Approximate reduction of non-linear discrete models with two time scales

The aim of this work is to present a general class of nonlinear discrete time models with two time scales whose dynamics is susceptible of being approached by means of a reduced system. The reduction process is included in the so-called approximate aggregation of variables methods which consist of describing the dynamics of a complex system involving many coupled variables through the dynamics of a reduced system formulated in terms of a few global variables. For the time unit of the discrete system we use that of the slow dynamics and assume that fast dynamics acts a large number of times during it. After introducing a general two-time scales nonlinear discrete model we present its reduced accompanying model and the relationships between them. The main result proves that certain asymptotic behaviours, hyperbolic asymptotically stable (A.S.) periodic solutions, to the aggregated system entail that to the original system.     

A structural study of new tetrakis(1H-pyrazol-1-yl)methanes

Tetrakis(1H-pyrazol-1-yl)methanes are very rare compounds of which only two are known: the unsubstituted 1 obtained classically by Hückel in 1937 from carbon tetrachloride and prepared again several times and the 3,5-dimethyl substituted 2 obtained serendipitously by Pombeiro in 2009. We have now extended this group to include four new derivatives 8, 9, 11 and 12 bearing methyl groups. The X-ray crystal structure of the four compounds has been determined. They have been studied by NMR both in solution (¹H, ¹³C, ¹⁵N) and in the solid state (¹³C and ¹⁵N). DFT calculations of the six compounds (geometries, energies and absolute shieldings) have been used to discuss the experimental observations.     

An [FeIII34] Molecular Metal Oxide

The dissolution of anhydrous iron bromide in a mixture of pyridine and acetonitrile, in the presence of an organic amine, results in the formation of an [Fe₃₄] metal oxide molecule, structurally characterised by alternate layers of tetrahedral and octahedral Fe^III ions connected by oxide and hydroxide ions. The outer shell of the complex is capped by a combination of pyridine molecules and bromide ions. Magnetic data, measured at temperatures as low as 0.4 K and fields up to 35 T, reveal competing antiferromagnetic exchange interactions; DFT calculations showing that the magnitudes of the coupling constants are highly dependent on both the Fe‐O‐Fe angles and Fe?O distances. The simplicity of the synthetic methodology, and the structural similarity between [Fe₃₄], bulk iron oxides, previous Fe^III–oxo cages, and polyoxometalates (POMs), hints that much larger molecular Fe^III oxides can be made.     

Excited state tracking during the relaxation of coordination compounds

The ability to locate minima on electronic excited states (ESs) potential energy surfaces both in the case of bright and dark states is crucial for a full understanding of photochemical reactions. This task has become a standard practice for small- to medium-sized organic chromophores thanks to the constant developments in the field of computational photochemistry. However, this remains a very challenging effort when it comes to the optimization of ESs of transition metal complexes (TMCs), not only due to the presence of several electronic ESs close in energy, but also due to the complex nature of the ESs involved. In this article, we present a simple yet powerful method to follow an ES of interest during a structural optimization in the case of TMCs, based on the use of a compact hole-particle representation of the electronic transition, namely the natural transition orbitals (NTOs). State tracking using NTOs is unambiguously accomplished by computing the mono-electronic wave function overlap between consecutive steps of the optimization. Here, we demonstrate that this simple but robust procedure works not only in the case of the cytosine but also in the case of the ES optimization of a ruthenium nitrosyl complex which is very problematic with standard approaches. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.     

The structure of fosfomycin salts in solution and in the solid state by nuclear magnetic resonance spectroscopy and DFT calculations

Two samples of fosfomycin salts, the calcium and the disodium ones, were used to record their NMR spectra both in solution and in the solid state. The existence of fosfomycin in a neutral and two ionized structures (mono and dianion) was considered to interpret the spectra that were solved using the GIAO calculated chemical shifts of the minimum energy conformations. Although the starting materials were dianions, the spectra in solution show the presence of monoanions.     

Influence of the melting conditions of heavy metal oxide glasses containing bismuth oxide on their optical absorption

Glasses of the systems Bi₂O₃-SiO₂, Bi₂O₃-PbO-Ga₂O₃, Bi₂O₃-PbO-Ga₂O₃-GeO₂ and Bi₂O₃-GeO₂-Li₂O have been prepared and the interaction of their melts with crucibles of different materials has been analytically determined. Silica and porcelain crucibles were very strongly corroded and the glass composition was noticeably altered. Instead platinum crucibles are not affected if the Bi₂O₃ content is not too high. The color of the glasses changes in all cases from pale yellow to deep brown when the melting temperature reaches approximately 1000 °C. The higher the temperature and the Bi₂O₃ content the darker the brown color, independently of the nature of the employed crucible. The addition of oxidizing ions (Sb⁵⁺, As⁵⁺ or Ce⁴⁺) to the glass batch prevents darkening. Nanoparticles of elementary bismuth Bi⁰ are observed by transmission electron microscopy in the glasses melted above 1000 °C. The partial thermoreduction of the Bi₂O₃ during the heating of the glass melt is proposed as the mechanism responsible for the observed darkening.     

AMP-activated protein kinase: structure and regulation

Mammalian AMP-activated protein kinase (AMPK) is a serine/threonine protein kinase that acts as a sensor of cellular energy status. It is activated by a large variety of cellular stresses that increase cellular AMP and decrease ATP levels and also by physiological stimuli, such as muscle contraction, or by hormones such as leptin and adiponectin. AMPK modulates multiple metabolic pathways. As a result, it has become a target for the development of new drugs for the treatment of type II diabetes, obesity or even cancer. In fact, it has been recently reported that drugs used in the treatment of diabetes, such as metformin and thiazolidinediones (TZDs), exert their beneficial effects through the activation of AMPK. AMPK is a heterotrimeric complex composed of a catalytic subunit (AMPK-alpha) and two regulatory subunits (AMPK-beta and AMPK-gamma). Functional orthologues of this kinase complex are found throughout eukaryotic kingdom, from yeast to humans, indicating that the function of this complex is evolutionarily conserved. This review summarizes the recent studies on the structure and regulation of the AMPK heterotrimeric complex.