J. M. Wills

Density functional theory for calculation of elastic properties of orthorhombic crystals: Application to TiSi2

A theoretical formalism to calculate the single crystal elastic constants for orthorhombic crystals from first principle calculations is described. This is applied for TiSi2 and we calculate the elastic constants using a full potential linear muffin-tin orbital method using the local density approximation (LDA) and generalized gradient approximation (GGA). The calculated values compare favorably with recent experimental results. An expression to calculate the bulk modulus along crystallographic axes of single crystals, using elastic constants, has been derived. From this the calculated linear bulk moduli are found to be in good agreement with the experiments. The shear modulus, Young’s modulus, and Poisson’s ratio for ideal polycrystalline TiSi2 are also calculated and compared with corresponding experimental values. The directional bulk modulus and the Young’s modulus for single crystal TiSi2 are estimated from the elastic constants obtained from LDA as well as GGA calculations and are compared with the ...

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.

Experimental and theoretical identification of a new high-pressure phase of silica

Following the discovery of stishovite (the highest-pressure polymorph of silica known from natural samples), many attempts have been made to investigate the possible existence of denser phases of silica at higher pressures. Based on the crystal structures observed in chemical analogues of silica, high-pressure experiments on silica and theoretical studies, several possible post-stishovite phases have been suggested. But the likely stable phase of silica at pressures and temperatures representative of Earths lower mantle remains uncertain. Here we report the results of an X-ray diffraction study of silica that has been heated to temperatures above ∼2,000 K and maintained at pressures between 68 and 85 GPa. We observe the occurrence of a new high-pressure phase which we identify with the aid of first-principles total-energy calculations. The structure of this phase (space group Pnc2) is intermediate between the α-PbO2 and ZrO2 structures, and is denser than other known silica phases.

Full-Potential Optical Calculations of Lead Chalcogenides

We report on ab initio calculations of the optical properties of the lead chalcogenides PbS, PbSe, and PbTe performed with a relativistic full-potential linear muffin-tin orbital method within the local density approximation. Our calculated spectra are in excellent agreement with recent ellipsometry measurements. The origin of the peaks in the spectra is discussed, as well as the effects of increasing the chalcogen atomic number. Q 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 349)358, 1998

The AM05 density functional applied to solids

We show that the AM05 functional [Armiento and Mattsson, Phys. Rev. B 72, 085108 (2005)] has the same excellent performance for solids as the hybrid density functionals tested in Paier et al. [J. Chem. Phys. 124, 154709 (2006); 125, 249901 (2006)]. This confirms the original finding that AM05 performs exceptionally well for solids and surfaces. Hartree-Fock hybrid calculations are typically an order of magnitude slower than local or semilocal density functionals such as AM05, which is of a regular semilocal generalized gradient approximation form. The performance of AM05 is on average found to be superior to selecting the best of local density approximation and PBE for each solid. By comparing data from several different electronic-structure codes, we have determined that the numerical errors in this study are equal to or smaller than the corresponding experimental uncertainties.

ELASTIC AND HIGH PRESSURE PROPERTIES OF ZNO

We have studied the elastic and structural properties of ZnO by means of accurate first-principles total energy calculations using the full potential linear muffin tin orbital method. The calculations are based on the density functional theory and we have used the local density Hedin–Lundqvist parametrization and the generalized gradient approximation of Perdew and Wang for the exchange and correlation potential. The calculated values for the equilibrium volume, bulk modulus, and elastic constants are generally in very good agreement with experiments. At elevated pressures ZnO undergoes a structural phase transition from the relatively open wurtzite structure into the more dense NaCl atomic arrangement. The calculated transition pressure is in good agreement with experiment.

Novel electronic configuration in ∂ - Pu

Abstract We present evidence for a unique electronic configuration, which we call the mixed-level state, that is consistent with most of the anomalous properties of ∂ –Pu. The unique properties of this state result from a subdivision of the 5f manifold into orthogonal sub-sets, one with localized character, contributing atomic-like correlation to the total energy, and the other of itinerant character, contributing 5f-electron bonding to the total energy. The near-degeneracy of α - and δ -phases of Pu and the unusual equilibrium volume, elastic constants, and thermal expansion of δ -phase are consistent with this configuration.

Photoemission and the electronic structure of PuCoGa5.

The electronic structure of the first Pu-based superconductor PuCoGa5 is explored using photoelectron spectroscopy and a novel theoretical scheme. Exceptional agreement between calculation and experiment defines a path forward for understanding the electronic structure aspects of Pu-based materials. The photoemission results show two separate regions of 5f electron spectral intensity, one at the Fermi energy and another centered 1.2 eV below the Fermi level. The results for PuCoGa5 clearly indicate 5f electron behavior on the threshold between localized and itinerant. Comparisons to delta phase Pu metal show a broader framework for understanding the fundamental electronic properties of the Pu 5f levels in general within two configurations, one localized and one itinerant.

The most incompressible metal osmium at static pressures above 750 gigapascals

Metallic osmium (Os) is one of the most exceptional elemental materials, having, at ambient pressure, the highest known density and one of the highest cohesive energies and melting temperatures. It is also very incompressible, but its high-pressure behaviour is not well understood because it has been studied so far only at pressures below 75 gigapascals. Here we report powder X-ray diffraction measurements on Os at multi-megabar pressures using both conventional and double-stage diamond anvil cells, with accurate pressure determination ensured by first obtaining self-consistent equations of state of gold, platinum, and tungsten in static experiments up to 500 gigapascals. These measurements allow us to show that Os retains its hexagonal close-packed structure upon compression to over 770 gigapascals. But although its molar volume monotonically decreases with pressure, the unit cell parameter ratio of Os exhibits anomalies at approximately 150 gigapascals and 440 gigapascals. Dynamical mean-field theory calculations suggest that the former anomaly is a signature of the topological change of the Fermi surface for valence electrons. However, the anomaly at 440 gigapascals might be related to an electronic transition associated with pressure-induced interactions between core electrons. The ability to affect the core electrons under static high-pressure experimental conditions, even for incompressible metals such as Os, opens up opportunities to search for new states of matter under extreme compression.

Electronic structure of CeRhIn 5 : de Haas–van Alphen and energy band calculations

The de Haas - van Alphen effect and energy band calculations are used to study angular dependent extremal areas and effective masses of the Fermi surface of the highly correlated antiferromagnetic material CeRhIn