Bounds on Codes Derived by Counting Components in Varshamov Graphs

We are interested in improving the Varshamov bound for finite values of length n and minimum distance d. We employ a counting lemma to this end which we find particularly useful in relation to Varshamov graphs. Since a Varshamov graph consists of components corresponding to low weight vectors in the cosets of a code it is a useful tool when trying to improve the estimates involved in the Varshamov bound. We consider how the graph can be iteratively constructed and using our observations are able to achieve a reduction in the over-counting which occurs. This tightens the lower bound for any choice of parameters n, k, d or q and is not dependent on information such as the weight distribution of a code. This work is taken from the author’s thesis [10]     

Phenylsulfonyl ene-allenes as efficient precursors to bicyclic systems via intramolecular [2 + 2]-cycloaddition reactions

Various phenylsulfonyl allene derivatives were prepared with double bonds tethered either to the alpha-position or the gamma-position of the allene. These substrates underwent a highly regio- and stereospecific thermal [2 + 2]-cycloaddition across the nonactivated cumulene double bond, forming distal cycloadducts (i.e., 57) in the case of alpha-tethered allenes and proximal adducts (i.e., 25) in the case of gamma-tethered allenes. The mechanistic rationale for the observed stereospecificity involves initial diradical formation, followed by a rapid ring closure to the more stable cis-fused ring system. The tether may be equipped with heteroatoms, allowing for the formation of fused heterocycles (e.g., 61), and the cycloaddition can be facilitated by the introduction of sterically bulky groups and/or by conformational rigidity to the tether. Other modes of cyclization were observed in the presence of sodium benzenesulfinate or Lewis acids, in which cases polar mechanisms prevail. The chemoselectivity is reversed for [4 + 2]-cycloadditions, which prefer instead to engage the vinyl sulfone moiety, independent of whether the tether is attached to the alpha- or gamma-position of the allene.     

Isolation and structure of [HC[CH(SiMe(3))(SnMe(3))](2)](+): a remarkably stable sec-alkyl cation

The reaction of the tin-substituted propene Me3Sn(R)CHCH=CHR (R = SiMe3) with MCl4 in dichloromethane in the presence of Me3SnCl gives the first examples of isolable sec-alkyl carbocation salts, [HC{CH(R)SnMe3}2]+M2Cl9- (M = Zr, Hf). The compounds are thermally stable and, unlike previously isolated trialkyl carbocations, do not require superacidic media or weakly coordinating anions for stability. The crystal structure and DFT calculations suggest polarization of the Sn substituents and hyperconjugation as the reason for the unexpected stability. The stabilizing effect of tin is significantly stronger than that of Si. The carbocations are effective initiators for the polymerization of isobutene, isoprene, and alpha-methylstyrene.     

Molar mass distributions by gradient liquid chromatography: predicting and tailoring selectivity

Interactive liquid chromatography (iLC) for polymer analysis is usually applied to the characterisation of distributions other than molar mass. In particular, its use for the determination of chemical-composition, functionality-type and tacticity distributions has been demonstrated. The application of iLC for the determination of molar mass distributions (MMDs), however, has not yet been fully explored. An expanded version of the reversed-phase liquid chromatography model has been developed to describe and predict how the retention behaviour of polydisperse polystyrene samples changes with molar mass. The relationship between molar mass and the parameters of the model has been investigated in some detail and non-linear correlations were found. From the model and the relationships between the model parameters and molar mass, calibration curves (retention time versus molar mass) were constructed to predict changes in chromatographic selectivity across a given molar mass range. These calibration curves were compared to experimentally obtained curves and, in most cases, excellent agreement was found. The dramatic enhancement in selectivity that can be obtained with iLC in comparison to size-exclusion chromatography (SEC) was illustrated by measuring matrix-assisted laser desorption ionisation (MALDI) MS spectra of fractions collected during a gradient-LC separation. In the low-molar mass range, essentially monodisperse fractions were obtained. Calibration curves, predicted by the model and validated experimentally using narrow-dispersity standards and MALDI-MS spectra of fractions, were used to determine the molar mass distribution of some narrowly distributed polystyrene samples. Molar mass distributions for such standards were found to be somewhat lower than the values reported by the manufacturers. The results also deviated from those obtained by MALDI-MS.     

Geometry optimised AB initio calculations on cyclopropenone and dimethylcyclopropenone adducts with borane and trifluoroborane

Geometry optimised ab initio calculations are reported for R₂C₃O.BY₃ (R = H, CH₃; Y = H, F). The results show that in the above series BH₃ is a stronger Lewis acid than BF₃, and that dimethylation increases the basicity of the cyclopropenone system.     

