José A. Flores-Livas

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.

Low-energy silicon allotropes with strong absorption in the visible for photovoltaic applications

We present state-of-the-art first-principle calculations of the electronic and optical properties of silicon allotropes with interesting characteristics for applications in thin-film solar cells. These new phases consist of distorted sp

High-pressure structures of disilane and their superconducting properties.

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Superconductivity in metastable phases of phosphorus-hydride compounds under high pressure

silicon networks and have a lower formation energy than other experimentally produced silicon phases. Some of these structures turned out to have quasi-direct and dipole-allowed band gaps in the range 0.8--1.5\,eV, and to display absorption coefficients comparable with those of chalcopyrites used in thin-film record solar cells.

Interplay between structure and superconductivity: Metastable phases of phosphorus under pressure

A systematic ab initio search for low-enthalpy phases of disilane (Si2H6) at high pressures was performed based on the minima hopping method. We found a novel metallic phase of disilane with Cmcm symmetry, which is enthalpically more favorable than the recently proposed structures of disilane up to 280 GPa, but revealing compositional instability below 190 GPa. The Cmcm phase has a moderate electron-phonon coupling yielding a superconducting transition temperature T(c) of around 20 K at 100 GPa, decreasing to 13 K at 220 GPa. These values are significantly smaller than previously predicted T(c))s for disilane at equivalent pressure. This shows that similar but different crystalline structures of a material can result in dramatically different T(c)s and stresses the need for a systematic search for a crystalline ground state.Through a systematic structural search we found an allotrope of carbon with Cmmm symmetry which we predict to be more stable than graphite for pressures above 10 GPa. This material, which we refer to as Z-carbon, is formed by pure sp(3) bonds and it provides an explanation to several features in experimental x-ray diffraction and Raman spectra of graphite under pressure. The transition from graphite to Z-carbon can occur through simple sliding and buckling of graphene sheets. Our calculations predict that Z-carbon is a transparent wide band-gap semiconductor with a hardness comparable to diamond.

The Elephant in the Room of Density Functional Theory Calculations

Hydrogen-rich compounds have been extensively studied both theoretically and experimentally in the quest for novel high-temperature superconductors. Reports on sulfur hydride attaining metallicity under pressure and exhibiting superconductivity at temperatures as high as 200 K have spurred an intense search for room-temperature superconductors in hydride materials. Recently, compressed phosphine was reported to metallize at pressures above 45 GPa, reaching a superconducting transition temperature (T-C) of 100 K at 200 GPa. However, neither the exact composition nor the crystal structure of the superconducting phase have been conclusively determined. In this work, the phase diagram of PHn (n = 1,2,3,4,5,6) was extensively explored by means of ab initio crystal structure predictions using the minima hopping method (MHM). The results do not support the existence of thermodynamically stable PHn compounds, which exhibit a tendency for elemental decomposition at high pressure even when vibrational contributions to the free energies are taken into account. Although the lowest energy phases of PH1,2,3 display T-C`s comparable to experiments, it remains uncertain if the measured values of T-C can be fully attributed to a phase-pure compound of PHn.

Superconductivity in intercalated group-IV honeycomb structures

Pressure-induced superconductivity and structural phase transitions in phosphorous (P) are studied by resistivity measurements under pressures up to 170 GPa and fully ab initio crystal structure and superconductivity calculations up to 350 GPa. Two distinct superconducting transition temperature (TC) vs. pressure (P) trends at low pressure have been reported more than 30 years ago, and for the first time we are able to reproduce them and devise a consistent explanation founded on thermodynamically metastable phases of black-phosphorous. Our experimental and theoretical results form a single, consistent picture which not only provides a clear understanding of elemental P under pressure but also sheds light on the long-standing and unsolved anomalous superconductivity trend. Moreover, at higher pressures we predict a similar scenario of multiple metastable structures which coexist beyond their thermodynamical stability range. Metastable phases of P experimentally accessible at pressures above 240 GPa should exhibit TC’s as high as 15 K, i.e. three times larger than the predicted value for the ground-state crystal structure. We observe that all the metastable structures systematically exhibit larger transition temperatures than the ground-state ones, indicating that the exploration of metastable phases represents a promising route to design materials with improved superconducting properties.

Ab initio Eliashberg Theory: Making Genuine Predictions of Superconducting Features

Using multiwavelets, we have obtained total energies and corresponding atomization energies for the GGA-PBE and hybrid-PBE0 density functionals for a test set of 211 molecules with an unprecedented and guaranteed μHartree accuracy. These quasi-exact references allow us to quantify the accuracy of standard all-electron basis sets that are believed to be highly accurate for molecules, such as Gaussian-type orbitals (GTOs), all-electron numeric atom-centered orbitals (NAOs), and full-potential augmented plane wave (APW) methods. We show that NAOs are able to achieve the so-called chemical accuracy (1 kcal/mol) for the typical basis set sizes used in applications, for both total and atomization energies. For GTOs, a triple-ζ quality basis has mean errors of ∼10 kcal/mol in total energies, while chemical accuracy is almost reached for a quintuple-ζ basis. Due to systematic error cancellations, atomization energy errors are reduced by almost an order of magnitude, placing chemical accuracy within reach also for medium to large GTO bases, albeit with significant outliers. In order to check the accuracy of the computed densities, we have also investigated the dipole moments, where in general only the largest NAO and GTO bases are able to yield errors below 0.01 D. The observed errors are similar across the different functionals considered here.

Emergence of superconductivity in doped H 2 O ice at high pressure

. Allthesecompoundsfeatureastronglyanisotropicsuperconductinggap.Our results show that despite the different doping and structural properties, the three families ofmaterialsfallintoasimilardescriptionofitssuperconductingbehavior. Thisallowsustoestimateanuppercriticaltemperatureofabout20Kfortheclassofintercalatedgroup-IVstructures,includingintercalatedgraphiteanddopedgraphene.

Superconductivity in an expanded phase of ZnO: an ab initio study

We present an application of Eliashberg theory of superconductivity to study a set of novel superconducting systems with a wide range of structural and chemical properties. The set includes three intercalated group-IV honeycomb layered structures, SH3 at 200 GPa (the superconductor with the highest measured critical temperature), the similar system SeH3 at 150 GPa, and a lithium doped mono-layer of black phosphorus. The theoretical approach we adopt is a recently developed, fully ab initio Eliashberg approach that takes into account the Coulomb interaction in a full energy-resolved fashion avoiding any free parameters like μ*. This method provides reasonable estimations of superconducting properties, including TC and the excitation spectra of superconductors.