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

In this work we examine critically the electronic structure of the rare-earth elements by use of the so-called Hubbard I approximation. From the theoretical side all measured features of both occupied and unoccupied states are reproduced, without significant deviations between observations and theory. We also examine cohesive properties like the equilibrium volume and bulk modulus, where we find, in general, a good agreement between theory and measurements. In addition we have reproduced the spin and orbital moments of these elements, as they are reflected from measurements of the saturation moment. We have also employed the Hubbard I approximation to extract the interatomic exchange parameters of an effective spin Hamiltonian for the heavy rare earths. We show that the Hubbard I approximation gives results which are consistent with calculations where 4f electrons are treated as core states for Gd. The latter approach was also used to address the series of the heavy/late rare-earths. Via Monte Carlo simulations we obtained ordering temperatures which reproduce measurements within about 20%. We have further illustrated the accuracy of these exchange parameters by comparing measured and calculated magnetic configurations for the heavy rare earths and the magnon dispersion for Gd. The Hubbard I approximation is compared to other theories of the electronic structure, and we argue that it is superior. We discuss the relevance of our results in general, and how this makes it possible to treat the electronic structure of materials containing rare-earth elements, such as permanent magnets, magnetostrictive compounds, photovoltaics, optical fibers, topological insulators, and molecular magnets.

Indeed, we find a correlation between the number of transition-metal (TM) 3d electrons and the stability of the hexagonal SmTM 5 (D2 d ) compound (TM = Fe, Co, or Ni), see Fig. 1 where we show results from calculations of formation energies. Notice that increasing the 3d electron count (more Ni) greatly stabilizes the compound. An obvious consequence of this behavior is that one should be able to recover crystal stability of a Sm-Fe alloy by doping with 3d electrons from nickel. We compare the theory with experiments [5,6] that closely reproduce the calculated behavior. Notice that an extrapolation of the experimental heats of formation suggests that an alloy with at least 7.2 3d electrons per TM atom is stable. This is important because SmCoNiFe 3 has about 7.3 3d electrons that is enough to stabilize the magnet. It has also recently been confirmed that the related alloy SmNi 2 Fe 3 , that has about 7.5 3d electrons, exist [7] in agreement with the experimental extrapolation outlined in Fig. 1.In a computational search for a thermodynamically viable compound with the maximum portion of iron atoms we recognize that no more than three iron atoms can be accommodated and those occupy the 3g sites that

The ill-posed analytic continuation problem for Green's functions and self-energies is investigated by revisiting the Padé approximants technique. We propose to remedy to the well-known problems of the Padé approximants by performing an average of several continuations, obtained by varying the number of fitted input points and Padé coefficients independently. The suggested approach is then applied to several test cases, including Sm and Pr atomic self-energies, the Green's functions of the Hubbard model for a Bethe lattice and of the Haldane model for a nano-ribbon, as well as two special test functions. The sensitivity to numerical noise and the dependence on the precision of the numerical libraries are analysed in detail. The present approach is compared to a number of other techniques, i.e. the non-negative least-square method, the non-negative Tikhonov method and the maximum entropy method, and is shown to perform well for the chosen test cases. This conclusion holds even when the noise on the input data is increased to reach values typical for quantum Monte Carlo simulations. The ability of the algorithm to resolve fine structures is finally illustrated for two relevant test functions.