Hybrid-DFT+Vw_w method for accurate band structure of correlated transition metal compounds: the case of cerium dioxide

Hybrid functionals' non-local exchange-correlation potential contains a derivative discontinuity that improves on standard semi-local density functional theory (DFT) band gaps. Moreover, by careful parameterization, hybrid functionals can provide self-interaction reduced description of selected states. On the other hand, the uniform description of all the electronic states of a given system is a know drawback of these functionals that causes varying accuracy in the description of states with different degrees of localization. This limitation can be remedied by the orbital dependent exact exchange extension of hybrid functionals; the hybrid-DFT+V$_w$ method [V. Iv{\'a}dy, et al., Phys. Rev. B 90, 035146 (2014)]. Based on the analogy of quasi-particle equations and hybrid-DFT single particle equations, here we demonstrate that parameters of hybrid-DFT+V$_w$ functional can be determined from approximate quasi-particle spectra. The proposed technique leads to a reduction of self-interaction and provides improved description for both $s$ / $p$ and $d$ / $f$-electrons of the simulated system. The performance of our charge self-consistent method is illustrated on the electronic structure calculation of cerium dioxide where good agreement with both quasi-particle and experimental spectra is achieved

The origin of the core-level binding energy shifts in nanoclusters

We investigate the shifts of the core-level binding energies in small gold nanoclusters by using {\it ab initio} density functional theory calculations. The shift of the 4$f$ states is calculated for magic number nanoclusters in a wide range of sizes and morphologies. We find a non-monotonous behavior of the core-level shift in nanoclusters depending on the size. We demonstrate that there are three main contributions to the Au 4$f$ shifts, which depend sensitively on the interatomic distances, coordination and quantum confinement. They are identified and explained by the change of the on-site electrostatic potential.Comment: 7 pages, 9 figure

Efficient and accurate determination of lattice-vacancy diffusion coefficients via non equilibrium ab initio molecular dynamics

We revisit the color-diffusion algorithm [P. C. Aeberhard et al., Phys. Rev. Lett. 108, 095901 (2012)] in nonequilibrium ab initio molecular dynamics (NE-AIMD), and propose a simple efficient approach for the estimation of monovacancy jump rates in crystalline solids at temperatures well below melting. Color-diffusion applied to monovacancy migration entails that one lattice atom (colored-atom) is accelerated toward the neighboring defect-site by an external constant force F. Considering bcc molybdenum between 1000 and 2800 K as a model system, NE-AIMD results show that the colored-atom jump rate k_{NE} increases exponentially with the force intensity F, up to F values far beyond the linear-fitting regime employed previously. Using a simple model, we derive an analytical expression which reproduces the observed k_{NE}(F) dependence on F. Equilibrium rates extrapolated by NE-AIMD results are in excellent agreement with those of unconstrained dynamics. The gain in computational efficiency achieved with our approach increases rapidly with decreasing temperatures, and reaches a factor of four orders of magnitude at the lowest temperature considered in the present study

Temperature dependent effective potential method for accurate free energy calculations of solids

We have developed a thorough and accurate method of determining anharmonic free energies, the temperature dependent effective potential technique (TDEP). It is based on \emph{ab initio} molecular dynamics followed by a mapping onto a model Hamiltonian that describes the lattice dynamics. The formalism and the numerical aspects of the technique are described in details. A number of practical examples are given, and results are presented, which confirm the usefulness of TDEP within \emph{ab initio} and classical molecular dynamics frameworks. In particular, we examine from first-principles the behavior of force constants upon the dynamical stabilization of body centered phase of Zr, and show that they become more localized. We also calculate phase diagram for $^4$He modeled with the Aziz \emph{et al.} potential and obtain results which are in favorable agreement both with respect to experiment and established techniques

A Test of Sovereignty: Franchise Tax Board of the State of California v. Gilbert P. Hyatt

In Franchise Tax Board of California v. Hyatt, the Supreme Court considers whether to overrule Nevada v. Hall, a 1979 Supreme Court decision. Hall permitted a State to be haled into the court of another State without its consent. In 2016, an evenly divided Supreme Court affirmed Hall 4-4 when faced with the same question, and following a remand to the Nevada Supreme Court, the Court has granted certiorari on this question once again. This Commentary contends that Hall was wrongly decided and should be overruled. The Constitution’s ratification did not alter the status of common-law State sovereign immunity, leaving intact not only State sovereign immunity in a State’s own court but also a State’s immunity to suits in the courts of another State without consent. However, this case, in which the Petitioner has already appeared in the court of another State, is not the appropriate vehicle for overruling Hall. State sovereign immunity should be restored at the next possible opportunity, when a State properly asks a federal court to enforce its common-law immunity from the courts of a sister State. Sovereigns should enjoy immunity not only in their own courts, but also in the courts of their peers

Defining Agency and Its Scope (II)