Inactivation of nitroalkane oxidase upon mutation of the active site base and rescue with a deprotonated substrate

Mutation of Asp402 in nitroalkane oxidase to Asn or Ala inactivates the enzyme with neutral nitroethane as substrate, but the activity can be rescued with the nitroethane anion. The V/K values of the D402N and D402A enzymes with the nitroethane anion are independent of pH, whereas the V/K values of the wild-type and D402E enzymes are pH dependent with both the protonated and the deprotonated forms of nitroethane. Moreover, although the V/K value of the D402E enzyme with neutral nitroethane is 20-fold less than that of the wild-type enzyme, there is only a 2-fold difference in the V/K values with the nitroethane anion. These results are fully consistent with a primary role for Asp402 as the active site base in nitroalkane oxidase which abstracts the substrate alpha-proton.     

The selenium-mercury interaction: synthesis,spectroscopic and x-ray structural studies of methylmercury-selenourea complexes

The synthesis of selenium bound selenourea complexes of methylmercury, [CH₃HgSeC(NH₂)₂]X (X=Cl, Br, NO₃, ClO₄) are described. A single crystal X-Ray analysis of the nitrate salt has provided for the first time bond length data pertinent to the biologically important mercury-selenium interaction. Crystals of [CH₃HgSeC(NH₂)₂] NO₃ belong to the space group PnZic with a = 7.524(1), b = 11.204(2), c = 9.738(2)Å, and z = 4. The structure was solved and refined using 561 observed reflections measured on a Syntex P2₁ diffractometer to a final R value of 0.037. The mercury atom is linearly coordinated to the methyl group and the selenium atom of the selenourea with Hg-Se of 2.477(3)Å. Strong Hg-Se bonding is indicated by the X-Ray data and by the ¹H - ¹⁹⁹Hg nmr coupling constants. A comparison of spectroscopic data for analogous thio and selenourea complexes is presented.     

Isomer-specific spectroscopy and conformational isomerization energetics of o-, m-, and p-ethynylstyrenes

The infrared and ultraviolet spectroscopy of o-, m-, and p-ethynylstyrene isomers (oES, mES, and pES) were studied by a combination of methods, including resonance-enhanced two-photon ionization (R2PI), UV-UV hole-burning spectroscopy (UVHB), resonant ion-dip infrared spectroscopy (RIDIRS), and rotationally resolved fluorescence excitation spectroscopy. In addition, the newly developed method of stimulated emission pumping-population transfer spectroscopy (SEP-PTS) was used to determine the energy threshold to conformational isomerization in m-ethynylstyrene. The S(1) <-- S(0) origin transitions of oES and pES occur at 32 369 and 33 407 cm(-1), respectively. In mES, the cis and trans conformations are calculated to be close in energy. In the R2PI spectrum of mES, the two most prominent peaks (32672 and 32926 cm(-1)) were confirmed by UVHB spectroscopy to be S(1) <-- S(0) origins of these two conformers. The red-shifted conformer was identified as the cis structure by least-squares fitting of the rotationally resolved fluorescence excitation spectrum of the origin band. There are also two possible conformations in oES, but transitions due to only one were observed experimentally, as confirmed by UVHB spectroscopy. Density functional theory calculations (B3LYP/6-31+G) predict that the cis-ortho conformer, in which the substituents point toward each other, is about 8 kJ/mol higher in energy than the trans-ortho isomer, and should only be about 5% of the room temperature population of oES. Ground-state infrared spectra in the C-H stretch region (3000-3300 cm(-1)) of each isomer were obtained with RIDIRS. In all three structural isomers, the acetylenic C-H stretch fundamental was split by Fermi resonance. Infrared spectra were also recorded in the excited electronic state, using a UV-IR-UV version of RIDIR spectroscopy. In all three isomers the acetylenic C-H stretch fundamental was unshifted from the ground state, but no Fermi resonance was seen. The first observed and last unobserved transitions in the SEP-PT spectrum were used to place lower and upper bounds on the barrier to cis --> trans isomerization in m-ethynylstyrene of 990-1070 cm(-1). Arguments are given for the lack of a kinetic shift in the measurement. The analogous trans --> cis barrier is in the same range (989-1065 cm(-1)), indicating that the relative energies of the zero-point levels of the two isomers are (E(ZPL)(cis) - E(ZPL)(trans))= -75 to +81 cm(-1). Both the barrier heights and relative energies of the minima are close to those determined by DFT (Becke3LYP/6-31+G) calculations.