The not-so-peculiar case of calcium oxide: a weakness in atomic natural orbital basis sets for calcium

Atomic natural orbital (ANO) basis sets for calcium may produce surprisingly poor atomic and molecular properties and energetics. The weaknesses in these basis sets may be traced primarily to deficiencies within the sets of d functions which are incapable of effectively correlating the 3s and 3p electrons. Examples are given which show that addition of tight d functions to the ANO basis is required to achieve qualitatively correct energetics and structures for conventionally bonded calcium compounds.     

A Quantum Chemical Study of the Abnormal Reactivity of 2‐Methoxyfuran

The gas‐phase pyrolytic and oxidative chemistry of furans has received much attention recently because of their potential as platform chemicals and biofuels. Typically these compounds exhibit very strong ring carbon to H or CH₃ bonds. 2‐Methoxyfuran had been reported to be exceptionally unstable in comparison to related substituted heterocycles in pyrolytic experiments. The origins of its reactivity are shown to be due to the very weak O–CH₃, which at 189.5 ± 1.9 kJ mol^?1 is some 200 kJ mol^?1 weaker than C–H bonds in the molecule. We show that the reported reactivity is somewhat overestimated but that does not alter the fact that 2‐methoxyfuran is exceptionally unstable. It may prove to be a useful alternative to azomethane as a thermal source of methyl radicals.     

Electrochemical Vicinal Difluorination of Alkenes: Scalable and Amenable to Electron-Rich Substrates

Fluorinated alkyl groups are important motifs in bioactive compounds, positively influencing pharmacokinetics, potency and conformation. The oxidative difluorination of alkenes represents an important strategy for their preparation, yet current methods are limited in their alkene-types and tolerance of electron-rich, readily oxidized functionalities, as well as in their safety and scalability. Herein, we report a method for the difluorination of a number of unactivated alkene-types that is tolerant of electron-rich functionality, giving products that are otherwise unattainable. Key to success is the electrochemical generation of a hypervalent iodine mediator using an “ex-cell” approach, which avoids oxidative substrate decomposition. The more sustainable conditions give good to excellent yields in up to decagram scales.     

Novel Separation Processes for Solid/Liquid Separations in Coal Derived Liquids

The removal of the mineral matter found in coal derived liquids is a very difficult solid/liquid separation process. Clays, pyrites and other minerals that occur in coal ultimately find their way into the liquefied product. This is the case, e.g., for both the solvent refined coal (SRC-I) and H-Coal processes. The ash content of bituminous coals which may be fed to coal liquefaction processes normally rangesfrom 6 to 11 wt.%. The ash content of the coal liquid product can range from 4 to 20 wt.% depending upon the lique-faction .process. Ash levels must be reduced to, e.g., 0.4 wt.% in the case of boiler fuel and less than 0.1 wt.% for gas turbine fuels.     

Hopf-algebraic renormalization of QED in the linear covariant gauge

In the context of massless quantum electrodynamics (QED) with a linear covariant gauge fixing, the connection between the counterterm and the Hopf-algebraic approach to renormalization is examined. The coproduct formula of Green’s functions contains two invariant charges, which give rise to different renormalization group functions. All formulas are tested by explicit computations to third loop order. The possibility of a finite electron self-energy by fixing a generalized linear covariant gauge is discussed. An analysis of subdivergences leads to the conclusion that such a gauge only exists in quenched QED.     

A trading mechanism contingent on several indices

We introduce a trading mechanism where the execution of an order on a security can be made contingent on the relation between the clearing price of the security and the clearing price of one or several indices. A mechanism similar to ours, but limited to only one index, was implemented on the Tel Aviv Stock Exchange. We argue that it is in some cases crucial to make the execution of an order contingent on several indices. Our mechanism consists of a particular implementation of a double-sided multi-unit combinatorial auction with substitutes (or DMCS auction), which we introduced in an earlier article.