Pentanuclear complexes with unusual structural topologies from the initial use of two aliphatic amino-alcohol ligands in Fe chemistry

Five novel pentanuclear Fe(3+) clusters with the aliphatic amino-alcohol ligands 3-amino-1-propanol (Hap) and 2-(hydroxymethyl)piperidine (Hhmpip) [Fe(5)(μ(3)-Ο)(2)(L)(4)(O(2)CR)(7)] [L = ap(-), R = Ph (1); L = ap(-), R = C(CH(3))(3) (2); L = hmpip(-), R = Ph (3); L = hmpip(-), R = C(CH(3))(3) (4)] and [Fe(5)(μ(4)-Ο)(μ(3)-Ο)(O(2)CC(CH(3))(3))(8)(ap)(2)Cl(HO(2)CC(CH(3))(3))] (5) are reported. Compounds 1-4 were prepared from reactions of preformed trinuclear Fe(3+) clusters with the ligands in a molar ratio 1 : 5 in MeCN (1, 3, 4) or DMF (2), whereas compound 5 was prepared from the reaction of FeCl(3) with Hap in the presence of HO(2)CC(CH(3))(3) in a molar ratio 1 : 3 : 2 in MeCN. To the best of our knowledge, 1-5 are the first examples of Fe(3+) complexes with the ligands Hap and Hhmpip. The structures of 1-4 are composed of a quasi-planar [Fe(5)(μ(3)-O)(2)](11+) core which consists of two vertex-sharing [Fe(3)(μ(3)-O)](7+) triangles. The structure of 5 is based on the [Fe(5)(μ(4)-O)(μ(3)-O)](11+) core, in which the five Fe(3+) ions adopt a monocapped trigonal pyramidal topology. Variable-temperature magnetic susceptibility measurements on powdered microcrystalline samples of 1 and 5 revealed the existence of antiferromagnetic interactions which led to an S = 5/2 ground state. M?ssbauer spectroscopy studies on powdered microcrystalline samples of 1 and 5 confirmed that all iron ions of both complexes are in the Fe(3+) (S = 5/2) state. The variation of the ligand environment in the various iron sites was reflected in their different quadruple splitting parameters. At T < 50 K the M?ssbauer spectra indicated the onset of spin relaxation effects in the time scale of the technique (10(-7)-10(-8) s).     

Antiferromagnetic Interactions in 1D Heisenberg Linear Chains of 7‐(4‐Fluorophenyl) and 7‐Phenyl‐Substituted 1,3‐Diphenyl‐1,4‐dihydro‐ 1,2,4‐benzotriazin‐4‐yl Radicals

7‐(4‐Fluorophenyl) and 7‐phenyl‐substituted 1,3‐diphenyl‐1,4‐dihydro‐1,2,4‐benzotriazin‐4‐yl radicals were characterized by X‐ray diffraction analysis and variable‐temperature magnetic susceptibility studies. The radicals pack in 1D π stacks of equally spaced slipped radicals with interplanar distances of 3.59 and 3.67 Å and longitudinal angles of 40.97 and 43.47°, respectively. Magnetic‐susceptibility studies showed that both radicals exhibit antiferromagnetic interactions. Fitting the magnetic data revealed that the behavior is consistent with 1D regular linear antiferromagnetic chain with J=?12.9 cm^?1, zJ′=?0.4 cm^?1, g=2.0069 and J=?11.8 cm^?1, zJ′=?6.5 cm^?1, g=2.0071, respectively. Magnetic‐exchange interactions in benzotriazinyl radicals are sensitive to the degree of slippage, and inter‐radical separation and subtle changes in structure alter the fine balance between ferro‐ and antiferromagnetic interactions.     

An improved multi-staged algorithmic process for the solution of the examination timetabling problem

The efficient creation of examination timetables is a recurring and important problem for universities worldwide. Good timetables typically are characterized by balanced distances between consecutive exams for all students. In this contribution an approach for the examination timetabling problem as defined in the second International Timetabling Competition () is presented. The solution approach is managed on the top level by GRASP (Greedy Randomized Adaptive Search Procedure) and it involves several optimization algorithms, heuristics and metaheuristics. A construction phase is executed first producing a relatively high quality feasible solution and an improvement phase follows that further ameliorates the produced timetable. Each phase consists of stages that are consumed in a circular fashion. The procedure produces feasible solutions for each dataset provided under the runtime limit imposed by the rules of the ITC07 competition. Results are presented and analyzed.     

General second-order scalar-tensor theory and self-tuning

Starting from the most general scalar-tensor theory with second-order field equations in four dimensions, we establish the unique action that will allow for the existence of a consistent self-tuning mechanism on Friedmann-Lema?tre-Robertson-Walker backgrounds, and show how it can be understood as a combination of just four base Lagrangians with an intriguing geometric structure dependent on the Ricci scalar, the Einstein tensor, the double dual of the Riemann tensor, and the Gauss-Bonnet combination. Spacetime curvature can be screened from the net cosmological constant at any given moment because we allow the scalar field to break Poincaré invariance on the self-tuning vacua, thereby evading the Weinberg no-go theorem. We show how the four arbitrary functions of the scalar field combine in an elegant way opening up the possibility of obtaining nontrivial cosmological solutions.     

