Stefano de Gironcoli

QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials

QUANTUM ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). The acronym ESPRESSO stands for opEn Source Package for Research in Electronic Structure, Simulation, and Optimization. It is freely available to researchers around the world under the terms of the GNU General Public License. QUANTUM ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively parallel architectures, and a great effort being devoted to user friendliness. QUANTUM ESPRESSO is evolving towards a distribution of independent and interoperable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.

Phonons and related crystal properties from density-functional perturbation theory

This article reviews the current status of lattice-dynamical calculations in crystals, using density-functional perturbation theory, with emphasis on the plane-wave pseudopotential method. Several specialized topics are treated, including the implementation for metals, the calculation of the response to macroscopic electric fields and their relevance to long-wavelength vibrations in polar materials, the response to strain deformations, and higher-order responses. The success of this methodology is demonstrated with a number of applications existing in the literature.

Linear response approach to the calculation of the effective interaction parameters in the LDA+U method

In this work we reexamine the LDA+U method of Anisimov and coworkers in the framework of a plane-wave pseudopotential approach. A simplified rotational-invariant formulation is adopted. The calculation of the Hubbard U entering the expression of the functional is discussed and a linear response approach is proposed that is internally consistent with the chosen definition for the occupation matrix of the relevant localized orbitals. In this way we obtain a scheme whose functionality should not depend strongly on the particular implementation of the model in ab-initio calculations. We demonstrate the accuracy of the method, computing structural and electronic properties of a few systems including transition and rare-earth correlated metals, transition metal monoxides and iron-silicate.

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.

Hubbard-corrected DFT energy functionals: The LDA+U description of correlated systems

The aim of this review article is to assess the descriptive capabilities of the Hubbard-rooted LDA+U method and to clarify the conditions under which it can be expected to be most predictive. The article illustrates the theoretical foundation of LDA+U and prototypical applications to the study of correlated materials, discusses the most relevant approximations used in its formulation, and makes a comparison with other approaches also developed for similar purposes. Open “issues” of the method are also discussed, including the calculation of the electronic couplings (the Hubbard U), the precise expression of the corrective functional and the possibility to use LDA+U for other classes of materials. The second part of the article presents recent extensions to the method and illustrates the significant improvements they have obtained in the description of several classes of different systems. The conclusive section finally discusses possible future developments of LDA+U to further enlarge its predictive power and its range of applicability.

First-principles codes for computational crystallography in the Quantum-ESPRESSO package

Abstract The Quantum-ESPRESSO package is a multi-purpose and multi-platform software for ab-initio calculations of condensed matter (periodic and disordered) systems. Codes in the package are based on density functional theory and on a plane wave/pseudopotential description of the electronic ground state and are ideally suited for structural optimizations (both at zero and at finite temperature), linear response calculations (phonons, elastic constants, dielectric and Raman tensors, etc.) and high-temperature molecular dynamics. Examples of applications of the codes included in the package are briefly discussed.

Efficient calculation of exact exchange and RPA correlation energies in the adiabatic-connection fluctuation-dissipation theory

Recently there has been a renewed interest in the calculation of exact-exchange and random-phase approximation (RPA) correlation energies for realistic systems. These quantities are main ingredients of the so-called

First principles thermoelasticity of MgSiO3-perovskite: Consequences for the inferred properties of the lower mantle

\text{EXX}/\text{RPA}+

Tuning the Morphology of Gold Clusters by Substrate Doping

scheme which has been shown to be a promising alternative approach to the standard local-density-approximation/generalized-gradient-approximation density-functional theory (LDA/GGA DFT) for weakly bound systems where LDA and GGA perform poorly. In this paper, we present an efficient approach to compute the RPA correlation energy in the framework of the adiabatic-connection fluctuation-dissipation formalism. The method is based on the calculation of a relatively small number of eigenmodes of RPA dielectric matrix, efficiently computed by iterative density response calculations in the framework of density functional perturbation theory. We will also discuss a careful treatment of the integrable divergence in the exact-exchange energy calculation which alleviates the problem of its slow convergence with respect to Brillouin-zone sampling. As an illustration of the method, we show the results of applications to bulk Si, Be dimer, and atomic systems.

Adsorption of atomic oxygen on Ag(001): a study based on density-functional theory

Some key thermoelastic properties of MgSiO3-perovskite (pv) have been determined at lower mantle (LM) pressures and temperatures using the quasi-harmonic approximation in conjunction with first principles phonon dispersions. The adiabatic bulk moduli (KS) of pv and of an assemblage of 80 vol% pv and 20 vol% MgO were obtained along the thermodynamically inferred adiabat and compared with the seismic counterpart given by the preliminary reference Earth model (KPREM). The discrepancy between calculated KSs and KPREM in the deep LM suggests a super-adiabatic gradient, or subtle changes of composition, or phase, or all beginning at about 1200 km. The Anderson Gruneisen parameter, δS=(∂lnKS/∂lnρ)P, was predicted to decrease rapidly with depth (from 2.7 to 1.2 across the LM) supporting the thermal origin for the lateral heterogeneities throughout most of the LM.