On [Fe4S4]2+ -(mu2-SR)-M II bridge formation in the synthesis of an A-cluster analogue of carbon monoxide dehydrogenase/acetylcoenzyme A synthase

The construction of a synthetic analogue of the A-cluster of carbon monoxide dehydrogenase/acetylcoenzyme synthase, the site of acetylcoenzyme A formation, requires as a final step the formation of an unsupported [Fe(4)S(4)]-(mu(2)-SR)-Ni(II) bridge to a preformed cluster. Our previous results (Rao, P. V.; Bhaduri, S.; Jiang, J.; Holm, R. H. Inorg. Chem. 2004, 43, 5833) and the work of others have addressed synthesis of dinuclear complexes relevant to the A-cluster. This investigation concentrates on reactions pertinent to bridge formation by examining systems containing dinuclear and mononuclear Ni(II) complexes and the 3:1 site-differentiated clusters [Fe(4)S(4)(LS(3))L'](2-) (L' = TfO(-) (14), SEt (15)). The system 14/[{Ni(L(O)-S(2)N(2))}M(SCH(2)CH(2)PPh(2))](+) results in cleavage of the dinuclear complex and formation of [{Ni(L(O)-S(2)N(2))}Fe(4)S(4)(LS(3))]- (18), in which the Ni(II) complex binds at the unique cluster site with formation of a Ni(mu(2)-SR)(2)Fe bridge rhomb. Cluster 18 and the related species [{Ni(phma)}Fe(4)S(4)(LS(3))](3)- (19) are obtainable by direct reaction of the corresponding cis-planar Ni(II)-S(2)N(2) complexes with 14. The mononuclear complexes [M(pdmt)(SEt)]- (M = Ni(II), Pd(II)) with 14 in acetonitrile or Me(2)SO solution react by thiolate transfer to give 15 and [M(2)(pdmt)(2)]. However, in dichloromethane the Ni(II) reaction product is interpreted as [{Ni(pdmt)(mu(2)-SEt)}Fe(4)S(4)(LS(3))](2-) (20). Reaction of Et(3)NH(+) and 15 affords the double cubane [{Fe(4)S(4)(LS(3))}(2)(mu(2)-SEt)](3-) (21). Cluster 18 contains two mutually supportive Fe-(mu(2)-SR)-Ni(II) bridges, 19 exhibits one strong and one weaker bridge, 20 has one unsupported bridge (inferred from the (1)H NMR spectrum), and 21 has one unsupported Fe-(mu(2)-SR)-Fe bridge. Bridges in 18, 19, and 21 were established by X-ray structures. This work demonstrates that a bridge of the type found in the enzyme A-clusters is achievable by synthesis and implies that more stable, unsupported single thiolate bridges may require reinforcement by an additional covalent linkage between the Fe(4)S(4) and nickel-containing components. (LS(3) = 1,3,5-tris((4,6-dimethyl-3-mercaptophenyl)thio)-2,4,6-tris(p-tolylthio)benzene(3-); L(O)-S(2)N(2) = N,N'-diethyl-3,7-diazanonane-1,9-dithiolate(2-); pdmt = pyridine-2,6-methanedithiolate(2-); phma = N,N'-1,2-phenylenebis(2-acetylthio)acetamidate(4-); TfO = triflate.).     

Spectroscopic and photophysical properties of hexanuclear rhenium(III) chalcogenide clusters

