The discontinuous nature of the exchange-correlation functional -- critical for strongly correlated systems

Standard approximations for the exchange-correlation functional have been found to give big errors for the linearity condition of fractional charges, leading to delocalization error, and the constancy condition of fractional spins, leading to static correlation error. These two conditions are now unified for states with both fractional charge and fractional spin: the exact energy functional is a plane, linear along the fractional charge coordinate and constant along the fractional spin coordinate with a line of discontinuity at the integer. This sheds light on the nature of the derivative discontinuity and calls for explicitly discontinuous functionals of the density or orbitals that go beyond currently used smooth approximations. This is key for the application of DFT to strongly correlated systems.Comment: 5 pages 2 figure

Localization and delocalization errors in density functional theory and implications for band-gap prediction

The band-gap problem and other systematic failures of approximate functionals are explained from an analysis of total energy for fractional charges. The deviation from the correct intrinsic linear behavior in finite systems leads to delocalization and localization errors in large or bulk systems. Functionals whose energy is convex for fractional charges such as LDA display an incorrect apparent linearity in the bulk limit, due to the delocalization error. Concave functionals also have an incorrect apparent linearity in the bulk calculation, due to the localization error and imposed symmetry. This resolves an important paradox and opens the possibility to obtain accurate band-gaps from DFT.Comment: 4 pages 4 figure

Broadening of the Derivative Discontinuity in Density Functional Theory

We clarify an important aspect of density functional theories, the broadening of the derivative discontinuity (DD) in a quantum system, with fluctuating particle number. Our focus is on a correlated model system, the single level quantum dot in the regime of the Coulomb blockade. We find that the DD-broadening is controlled by the small parameter $\Gamma/U$, where $\Gamma$ is the level broadening due to contacting and $U$ is a measure of the charging energy. Our analysis suggests, that Kondoesque fluctuations have a tendency to increase the DD-broadening, in our model by a factor of two.Comment: 4 pages, 2 figure

Global hybrids from the semiclassical atom theory satisfying the local density linear response

We propose global hybrid approximations of the exchange-correlation (XC) energy functional which reproduce well the modified fourth-order gradient expansion of the exchange energy in the semiclassical limit of many-electron neutral atoms and recover the full local density approximation (LDA) linear response. These XC functionals represent the hybrid versions of the APBE functional [Phys. Rev. Lett. 106, 186406, (2011)] yet employing an additional correlation functional which uses the localization concept of the correlation energy density to improve the compatibility with the Hartree-Fock exchange as well as the coupling-constant-resolved XC potential energy. Broad energetical and structural testings, including thermochemistry and geometry, transition metal complexes, non-covalent interactions, gold clusters and small gold-molecule interfaces, as well as an analysis of the hybrid parameters, show that our construction is quite robust. In particular, our testing shows that the resulting hybrid, including 20\% of Hartree-Fock exchange and named hAPBE, performs remarkably well for a broad palette of systems and properties, being generally better than popular hybrids (PBE0 and B3LYP). Semi-empirical dispersion corrections are also provided.Comment: 12 pages, 4 figure

Obliquity measurement and atmospheric characterization of the WASP-74 planetary system

We present new transit observations of the hot Jupiter WASP-74 b ($T_\mathrm{eq} \sim$ 1860 K) using the high-resolution spectrograph HARPS-N and the multi-colour simultaneous imager MuSCAT2. We refine the orbital properties of the planet and its host star, and measure its obliquity for the first time. The measured sky-projected angle between the stellar spin-axis and the planet's orbital axis is compatible with an orbit well-aligned with the equator of the host star ($\lambda = 0.77\pm0.99 \mathrm{deg}$). We are not able to detect any absorption feature of H$\alpha$, or any other atomic spectral features, in its high-resolution transmission spectra due to low S/N at the line cores. Despite previous claims regarding the presence of strong optical absorbers such TiO and VO gases in the atmosphere of WASP-74 b, the new ground-based photometry combined with a reanalysis of previously reported observations from the literature shows a slope in the low-resolution transmission spectrum steeper than expected from Rayleigh scattering alone.Comment: Accepted for publication in Astronomy & Astrophysics. 12 pages, 8 figures, 5 table

The Hubbard model within the equations of motion approach

The Hubbard model has a special role in Condensed Matter Theory as it is considered as the simplest Hamiltonian model one can write in order to describe anomalous physical properties of some class of real materials. Unfortunately, this model is not exactly solved except for some limits and therefore one should resort to analytical methods, like the Equations of Motion Approach, or to numerical techniques in order to attain a description of its relevant features in the whole range of physical parameters (interaction, filling and temperature). In this manuscript, the Composite Operator Method, which exploits the above mentioned analytical technique, is presented and systematically applied in order to get information about the behavior of all relevant properties of the model (local, thermodynamic, single- and two- particle ones) in comparison with many other analytical techniques, the above cited known limits and numerical simulations. Within this approach, the Hubbard model is shown to be also capable to describe some anomalous behaviors of the cuprate superconductors.Comment: 232 pages, more than 300 figures, more than 500 reference

Mu-Opioid Receptors Transiently Activate the Akt-nNOS Pathway to Produce Sustained Potentiation of PKC-Mediated NMDAR-CaMKII Signaling

BACKGROUND: In periaqueductal grey (PAG) matter, cross-talk between the Mu-opioid receptor (MOR) and the glutamate N-methyl-D-Aspartate receptor (NMDAR)-CaMKII pathway supports the development of analgesic tolerance to morphine. In neurons, histidine triad nucleotide binding protein 1 (HINT1) connects the regulators of G protein signaling RGSZ1 and RGSZ2 to the C terminus of the MOR. In response to morphine, this HINT1-RGSZ complex binds PKCgamma, and afterwards, the interplay between PKCgamma, Src and Gz/Gi proteins leads to sustained potentiation of NMDAR-mediated glutamate responses. METHODOLOGY/PRINCIPAL FINDINGS: Following an intracerebroventricular (icv) injection of 10 nmol morphine, Akt was recruited to the synaptosomal membrane and activated by Thr308 and Ser473 phosphorylation. The Akt activation was immediately transferred to neural Nitric Oxide Synthase (nNOS) Ser1417. Afterwards, nitric oxide (NO)-released zinc ions recruited PKCgamma to the MOR to promote the Src-mediated phosphorylation of the Tyr1325 NMDAR2A subunit. This action increased NMDAR calcium flux and CaMKII was activated in a calcium-calmodulin dependent manner. CaMKII then acted on nNOS Ser847 to produce a sustained reduction in NO levels. The activation of the Akt-nNOS pathway was also reduced by the binding of these proteins to the MOR-HINT1 complex where they remained inactive. Tolerance to acute morphine developed as a result of phosphorylation of MOR cytosolic residues, uncoupling from the regulated G proteins which are transferred to RGSZ2 proteins. The diminished effect of morphine was prevented by LNNA, an inhibitor of nNOS function, and naltrindole, a delta-opioid receptor antagonist that also inhibits Akt. CONCLUSIONS/SIGNIFICANCE: Analysis of the regulatory phosphorylation of the proteins included in the study indicated that morphine produces a transient activation of the Akt/PKB-nNOS pathway. This activation occurs upstream of PKCgamma and Src mediated potentiation of NMDAR activity, ultimately leading to morphine tolerance. In summary, the Akt-nNOS pathway acts as a primer for morphine-triggered events which leads to the sustained potentiation of the NMDAR-CaMKII pathway and MOR inhibition