Competition between N and O: use of diazine N-oxides as a test case for the Marcus theory rationale for ambident reactivity

The preferred site of alkylation of diazine N-oxides by representative hard and soft alkylating agents was established conclusively using the ¹H–¹⁵N HMBC NMR technique in combination with other NMR spectroscopic methods. Alkylation of pyrazine N-oxides (1 and 2) occurs preferentially on nitrogen regardless of the alkylating agent employed, while O-methylation of pyrimidine N-oxide (3) is favoured in its reaction with MeOTf. As these outcomes cannot be explained in the context of the hard/soft acid/base (HSAB) principle, we have instead turned to Marcus theory to rationalise these results. Marcus intrinsic barriers (ΔG^‡₀) and Δ_rG° values were calculated at the DLPNO-CCSD(T)/def2-TZVPPD/SMD//M06-2X-D3/6-311+G(d,p)/SMD level of theory for methylation reactions of 1 and 3 by MeI and MeOTf, and used to derive Gibbs energies of activation (ΔG^‡) for the processes of N- and O-methylation, respectively. These values, as well as those derived directly from the DFT calculations, closely reproduce the observed experimental N- vs. O-alkylation selectivities for methylation reactions of 1 and 3, indicating that Marcus theory can be used in a semi-quantitative manner to understand how the activation barriers for these reactions are constructed. It was found that N-alkylation of 1 is favoured due to the dominant contribution of Δ_rG° to the activation barrier in this case, while O-alkylation of 3 is favoured due to the dominant contribution of the intrinsic barrier (ΔG^‡₀) for this process. These results are of profound significance in understanding the outcomes of reactions of ambident reactants in general.

Marcus theory enables rationalisation and quantification of selectivities in reactions of ambident nucleophiles for which the HSAB principle cannot operate.     

Functionalized nanoparticles for liquid atmospheric pressure matrix-assisted laser desorption/ionization peptide analysis

Nanoparticles for the extraction of peptides and subsequent analysis using atmospheric pressure matrix-assisted laser desorption/ionization (APMALDI) have been evaluated. The atmospheric pressure source allows for particles to be directly introduced in the liquid matrix, minimizing sample loss and analysis time. Described in this work are two sample preparation procedures for liquid APMALDI analysis: a C18 functionalized silica nanoparticle for hydrophobic extractions, and an aptamer functionalized magnetite core nanoparticle for rapid, affinity extractions. The C18 particles provide a non-selective support for rapid profiling applications, while the aptamer particles are directed towards reducing the complexity in biological samples. The aptamer functionalized particles provide a more selective analyte-nanoparticle interaction whereby the tertiary structure of the analyte becomes more critical to the extraction. In both cases, the liquid APMALDI matrix provides a support for ionization, and acts as the releasing agent for the analyte-particle interaction. Additionally, analyte enrichment was possible due to the large surface-to-volume ratio of the particles. The experiments conducted with functionalized nanoparticles, in an atmospheric pressure liquid matrix, present a basis for further methodologies and utilities of silica nanoparticles to be developed.     

Dynamics of curved DNA molecules: prediction and experiment

We have developed a quantitative predictive model capable of describing the dynamics of migration of intrinsically curved DNA fragments on polyacrylamide gels. The model takes into account structural features of DNA, end-to-end distance, screening of hydrodynamic interactions, ionic strength of buffer, electrostatic persistence length, structural fluctuations of the macromolecule, counter condensation, and variation of dielectric constant and viscosity of water with MPD. In doing so, we have also addressed a decade old issue on the effect of the organic solvent 2-methyl-2,4-pentanediol on gel migration of phased A-tracts. We show here that A-tract-solvent interactions are less favored compared with A-tract-A-tract and solvent-solvent interactions.     

An experimental study of chromatographic dynamics in open and packed non-cylindrical conduits

A systematic investigation of the influence of the perimeter shape of open and particle packed fused silica capillaries on chromatographic properties such as resistance to flow and dispersion of solutes propelled through these channels has been conducted. Verifications of these uncommon experiments with existing theoretical treatments are presented and the insights transferred to a novel polymer chip design with integrated facilities for complex separations. A comparison of the chromatographic performance of a real life proteomics sample on this chip with a capillary column of "similar" dimensions is presented.     

The NMR spectra of porphyrins—19: 13C and proton NMR spectra of metal-free porphyrins with the Type-IX substituent orientation,and of their zinc(II) complexes

The ¹³C and proton NMR spectra of six porphyrins bearing the substituent orientation characteristic of the natural “Type-IX” arrangement are reported and assigned. Significant concentration effects in the spectra of the free base porphyrins, together with the broadening of the C_α (and occasionally C_β) carbon resonances due to NH tautomerism caused a significant loss of data in these spectra. However, the spectra of the corresponding zinc(II) porphyrins (with addition of excess pyrrolidine) show that both these extraneous effects are completely removed to give well-resolved spectra with accurately reproducible chemical shifts. These spectra are assigned and an analysis of the chemical shifts allows the deduction of substituent chemical shift (SCS) parameters for the peripheral substituents at the beta and meso carbons. There is no global effect of these beta substituents, the beta carbon SCS being confined to the immediate pyrrole ring, and the meso carbon SCS to the two adjacent pyrrole rings. The SCS parameters are analyzed and it is shown how they can be used to predict the peripheral and meso carbon chemical shifts of any porphyrin bearing the substituents discussed.     

Isomorphism of maximum length circuit codes

Designs, Codes and Cryptography - Douglas (J Comb Theory 6(4):323–339, 1969) proved that for odd spread k and dimension $$d={\frac{1}{2}(3k+3)}$$ all maximum length (d, k) circuit...     

Frobenius distributions of elliptic curves in short intervals on average

The Ramanujan Journal - For an elliptic curve $$E/{\mathbb {Q}}$$ , let $$a_p$$ denote the trace of its Frobenius endomorphism over $${\mathbb {F}}_p$$ , where p is a prime of good reduction for E....     

On some global well-posedness and asymptotic results for quasilinear parabolic equations

We prove that the quasilinear parabolic initial-boundary value problem (1.1) below is globally well-posed in a class of high order Sobolev solutions, and that these solutions possess compact, regular attractors ast+.     

Stability of rarefaction waves in viscous media

We study the time-asymptotic behavior of weak rarefaction waves of systems of conservation laws describing one-dimensional viscous media, with strictly hyperbolic flux functions. Our main result is to show that solutions of perturbed rarefaction data converge to an approximate, Burgers rarefaction wave, for initial perturbations w ₀ with small mass and localized as w ₀(x)= The proof proceeds by iteration of a pointwise ansatz for the error, using integral representations of its various components, based on Green's functions. We estimate the Green's functions by careful use of the Hopf-Cole transformation, combined with a refined parametrix method. As a consequence of our method, we also obtain rates of decay and detailed pointwise estimates for the error.This pointwise method has been used successfully in studying stability of shock and constant-state solutions. New features in the rarefaction case are time-varying coefficients in the linearized equations and error waves of unbounded mass (log (t)). These diffusion waves have amplitude (t ^-1/2logt) in linear degenerate transversal fields and (t ^-1/2logt) in genuinely nonlinear transversal fields, a distinction which is critical in the stability proof.