The electronic, vibrational, and excited-state properties of hexanuclear rhenium(III) chalcogenide clusters based on the [Re(6)(mu(3)-Q)(8)](2+) (Q = S, Se) core have been investigated by spectroscopic and theoretical methods. Ultraviolet or visible excitation of [Re(6)Q(8)](2+) clusters produces luminescence with ranges in maxima of 12 500-15 100 cm(-)(1), emission quantum yields of 1-24%, and emission lifetimes of 2.6-22.4 microseconds. Nonradiative decay rate constants and the luminescence maxima follow the trend predicted by the energy gap law (EGL). Examination of 24 clusters in solution and 14 in the solid phase establish that exocluster ligands engender the observed EGL behavior; clusters with oxygen- or nitrogen-based apical ligands achieve maximal quantum yields and the longest lifetimes. The excited-state decay mechanism was investigated by applying nonradiative decay models to temperature-dependent emission experiments. Solid-state Raman spectra were recorded to identify vibrational contributions to excited-state deactivation; spectral assignments were enabled by normal coordinate analysis afforded from Hartree-Fock and DFT calculations. Excited-state decay is interpreted with a model where normal modes largely centered on the [Re(6)Q(8)](2+) core induce nonradiative relaxation. Hartree-Fock and DFT calculations of the electronic structure of the hexarhenium family of compounds support such a model. These experimental and theoretical studies of [Re(6)Q(8)](2+) luminescence provide a framework for elaborating a variety of luminescence-based applications of the largest series of isoelectronic clusters yet discovered.     

Unexpected reactivity of pyridinium salts toward alkynyl Fischer complexes to produce oxo‐heterocycles

The unprecedented reaction of ketone‐containing aromatic pyridinium salts 3a ‐ e and alkynyl Fischer complexes 1a ‐ f proceeds via a mild domino process to provide 4,6‐disubstituted pyran‐2‐ones 5a ‐ k and 2,3,5‐trisubstituted furans 6a ‐ h (45‐97%). According of the results of isotopic labeling experiments, a mechanism involving an initial Michael addition appears to be the key step, obtaining a mesomeric structure responsible for the formation of both products.     

Automatic generation of linear programming problems for computer aided instruction

The paper presents a method for generating random linear programming problems with a previously selected type of solution. The user can choose a problem whose solution is unbounded, bounded for minima, maxima or both, unique or multiple, with given structure, at wish. Initially, the feasible solution of the LPP is generated as the sum of a linear space, a cone, and a polytope, depending on the desired properties of the solution. With the aim of obtaining a simple set of constraints, the generators of these three structures are selected as random vectors with integer simple components, the range of which can be given. Next, an objective function that satisfies the required conditions, i.e. leads to a solution of the desired type, is obtained. The generating algorithms have been implemented in Mathematica and some illustrative examples are given to clarify the generation process. With this tool, a LPP can be generated, according to the instructor requirements, where this is a human or an expert system. They can control student progress and generate a sequence of problems covering all possible cases, in steps of increasing difficulty. Combining this tool with another (also produced by the same authors) that solves the problems and explains the whole process, step by step, a computer aided module for learning LPP, which is completely autonomous, can be easily obtained.     

Extending the hydrophobic cavity of β-cyclodextrin results in more negative heat capacity changes but reduced binding affinities

The formation of inclusion complexes of hydroxypropylated β-cyclodextrins (CDs) with three bile salts are investigated to shed light on the role played by the hydroxypropyl (HP) substituents. The HP-chains are situated at the rim of the CD and may thus extend the hydrophobic cavity of the CD. Calorimetric titrations in a broad temperature range and molecular dynamics simulations confirm previous speculations that the HP-chains cause an increase in dehydrated nonpolar surface area upon formation of the complexes. This additional burial of nonpolar surface area, 12–16 Å² per HP-chain according to the MD simulations, results in more negative values of ΔC _p °, which are in quantitative agreement with what is expected for hydrophobic dehydration. Although these observations support the picture of an extended hydrophobic cavity, HPβCD complexes were less stable than their unsubstituted counterparts. This indicates that increased hydrophobic contacts are not always accompanied by increased binding strength. The linear dependence of ΔC _p °, ΔH° and ΔS° on the number of HP-chains give rise to isoentropic and isoenthalpic temperatures at which ΔH° and ΔS° are independent of the number of HP-chains on the host CD (but depend on the type of bile salt). Interestingly, these convergence temperatures are close to what is observed for unfolding of proteins and may be a common feature of hydrophobic dehydration.     

