Enantiodifferentiating photocyclodimerization of 2-anthracenecarboxylic acid mediated by gamma-cyclodextrins with a flexible or rigid cap

[reaction: see text] A series of modified gamma-cyclodextrins (CDs) with a flexible or rigid cap, synthesized and used as chiral supramolecular hosts for mediating the enantiodifferentiating photocyclodimerization of 2-anthracenecarboxylic acid, significantly improved the chemical and optical yields of chiral head-to-head cyclodimer 3, while the gamma-CD with a rigid cap dramatically inverted the stereochemical outcomes and further improved the enantioselectivities of both head-to-tail and head-to-head dimers 2 and 3.     

The crystal structure of Mg51Zn20

The crystal structure of Mg₅₁Zn₂₀, a phase designated conventionally as “Mg₇Zn₃,” has been determined by the single-crystal X-ray diffraction method. It was solved by the examination of a Patterson synthesis, and refined by the ordinary Fourier and least-squares method; the R value obtained was 4.8% for 1167 observed reflections. The crystal is orthorhombic, space group Immm, with a = 14.083(3), b = 14.486(3), c = 14.025(3) Å, and Z = 2. There are 18 independent atomic sites, Zn1Zn6, Mg1Mg10, A, and B, and the last two sites are statistically occupied by Zn and Mg atoms with the occupancies; 0.46(2)Zn7 + 0.52(2)Mg11 and 0.24(2)Zn8 + 0.74(2)Mg12, for A and B, respectively. The structure of the crystal is described as an arrangement of icosahedral coordination polyhedra, to which all the atomic sites but Zn3 site belong. In this arrangement the Zn atoms other than the Zn3 and Zn8(B) center the icosahedral coordination polyhedra with coordination number 12. The Zn3, Zn8 atoms, and all the Mg atoms except Mg11(A) are located at the centers of various coordination polyhedra with the coordination numbers from 11 to 15. The distances between neighboring atoms are 2.71–3.07, 2.82–3.65, and 2.60–3.20 Å for ZnZn, MgMg, and ZnMg, respectively.     

Lewis acid catalyzed stereoselective carbosilylation. Intramolecular trans-vinylsilylation and trans-arylsilylation of unactivated alkynes.

Intramolecular trans-vinylsilylation using silicon-tethered alkynylvinylsilanes 3b-c was catalyzed dramatically by Lewis acids such as EtAlCl(2) to give the corresponding six-membered silacycles 4b-c in high yields. The reaction proceeded via an exo-mode cyclization. In addition to the vinylsilylation, the intramolecular trans-arylsilylations using carbon-tethered alkynylarylsilanes 8a-b were also catalyzed by Lewis acids such as HfCl(4) to give six- and seven-membered cyclic (E)-vinylsilanes 9a-b, respectively. The cyclization of silicon-tethered substrates 13a-d afforded five- and six-membered silacycle products 14a-d in low to high yields. All arylsilylation reactions proceeded via an exo-mode fashion exclusively.     

Infinite-Dimensional Analysis and Analytic Number Theory

We consider arithmetical aspects of analysis on Fock spaces (Boson Fock space, Fermion Fock space, and Boson–Fermion Fock space) with applications to analytic number theory.     

Gravimetric study of high-pressure sorption of gases in polymers

A gravimetric method for determining precisely the solubility of gases in polymers at high pressure is described. The solubilities of N₂ and CO₂ in low-density polyethylene (LDPE); CO₂ in polycarbonate (PC); and N₂, CH₄, C₂H₆, and CO₂ in polysulfone (PSUL) have been measured as a function of pressure up to 50 atm. Most of the measured sorption isotherms agreed closely with published data, but reproducible and time-dependent hysteresis in the sorption of CO₂, C₂H₆, and CH₄ in glassy polymers, PC, and PSUL, was observed in this study for the first time. Like the well known conditioning effect of high-pressure CO₂ on the sorption capacity of glassy polymers, these hysteresis phenomena are believed to be due to the plasticizing effect of sorbed gases. On the basis of the current data, the dual-mode sorption model including the plasticization by sorbed gas is discussed and a primitive equation for the concentration of sorbed gases in a quasiequilibrium state of sorption or desorption is proposed.