Gian-Marco Rignanese

First-principles computation of material properties: the ABINIT software project

The density functional theory (DFT) computation of electronic structure, total energy and other properties of materials, is a field in constant progress. In order to stay at the forefront of knowledge, a DFT software project can benefit enormously from widespread collaboration, if handled properly. Also, modern software engineering concepts can considerably ease its development. The ABINIT project relies upon these ideas: freedom of sources, reliability, portability, and self-documentation are emphasised, in the development of a sophisticated plane-wave pseudopotential code. We describe ABINITv3.0, distributed under the GNU General Public License. The list of ABINITv3.0 capabilities is presented, as well as the different software techniques that have been used until now: PERL scripts and CPP directives treat a unique set of FORTRAN90 source files to generate sequential (or parallel) object code for many different platforms; more than 200 automated tests secure existing capabilities; strict coding rules are followed; the documentation is extensive, including online help files, tutorials, and HTML-formatted sources

A brief introduction to the ABINIT software package

Abstract A brief introduction to the ABINIT software package is given. Available under a free software license, it allows to compute directly a large set of properties useful for solid state studies, including structural and elastic properties, prediction of phase (meta)stability or instability, specific heat and free energy, spectroscopic and vibrational properties. These are described, and corresponding applications are presented. The emphasis is also laid on its ease of use and extensive documentation, allowing newcomers to quickly step in.

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.

Hybrid exchange-correlation functional for accurate prediction of the electronic and structural properties of ferroelectric oxides

Using a linear combination of atomic orbitals approach, we report a systematic comparison of various density functional theory (DFT) and hybrid exchange-correlation functionals for the prediction of the electronic and structural properties of prototypical ferroelectric oxides. It is found that none of the available functionals is able to provide, at the same time, accurate electronic and structural properties of the cubic and tetragonal phases of BaTiO3 and PbTiO3. Some, although not all, usual DFT functionals predict the structure with acceptable accuracy, but always underestimate the electronic band gaps. Conversely, common hybrid functionals yield an improved description of the band gaps, but overestimate the volume and atomic distortions associated with ferroelectricity, giving rise to an unacceptably large c/a ratio for the tetragonal phases of both compounds. This supertetragonality is found to be induced mainly by the exchange energy corresponding to the generalized gradient approximation (GGA) and, to a lesser extent, by the exact exchange term of the hybrid functional. We thus propose an alternative functional that mixes exact exchange with the recently proposed GGA of Wu and Cohen [Phys. Rev. B 73, 235116 (2006)] which, for solids, improves over the treatment of exchange of the most usual GGAs. The new functional renders an accurate description of both the structural and electronic properties of typical ferroelectric oxides.

FireWorks: a dynamic workflow system designed for high-throughput applications

This paper introduces FireWorks, a workflow software for running high‐throughput calculation workflows at supercomputing centers. FireWorks has been used to complete over 50 million CPU‐hours worth of computational chemistry and materials science calculations at the National Energy Research Supercomputing Center. It has been designed to serve the demanding high‐throughput computing needs of these applications, with extensive support for (i) concurrent execution through job packing, (ii) failure detection and correction, (iii) provenance and reporting for long‐running projects, (iv) automated duplicate detection, and (v) dynamic workflows (i.e., modifying the workflow graph during runtime). We have found that these features are highly relevant to enabling modern data‐driven and high‐throughput science applications, and we discuss our implementation strategy that rests on Python and NoSQL databases (MongoDB). Finally, we present performance data and limitations of our approach along with planned future work. Copyright

Dielectric properties of crystalline and amorphous transition metal oxides and silicates as potential high-κ candidates: the contribution of density-functional theory

A review is given of various first-principles studies of the dielectric properties of crystalline and amorphous transition metal oxides and silicates, which have drawn considerable attention as potential high-kappa materials. After a brief summary of the principal equations of density-functional theory related to the dielectric properties of solids, the results obtained for group IVb M = (Hf, Zr, Ti) and IIIb M = (Y, La, Lu) transition metals crystalline oxides and/or silicates are discussed. For the group IVb transition metals, four crystalline phases (cubic, tetragonal, monoclinic and rutile) of dioxide MO2 with M = (Hf, Zr, Ti) have been considered in the literature. The results of density-functional theory calculations of the dielectric properties of three crystalline transition metal silicates (hafnon HfSiO4, zircon ZrSiO4 and a hypothetical TiSiO4 structure) are also presented. For the group IIIb transition metals, two crystalline phases (cubic and hexagonal) of sesquioxides M2O3 with M = Lu have been investigated within density-functional theory. Finally, the first-principles results that have been obtained for the amorphous silicates are discussed. A presentation is given of a scheme recently introduced which relates the dielectric constants to the local bonding of Si and metal atoms. It is based on the definition of parameters characteristic of the basic structural units centred on Si and metals atoms and including their nearest O neighbours. Applied to amorphous Zr silicates, it provides a good description of the measured dielectric constants, both of the optical and the static ones.