Self-induced transparency in diblock copolymer dispersions

We report on the versatile effect of weak red laser light impinging on diblock copolymer [poly(isoprene-b-styrene)] dispersions in two selective solvents for each block. In the strongly scattering but transparent micellar solutions in hexane (a good solvent for polyisoprene), higher refractive index copolymer-rich fibers were formed. In the turbid dispersions of the same copolymer in ethyl acetate (a good solvent for polystyrene), the effect of self-induced transparency was observed. A two-step patterning mechanism caused the generation of a transparent microchannel, increasing light transmission. The analogy between the current effect and that observed in homopolymer polyisoprene solutions in different solvents is discussed toward an understanding of the unanticipated light-soft-matter interaction.     

On the mechanism of the palladium-catalyzed β-arylation of ester enolates

The palladium‐catalyzed β‐arylation of ester enolates with aryl bromides was studied both experimentally and computationally. First, the effect of the ligand on the selectivity of the α/β‐arylation reactions of ortho‐ and meta‐fluorobromobenzene was described. Selective β‐arylation was observed for the reaction of o‐fluorobromobenzene with a range of biarylphosphine ligands, whereas α‐arylation was predominantly observed with m‐fluorobromobenzene for all ligands except DavePhos, which gave an approximate 1:1 mixture of α‐/β‐arylated products. Next, the effect of the substitution pattern of the aryl bromide reactant was studied with DavePhos as the ligand. We showed that electronic factors played a major role in the α/β‐arylation selectivity, with electron‐withdrawing substituents favoring β‐arylation. Kinetic and deuterium‐labeling experiments suggested that the rate‐limiting step of β‐arylation with DavePhos as the ligand was the palladium–enolate‐to‐homoenolate isomerization, which occurs by a β? H‐elimination, olefin‐rotation, and olefin‐insertion sequence. A dimeric oxidative‐addition complex, which was shown to be catalytically competent, was isolated and structurally characterized. A common mechanism for α‐ and β‐arylation was described by DFT calculations. With DavePhos as the ligand, the pathway leading to β‐arylation was kinetically favored over the pathway leading to α‐arylation, with the palladium–enolate‐to‐homoenolate isomerization being the rate‐limiting step of the β‐arylation pathway and the transition state for olefin insertion its highest point. The nature of the rate‐limiting step changed with PCy₃ and PtBu₃ ligands, and with the latter, α‐arylation became kinetically favored. The trend in selectivity observed experimentally with differently substituted aryl bromides agreed well with that observed from the calculations. The presence of electron‐withdrawing groups on these bromides mainly affected the α‐arylation pathway by disfavoring C? C reductive elimination. The higher activity of the ligands of the biaryldialkylphosphine ligands compared to their corresponding trialkylphosphines could be attributed to stabilizing interactions between the biaryl backbone of the ligands and the metal center, thereby preventing deactivation of the β‐arylation pathway.     

Measured and calculated oxidation potentials of 1-X-12-Y-CB11Me10- anions

Cyclic voltammetry of 31 icosahedral carborane anions 1-X-12-Y-CB(11)Me(10)(-) at a Pt electrode in liquid SO(2) revealed a completely reversible one-electron oxidation even at low scan rates, except for the anions with Y = I, which are oxidized irreversibly up to a scan rate of 5.0 V/s, and the anion with X = COOH and Y = H, whose oxidation is irreversible at scan rates below 1.0 V/s. Relative reversible oxidation potentials agree well with RI-B3LYP/TZVPP,COSMO and significantly less well with RI-BP86/TZVPP,COSMO or RI-HF/TZVPP,COSMO calculated adiabatic electron detachment energies. Correlations with HOMO energies of the anions are nearly as good, even though the oxidized forms are subject to considerable Jahn-Teller distortion. Except for the anion with X = F and Y = Me, the oxidation potentials vary linearly with substituent σ(p) Hammett constants. The slopes (reaction constants) are ~0.31 and ~0.55 V for positions 1 and 12, respectively.     

A singular function boundary integral method for elliptic problems with singularities

In this work we present a singular function boundary integral method for elliptic problems with boundary singularities. In this method, the approximation is constructed from the truncated asymptotic expansion for the solution near the singular point and the Dirichlet boundary conditions are weakly enforced by means of Lagrange multiplier functions. The resulting discrete problem is posed and solved on the boundary of the domain, away from the point of singularity. We are able to show that the method approximates the generalized stress intensity factors, i.e. the coe cients in the asymptotic expansion, at an exponential rate. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An hp finite element method for singularly perturbed systems of reactiondiffusion equations

We consider the approximation of a coupled system of two singularly perturbed reaction-diffusion equations by the finite element method. The solution to such problems contains boundary layers which overlap and interact, and the numerical approximation must take this into account in order for the resulting scheme to converge uniformly with respect to the singular perturbation parameters. We present results on a high order hp finite element scheme which includes elements of size O (εp) and O (μp) near the boundary, where ε, μ are the singular perturbation parameters and p is the degree of the approximating polynomials. Under the assumption of analytic input data, the method yields exponential rates of convergence as p → ∞, independently of ε and μ. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Scheduling Three-Operation Jobs in a Two-Machine Flow Shop to Minimize Makespan

This paper considers a variant of the classical problem of minimizing makespan in a two-machine flow shop. In this variant, each job has three operations, where the first operation must be performed on the first machine, the second operation can be performed on either machine but cannot be preempted, and the third operation must be performed on the second machine. The NP-hard nature of the problem motivates the design and analysis of approximation algorithms. It is shown that a schedule in which the operations are sequenced arbitrarily, but without inserted machine idle time, has a worst-case performance ratio of 2. Also, an algorithm that constructs four schedules and selects the best is shown to have a worst-case performance ratio of 3/2. A polynomial time approximation scheme (PTAS) is also presented.