Oscar Grånäs

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.

Itinerant Magnetic Multipole Moments of Rank Five as the Hidden Order in URu2Si2

A broken symmetry ground state without any magnetic moments has been calculated by means of the local-density approximation to density functional theory plus a local exchange term, the so-called LDA+U approach, for URu(2)Si(2). The solution is analyzed in terms of a multipole tensor expansion of the itinerant density matrix and is found to be a nontrivial magnetic multipole. Analysis and further calculations show that this type of multipole enters naturally in time reversal breaking in the presence of large effective spin-orbit coupling and coexists with magnetic moments for most magnetic actinides.

Charge self-consistent dynamical mean-field theory based on the full-potential linear muffin-tin orbital method: methodology and applications.

Full charge self-consistence (CSC) over the electron density has been implemented into the local density approximation plus dynamical mean-field theory (LDA + DMFT) scheme based on a full-potential ...

Multipole decomposition of LDA+U energy and its application to actinides compounds

This work presents new development and applications of ab-initio simulation tools for material science. Focus lies on materials with strong electronic correlation and strong spin-orbit coupling. Improvements on methods for solving the impurity problem in LDA+DMFT is presented, as well as a reliant method for charge self-consistency in a LMTO based electronic structure code. A new adaptive scheme for Brillouin zone integration is developed, where we show a strong reduction of numerical noise compared to standard techniques. A reformulation of the standard LDA+U method aiming to reduce the number of free parameters is introduced. Fast and realistic reduction of the number of free parameters provides the possibility of high throughput calculations and enabled us to study a large number of compounds. An analysis method for polarization in terms of coupled multipoles, and their corresponding energy contributions is developed and applied. This led to the formulation of Katts rules, a set of rules complementary to Hunds rules. Katts rules applies for occupying the orbitals of an electronic shell with strong spin-orbit coupling. The analysis is also used to investigate the unconventional Uranium based superconductors URu2Si2, UPt3, UPd2Al3 and UNi2Al3, as well as the high temperature superconductor LaOFeAs. We also investigate the non-magnetic delta-phase of Plutonium, providing insight to the electronic structure and the branching ratios of 4d to 5f transitions seen in photo emission spectra.The influence of surface reconstruction on the magneto crystalline anisotropy is investigated in multilayer Fe/ZnSe, showing that Fe deposited on an unreconstructed interface strongly reduces the uniaxial component of the MAE. We provide a detailed understanding of the magnetic properties of Fe2P, opening possible routes for enhancing the MAE in this system. A general route to strong MAE in nano-laminates is presented, we apply this to propose a candidate with extremely strong anisotropy energy density, 5Fe/2W1-xReX for x=[0.6-0.8].

Large magnetic anisotropy of Fe2P investigated via ab initio density functional theory calculations

We present an investigation of the large magnetic anisotropy of Fe2P, based on ab initio density functional theory calculations, with a full-potential linear muffin-tin orbital basis. We obtain a uniaxial magnetic anisotropy energy (MAE) of 664 mu eV/f.u., which is in decent agreement with experimental observations. Based on a band structure analysis the microscopic origin of the large magnetic anisotropy is explained. We also show that by straining the crystal structure, the MAE can be enhanced further.We present an investigation of the large magnetic anisotropy of Fe2P, based on ab initio density functional theory calculations, with a full-potential linear muffin-tin orbital basis. We obtain a uniaxial magnetic anisotropy energy (MAE) of 664 mu eV/f.u., which is in decent agreement with experimental observations. Based on a band structure analysis the microscopic origin of the large magnetic anisotropy is explained. We also show that by straining the crystal structure, the MAE can be enhanced further.

Inhomogeneity in Co doped ZnO diluted magnetic semiconductor

Here, we have studied the chemical and magnetic interactions in Co doped ZnO diluted magnetic semiconductor by ab initio density functional calculations. The calculated chemical pair interaction pa ...

A new first principles approach to calculate phonon spectra of disordered alloys

The lattice dynamics in substitutional disordered alloys with constituents having large size differences is driven by strong disorder in masses, inter-atomic force constants and local environments. In this paper, a new first principles approach based on special quasirandom structures and an itinerant coherent potential approximation to compute the phonon spectra of such alloys is proposed and applied to Ni₀.₅Pt₀.₅ alloy. The agreement between our results and experiments is found to be much better than for previous models of disorder due to an accurate treatment of the interplay of inter-atomic forces among various pairs of chemical species. This new formalism serves as a potential solution to the longstanding problem of a proper microscopic understanding of lattice dynamical behavior of disordered alloys.

Analytic continuation by averaging Pade approximants

The ill-posed analytic continuation problem for Greens functions and self-energies is investigated by revisiting the Pade approximants technique. We propose to remedy the well-known problems of th ...

Electronic structure, cohesive properties and magnetism of SrRuO3; a theoretical investigation

We have performed an extensive test of the ability of density functional theory within several approximations for the exchange-correlation functional, local density approximation + Hubbard U, and l ...

Electronic and magnetic properties of single Fe atoms on a CuN surface : Effects of electron correlations

The electronic structure and magnetic properties of a single Fe adatom on a CuN surface have been studied using density functional theory in the local spin density approximation (LSDA), the LSDA+U approach, and the local density approximation plus dynamical mean-field theory (LDA+DMFT). The impurity problem in LDA+DMFT is solved through exact diagonalization and in the Hubbard-I approximation. The comparison of the one-particle spectral functions obtained from LSDA, LSDA+U, and LDA+DMFT show the importance of dynamical correlations for the electronic structure of this system. Most importantly, we focused on the magnetic anisotropy and found that neither LSDA nor LSDA+U can explain the measured high values of the axial and transverse anisotropy parameters. Instead, the spin excitation energies obtained from our LDA+DMFT approach with exact diagonalization agree significantly better with experimental data. This affirms the importance of treating fluctuating magnetic moments through a realistic many-body treatment when describing this class of nanomagnetic systems. Moreover, it facilitates insight to the role of the hybridization with surrounding orbitals.