How do nitriles compare with isoelectronic alkynyl groups in the electronic communication between iron centers bridged by phenylenebis- and -tris(nitrile) ligands? An electronic and crystal-structure study

Density functional theory (DFT) calculations on the model [{FeCp(dpe)}(2){1,4-C(6)H(4)(CN)(2)}](2+) (3(2+); dpe = diphosphinoethane) of salts of the cations [{FeCp(dppe)}(2){1,4-C(6)H(4)(CN)(2)}](2+) (1(2+); dppe = 1,2-bis[diphenyldiphosphino]ethane) and [{FeCp*(CO)(2)}(2){1,4-C(6)H(4)(CN)(2)}](2+) (2(2+)), for which the X-ray crystal structures have been determined, as well as on its isomer [{FeCp(dpe)}(2){1,3-C(6)H(4)(CN)(2)}](2+) (4(2+)) and on the related complex [{FeCp(dpe)}(3){1,3,5-C(6)H(3)(CN)(3)}](3+) (5(2+)), indicate that the highest occupied molecular orbitals (HOMOs) of these compounds are localized on the metal centers with negligible participation of the C(6) ring. Thus, the poly(nitrile)phenylene ligand efficiently quenches the electronic communication between the metal centers. This is at variance with the related isoelectronic polyacetylene phenylene complexes, in which the iron centers have been shown to be electronically coupled. Consistently, apart from the case of 3(3+), which shows some degree of delocalization, all of the oxidized forms of 3(2+), 4(2+), and 5(2+) can be described as class II, localized mixed-valent species, in agreement with the electrochemical data showing two close oxidation potentials around 1 V vs FeCp*(2). This is at variance with the p-phenylene-bridged biethynyldiiron analogue, for which extended electronic delocalization was earlier shown to provide greater degree of delocalization of the mixed valency. Time-dependent DFT calculations on 3(2+), 4(2+), and 5(2+) indicate that the lowest-energy absorption band is associated with metal-to-ligand charge-transfer transitions involving the metallic HOMOs and the two lowest unoccupied molecular orbitals that derive from the lowest π*(phenylene) orbitals with some π*(CN) bonding admixture.     

The $(1-\mathbb{E})$-transform in combinatorial Hopf algebras

We extend to several combinatorial Hopf algebras the endomorphism of symmetric functions sending the first power-sum to zero and leaving the other ones invariant. As a “transformation of alphabets”, this is the (1-\mathbbE)(1-\mathbb{E})-transform, where \mathbbE\mathbb{E} is the “exponential alphabet,” whose elementary symmetric functions are e_n=\frac1n!e_{n}=\frac{1}{n!}. In the case of noncommutative symmetric functions, we recover Schocker’s idempotents for derangement numbers (Schocker, Discrete Math. 269:239–248, 2003). From these idempotents, we construct subalgebras of the descent algebras analogous to the peak algebras and study their representation theory. The case of WQSym leads to similar subalgebras of the Solomon–Tits algebras. In FQSym, the study of the transformation boils down to a simple solution of the Tsetlin library in the uniform case.     

On the measurement of dislocation core distributions in a GaAs/ZnTe/CdTe heterostructure by high-resolution transmission electron microscopy

Tensorial maps of misfit dislocations at the strained GaAs-ZnTe-CdTe interfacial zone are reconstructed by use of digital processing of high-resolution transmission electron micrographs. Large distortions of the crystal lattice around Lomer dislocations are measured using the geometric phase technique. The integration of the dislocation distribution tensor field over a dislocation core region gives the in-plane components of their Burgers vectors. The accuracy of the method for the dislocation map reconstruction is tested by comparing the theoretical values of the so-called true Burgers vectors with those obtained from the integration of tensorial maps.     

Stability by rescaled weak convergence for the Navier–Stokes equations

We study a weak stability problem for the three-dimensional Navier–Stokes system: if a sequence (u_0,n)_n∈N${(u_{0,n})}_{n\in \mathbb{N}}$ of initial data, bounded in some scaling invariant space, converges weakly to an initial data u₀$u_0$ which generates a global regular solution, does u_0,n$u_{0,n}$ generate a global regular solution? Because of the invariances of the Navier–Stokes equations, a positive answer in general to this question would imply global regularity for any data, so we introduce a new concept of weak convergence (rescaled weak convergence) under which we are able to give a positive answer. The proof relies on profile decompositions in anisotropic spaces and their propagation by the Navier–Stokes equations.     

A tabu search heuristic for the vehicle routing problem with private fleet and common carrier

This paper describes a tabu search heuristic for a vehicle routing problem where the owner of a private fleet can either visit a customer with one of his vehicles or assign the customer to a common carrier. The owner’s objective is to minimize the variable and fixed costs for operating his fleet plus the total costs charged by the common carrier. The proposed tabu search is shown to outperform the best approach reported in the literature on 34 benchmark instances with a homogeneous fleet.     

