Preparation of [5,6]- and [6,6]-oxahomofullerene derivatives and their interconversion by Lewis acid assisted reactions of fullerene mixed peroxides

[60]Fullerene mixed peroxides C60(O)(OOtBu)4 exhibit chemo- and regioselective reactions under mild conditions. The epoxy moiety is opened by ferric chloride to form vicinal hydroxy chloride C60Cl(OH)(OOtBu)4. BF3 is also effective in opening the epoxy moiety. The O-O bond of the fullerene mixed peroxide is cleaved by aluminum chloride to form both [5,6]- and [6,6]-fullerene hemiketals (oxohomo[60]fullerenes). A Hock-type rearrangement is proposed for the formation of the hemiketals, in which a fullerene C-C bond is cleaved. Lewis acids and/or visible light can initiate isomerization of the hemiketal isomers. Single-crystal X-ray analysis and theoretical calculations confirmed the results.     

Extension of MNDO to d orbitals: Parameters and results for the halogens

A recently proposed extension of the MNDO formalism to d orbitals has been parameterized for the halogens CI, Br, and I. Extensive test calculations indicate slight consistent improvements for normalvalent molecules and dramatic improvements for hypervalent molecules, in comparison with established MNDO -type methods without d orbitals. The mean absolute errors in calculated heats of formation are 3.9 kcal/mol for 155 normalvalent compounds and 2.8 kcal/mol for 23 hypervalent compounds. The predicted structures of the hypervalent molecules are qualitatively correct, with a mean absolute error of 2° in 19 bond angles.     

A chemically consistent graph architecture for massive reaction networks applied to solid-electrolyte interphase formation

Modeling reactivity with chemical reaction networks could yield fundamental mechanistic understanding that would expedite the development of processes and technologies for energy storage, medicine, catalysis, and more. Thus far, reaction networks have been limited in size by chemically inconsistent graph representations of multi-reactant reactions (e.g. A + B → C) that cannot enforce stoichiometric constraints, precluding the use of optimized shortest-path algorithms. Here, we report a chemically consistent graph architecture that overcomes these limitations using a novel multi-reactant representation and iterative cost-solving procedure. Our approach enables the identification of all low-cost pathways to desired products in massive reaction networks containing reactions of any stoichiometry, allowing for the investigation of vastly more complex systems than previously possible. Leveraging our architecture, we construct the first ever electrochemical reaction network from first-principles thermodynamic calculations to describe the formation of the Li-ion solid electrolyte interphase (SEI), which is critical for passivation of the negative electrode. Using this network comprised of nearly 6000 species and 4.5 million reactions, we interrogate the formation of a key SEI component, lithium ethylene dicarbonate. We automatically identify previously proposed mechanisms as well as multiple novel pathways containing counter-intuitive reactions that have not, to our knowledge, been reported in the literature. We envision that our framework and data-driven methodology will facilitate efforts to engineer the composition-related properties of the SEI – or of any complex chemical process – through selective control of reactivity.

A chemically consistent graph architecture enables autonomous identification of novel solid-electrolyte interphase formation pathways from a massive reaction network.     

Synthesis, Structure, and Properties of a Model for Galactose Oxidase

An active-site analog of the radical copper enzyme galactose oxidase has been prepared from a synthetic tripod chelate ((2-pyridylmethyl)[(2-hydroxy-3,5-dimethylphenyl)methyl][(2-hydroxy-5-methyl-3-(methylthio)phenyl)methyl]amine, duncamine (dnc)) that binds a single Cu(II) ion through phenolate, thioether-substituted phenolate, and pyridylamine arms. The Cu complex crystallizes as a dinucleated dimer bridged by phenolate oxygens, and the structure has been determined by X-ray crystallography. Addition of pyridine (or other coordinating bases) dissociates the complex into a monomeric derivative that has been characterized spectroscopically (optical absorption and EPR) and electrochemically. The model provides insight into the properties of a mutant form of galactose oxidase which retains the same copper ligand complement as the wild type protein but lacks catalytic activity.     

Chemie der lithium-enolat-heptafulvene: regiospezifische aldol-addition

Aldehydes and ketones add to the cycloheptatriene ester anion $\text{2a}$ and to the carboxylic acid dianion $\text{2b}$ at C-7 (α-attack) or C-2 (C-5) (γ-attack), depending on the starting compounds.     

PHOTOCHEMISTRY OF ALL-TRANS- AND 13-CIS-14,15-DIDEUTERIORETINAL

Abstract— All- trans - and 13- cis -14,15-dideuterioretinal were synthesized and their solution photochemistry examined. Quantum yields of trans → cis or cis → trans photoisomerization and the number and ratio of primary photoproducts, determined by high pressure liquid chromatographic analysis, are essentially identical to that of their corresponding retinal isomer. The C-14, C-15 carbon-hydrogen modes play no particularly important role in the deactivation of electronically excited linear polyenes related to retinal.     

Automatic structures,rational growth,and geometrically finite hyperbolic groups

Summary We show that the set of equivalence classes of synchronously automatic structures on a geometrically finite hyperbolic groupG is dense in the product of the sets over all maximal parabolic subgroupsP. The set of equivalence classes of biautomatic structures onG is isomorphic to the product of the sets over the cusps (conjugacy classes of maximal parabolic subgroups) ofG. Each maximal parabolicP is a virtually abelian group, so and were computed in [NS1].We show that any geometrically finite hyperbolic group has a generating set for which the full language of geodesics forG is regular. Moreover, the growth function ofG with respect to this generating set is rational. We also determine which automatic structures on such a group are equivalent to geodesic ones. Not all are, though all biautomatic structures are.Oblatum 14-VI-1993 & 4-I-1994Both authors acknowledge support from the NSF for this research.     

Safety Stock Determination with Serially Correlated Demand in a Periodic-Review Inventory System

We consider a periodic-review inventory replenishment model with an order-up-to-R operating doctrine for the case of deterministic lead times and a covariance-stationary stochastic demand process. A method is derived for setting the inventory safety stock to achieve an exact desired stockout probability when the autocovariance function for Gaussian demand is known. Because the method does not require that parametric time-series models be fit to the data, it is easily implemented in practice. Moreover, the method is shown to be asymptotically valid when the autocovariance function of demand is estimated from historical data. The effects on the stockout rate of various levels of autocorrelated demand are demonstrated for situations in which autocorrelation in demand goes undetected or is ignored by the inventory manager. Similarly, the changes to the required level of safety stock are demonstrated for varying levels of autocorrelation.     

Frobenius-Perron operators and approximation of invariant measures for set-valued dynamical systems

A set-valued dynamical systemF on a Borel spaceX induces a set-valued operatorF onM(X) — the set of probability measures onX. We define arepresentation ofF, each of which induces an explicitly defined selection ofF; and use this to extend the notions of invariant measure and Frobenius-Perron operators to set-valued maps. We also extend a method ofS. Ulam to Markov finite approximations of invariant measures to the set-valued case and show how this leads to the approximation ofT-invariant measures for transformations , whereT corresponds to the closure of the graph of .