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 general reformulation of the exchange energy of 5f -shell is applied in the analysis of the magnetic structure of various actinides compounds in the framework of LDA+U method. The calculations are performed in a convenient scheme with essentially only one free parameter, the screening length. The results are analyzed in terms of different polarization channels, due to different multipoles. Generally it is found that the spin-orbital polarization is dominating. This can be viewed as a strong enhancement of the spin-orbit coupling in these systems. This leads to a drastic decrease in spin polarization, in accordance with experiments. The calculations are able to correctly differentiate magnetic and non-magnetic Pu system. Finally, in all magnetic systems a new multipolar order is observed, whose polarization energy is often larger in magnitude than one of spin polarization. INTRODUCTIONThe magnetism of actinide systems shows a very rich variety of magnetic properties [1]. There are variations from itinerant magnetic systems to systems showing characteristics of localized magnetism. In the border between these extremes one have the so-called heavy fermions, which show many peculiar and anomalous properties, one of which is the co-existence of superconductivity and magnetism [2]. One aspect that makes the magnetism of the actinides unique is the presence of strong spin-orbit coupling (SOC) together with strong exchange interactions for the 5f electrons, which are the ones responsible for the magnetism.From a theoretical point of view, a standard density functional approach, either in the local density approximation (LDA) or generalized gradient approximation (GGA), describes quite well the equilibrium properties of at least metallic systems. However, these functionals are known to underestimate the orbital moments which are induced by the relatively strong SOC [3,4,5]. This can be remedied by allowing for the so-called orbital polarization [5], responsible for Hund's second rule in atomic physics, either through adding an appropriate orbital depending term to the Hamiltonian or by adopting the so-called LDA+U approach [6,7,8]. In the latter method a screened Hartree-Fock (HF) interaction is included among the 5f states only.There is a drastic difference between the itinerant magnetism of a 3d shell and that of the 5f shell. In the former the orbital degrees of freedom are quenched due to the process of hopping between different atoms, while in the latter case the stronger SOC un-quenches them again. Magnetic ordering is relatively abundant among actinide systems due to the strong exchange interactions, but generally the spin moments are strongly reduced compared to a fully spin polarized value, which sometimes is ascribed to crystal field effects and other times to hybridization. This paper will focus on the role of the local screened exchange interactions and it will aim to convincingly argue that these interactions, together with an appreciable SOC interaction, are responsible for the reduced spin polarizations ...

In this paper we present an accurate numerical scheme for extracting interatomic exchange parameters (J ij ) of strongly correlated systems, based on first-principles full-potential electronic structure theory. The electronic structure is modeled with the help of a full-potential linear muffin-tin orbital method. The effects of strong electron correlations are considered within the charge self-consistent density functional theory plus dynamical mean-field theory. The exchange parameters are then extracted using the magnetic force theorem; hence all the calculations are performed within a single computational framework. The method allows us to investigate how the J ij parameters are affected by dynamical electron correlations. In addition to describing the formalism and details of the implementation, we also present magnetic properties of a few commonly discussed systems, characterized by different degrees of electron localization. In bcc Fe, treated as a moderately correlated metal, we found a minor renormalization of the J ij interactions once the dynamical correlations are introduced. However, generally, if the magnetic coupling has several competing contributions from different orbitals, the redistribution of the spectral weight and changes in the exchange splitting of these states can lead to a dramatic modification of the total interaction parameter. In NiO we found that both static and dynamical mean-field results provide an adequate description of the exchange interactions, which is somewhat surprising given the fact that these two methods result in quite different electronic structures. By employing the Hubbard-I approximation for the treatment of the 4f states in hcp Gd we reproduce the experimentally observed multiplet structure. The calculated exchange parameters result in being rather close to the ones obtained by treating the 4f electrons as noninteracting core states.