ZrO2 is thus established as a previously unrecognized lead-free antiferroelectric with excellent dielectric properties and compatibility with silicon. In addition, we demonstrate that a ferroelectric phase of ZrO2 can be stabilized through epitaxial strain, and suggest an alternative stabilization mechanism through continuous substitution of Zr by Hf.

Hexagonal ABC semiconductors as ferroelectrics.

We use a first-principles rational-design approach to identify a previously unrecognized class of ferroelectric materials in the P6(3)mc LiGaGe structure type. We calculate structural parameters, polarization, and ferroelectric well depths both for reported and as-yet hypothetical representatives of this class. Our results provide guidance for the experimental realization and further investigation of high-performance materials suitable for practical applications.

Wannier Center Sheets in Topological Insulators

We argue that various kinds of topological insulators (TIs) can be insightfully characterized by an inspection of the charge centers of the hybrid Wannier functions, defined as the orbitals obtained by carrying out a Wannier transform on the Bloch functions in one dimension while leaving them Bloch-like in the other two. From this procedure, one can obtain the Wannier charge centers (WCCs) and plot them in the two-dimensional projected Brillouin zone. We show that these WCC sheets contain the same kind of topological information as is carried in the surface energy bands, with the crucial advantage that the topological properties of the bulk can be deduced from bulk calculations alone. The distinct topological behaviors of these WCC sheets in trivial, Chern, weak, strong, and crystalline TIs are first illustrated by calculating them for simple tight-binding models. We then present the results of first-principles calculations of the WCC sheets in the trivial insulator

Orthorhombic ABC Semiconductors as Antiferroelectrics

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Dynamic Evanescent Phonon Coupling Across the La 1 − x Sr x MnO 3 / SrTiO 3 Interface

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Hyperferroelectrics: Proper Ferroelectrics with Persistent Polarization

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