Iterated souslin forcing,the principles ⋄(E) and a generalisation of the axiom SAD

The axiom SAD was introduced in our paper with Avraham and Shelah [1]. It is a Martin’s Axiom type of principle, having some of the consequences of MA plus , but nonetheless provably consistent with GCH. In [1] it was shown to be consistent (with GCH) and used to demonstrate the consistency with CH of some known consequences of MA + . In particular, SAD implies the negation of Jensen’s ⋄ principle. In this paper we present a generalisation of SAD, let us call it SAD(E), whereE will be an arbitrary stationary subset ofω ₁, and show that although SAD(E) implies the negation of ⋄(E), it is consistent with ⋄. SAD(E) resembles the axiom SA of Shelah, described in our survey article [2], and indeed is a sort of blending of the two principles SA and SAD. (In particular, Shelah proved that SA is consistent with ⋄ but implies the failure of some ⋄(E).) Our proof (of the consistency of SAD(E) with ⋄) will be of interest to forcing enthusiasts, since it shows that iterated Souslin forcingcan distinguish between different stationary sets (it was previously thought that this was not the case), and can indeed be used to establish the non-provability of the principles ⋄(E) from ⋄ alone.     

Determination of absolute configuration using optical rotation calculated using density functional theory

[structure: see text] We report the first determinations of the absolute configurations (ACs) of chiral molecules using discrete frequency, transparent spectral region optical rotations calculated using density functional theory (DFT). The ACs of 2H-naphtho[1,8-bc]thiophene 1-oxide (3), naphtho[1,8-cd]-1,2-dithiole 1-oxide (4), and 9-phenanthryl methyl sulfoxide (5) are determined by comparison of their specific rotations to values calculated via the time-dependent DFT/gauge-invariant atomic orbital (TDDFT/GIAO) methodology using the B3LYP functional and the aug-cc-pVDZ basis set.     

Determination of absolute configuration using vibrational circular dichroism spectroscopy: the chiral sulfoxide 1-(2-methylnaphthyl) methyl sulfoxide

We report the determination of the absolute configuration (AC) of the chiral sulfoxide, 1-(2-methylnaphthyl) methyl sulfoxide, 1, using vibrational circular dichroism (VCD) spectroscopy. The VCD of 1 has been measured in the mid-IR spectral region in CCl(4) solution. Analysis employs the ab initio DFT/GIAO methodology. DFT calculations predict two stable conformations of 1, E and Z, Z being lower in energy than E by <1 kcal/mol. In both conformations the S-O bond is rotated from coplanarity with the naphthyl moiety by 30-40 degrees. The predicted unpolarized absorption ("IR") spectrum of the equilibrium mixture of the two conformations permits assignment of the experimental IR spectrum in the mid-IR spectral region. The presence of both E and Z conformations is clearly evident. The VCD spectrum predicted for S-1 is in excellent agreement with the experimental spectrum of (-)-1, unambiguously defining the AC of 1 as R(+)/S(-).     

X-ray scattering study of the effect of hydration on the cross-beta structure of amyloid fibrils

We have investigated the effect of sample hydration on the wide-angle X-ray scattering patterns of amyloid fibrils from two different sources, hen egg white lysozyme (HEWL) and an 11-residue peptide taken from the sequence of transthyretin (TTR105-115). Both samples show an inter-strand reflection at 4.7 A and an inter-sheet reflection which occurs at 8.8 and approximately 10 A for TTR105-115 and HEWL fibrils, respectively. The positions, widths, and relative intensities of these reflections are conserved in patterns obtained from dried stalks and hydrated samples over a range of fibril concentrations. In 2D scattering patterns obtained from flow-aligned hydrated samples, the inter-strand and inter-sheet reflections showed, respectively, axial and equatorial alignment relative to the fibril axis, characteristic of the cross-beta structure. Our results show that the cross-beta structure of the fibrils is not a product of the dehydrating conditions typically employed to produce aligned samples, but is conserved in individual fibrils in hydrated samples under dilute conditions comparable to those associated with other biophysical and spectroscopic techniques. This suggests a structure consisting of a stack of two or more sheets whose interfaces are inaccessible to bulk water.     

