On a monotonic trigonometric sum

By establishing a cosine analogue of a result of Askey and Steinig on a monotonic sine sum, this paper sharpens and unifies several results associated with Young's inequality for the partial sums of k ^–1 cosk.     

Predictions of substituent effects in thermal azide 1,3-dipolar cycloadditions: implications for dynamic combinatorial (reversible) and click (irreversible) chemistry

Substituent effects in 1,3-dipolar cycloadditions of azides with alkenes and alkynes were investigated with the high-accuracy CBS-QB3 method. The possibilities for noncatalytic activation and the reversibility or irreversibility of these reactions was explored; the possibilities for uses in dynamic combinatorial chemistry (DCC) or click chemistry were explored. The activation enthalpies for reactions of ethylene and acetylene with hydrazoic acid, formyl, phenyl-, methyl-, and methanesulfonylazides exhibit modest variation, with Delta H++ ranging from 17 to 20 kcal/mol. A detailed study of formylazide cycloadditions with various alkenes and alkynes reveals a narrow range of activation enthalpies (17-21 kcal/mol). The activation enthalpies for the reactions of azides with alkenes and alkynes are similar. FMO theory and distortion/interaction energy control have been used to rationalize the rates and regiochemistries of cycloadditions involving alkene dipolarophiles. Significantly, triazoles, formed from alkynes, are 30-40 kcal/mol more stable than tetrazolines formed from alkenes. On the basis of initial reactant concentrations, kinetic and thermodynamic values are suggested for the identification of reversible reactions that approach equilibrium over 24 h, as well as for fast irreversible reactions. Although azide cycloadditions are suitable for irreversible chemistry and are typically unsuitable for reversible applications, theoretical procedures established by these studies have provided guidelines for the prediction of useful reversible libraries.     

Mechanistic Evidence of a Ni(0/II/III) Cycle for Nickel Photoredox Amide Arylation

This work demonstrates the dominance of a Ni(0/II/III) cycle for Ni-photoredox amide arylation, which contrasts with other Ni-photoredox C-heteroatom couplings that operate via Ni(I/III) self-sustained cycles. The kinetic data gathered when using different Ni precatalysts supports an initial Ni(0)-mediated oxidative addition into the aryl bromide. Using NiCl₂ as the precatalyst resulted in an observable induction period, which was found to arise from a photochemical activation event to generate Ni(0) and to be prolonged by unproductive comproportionation between the Ni(II) precatalyst and the in situ generated Ni(0) active species. Ligand exchange after oxidative addition yields a Ni(II) aryl amido complex, which was identified as the catalyst resting state for the reaction. Stoichiometric experiments showed that oxidation of this Ni(II) aryl amido intermediate was required to yield functionalized amide products. The kinetic data presented supports a rate-limiting photochemically-mediated Ni(II/III) oxidation to enable C−N reductive elimination. An alternative Ni(I/III) self-sustained manifold was discarded based on EPR and kinetic measurements. The mechanistic insights uncovered herein will inform the community on how subtle changes in Ni-photoredox reaction conditions may impact the reaction pathway, and have enabled us to include aryl chlorides as coupling partners and to reduce the Ni loading by 20-fold without any reactivity loss.     

Self Organising Maps for distinguishing polymer groups using thermal response curves obtained by dynamic mechanical analysis

Self Organising Maps are described including the U-Matrix, component planes, hit histograms, quality indicators as mean quantisation error and topological error. Software was written in Matlab and several new approaches for visualising multiclass maps are employed. The method is applied to a dataset consisting of the Dynamic Mechanical Analysis of 293 polymers, involving heating the polymers over a temperature range of -51 degrees C to 270 degrees C. These can be characterised in three different ways (a) amorphous or semi-crystalline (b) as 9 groups (c) as 30 grades.     

Linkage isomerism in the binding of pentapeptide Ac-His(Ala)3His-NH2 to (ethylenediamine)palladium(II): effect of the binding mode on peptide conformation

