How tight is the Lieb-Oxford bound?

Density-functional theory requires ever better exchange-correlation (xc) functionals for the ever more precise description of many-body effects on electronic structure. Universal constraints on the xc energy are important ingredients in the construction of improved functionals. Here we investigate one such universal property of xc functionals: the Lieb-Oxford lower bound on the exchange-correlation energy, $E_{xc}[n] \ge -C \int d^3r n^{4/3}$, where $C\leq C_{LO}=1.68$. To this end, we perform a survey of available exact or near-exact data on xc energies of atoms, ions, molecules, solids, and some model Hamiltonians (the electron liquid, Hooke's atom and the Hubbard model). All physically realistic density distributions investigated are consistent with the tighter limit $C \leq 1$. For large classes of systems one can obtain class-specific (but not fully universal) similar bounds. The Lieb-Oxford bound with $C_{LO}=1.68$ is a key ingredient in the construction of modern xc functionals, and a substantial change in the prefactor $C$ will have consequences for the performance of these functionals.Comment: 10 pages, 3 figure

Non-empirical hyper-generalized-gradient functionals constructed from the Lieb-Oxford bound

A simple and completely general representation of the exact exchange-correlation functional of density-functional theory is derived from the universal Lieb-Oxford bound, which holds for any Coulomb-interacting system. This representation leads to an alternative point of view on popular hybrid functionals, providing a rationale for why they work and how they can be constructed. A similar representation of the exact correlation functional allows to construct fully non-empirical hyper-generalized-gradient approximations (HGGAs), radically departing from established paradigms of functional construction. Numerical tests of these HGGAs for atomic and molecular correlation energies and molecular atomization energies show that even simple HGGAs match or outperform state-of-the-art correlation functionals currently used in solid-state physics and quantum chemistry.Comment: v2: Major revison. Added information on relation to the gradient expansion and to local hybrids, improved discussion of size consistency and of performance relative to other functional

Ecdysteroids: A novel class of anabolic agents?

Increasing numbers of dietary supplements with ecdysteroids are marketed as “natural anabolic agents”. Results of recent studies suggested that their anabolic effect is mediated by estrogen receptor (ER) binding. Within this study the anabolic potency of ecdysterone was compared to well characterized anabolic substances. Effects on the fiber sizes of the soleus muscle in rats as well the diameter of C2C12 derived myotubes were used as biological readouts. Ecdysterone exhibited a strong hypertrophic effect on the fiber size of rat soleus muscle that was found even stronger compared to the test compounds metandienone (dianabol), estradienedione (trenbolox), and SARM S 1, all administered in the same dose (5 mg/kg body weight, for 21 days). In C2C12 myotubes ecdysterone (1 µM) induced a significant increase of the diameter comparable to dihydrotestosterone (1 µM) and IGF 1 (1.3 nM). Molecular docking experiments supported the ERβ mediated action of ecdysterone. To clarify its status in sports, ecdysterone should be considered to be included in the class “S1.2 Other Anabolic Agents” of the list of prohibited substances of the World Anti-Doping Agency

The Fermionic Density-functional at Feshbach Resonance

We consider a dilute gas of neutral unpolarized fermionic atoms at zero temperature.The atoms interact via a short range (tunable) attractive interaction. We demonstrate analytically a curious property of the gas at unitarity. Namely, the correlation energy of the gas, evaluated by second order perturbation theory, has the same density dependence as the first order exchange energy, and the two almost exactly cancel each other at Feshbach resonance irrespective of the shape of the potential, provided $(\mu r_s) >> 1$. Here $(\mu)^{-1}$ is the range of the two-body potential, and $r_s$ is defined through the number density $n=3/(4\pi r_s^3)$. The implications of this result for universality is discussed.Comment: Five pages, one table. accepted for publication in PR

Determination of the gaseous hydrogen ductile-brittle transition in copper-nickel alloys

A series of copper-nickel alloys were fabricated, notched tensile specimens machined for each alloy, and the specimens tested in 34.5 MPa hydrogen and in air. A notched tensile ratio was determined for each alloy and the hydrogen environment embrittlement (HEE) determined for the alloys of 47.7 weight percent nickel to 73.5 weight percent nickel. Stacking fault probability and stacking fault energies were determined for each alloy using the x ray diffraction line shift and line profiles technique. Hydrogen environment embrittlement was determined to be influenced by stacking fault energies; however, the correlation is believed to be indirect and only partially responsible for the HEE behavior of these alloys

