Exceptionally Simple Enantioselective Syntheses of Chiral Hexa- and Tetracyclic Polyprenoids of Sedimentary Origin

Coupling between a sulfone and an acylsilane fragment (see below) constitutes the first step in the exceptionally short total syntheses of two chiral hexacyclic hydrocarbons isolated from Eocene Messel shale (Germany). Like the first step, subsequent steps also employ a powerful synthetic tactic: polycyclization of a specially constructed chiral, multiply unsaturated oxirane. TBS=tBuMe₂Si.     

Strongly transitive actions on euclidean buildings

We prove a decomposition result for a group G acting strongly transitively on the Tits boundary of a Euclidean building. As an application we provide a local to global result for discrete Euclidean buildings, which generalizes results in the locally compact case by Caprace–Ciobotaru and Burger–Mozes. Let X be a Euclidean building without cone factors. If a group G of automorphisms of X acts strongly transitively on the spherical building at infinity ?X, then the G-stabilizer of every affine apartment in X contains all reflections along thick walls. In particular G acts strongly transitively on X if X is simplicial and thick.     

Analysis of environment response effects on excitation energies within subsystem-based time-dependent density-functional theory

We analyze the ability of subsystem time-dependent density-functional theory (sTDDFT) to describe environmental response effects. To this end, we utilize the recently proposed “exact” version of sTDDFT relying on projection-based embedding (PbE), which so far was applied only for the special case of two subsystems. We confirm that PbE-sTDDFT in combination with supersystem bases yields results equivalent to those of supermolecular TDDFT calculations for systems solvated by many solvent molecules, using the previously studied system of methylene-cyclopropene⋯(H₂O)₁₇ as an example. By means of this exact reference embedding framework, we are able to disentangle solvent effects introduced in terms of the embedding potential from those caused by solvent response couplings, both for the PbE variant and for sTDDFT with approximate non-additive kinetic energy functionals. Furthermore, we show that the use of a monomer basis introduces significant errors for the environmental response contribution. Employing a virtual-orbital localization strategy on top of PbE-sTDDFT, we can also directly assess the impact of inter-subsystem charge-transfer excitations on the entire solvent effect, which turn out to play a significant role for the environmental response. Finally, we analyze the response effects introduced by the individual solvent molecules and their interdependence, and show that a simple, pair-wise additive correction for solvent response yields excellent results in the present example.     

A highly active catalyst system for the heteroarylation of acetone

A highly active catalyst system for the heteroarylation of acetone has been identified. The coupling between the in situ generated tributyltin enolate of acetone and a variety of heteroaromatic bromides, chlorides, and triflates in the presence of this catalyst system provided arylacetones in good yields.     

Enantioselective Desymmetrization of Prochiral Cyclohexanones by Organocatalytic Intramolecular Michael Additions to α,β‐Unsaturated Esters

A new catalytic asymmetric desymmetrization reaction for the synthesis of enantioenriched derivatives of 2‐azabicyclo[3.3.1]nonane, a key motif common to many alkaloids, has been developed. Employing a cyclohexanediamine‐derived primary amine organocatalyst, a range of prochiral cyclohexanone derivatives possessing an α,β‐unsaturated ester moiety linked to the 4‐position afforded the bicyclic products, which possess three stereogenic centers, as single diastereoisomers in high enantioselectivity (83–99 % ee) and in good yields (60–90 %). Calculations revealed that stepwise C? C bond formation and proton transfer via a chair‐shaped transition state dictate the exclusive endo selectivity and enabled the development of a highly enantioselective primary amine catalyst.     

The value of rough quantum mechanical calculations

During a few years beginning in 1927 rough quantum mechanical calculations of the energy of the ground states with simple wave functions based upon certain models were made for H ₂ ⁺ , H₂, and He ₂ ⁺ . These calculations provided much insight into the nature of the chemical bond, a concept formulated empirically in the 19th century, and of the chemists' classical valence-bond theory, also formulated in the 19th century. Moreover, ideas suggested by the rough calculations permitted the valence-bond theory to be greatly refined and made more powerful. Extensive knowledge about the properties of atomic nuclei was obtained only after quantum mechanics had been discovered. Nuclear physicists have for the most part striven to carry out very accurate quantum mechanical calculations of nuclear properties, with results that are often in excellent agreement with experiment. I suggest that rough calculations based on simple models might give additional insight and suggest new experiments.     

Spectrum of the Kerzman-Stein Operator for the Ellipse

The skew-hermitian part of the Cauchy operator, defined with respect to arclength measure on the boundary, is known as the Kerzman-Stein operator. For an ellipse, the eigenvalues of this operator are shown to have multiplicity two. For an ellipse with small eccentricity, we compute the leading coefficient in the asymptotic expansion of the eigenvalues.