The reaction of the pentapeptide Ac-His1-Ala2-Ala3-Ala4-His5-NH2 (AcHAAAHNH2) (1) with [Pd(en)(ONO2)2] (en = NH2CH2CH2NH2) in either DMF-d(7) or H2O:D2O (90%:10%) gave three linkage isomers of [Pd(en)(AcHAAAHNH2)](2+) (2), 2a, 2b, and 2c, which differ only in which pair of imidazole nitrogen atoms bind to Pd. In the most abundant isomer, 2a, Pd is bound by N1 from each of the two imidazole rings. In the minor isomers 2b and 2c, Pd is bound by N1(His1) and N3(His5) and by N3(His1) and N1(His5), respectively. The reactions of [Pd(en)(ONO2)2] with the N-methylated peptides Ac-(N3-MeHis)-Ala-Ala-Ala-(N3-MeHis)-NH2 (AcH*AAAH*NH2) (3), Ac-(N3-MeHis)-Ala-Ala-Ala-(N1-MeHis)-NH2 (AcH(*)AAAH(#)NH2) (4), and Ac-(N1-MeHis)-Ala-Ala-Ala-(N3-Me-His)-NH2 (AcH(#)AAAH(*)NH2) (5) each gave a single species [Pd(en)(peptide)](2+) in N,N-dimethylformamide (DMF) or aqueous solution, 7, 8, and 9, respectively, with Pd bound by the two nonmethylated imidazole nitrogen atoms in each case. These complexes were analogous to 2a, 2b, and 2c, respectively. Ac-(N1-MeHis)-Ala-Ala-Ala-(N1-MeHis)-NH2 (AcH(#)AAAH(#)NH2) (6) with [Pd(en)(ONO2)2] in DMF slowly gave a single product, [Pd(en)(AcH(#)AAAH(#)NH2)](2+) (10), in which Pd was bound by the N3 of each imidazole ring. The corresponding linkage isomer of 2 was not observed. Complex 10 was also the major product in aqueous solution, but other species were also present. All compounds were exhaustively characterized in solution by multinuclear 1D ((1)H , (13)C, and, with (15)N-labeled ethylenediamine, (15)N) and 2D (correlation spectroscopy, total correlation spectroscopy, transverse rotating-frame Overhauser effect spectroscopy (T-ROESY), heteronuclear multiple-bond correlation, and heteronuclear single quantum coherence) NMR spectra, circular dichroism (CD) spectra, electrospray mass spectroscopy, and reversed-phase high-performance liquid chromatography. ROESY spectra were used to calculate the structure of 2a, which contained a single turn of a peptide alpha helix in both DMF and water, the helix being better defined in DMF. The Pd(en)(2+) moiety was not used in structure calculations, but its location and coordination by one imidazole N1 from each histidine to form a 22-membered metallocycle were unambiguously established. Convergence of the structures was greatest when calculated with two hydrogen-bond constraints (Ala4 peptide NH...OC acetyl and His5 peptide NH...OC-His1) that were indicated by the low temperature dependence of these NH chemical shifts. Vicinal HN-CHalpha coupling constants and chemical shifts of alpha-H atoms were also consistent with a helical conformation. Similar long-range ROE correlations were observed for [Pd(en)(AcH(*)AAAH(*)NH2)](2+) (7), which displayed a CD spectrum in aqueous solution that suggested the presence of some helicity. Long-range ROE correlations were not observed for 8, 9, or 10, but a combination of NMR data and CD spectroscopy was interpreted in terms of the conformational behavior of the coordinated pentapeptide. Only for the linkage isomer [Pd(en)(AcH(*)AAAH(#)NH2)](2+) (8) was there evidence of a contribution from a helical conformation. The data for 8 were interpreted as interconversion between the helix and random coil conformations. Zn(2+) with peptides gave broad NMR peaks attributed to lability of this metal ion, while reactions of cis-[Pt(NH3)2(ONO2)2] were slow, giving a complex mixture of products rather than the macrochelate ring observed with Pd(en)(2+). In summary, these studies indicate that Pd(en)(2+) coordinates to histidine with similar preference for each of the two imidazole nitrogens, enabling the formation of up to four linkage isomers in its complexes with pentapeptides His-xxx-His. Only the N1-N1 linkage isomer that forms a 22-membered macrochelate ring is able to induce an alpha-helical peptide conformation, whereas the 20- and 21-membered rings of linkage isomers do not. This suggests that linkage isomeric mixtures may compromise histidine coordination to metal ions and reduce alpha-helicity.     

Hartree-Fock complete basis set limit properties for transition metal diatomics

Numerical Hartree-Fock (HF) energies accurate to at least 1 microhartree are reported for 27 diatomic transition-metal-containing species. The convergence of HF energies toward this numerical limit upon increasing the basis set size has been investigated, where standard nonrelativistic all-electron correlation consistent basis sets and augmented basis sets, developed by Balabanov and Peterson [J. Chem. Phys. 123, 064107 (2005)], were employed. Several schemes which enable the complete basis set (CBS) limit to be determined have been investigated, and the resulting energies have been compared to the numerical Hartree-Fock energies. When comparing basis set extrapolation schemes, those in the form of exponential functions perform well for our test set, with mean absolute deviations from numerical HF energies of 234 and 153 microE(h), when the CBS limit has been determined using a two-point fit as proposed by Halkier et al. [Chem. Phys. Lett. 302, 437 (1999)] on calculations of triple- and quadruple-zeta basis set qualities and calculations of quadruple- and quintuple-zeta basis set qualities, respectively. Overall, extrapolation schemes in the form of a power series are not recommended for the extrapolation of transition metal HF energies. The impact of basis set superposition error has also been examined.     

Biology-enabling inositol phosphates, phosphatidylinositol phosphates and derivatives

This review highlights inositol polyphosphate- and phosphatidylinositol-based small molecule probes that have advanced our understanding of intracellular signalling.     

Emerging methods in proteomics: top-down protein characterization by multistage tandem mass spectrometry

"Top-down" mass spectrometry methods have emerged as an attractive alternative to conventional "bottom-up" approaches for the comprehensive characterization of co- and post-translational protein modifications. Here we present a brief overview of current strategies employed for top-down protein characterization and discuss the key technical challenges and solutions associated with their implementation on a range of mass spectrometry instrument platforms. For more specific details regarding the individual strategies described herein, interested readers are referred to the references cited at the end of this article.     

Fano 3-folds with divisible anticanonical class

We show the nonvanishing of H ⁰(X,−K _X ) for any a Fano 3-fold X for which −K _X is a multiple of another Weil divisor in Cl(X). The main case we study is Fano 3-folds with Fano index 2: that is, 3-folds X with rank Pic(X)=1, -factorial terminal singularities and −K _X  = 2A for an ample Weil divisor A. We give a first classification of all possible Hilbert series of such polarised varieties (X,A) and deduce both the nonvanishing of H ⁰(X,−K _X ) and the sharp bound (−K _X )³≥ 8/165. We find the families that can be realised in codimension up to 4.