Confinement effects on the spin potential of first row transition metal cations

Abstract

By using a spherical confinement method, the behaviour of spin potential and pairing energy is studied and compared to the free ion limit for a representative sample of first row transition metal cations. The study was carried out using three approximations within the Kohn–Sham model; exchange-only, exchange plus correlation contribution and correcting the self-interaction error. For the three approaches, the spin potential shows a close connection with the capability of a system to perform a spin-flip process. Namely, in accordance with Hund’s rule, the spin potential increases from low d occupation up to maximum for the half filled configurations; and it decreases from that point on, as d occupation grows. Such a conclusion is reached for confined and non-confined cations, even under extreme confinement conditions. In addition, two important observations are obtained: (a) In contrast to the neutral atoms situation, in the case of cations no eigenvalue crossings are observed under confinement conditions for the whole sample of ions tested. (b) The self-interaction error found in many exchange–correlation functionals does not affect the pairing energy over confined atoms, even when this error has an important contribution on a single eigenvalue. Therefore, pairing energy predicted by exchange–correlation functionals non-corrected by the self-interaction error can be made safely on transition metal cations under high pressures.     

Biomass-derived electrodes for flexible supercapacitors

At present, supercapacitors constitute, along with batteries, one of the most promising electrochemical energy storage technology. The recent emerging generation of bendable portable electronic devices has boosted the research of new materials, new processing techniques and new designs that can meet the demands in terms of mechanical stability upon bending or stretching, without compromising their electrochemical performance, at an acceptable cost. Among all the electrode materials currently explored, biomass-derived carbons hold a great potential, due to their low-cost, easy processing techniques, stability and versatility. Here we introduce the range of renewable precursors available and current state-of-the-art performances, and explore the challenges regarding flexibility and sustainability.     

Charged black rings from inverse scattering

The inverse scattering method of Belinsky and Zakharov is a powerful method to construct solutions of vacuum Einstein equations. In particular, in five dimensions this method has been successfully applied to construct a large variety of black hole solutions. Recent applications of this method to Einstein–Maxwell-dilaton (EMd) theory, for the special case of Kaluza–Klein dilaton coupling, has led to the construction of the most general black ring in this theory. In this contribution, we review the inverse scattering method and its application to the EMd theory. We illustrate the efficiency of these methods with a detailed construction of an electrically charged black ring.     

Heavy-tailed phase-type distributions: a unified approach

Extremes - A phase-type distribution is the distribution of the time until absorption in a finite state-space time-homogeneous Markov jump process, with one absorbing state and the rest being...     

Fractional square functions and potential spaces

Carlos Segovia and Richard Wheeden defined fractional square functions involving fractional derivatives. They obtained characterizations of potential spaces via square functions. Our aim in this paper is to reconsider the ideas of Segovia and Wheeden under the light of the semigroups of operators. We develop a quite general theory of fractional square functions associated to certain classes of operators. We present some examples of differential operators where our theory applies. We recover in a more compact way the results of Segovia and Wheeden and we obtain new characterizations of the potential spaces associated to the harmonic oscillator and Ornstein–Uhlenbeck operators.     

Organotin catalysts in organosilicon chemistry

Organotin compounds are best known in the chemical industry as PVC stabilizers, polyurethane foam formers and antifungal agents. However, they have also been widely used in the silicon industry for decades for curing organosilicon polymers, despite the fact that neither the mechanism through which the siloxane bonds are formed nor their inherent toxicity are completely understood. This review gives an account of the use of organotin compounds in the preparation of diverse polysiloxane‐containing materials via cross‐linking with either organic or inorganic polymers. As they are common ingredients for this application, a brief outline of the preparation of relevant silicon‐containing compounds, as well as their reactivity, are given. In addition, since there is some evidence that stannasiloxanes formed in situ during the reaction play a determinant role as intermediates in the reaction mechanism, an overview of the synthesis and reactivity of Sn‐O‐Si‐containing compounds is also presented. Copyright © 2012 John Wiley & Sons, Ltd.     

The Compound Poisson Limit Ruling Periodic Extreme Behaviour of Non-Uniformly Hyperbolic Dynamics

We prove that the distributional limit of the normalised number of returns to small neighbourhoods of periodic points of certain non-uniformly hyperbolic dynamical systems is compound Poisson. The returns to small balls around a fixed point in the phase space correspond to the occurrence of rare events, or exceedances of high thresholds, so that there is a connection between the laws of Return Times Statistics and Extreme Value Laws. The fact that the fixed point in the phase space is a repelling periodic point implies that there is a tendency for the exceedances to appear in clusters whose average sizes is given by the Extremal Index, which depends on the expansion of the system at the periodic point. We recall that for generic points, the exceedances, in the limit, are singular and occur at Poisson times. However, around periodic points, the picture is different: the respective point processes of exceedances converge to a compound Poisson process, so instead of single exceedances, we have entire clusters of exceedances occurring at Poisson times with a geometric distribution ruling its multiplicity. The systems to which our results apply include: general piecewise expanding maps of the interval (Rychlik maps), maps with indifferent fixed points (Manneville-Pomeau maps) and Benedicks-Carleson quadratic maps.