Homomorphisms of matrix algebras and constructions of Butson–Hadamard matrices

An $n\times n$ matrix $H$ is Butson–Hadamard if its entries are $k$th roots of unity and it satisfies $H{H}^1=n{I}_n$. Write $\mathrm{BH}(n,k)$ for the set of such matrices.Suppose that $k=p^{\alpha }{q}^{\beta }$ where $p$ and $q$ are primes and $\alpha \ge 1$. A recent result of Östergård and Paavola uses a matrix $H\in \mathrm{BH}(n,pk)$ to construct $H^{\prime }\in \mathrm{BH}(pn,k)$. We simplify the proof of this result and remove the restriction on the number of prime divisors of $k$. More precisely, we prove that if $k=mt$, and each prime divisor of $k$ divides $t$, then we can construct a matrix $H^{\prime }\in \mathrm{BH}(mn,t)$ from any $H\in \mathrm{BH}(n,k)$.     

Cluster integrals of convex molecule systems

Cluster integrals assigned to particles interacting via the Kihara non-spherical potential are studied theoretically. An exact formula is derived which allows one to consider the effect of molecular shape separately from the effect of soft interactions. Employing the proposed formalism, the cluster integrals are analysed. The approach is applied to determine the third virial coefficient and an efficient computational method is developed. The third virial coefficient was calculated for a combination of molecules with hard cores of prolate spher-ocylindrical- and spherical shapes interacting via the square-well, triangle-well and 12-6 pair potentials. Comparison with numerical results obtained by Monte Carlo integration is made and fair agreement is found.     

Mediated glucose enzyme electrodes by cross-linking films of osmium redox complexes and glucose oxidase on electrodes

Here, we report on a novel, versatile approach for the preparation of mediated enzyme electrodes, demonstrated using cross-linked films of glucose oxidase and a range of functionalised osmium complexes on graphite electrodes. Response of enzyme electrodes are optimised by evaluation of glucose response as a function of variation in ratios of [Os(2,2′-bipyridine)₂(4-aminomethyl pyridine)Cl]⁺ redox mediator, polyallylamine support and glucose oxidase enzyme cross-linked using a di-epoxide reagent in films on graphite. Lowering of the redox potential required to mediate glucose oxidation is achieved by synthesis of complexes using (4,4′-dimethyl-2,2′-bipyridine) or (4,4′-dimethoxy-2,2′-bipyridine) as a ligand instead of (2,2′-bipyridine). Enzyme electrodes prepared using the complexes based on dimethoxy- or dimethyl-substituted bipyridines provide glucose oxidation current densities of 30 and 70 μA?cm^?2 at 0.2 and 0.35 V applied potential compared to 120 μA?cm^?2 at 0.45 V for the initial enzyme electrode, under pseudo-physiological conditions in 5 mM glucose, with stability of signals proving inadequate for long-term operation. Current output and stability may be improved by selection of alternate anchoring and cross-linking methodology, to provide enzyme electrodes capable for application to long-term glucose biosensors and anodes in enzymatic fuel cells.

Modelling the growth rate of a tracer gradient using stochastic differential equations

We develop a model in two dimensions to characterise the growth rate of a tracer gradient mixed by a statistically homogeneous flow that varies on arbitrary timescales. The model is based on the orientation dynamics of the passive-tracer gradient with respect to the straining (compressive) direction of the flow, and involves reducing the dynamics to a set of stochastic differential equations. The statistical properties of the system emerge from solving the associated Fokker–Planck equation. Within the model framework, the tracer gradient aligns with the compressive direction when the mean effective rotation in the flow is zero. At finite values of rotation, the tracer gradient aligns with a different direction, but the mean growth rate of the gradient is positive in all cases. In a certain limiting case, namely temporally decorrelated (rapidly varying) flows, exact, analytical expressions exist for the mean growth rate. Using numerical simulations, we assess the extent to which our model applies to real mixing protocols, and map the stochastic parameters on to flow parameters.