The maximum and the addition of assignment games

In the framework of two-sided assignment markets, we first consider that, with several markets available, the players may choose where to trade. It is shown that the corresponding game, represented by the maximum of a finite set of assignment games, may not be balanced. Some conditions for balancedness are provided and, in that case, properties of the core are analyzed. Secondly, we consider that players may trade simultaneously in more than one market and then add up the profits. The corresponding game, represented by the sum of a finite set of assignment games, is balanced. Moreover, under some conditions, the sum of the cores of two assignment games coincides with the core of the sum game.     

Zero-finder methods derived using Runge-Kutta techniques

In this paper some families of zero-finding iterative methods for nonlinear equations are presented. The key idea to derive them is to solve an initial value problem applying Runge-Kutta techniques. More explicitly, these methods are used to solve the problem that consists in a differential equation in what appears the inverse function of the one which zero will be computed and the condition given by the value attained by it at the initial approximation. Carrying out this procedure several families of different orders of local convergence are obtained. Furthermore, the efficiency of these families are computed and two new families using like-Newton’s methods that improve the most efficient one are also given.     

Optimizing microwind rural electrification projects. A case study in Peru

Electrification systems based on the use of renewable energy sources are suitable for providing electricity to isolated communities autonomously. Specifically, electrification by wind power is one of the technological options that have been used recently in projects implemented in the Andean highlands of Peru. To date, these projects have tended to install individual microwind turbines at each demand point. Alternatively, we propose a solution that considers both individual generators and microgrids. We develop a mathematical model that gives the location and size or type of the wind turbines and the design of the microgrids, taking into account the demand of the consumption points and the wind potential. The criterion is the minimization of the initial investment cost required to meet the demand. The model is validated by application to a real case in the northern highlands of Peru. Results show that microgrids are used despite the village dispersion, and the solutions significantly reduce the initial investment costs.     

Aryl-O reductive elimination from reaction of well-defined aryl-Cu(III) species with phenolates: the importance of ligand reactivity

Well-defined aryl-Cu(III) species undergo rapid reductive elimination upon reaction with phenolates (PhO(-)), to form aryl-OPh cross-coupling products. Kinetic studies show that the reaction follows a different mechanistic pathway compared to the reaction with phenols. The pH active cyclized pincer-like ligand undergoes an initial amine deprotonation that triggers a faster reactivity at room temperature. A mechanistic proposal for the enhanced reactivity and the role of EPR-detected Cu(II) species will be discussed in detail.     

Measuring electron sharing between atoms in first-principle simulations

Calculations of large scale electronic structure within periodic boundary conditions, mostly based on solid state physics, allow the modeling of atomic forces and molecular dynamics for atomic assemblies of 100–1000 atoms, thus providing complementary information in material and macromolecular sciences. Nevertheless, these methods lack connections with the chemistry of simple molecules as isolated entities. In order to contribute to establish a conceptual connection between solid state physics and chemistry, the calculation of the extent of electron sharing between atoms, also known as delocalization index, is performed on simple molecules and on complexes with transition metal atoms, using density functional calculations where the Kohn–Sham molecular orbitals are represented in terms of plane waves and in periodic boundary conditions. These applications show that the useful measure of electron sharing between atomic pairs can be recovered from density functional calculations using the same set-up applied to large atomic assemblies in condensed phases, with no projections of molecular orbitals onto atomic orbitals.     

All-metal aromatic clusters M4(2-) (M = B, Al, and Ga). Are π-electrons distortive or not?

The π-electrons in benzene, the quintessential aromatic molecule, were previously shown to be distortive, i.e., they prefer localized double bonds alternating with single bonds. It is the σ-electrons that force the double bonds to delocalize, leading to a regular, D(6h) geometry. Herein, we computationally investigate the double-bond localizing or delocalizing propensities of σ- and π-electrons in the archetypal all-metal aromatic cluster Al(4)(2-) and its second- and fourth-period analogs B(4)(2-) and Ga(4)(2-), using Kohn-Sham molecular orbital (MO) theory at BP86/TZ2P in combination with quantitative bond energy decomposition analyses (EDA). We compare the three all-metal aromatic clusters with the structurally related organic species C(4)H(4)(2+), C(4)H(4), and C(4)H(4)(2-). Our analyses reveal that the π-electrons in the group-13 M(4)(2-) molecules have a weak preference for localizing the double bonds. Instead, the σ-electrons enforce the regular D(4h) equilibrium geometry with delocalized double bonds.     

Nuclear shieldings with the SSB-D functional

The recently reported SSB-D functional [J. Chem. Phys. 2009, 131, 094103] is used to check the performance for obtaining nuclear magnetic resonance (NMR) shielding constants. Four different databases were studied, which contain a diversity of molecules and nuclear shielding constants. The SSB-D functional is compared with its "parent" functionals (PBE, OPBE), the KT2 functional that was designed specially for NMR applications and the coupled cluster CCSD(T) method. The best performance for the experimentally most-used elements ((1)H, (13)C) is obtained for the SSB-D and KT2 functionals.