Marc Torrent

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.

Ab initiomodel of optical properties of two-temperature warm dense matter

We present a model to describe thermophysical and optical properties of two-temperature systems consisted of heated electrons and cold ions in a solid lattice that occur during ultrafast heating experiments. Our model is based on ab initio simulations within the framework of density functional theory. The optical properties are obtained by evaluating the Kubo-Greenwood formula. By applying the material parameters of our ab initio model to a two-temperature model we are able to describe the temperature relaxation process of femtosecond-laser-heated gold and its optical properties within the same theoretical framework. Recent time-resolved measurements of optical properties of ultrafast heated gold revealed the dynamics of the interaction between femtosecond laser pulses and solid state matter. Different scenarios obtained from simulations of our study are compared with experimental data [Chen, Holst, Kirkwood, Sametoglu, Reid, Tsui, Recoules, and Ng, Phys. Rev. Lett. 110, 135001 (2013)].

Interatomic force constants including the DFT-D dispersion contribution

Grimme’s DFT-D dispersion contribution to interatomic forces constants, required for the computation of the phonon band structures in density-functional perturbation theory, has been derived analytically. The implementation has then been validated with respect to frozen phonons, and applied on materials where weak cohesive forces play a major role, i.e., argon, graphite, benzene, etc. We show that these dispersive contributions have to be considered to properly reproduce the experimental vibrational properties of these materials, although the lattice parameter change, coming from the ground-state relaxation with the proper functional, induces the most important change with respect to a treatment without dispersion corrections. In the current implementation, the contribution of these dispersion corrections to the dynamical matrices (with a number of elements that is proportional to the square of the number of atoms) has only a cubic scaling with the number of atoms. In practice, the overload with respect to density-functional calculations is small, making this methodology promising to study vibrational properties of large dispersive systems.

Parallel eigensolvers in plane-wave Density Functional Theory

We consider the problem of parallelizing electronic structure computations in plane-wave Density Functional Theory. Because of the limited scalability of Fourier transforms, parallelism has to be found at the eigensolver level. We show how a recently proposed algorithm based on Chebyshev polynomials can scale into the tens of thousands of processors, outperforming block conjugate gradient algorithms for large computations.

Strong isotope effect in phase II of dense solid hydrogen and deuterium.

Quantum nuclear zero-point motions in solid H(2) and D(2) under pressure are investigated at 80 K up to 160 GPa by first-principles path-integral molecular dynamics calculations. Molecular orientations are well defined in phase II of D(2), while solid H(2) exhibits large and very asymmetric angular quantum fluctuations in this phase, with possible rotation in the (bc) plane, making it difficult to associate a well-identified single classical structure. The mechanism for the transition to phase III is also described. Existing structural data support this microscopic interpretation.

Electronic structure packages: Two implementations of the projector augmented wave (PAW) formalism

The projector augmented wave (PAW) formalism developed by Blochl [Phys. Rev. B 50 (1994) 17953] is an accurate and efficient pseudopotential-like scheme for electronic structure calculations within density functional theory and is now implemented in several electronic structure codes. Some of these codes use an implementation of the formalism developed by Kresse et al. [Phys. Rev. B 59 (1999) 1758] which differs slightly from the original Blochl formalism and which can lead to different electronic structure results. In this paper, we analyze and illustrate the difference between the Blochl and Kresse PAW formulations.

First-principles study of paraelectric and ferroelectric CsH2PO4 including dispersion forces: Stability and related vibrational, dielectric, and elastic properties

Using density functional theory (DFT) and density functional perturbation theory (DFPT), we investigate the stability and response functions of CsH

Oxide ion and proton transport in Gd-doped barium cerate: a combined first-principles and kinetic Monte Carlo study

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Influence of point defects and impurities on the dynamical stability of δ-plutonium

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First-principles calculations of momentum distributions of annihilating electron-positron pairs in defects in UO2

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