Klaus Koepernik

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.

Density functional application to strongly correlated electron systems

Abstract The local spin density approximation plus onsite Coulomb repulsion approach (LSDA+U) to density functional theory is carefully reanalyzed. Its possible link to single-particle Greens function theory is occasionally discussed. A simple and elegant derivation of the important sum rules for the on-site interaction matrix elements linking them to the values of U and J is presented. All necessary expressions for an implementation of LSDA+U into a non-orthogonal basis solver for the Kohn–Sham equations are given, and implementation into the full-potential local-orbital solver (Phys. Rev. B 59 (1999) 1743) is made. Results of application to several planar cuprate structures are reported in detail and conclusions on the interpretation of the physics of the electronic structure of the cuprates are drawn.

Co dimers on hexagonal carbon rings proposed as subnanometer magnetic storage bits.

It is demonstrated by means of density functional and ab initio quantum chemical calculations, that transition-metal-carbon systems have the potential to enhance the presently available area density of magnetic recording by 3 orders of magnitude. As a model system, Co2 benzene with a diameter of 0.5 nm is investigated. It shows a magnetic anisotropy of the order of 0.1 eV per molecule, large enough to store permanently 1 bit of information at temperatures considerably larger than 4 K. A similar performance can be expected, if cobalt dimers are deposited on graphene or on graphite.

Electric-field control of surface magnetic anisotropy: a density functional approach

In a recent experiment, Weisheit et al (2007 Science 315 349) demonstrated that the coercivity of thin L10 FePt and FePd films can be modified by the external electric field in an electrochemical environment. Here, this observation is confirmed by density functional calculations for the intrinsic magnetic anisotropy. The origin of the effect is clarified by means of a general and simple method to simulate charged metal surfaces. It is predicted that the coercivity of thin CoPt films is much more susceptible to electric field than that of FePt films.

Orbital textures and charge density waves in transition metal dichalcogenides

A theoretical and experimental study reveals the relation between charge density waves and orbital textures for different stackings in a two-dimensional layered material.

Mott transition of MnO under pressure : A comparison of correlated band theories

The electronic structure, magnetic moment, and volume collapse of MnO under pressure are obtained from four different correlated band theory methods; local density approximation+ Hubbard U LDA+U, pseudopotential self-interaction correction pseudo-SIC, the hybrid functional combined local exchange plus Hartree-Fock exchange, and the local spin density SIC SIC-LSD method. Each method treats correlation among the five Mn 3d orbitals per spin, including their hybridization with three O 2p orbitals in the valence bands and their changes with pressure. The focus is on comparison of the methods for rocksalt MnO neglecting the observed transition to the NiAs structure in the 90– 100 GPa range. Each method predicts a first-order volume collapse, but with variation in the predicted volume and critical pressure. Accompanying the volume collapse is a moment collapse, which for all methods is from high-spin to low-spin 5 → 1 , not to nonmagnetic as the simplest scenario would have. The specific manner in which the transition occurs varies considerably among the methods: pseudo-SIC and SIC-LSD give insulator-to-metal, while LDA+U gives insulator-toinsulator and the hybrid method gives an insulator-to-semimetal transition. Projected densities of states above and below the transition are presented for each of the methods and used to analyze the character of each transition. In some cases the rhombohedral symmetry of the antiferromagnetically ordered phase clearly influences the character of the transition.

TaIrTe4: A ternary type-II Weyl semimetal

In metallic condensed matter systems two different types of Weyl fermions can in principle emerge, with either a vanishing (type-I) or with a finite (type-II) density of states at the Weyl node energy. So far only WTe2 and MoTe2 were predicted to be type-II Weyl semi-metals. Here we identify TaIrTe4 as a third member of this family of topological semi-metals. TaIrTe4 has the attractive feature that it hosts only four well-separated Weyl points, the minimum imposed by symmetry. Moreover, the resulting topological surface states - Fermi arcs connecting Weyl nodes of opposite chirality - extend to about 1/3 of the surface Brillouin zone. This large momentum-space separation is very favorable for detecting the Fermi arcs spectroscopically and in transport experiments.

Tight-binding models for the iron-based superconductors

The rich materials class of iron-based superconductors turned out to exhibit a very complex electronic structure despite the simplicity of their crystal structures. For various approaches to study the instability against magnetic order or superconductivity, a real-space description of the electronic structure is required. Here, the bonding situation and the orbital structure of the electronic state are analyzed and minimum tight-binding models quantitatively correctly describing the low-energy electronic structure are provided.

Superconducting rare earth transition metal borocarbides

Abstract We present an overview of selected properties of quaternary intermetallic rare earth transition metal borocarbides and related boronitride compounds, as well as of theoretical calculations with possible relevance to the mechanism of superconductivity. The interplay of superconductivity and magnetism for compounds with pure and mixed rare earth components is considered. We suggest that the incommensurate magnetic structure modulated along the a -axis is responsible for the pair breaking in Ho x R 1− x Ni 2 B 2 C; R=Y, Lu samples. The effect of doping (Cu, Co) at the transition metal site is considered experimentally and theoretically. The possible role of correlation effects due to the presence of the transition metal component in determining the electronic structure is discussed comparing the band structure calculation results with various electronic spectroscopies as well as de Haas–van Alphen data. Important thermodynamic properties of these systems are analyzed within multiband Eliashberg theory with special emphasis on the upper critical field H c2 ( T ) and the specific heat. In particular, the unusual positive curvature of H c2 ( T ) near T c observed for high-quality single crystals, polycrystalline samples of YNi 2 B 2 C, LuNi 2 B 2 C as well as to a somewhat reduced extent also for the mixed system Y 1− x Lu x Ni 2 B 2 C is explained microscopically. It is shown that in these well-defined samples the clean limit of type II superconductors is achieved. The values of H c2 ( T ) and of its positive curvature near T c (as determined both resistively and from magnetization as well as from specific heat measurements is an intrinsic quantity generic for such samples) decrease with growing impurity content. Both quantities thus provide a direct measure of the sample quality.

Jahn–Teller-like origin of the tetragonal distortion in disordered Fe–Pd magnetic shape memory alloys

The electronic structure and magnetic properties of disordered FexPd100−x alloys (50<x<85) are investigated in the framework of density functional theory using the full potential local orbital method. Disorder is treated in the coherent potential approximation. Our calculations explain the experimental magnetization data. The origin of the tetragonal distortion in the Fe–Pd magnetic shape memory alloys is found to be a Jahn–Teller-like effect, which allows the system to reduce its band energy in a narrow composition range. Prospects for an optimization of the alloys’ properties by adding third elements are discussed.