Lars Nordström

Planewaves, pseudopotentials and the LAPW method

With its extreme accuracy and reasonable computational efficiency, the linearized augmented planewave (LAPW) method has emerged as the standard by which density functional calculations for transition metal and rare-earth containing materials are judged. This volume presents a thorough and self-conta

An alternative way of linearizing the augmented plane-wave method

A new basis set for a full potential treatment of crystal electronic structures is presented and compared to that of the well-known linearized augmented plane-wave (LAPW) method. The basis set consists of energy-independent augmented plane-wave functions combined with local orbitals. Each basis function is continuous over the whole unit cell but it may have a discontinuous slope at the muffin-tin boundaries, i.e. at the surfaces of atomic centered, non-overlapping spheres. This alternative way to linearize the augmented plane-wave method is shown to reproduce the accurate results of the LAPW method, but using a smaller basis set size. The reduction in number of basis functions is most significant for open structures.

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.

A method for atomistic spin dynamics simulations: implementation and examples

We present a method for performing atomistic spin dynamic simulations. A comprehensive summary of all pertinent details for performing the simulations such as equations of motions, models for inclu ...

Rare-earth transition-metal intermetallics

Abstract The combination of itinerant transition metal (M = Fe) and localized rare-earth (R = Gd-Y) magnetism in RFe 2 compounds has been investigated in self-consistent energy band calculations. The computed and measured total moments are in good agreement for all cases where single crystal data are available. We find, however, that there is a significant contribution to the moment from the R-5d partial moments coupled antiparallel to the Fe-3d moment which results from 3d–5d hybridization. The R-4f moments interact with the conduction band system solely by local exchange interactions, which are calculated ab initio from density functional theory. A sum rule for the total 3d + 5d moment is shown to be obeyed and the effective ferrimagnetic exchange interaction between rare-earth and transition-metal moments is discussed. Finally, the spin wave spectra of these materials are evaluated in terms of a model arising from these calculations.

Theory of phase stabilities and bonding mechanisms in stoichiometric and substoichiometric molybdenum carbide

First principles, total energy methods have been applied to predict the relative stabilities of the four experimentally verified MoC phases: the cubic delta(NaCl) phase and the three hexagonal gamm ...

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.

First-principles calculations of spin spirals in Ni2MnGa and Ni2MnAl

We report here noncollinear magnetic configurations in the Heusler alloys Ni 2 MnGa and Ni 2 MnAl which are interesting in the context of the magnetic shape memory effect. The total energies for different spin spirals are calculated and the ground-state magnetic structures are identified. The calculated dispersion curves are used to estimate the Curie temperature which is found to be in good agreement with experiments. In addition, the variation of the magnetic moment as a function of the spiral structure is studied. Most of the variation is associated with Ni, and symmetry constraints relevant for the magnetization are identified. Based on the calculated results, the effect of the constituent atoms in determining the Curie temperature is discussed.

Calculation of orbital magnetism and magnetocrystalline anisotropy energy in YCo5

First-principles electronic structure calculations have been performed for the intermetallic compound YCo5. This compound is known to have unusually large cobalt orbital magnetic moments and one of the largest magnetocrystalline anisotropies among itinerant ferromagnets. By including spin-orbit coupling and orbital polarization in the theoretical treatment the orbital magnetic moments and the magnetocrystalline anisotropy energy were calculated. It was found that in order to obtain reasonable agreement with experiments the inclusions of orbital correlation (here in the form of orbital polarization) is essential. The different contributions from the two inequivalent cobalt sites to the orbital magnetization and the anisotropy are discussed.

Ab initio calculation of molecular field interactions in rare‐earth transition‐metal intermetallics (invited)

The interaction, KRM, between the rare‐earth 4f moment and the transition‐metal 3d moments in rare‐earth transition‐metal intermetallics is shown to depend upon the R‐5d moment, which is due to 3d–5d hybridization, and local 4f–5d exchange integrals. Both the R‐5d moment and KRM may be calculated ab initio from the local spin‐density approximation to density functional theory in self‐consistent energy‐band calculations with the localized 4f‐moments fixed at their Russel–Saunders values. Detailed examples are given for the RFe2 (R=Gd−Yb) series. The exchange integrals are similar to those entering into the density functional version of Stoner theory and their energy dependence must be treated carefully. The calculated local exchange integrals are shown to be related to the molecular fields derived from spin Hamiltonians, hence to the spin‐wave spectra. Reasonable agreement with values of the molecular fields extracted from inelastic neutron scattering and high field susceptibility measurements is obtained.