Basic ancillary ligands promote O-O bond formation in iridium-catalyzed water oxidation: a DFT study

The cationic iridium complex [Ir(OH(2))(2)(phpy)(2)](+) (phpy = o-phenylpyridine) is among the most efficient mononuclear catalysts for water oxidation. The postulated active species is the oxo complex [Ir(O)(X)(phpy)(2)](n), with X = OH(2) (n = +1), OH(-) (n = 0) or O(2-) (n = -1), depending on the pH. The reactivity of these species has been studied computationally at the DFT(B3LYP) level. The three [Ir(O)(X)(phpy)(2)](n) complexes have an electrophilic Ir(v)-oxo moiety, which yields an O-O bond by undergoing a nucleophilic attack of water in the critical step of the mechanism. In this step, water transfers one proton to either the Ir(V)-oxo moiety or the ancillary X ligand. Five different reaction pathways associated with this acid/base mechanism have been characterized. The calculations show that the proton is preferably accepted by the X ligand, which plays a key role in the reaction. The higher the basicity of X, the lower the energy barrier associated with O-O bond formation. The anionic species, [Ir(O)(2)(phpy)(2)](-), which has the less electrophilic Ir(V)-oxo moiety but the most basic X ligand, promotes O-O bond formation through the lowest energy barrier, 14.5 kcal mol(-1). The other two active species, [Ir(O)(OH)(phpy)(2)] and [Ir(O)(OH(2))(phpy)(2)](+), which have more electrophilic Ir(V)-oxo moieties but less basic X ligands, involve higher energy barriers, 20.2 kcal mol(-1) and 25.9 kcal mol(-1), respectively. These results are in good agreement with experiments showing important pH effects in similar catalytic systems. The theoretical insight given by the present study can be useful in the design of more efficient water oxidation catalysts. The catalytic activity may increase by using ligand scaffolds bearing internal bases.     

High‐order implicit Runge–Kutta time integrators for fluid‐structure interactions

This paper presents an approach to develop high‐order, temporally accurate, finite element approximations of fluid‐structure interaction (FSI) problems. The proposed numerical method uses an implicit monolithic formulation in which the same implicit Runge–Kutta (IRK) temporal integrator is used for the incompressible flow, the structural equations undergoing large displacements, and the coupling terms at the fluid‐solid interface. In this context of stiff interaction problems, the fully implicit one‐step approach presented is an original alternative to traditional multistep or explicit one‐step finite element approaches. The numerical scheme takes advantage of an arbitrary Lagrangian–Eulerian formulation of the equations designed to satisfy the geometric conservation law and to guarantee that the high‐order temporal accuracy of the IRK time integrators observed on fixed meshes is preserved on arbitrary Lagrangian–Eulerian deforming meshes. A thorough review of the literature reveals that in most previous works, high‐order time accuracy (higher than second order) is seldom achieved for FSI problems. We present thorough time‐step refinement studies for a rigid oscillating‐airfoil on deforming meshes to confirm the time accuracy on the extracted aerodynamics reactions of IRK time integrators up to fifth order. Efficiency of the proposed approach is then tested on a stiff FSI problem of flow‐induced vibrations of a flexible strip. The time‐step refinement studies indicate the following: stability of the proposed approach is always observed even with large time step and spurious oscillations on the structure are avoided without added damping. While higher order IRK schemes require more memory than classical schemes (implicit Euler), they are faster for a given level of temporal accuracy in two dimensions. Copyright © 2015 John Wiley & Sons, Ltd.     

Enumeration of (p,q)-parking functions

Parking functions are central in many aspects of combinatorics. We define in this communication a generalization of parking functions which we call (p₁,…,p_k)-parking functions. We give a characterization of them in terms of parking functions and we show that they can be interpreted as recurrent configurations in the sandpile model for some graphs. We also establish a correspondence with a Lukasiewicz language, which enables to enumerate (p₁,…,p_k)-parking functions as well as increasing ones.     

Chaines maximales de préordres

Résumé La famille des préordres sur un ensemble fixé constitue un treillis pour l'inclusion. Répondant à une question rencontrée par S. Eilenberg dans l'étude des automates non déterministes on établit une propriété des chaînes maximales de préordres sur un ensemble fini.On en déduit que si l'ensemble a n éléments, de telles chaînes contiennent au plus [n(n + 1)]/2 préordres.

---

     

Exploration of chiral Lewis acid Mg2+ catalysts in the synthesis of aryl organophosphate triesters from phosphorus oxychloride through a three-step,two-pot substitution sequence

A variety of nucleophilic and Lewis acid catalysts were examined for use in promoting the synthesis of organophosphate triesters. Eight novel organophosphate triesters are reported here for the first time. MgSO₄ was discovered as an inexpensive catalyst capable of improving the synthesis of a variety of aryl organophosphate triesters from the readily available and low cost precursor phosphorus oxychloride in a three-step, two-pot sequence. Yields for this method improve upon the uncatalyzed method by 8–36%. Several chiral catalysts were tested, but none were able to induce enantioselectivity in the reaction.