Band Offsets at the Si/SiO2 Interface from Many-Body Perturbation Theory.

We use many-body perturbation theory, the state-of-the-art method for band-gap calculations, to compute the band offsets at the Si/SiO2 interface. We examine the adequacy of the usual approximations in this context. We show that (i) the separate treatment of band structure and potential lineup contributions, the latter being evaluated within density-functional theory, is justified, (ii) most plasmon-pole models lead to inaccuracies in the absolute quasiparticle corrections, (iii) vertex corrections can be neglected, and (iv) eigenenergy self-consistency is adequate. Our theoretical offsets agree with the experimental ones within 0.3 eV.

Room Temperature Peierls Distortion in Small Diameter Nanotubes

By means of ab initio simulations, we investigate the phonon band structure and electron-phonon coupling in small 4-A diameter nanotubes. We show that both the C(5,0) and C(3,3) tubes undergo above room temperature a Peierls transition mediated by an acoustical long wavelength and an optical q=2k(F) phonon, respectively. In the armchair geometry, we verify that the electron-phonon coupling parameter lambda originates mainly from phonons at q=2k(F) and is strongly enhanced when the diameter decreases. These results question the origin of superconductivity in small diameter nanotubes.

Accuracy of generalized gradient approximation functionals for density-functional perturbation theory calculations

We assess the validity of various exchange-correlation functionals for computing the structural, vibrational, dielectric, and thermodynamical properties of materials in the framework of density-functional perturbation theory (DFPT). We consider five generalized-gradient approximation (GGA) functionals (PBE, PBEsol, WC, AM05, and HTBS) as well as the local density approximation (LDA) functional. We investigate a wide variety of materials including a semiconductor (silicon), a metal (copper), and various insulators (SiO2 α-quartz and stishovite, ZrSiO4 zircon, and MgO periclase). For the structural properties, we find that PBEsol and WC are the closest to the experiments and AM05 performs only slightly worse. All three functionals actually improve over LDA and PBE in contrast with HTBS, which is shown to fail dramatically for α-quartz. For the vibrational and thermodynamical properties, LDA performs surprisingly very well. In the majority of the test cases, it outperforms PBE significantly and also the WC, PBEsol and AM05 functionals though by a smaller margin (and to the detriment of structural parameters). On the other hand, HTBS performs also poorly for vibrational quantities. For the dielectric properties, none of the functionals can be put forward. They all (i) fail to reproduce the electronic dielectric constant due to the well-known band gap problem and (ii) tend to overestimate the oscillator strengths (and hence the static dielectric constant).

Low-Dimensional Transport and Large Thermoelectric Power Factors in Bulk Semiconductors by Band Engineering of Highly Directional Electronic States

Thermoelectrics are promising for addressing energy issues but their exploitation is still hampered by low efficiencies. So far, much improvement has been achieved by reducing the thermal conductivity but less by maximizing the power factor. The latter imposes apparently conflicting requirements on the band structure: a narrow energy distribution and a low effective mass. Quantum confinement in nanostructures and the introduction of resonant states were suggested as possible solutions to this paradox, but with limited success. Here, we propose an original approach to fulfill both requirements in bulk semiconductors. It exploits the highly directional character of some orbitals to engineer the band structure and produce a type of low-dimensional transport similar to that targeted in nanostructures, while retaining isotropic properties. Using first-principle calculations, the theoretical concept is demonstrated in Fe2YZ Heusler compounds, yielding power factors 4 to 5 times larger than in classical thermoelectrics at room temperature. Our findings are totally generic and rationalize the search of alternative compounds with similar behavior. Beyond thermoelectricity, these might be relevant also in the context of electronic, superconducting, or photovoltaic applications.