Counterexamples to a proposed algorithm for Fries structures of benzenoids

The Fries number of a benzenoid is the maximum number of benzenoid hexagons over all of its Kekulé structures (perfect matchings), and a Fries canonical structure is a perfect matching that realises this maximum. A recently published algorithm claims to determine Fries canonical structures of benzenoids via iterated Hadamard products based on the adjacency matrix (Ciesielski et?al. in Symmetry 2:1390–1400, 2010). This algorithm is re-examined here. Convergence is typically rapid and often yields a single candidate perfect matching, but the algorithm can give an exponential number of choices, of which only a small number are canonical. More worryingly, the algorithm is found to give incorrect results for the Fries number for some benzenoids with as few as seven hexagonal faces. We give a combinatorial reformulation of the algorithm in terms of linear combinations of perfect matchings (with weights at each stage proportional to the products of weights of the edges included in a matching). In all the cases we have examined, the algorithm converges to a maximum-weight matching (or combination of maximum-weight matchings), and where the algorithm fails, either no best Fries matching is of maximum weight, or a best Fries matching is of maximum weight but a sub-optimal matching of the same weight is chosen.     

Symmetry preservation in a new noncentrosymmetric lattice comprised of acentric POM clusters residing in bowls of Cs(+)-based half SOD β-cage

In light of ever growing interests in noncentrosymmetric materials, a fascinating reticular chemistry is illustrated via the structure of a new family of solids where the acentric symmetry of the well-known [V(4+)(14)As(3+)(8)O(42)Cl](5-) POM cluster is manifested through the network construction of counter cations featuring slabs of Cs(+)-based half SOD β-cages.     

Sodium periodate as a primary oxidant for water-oxidation catalysts

Sodium periodate was characterized as a primary chemical oxidant for the catalytic evolution of oxygen at neutral pH using a variety of water-oxidation catalysts. The visible spectra of solutions formed from Cp*Ir(bpy)SO(4) during oxygen-evolution catalysis were measured. NMR spectroscopy suggests that the catalyst remains molecular after several turnovers with sodium periodate. Two of our [Cp*Ir(bis-NHC)][PF(6)](2) complexes, along with other literature catalysts, such as the manganese terpyridyl dimer, Hill's cobalt polyoxometallate, and Meyer's blue dimer, were also tested for activity. Sodium periodate was found to function only for water-oxidation catalysts with low overpotentials. This specificity is attributed to the relatively low oxidizing capability of sodium periodate solutions relative to solutions of other common primary oxidants. Studying oxygen-evolution catalysis by using sodium periodate as a primary oxidant may, therefore, provide preliminary evidence that a given catalyst has a low overpotential.     

Synthesis of 5-Iodo-1,4-disubstituted-1,2,3-triazoles Mediated by in Situ Generated Copper(I) Catalyst and Electrophilic Triiodide Ion

Mixing copper(II) perchlorate and sodium iodide solutions results in copper(I) species and the electrophilic triiodide ions, which collectively mediate the cycloaddition reaction of organic azide and terminal alkyne to afford 5-iodo-1,4-disubstituted-1,2,3-triazoles. One molar equivalent of an amine additive is required for achieving a full conversion. Excessive addition of the amine compromises the selectivity for 5-iodo-1,2,3-triazole by promoting the formation of 5-proto-1,2,3-triazole. Based on preliminary kinetic and structural evidence, a mechanistic model is formulated in which a 5-iodo-1,2,3-triazole is formed via iodination of a copper(I) triazolide intermediate by the electrophilic triiodide ions (and possibly triethyliodoammonium ions). The experimental evidence explains the higher reactivity of the in situ generated copper(I) species and triiodide ion in the formation of 5-iodo-1,2,3-triazoles than that of the pure forms of copper(I) iodide and iodine.     

Global Optimization of Econometric Functions

Estimating the values of the parameter estimates of econometric functions (maximum likelihood functions or nonlinear least squares functions) are often challenging global optimization problems. Determining the global optimum for these functions is necessary to understand economic behavior and to develop effective economic policies. These functions often have flat surfaces or surfaces characterized by many local optima. Classical deterministic optimization methods often do not yield successful results. For that reason, stochastic optimization methods are becoming widely used in econometrics. Selected stochastic methods are applied to two difficult econometric functions to determine if they might be useful in estimating the parameters of these functions.     

Development of Non-Hydrolysable Oligosaccharide Activity-Based Inactivators for Endoglycanases: A Case Study on α-1,6 Mannanases

There is a vast genomic resource for enzymes active on carbohydrates. Lagging far behind, however, are functional chemical tools for the rapid characterization of carbohydrate-active enzymes. Activity-based probes (ABPs) offer one chemical solution to these issues with ABPs based upon cyclophellitol epoxide and aziridine covalent and irreversible inhibitors representing a potent and widespread approach. Such inhibitors for enzymes active on polysaccharides are potentially limited by the requirement for several glycosidic bonds, themselves substrates for the enzyme targets. Here, it is shown that non-hydrolysable trisaccharide can be synthesized and applied even to enzymes with challenging subsite requirements. It was found that incorporation of carbasugar moieties, which was accomplished by cuprate-assisted regioselective trans-diaxial epoxide opening of carba-mannal synthesised for this purpose, yields inactivators that act as powerful activity-based inhibitors for α-1,6 endo-mannanases. 3-D structures at 1.35–1.47 Å resolutions confirm the design rationale and binding to the enzymatic nucleophile. Carbasugar oligosaccharide cyclophellitols offer a powerful new approach for the design of robust endoglycosidase inhibitors, while the synthesis procedures presented here should allow adaptation towards activity-based endoglycosidase probes as well as configurational isosteres targeting other endoglycosidase families.     

Quantification of hard X-ray photoelectron spectroscopy: Calculating relative sensitivity factors for 1.5- to 10-keV photons in any instrument geometry

A method for the rapid determination of theoretical relative sensitivity factors (RSFs) for hard X-ray photoelectron spectroscopy (HAXPES) instruments of any type and photon energy has been developed. We develop empirical functions to describe discrete theoretically calculated values for photoemission cross sections and asymmetry parameters across the photon energy range from 1.5 to 10 keV for all elements from lithium to californium. The formulae describing these parameters, in conjunction with similar practical estimates for inelastic mean free paths, allow the calculation of a full set of theoretical sensitivity factors for a given X-ray photon energy, X-ray polarisation and instrument geometry. We show that the anticipated errors on these RSFs are less than the typical errors generated by extracting X-ray photoelectron spectroscopy (XPS) intensities from the spectra and thus enable adequate quantification for any XPS/HAXPES experiment up to 10 keV. A spreadsheet implementation of this method is provided in the supporting information, along with example RSFs for existing commercial instruments.