Hole polaron formation and migration in olivine phosphate materials

By combining first principles calculations and experimental XPS measurements, we investigate the electronic structure of potential Li-ion battery cathode materials LiMPO4 (M=Mn,Fe,Co,Ni) to uncover the underlying mechanisms that determine small hole polaron formation and migration. We show that small hole polaron formation depends on features in the electronic structure near the valence-band maximum and that, calculationally, these features depend on the methodology chosen for dealing with the correlated nature of the transition-metal d-derived states in these systems. Comparison with experiment reveals that a hybrid functional approach is superior to GGA+U in correctly reproducing the XPS spectra. Using this approach we find that LiNiPO4 cannot support small hole polarons, but that the other three compounds can. The migration barrier is determined mainly by the strong or weak bonding nature of the states at the top of the valence band, resulting in a substantially higher barrier for LiMnPO4 than for LiCoPO4 or LiFePO4

Alchemical normal modes unify chemical space

In silico design of new molecules and materials with desirable quantum properties by high-throughput screening is a major challenge due to the high dimensionality of chemical space. To facilitate its navigation, we present a unification of coordinate and composition space in terms of alchemical normal modes (ANMs) which result from second order perturbation theory. ANMs assume a predominantly smooth nature of chemical space and form a basis in which new compounds can be expanded and identified. We showcase the use of ANMs for the energetics of the iso-electronic series of diatomics with 14 electrons, BN doped benzene derivatives (C$_{6-2x}$(BN)$_{x}$H$_6$ with $x = 0, 1, 2, 3$), predictions for over 1.8 million BN doped coronene derivatives, and genetic energy optimizations in the entire BN doped coronene space. Using Ge lattice scans as reference, the applicability ANMs across the periodic table is demonstrated for III-V and IV-IV-semiconductors Si, Sn, SiGe, SnGe, SiSn, as well as AlP, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs, and InSb. Analysis of our results indicates simple qualitative structure property rules for estimating energetic rankings among isomers. Useful quantitative estimates can also be obtained when few atoms are changed to neighboring or lower lying elements in the periodic table. The quality of the predictions often increases with the symmetry of system chosen as reference due to cancellation of odd order terms. Rooted in perturbation theory the ANM approach promises to generally enable unbiased compound exploration campaigns at reduced computational cost

Immunoceptive inference: why are psychiatric disorders and immune responses intertwined?

There is a steadily growing literature on the role of the immune system in psychiatric disorders. So far, these advances have largely taken the form of correlations between specific aspects of inflammation (e.g. blood plasma levels of inflammatory markers, genetic mutations in immune pathways, viral or bacterial infection) with the development of neuropsychiatric conditions such as autism, bipolar disorder, schizophrenia and depression. A fundamental question remains open: why are psychiatric disorders and immune responses intertwined? To address this would require a step back from a historical mind-body dualism that has created such a dichotomy. We propose three contributions of active inference when addressing this question: translation, unification, and simulation. To illustrate these contributions, we consider the following questions. Is there an immunological analogue of sensory attenuation? Is there a common generative model that the brain and immune system jointly optimise? Can the immune response and psychiatric illness both be explained in terms of self-organising systems responding to threatening stimuli in their external environment, whether those stimuli happen to be pathogens, predators, or people? Does false inference at an immunological level alter the message passing at a psychological level (or vice versa) through a principled exchange between the two systems

Thermodynamic Limit and Decoherence: Rigorous Results

Time evolution operator in quantum mechanics can be changed into a statistical operator by a Wick rotation. This strict relation between statistical mechanics and quantum evolution can reveal deep results when the thermodynamic limit is considered. These results translate in a set of theorems proving that these effects can be effectively at work producing an emerging classical world without recurring to any external entity that in some cases cannot be properly defined. In a many-body system has been recently shown that Gaussian decay of the coherence is the rule with a duration of recurrence more and more small as the number of particles increases. This effect has been observed experimentally. More generally, a theorem about coherence of bulk matter can be proved. All this takes us to the conclusion that a well definite boundary for the quantum to classical world does exist and that can be drawn by the thermodynamic limit, extending in this way the deep link between statistical mechanics and quantum evolution to a high degree.Comment: 5 pages, no figures. Contribution to proceedings of DICE 2006 (Piombino, Italy, September 11-15, 2006

A self-consistent first-principles calculation scheme for correlated electron systems

A self-consistent calculation scheme for correlated electron systems is created based on the density-functional theory (DFT). Our scheme is a multi-reference DFT (MR-DFT) calculation in which the electron charge density is reproduced by an auxiliary interacting Fermion system. A short-range Hubbard-type interaction is introduced by a rigorous manner with a residual term for the exchange-correlation energy. The Hubbard term is determined uniquely by referencing the density fluctuation at a selected localized orbital. This strategy to obtain an extension of the Kohn-Sham scheme provides a self-consistent electronic structure calculation for the materials design. Introducing an approximation for the residual exchange-correlation energy functional, we have the LDA+U energy functional. Practical self-consistent calculations are exemplified by simulations of Hydrogen systems, i.e. a molecule and a periodic one-dimensional array, which is a proof of existence of the interaction strength U as a continuous function of the local fluctuation and structural parameters of the system.Comment: 23 pages, 8 figures, to appear in J. Phys. Condens. Matte