Rates and mechanisms of conversion of ice nanocrystals to hydrates of HCl and HBr: acid diffusion in the ionic hydrates

This FTIR study focuses on solid-state chemistry associated with formation and interconversion of the ionic HX (X = Cl, Br) hydrates. Kinetic data are reported for conversions of ice nanocrystal arrays exposed to the saturation pressure of the acids in the 110 approximately 125 K range. The product is amorphous acid dihydrate in the case of HBr, and amorphous monohydrate for HCl. The rate-determining step is identified as HX diffusion through the hydrate product crust toward the interfacial reaction zone, rather than diffusion through ice, as commonly believed. Slowing of the conversion process is thus observed with increasing thickness of the crust. The diffusion coefficient (D(e)) and activation energy values for HX diffusion through the hydrates were evaluated with the help of the shrinking-core model. Hydrate crystallization occurs as a separate step, upon heating above 130 K. Subsequently, rates of reversible transitions between crystal di- and monohydrates were observed upon exposure to acid vapor and acid evacuation. In conversion from di- to monohydrate, the rate slows after fast formation of several layers; subsequently, diffusion through the product crust appears to be the rate-controlling step. The activation energy for HBr diffusion through crystal dihydrate is found to be significantly higher than that for the amorphous analogue. Conjecture is offered for a molecular mechanism of HX transport through the crystal hydrate, based on (i) spectroscopic/computational evidence for the presence of molecular HX bonded to X(-) in each of the ionic hydrate phases and (ii) the relative E(a) values found for HBr and HCl diffusion. Monte Carlo modeling suggests acid transport to the reaction zone along boundaries between "nanocrystallites" generated by multiple hydrate nucleation events at the particle surfaces. The reverse conversion, of crystalline monohydrate particles to the dihydrate phase, as well as dihydrate to trihydrate, displays nearly constant rate throughout the particle conversion; suggesting desorption of HX from the particle surface as the rate-limiting factor. Like for D(e), the activation energies for desorption were found to be approximately 20% greater for HCl than HBr for related hydrate phases.     

Quadrupole moments of highly deformed structures in the A approximately 135 region: probing the single-particle motion in a rotating potential

The latest generation gamma-ray detection system, GAMMASPHERE, coupled with the Microball charged-particle detector, has made possible a new class of nuclear lifetime measurement. For the first time differential lifetime measurements free from common systematic errors for over 15 different nuclei ( >30 rotational bands in various isotopes of Ce, Pr, Nd, Pm, and Sm) have been extracted at high spin within a single experiment. This comprehensive study establishes the effective single-particle transition quadrupole moments in the A approximately 135 light rare-earth region. Detailed comparisons are made with theoretical calculations using the self-consistent cranked mean-field theory which convincingly demonstrates the validity of the additivity of single-particle quadrupole moments in this mass region.     

Polymerization of olefin oxides with zinc n-butyl xanthate and zinc dimethyldithiocarbamate catalysts: Mechanism of initiation

Xanthates and dithiocarbamates of metals have been reported to be effective as catalysts for the polymerization of olefin oxides. To investigate the mechanism of initiation, the bulk polymerization at 50°C of 1,2-butene oxide with zinc n-butyl xanthate (ZBX) at a monomer: ZBX molar ratio of 584: 1 was studied by ultraviolet and infrared spectroscopy. There is a rapid conversion of the sulfur–zinc bond in the metal xanthate to a structure containing sulfur–carbon and oxygen–zinc bonds, the latter acting as the site of the propagation step during polymerization. The xanthate ester moiety is subsequently converted to the oxygenated analogs, namely, O,O-dialkylthiocarbonate and dialkyl carbonate. These changes are independent of the propagation step. The changes observed in the polymerization of butene oxide with zinc dimethyldithiocarbamate are similar, but much slower than in the case of ZBX. The presence of the carbonate ester moiety was also shown in the benzene-insoluble, catalytically active fraction isolated from seeded catalyst, i.e., from the reaction product of propylene oxide and ZBX at a molar ratio of 8:1 or lower. This fraction also contained ionic sulfur.     

Direct spectroscopic observation of proton transfer rates: activation energy for proton exchange in ice Ic

Advantage has been taken of the ability to matrix isolate D₂O in H₂O ice I_c to determine the activation energy for proton transfer. The value computed from spectroscopic data is 9.3 ± 0.3 kcal which is comparable to accepted values of E_a for conduction (8.5–9.0 kcal) and the excitation energy for the OH stretching mode in H₂O ice I_c (≈ 9.2 kcal).