Logic Prizes <Emphasis Type="Italic">et Cætera</Emphasis>

I discuss the origin and development of logic prizes around the world. In a first section I describe how I started this project by creating the Newton da Costa Logic Prize in Brazil in 2014. In a second section I explain how this idea was extended into the world through the manifesto A Logic Prize in Every Country! and how was organized the Logic Prizes Contest at the 6th UNILOG (World Congress and School on Universal Logic) in Vichy in June 2018 with the participation of 9 logic prizes winners from 9 countries. In a third section I discuss how this project will develop in the future with the creation of more logic prizes, an Encyclopædia of Logic, the book series Logic PhDs, as well as the creation of a World Logic Day, January 14, day of birth of Alfred Tarski and of death of Kurt Gödel.     

de Haas-van Alphen oscillations with non-parabolic dispersions

de Haas-van Alphen oscillation spectrum of two-dimensional systems is studied for general power law energy dispersion, yielding a Fermi surface area of the form S(E) ∝ E ^α for a given energy E. The case α = 1 stands for the parabolic energy dispersion. It is demonstrated that the periodicity of the magnetic oscillations in inverse field can depend notably on the temperature. We evaluated analytically the Fourier spectrum of these oscillations to evidence the frequency shift and smearing of the main peak structure as the temperature increases.     

Nickel(II)-Based Building Blocks with Schiff Base Derivatives: Experimental Insights and DFT Calculations

We have recently reported a series of neutral square planar tridentate Schiff base (L) complexes of the general formula [(L)M(py)], showing relatively high first-order hyperpolarizabilities and NLO redox switching behavior. In the present study, new members of this family of compounds have been prepared with the objective to investigate their potential as building blocks in the on-demand construction of D-π-A push–pull systems. Namely, ternary nickel(II) building blocks of general formula [(L^A/D)Ni(4-pyX)] (4–7), where L^A/D stands for an electron accepting or donating dianionic O,N,O-tridentate Schiff base ligand resulting from the monocondensation of 2-aminophenol or its 4-substituted nitro derivative and β-diketones R-C(=O)CH₂C(=O)CH₃ (R = methyl, anisyl, ferrocenyl), and 4-pyX is 4-iodopyridine or 4-ethynylpyridine, were synthesized and isolated in 60–78% yields. Unexpectedly, the Sonogashira cross-coupling reaction between the 4-iodopyridine derivative 6 and 4-ethynylpyridine led to the formation of the bis(4-pyridyl) acetylene bridged centrosymmetric dimer [{(L^D)Ni}₂(µ²-py-C≡C-py)] (8). Complexes 4–8 were characterized by elemental analysis, FT-IR and NMR spectroscopy, single crystal X-ray diffraction and computational methods. In each compound, the four-coordinate Ni(II) metal ion adopts a square planar geometry with two nitrogen and two oxygen atoms as donors occupying trans positions. In 8, the Ni…Ni separation is of 13.62(14) Å. Experimental results were proved and explained theoretically exploiting Density Functional Theory calculations.     

An expanded halogen bonding scale using astatine

As a non-covalent interaction, halogen bonding is now acknowledged to be useful in all fields where the control of intermolecular recognition plays a pivotal role. Halogen-bond basicity scales allow quantification of the halogen bonding of referential donors with organic functional groups from a thermodynamic point of view. Herein we present the pK_BAtI basicity scale to provide the community an overview of halogen-bond acceptor strength towards astatine, the most potent halogen-bond donor element. This experimental scale is erected on the basis of complexation constants measured between astatine monoiodide (AtI) and sixteen selected Lewis bases. It spans over 6 log units and culminates with a value of 5.69 ± 0.32 for N,N,N′,N′-tetramethylthiourea. On this scale, the carbon π-bases are the weakest acceptors, the oxygen derivatives cover almost two-thirds of the scale, and sulphur bases exhibit the highest AtI basicity. Regarding the applications of ²¹¹At in targeted radionuclide therapy, stronger labelling of carrier agents could be envisaged on the basis of the pK_BAtI scale.

Based on the halogen bonding between astatine monoiodide (AtI) and 16 Lewis bases, the newly established pK_BAtI scale indicates that the halogen bond basicity of AtI follows the order C ≤ O ≤ S ≈ Se for the acceptor atomic site.     

A composite grid approach for the Euler equations

A zonal grid methodology has been developed for the calculation of compressible fluid flows. The domain subdivision is based on patched grid systems composed of zones or blocks within which a distinct curvilinear grid is generated. The flow simulation is then carried out with a modified scheme based on the Euler finite volume solver of Ni. This scheme uses a distribution procedure that provides an easy and accurate way for the transfer of information from one block to another. This method results in a naturally conservative computation at the interfaces. It is analysed and developed for the treatment of embedded grids with a grid point common to more than four blocks.