Fiduciary law necessarily raises issues of delineation and demarcation, which this paper demonstrates through examples involving common-law agents. Serving as an agent, and thus as a fiduciary, does not necessarily mean that agency law prescribes all duties that the agent owes the principal. The agent may have rights external to the relationship that the agent may exercise, distinct from the duty of loyalty owed the principal. When an agent acts outside the bounds of an agency relationship, the principal’s consent is not requisite to conduct that would constitute disloyalty within the bounds of the agency relationship. The paper illustrates the significance of this point through a series of examples drawn from a range of contexts, including auctions of art objects. Prior scholarship neglects the implications of demarcations that define the scope of an agency relationship and of fiduciary relationships more generically. More generally or theoretically, the paper examines the qualities of fiduciary duty as a default rule, arguing that the relative “stickiness” of the default varies. Agency law contains two different kinds of altering rules—necessary and sufficient conditions to vary a default rule—consisting of agreements that define the scope of the agent’s representative role on behalf of the principal, and consent by the principal to actions by the agent within that scope that relieve the agent of liability for breach of fiduciary duty, which impose significantly different requisites. The basic distinction between agreement and consent has parallels elsewhere in agency law; for example, ratification, like consent, requires specificity because to be legally effective ratification requires that the principal know, as a matter of historical fact, what the agent has done. Agreement, on the other hand, requires less specificity, comparable to manifestations that confer actual authority on an agent which necessarily does not require that the principal foresee all actions that the agent may take that fall within the scope of the grant of authority. And ratification, like effective consent, is a matter of historical fact, not hypothesis. These implications follow because agency law, by positioning an agent as the principal’s representative for purposes of legally-salient interactions with third parties and facts about the world, frames the agent as an extension of the principal, not the principal’s substitute

Finite temperature elastic constants of paramagnetic materials within the disordered local moment picture from ab initio molecular dynamics calculations

We present a theoretical scheme to calculate the elastic constants of magnetic materials in the high-temperature paramagnetic state. Our approach is based on a combination of disordered local moments picture and ab initio molecular dynamics (DLM-MD). Moreover, we investigate a possibility to enhance the efficiency of the simulations of elastic properties using recently introduced method: symmetry imposed force constant temperature dependent effective potential (SIFC-TDEP). We have chosen cubic paramagnetic CrN as a model system. This is done due to its technological importance and its demonstrated strong coupling between magnetic and lattice degrees of freedom. We have studied the temperature dependent single-crystal and polycrystalline elastic constants of paramagentic CrN up to 1200 K. The obtained results at T= 300 K agree well with the experimental values of polycrystalline elastic constants as well as Poisson ratio at room temperature. We observe that the Young's modulus is strongly dependent on temperature, decreasing by ~14% from T=300 K to 1200 K. In addition we have studied the elastic anisotropy of CrN as a function of temperature and we observe that CrN becomes substantially more isotropic as the temperature increases. We demonstrate that the use of Birch law may lead to substantial errors for calculations of temperature induced changes of elastic moduli. The proposed methodology can be used for accurate predictions of mechanical properties of magnetic materials at temperatures above their magnetic order-disorder phase transition.Comment: 1 table, 3 figure

Ab-initio elastic tensor of cubic Ti0.5_{0.5}Al0.5_{0.5}N alloy: the dependence of the elastic constants on the size and shape of the supercell model

In this study we discuss the performance of approximate SQS supercell models in describing the cubic elastic properties of B1 (rocksalt) Ti$_{0.5}$Al$_{0.5}$N alloy by using a symmetry based projection technique. We show on the example of Ti$_{0.5}$Al$_{0.5}$N alloy, that this projection technique can be used to align the differently shaped and sized SQS structures for a comparison in modeling elasticity. Moreover, we focus to accurately determine the cubic elastic constants and Zener's type elastic anisotropy of Ti$_{0.5}$Al$_{0.5}$N. Our best supercell model, that captures accurately both the randomness and cubic elastic symmetry, results in $C_{11}=447$ GPa, $C_{12}=158$ GPa and $C_{44}=203$ GPa with 3% of error and $A=1.40$ for Zener's elastic anisotropy with 6% of error. In addition, we establish the general importance of selecting proper approximate SQS supercells with symmetry arguments to reliably model elasticity of alloys. In general, we suggest the calculation of nine elastic tensor elements - $C_{11}$, $C_{22}$, $C_{33}$, $C_{12}$, $C_{13}$, $C_{23}$, $C_{44}$, $C_{55}$ and $C_{66}$, to evaluate and analyze the performance of SQS supercells in predicting elasticity of cubic alloys via projecting out the closest cubic approximate of the elastic tensor. The here described methodology is general enough to be applied in discussing elasticity of substitutional alloys with any symmetry and at arbitrary composition.Comment: Submitted to Physical Review