Norms on Free Topological Groups

A norm on a group G is a function N mapping G into the set ofnon-negative real numbers such that for each x and y in G, N(xy^–1) N(x)+N(y) and N(e) = 0, where e is the identity element ofG. It is shown here that if F(X) is the free topological groupon any completely regular Hausdorff space X and H is a subgroupof F(X) generated by a finite subset of X, then any norm onH can be extended to a continuous norm on F(X).     

On the conformational stability and dimerization of phosphotransferase enzyme I from Escherichia coli

The activity of enzyme I (EI), the first protein in the bacterial PEP:sugar phosphotransferase system, is regulated by a monomer–dimer equilibrium where a Mg²⁺-dependent autophosphorylation by PEP requires the homodimer. Using inactive EI(H189A), in which alanine is substituted for the active-site His189, substrate binding effects can be separated from those of phosphorylation. Whereas 1 mM PEP (with 2 mM Mg²⁺) strongly promotes dimerization of EI(H189A) at pH 7.5 and 20 °C, 5 mM pyruvate (with 2 mM Mg²⁺) has the opposite effect. A correlation between the coupling of N- and C-terminal domain unfolding, measured by differential scanning calorimetry, and the dimerization constant for EI, determined by sedimentation equilibrium, is observed. That is, when the coupling between N- and C-terminal domain unfolding produced by 0.2 or 1.0 mM PEP and 2 mM Mg²⁺ is inhibited by 5 mM pyruvate, the dimerization constant for EI(H189A) decreases from >10⁸ to <5 × 10⁵ or 3 × 10⁷ M⁻¹, respectively. With 2 mM Mg²⁺ at 15–25 °C and pH 7.5, PEP has been found to bind to one site/monomer of EI(H189A) with K_A′10⁶ M⁻¹ (ΔG′=−33.7±0.2 kJ mol⁻¹ and ΔH=+16.3 kJ mol⁻¹ at 20 °C with ΔC_p=−1.4 kJ K⁻¹ mol⁻¹). The binding of PEP to EI(H189A) is synergistic with that of Mg²⁺. Thus, physiological concentrations of PEP and Mg²⁺ increase, whereas pyruvate and Mg²⁺ decrease the amount of dimeric, active, dephospho-enzyme I.     

Vibrational exciton delocalization precludes the use of infrared intensities as proxies for surfactant accumulation on aqueous surfaces

Surface-sensitive vibrational spectroscopy is a common tool for measuring molecular organization and intermolecular interactions at interfaces. Peak intensity ratios are typically used to extract molecular information from one-dimensional spectra but vibrational coupling between surfactant molecules can manifest as signal depletion in one-dimensional spectra. Through a combination of experiment and theory, we demonstrate the emergence of vibrational exciton delocalization in infrared reflection–absorption spectra of soluble and insoluble surfactants at the air/water interface. Vibrational coupling causes a significant decrease in peak intensities corresponding to C–F vibrational modes of perfluorooctanoic acid molecules. Vibrational excitons also form between arachidic acid surfactants within a compressed monolayer, manifesting as signal reduction of C–H stretching modes. Ionic composition of the aqueous phase impacts surfactant intermolecular distance, thereby modulating vibrational coupling strength between surfactants. Our results serve as a cautionary tale against employing alkyl and fluoroalkyl vibrational peak intensities as proxies for concentration, although such analysis is ubiquitous in interface science.

Coupling between surfactant molecules at the air/water interface bleeds intensity into a diffuse background, such that single-wavelength vibrational intensity is effectively depleted at high surface coverage.     

Palladium-catalyzed amination of aryl nonaflates

The first detailed study of the palladium-catalyzed amination of aryl nonaflates is reported. Use of ligands 2-4 and 6 allows for the catalytic amination of electron-rich and -neutral aryl nonaflates with both primary and secondary amines. With use of Xantphos 5, the catalytic amination of a variety of functionalized aryl nonaflates resulted in excellent yields of anilines; even 2-carboxymethyl aryl nonaflate is effectively coupled with a primary alkylamine. Moderate yields were obtained when coupling halo-aryl nonaflates with a variety of amines, where in most cases the aryl nonaflate reacted in preference to the aryl halide. Overall, aryl nonaflates are an effective alternative to triflates in palladium-catalyzed C-N bond-forming processes due to their increased stability under the reaction conditions.     

Preparation of high molecular weight polyurethane particles by nonaqueous emulsion polyaddition

A versatile nonaqueous emulsion polyaddition process for the one-step fabrication of spherical polyurethane nanoparticles is presented. Three different emulsion systems were used consisting of N,N′-dimethylformamide (DMF) dispersed in n-hexane, acetonitrile dispersed in cyclohexane, and acetonitrile dispersed in tetradecane. After successful stabilization of the emulsion systems by using a poly(isoprene)-poly(methylmethacrylate) block copolymer, the fabrication of the polyurethanes was carried out within the dispersed polar phase. The polyurethane particles showed average diameters as small as 35 nm. Additionally, infrared (IR) characterization revealed that the formation of any urea, which decreases the mechanical properties of the polyurethanes, was prevented during the polyaddition. This was attributed to the anhydrous reaction conditions. Gel permeation chromatography (GPC) analysis demonstrated the average molecular weights (M _n) of the polyurethanes to be as high as 16,500 g/mol, corresponding to conversions of 0.98. Comparable molecular weights and conversions have not previously been achieved without the formation of urea.     

S0 ring-puckering potential energy function for coumaran

With the aid of a reported inversion splitting value, the far-infrared spectrum resulting from the ring-puckering vibration of coumaran has been reassigned and the one-dimensional potential energy function has been determined. The barrier to planarity is 155 +/- 4 cm(-1) and the dihedral angle is 25 degrees . These results agree well with the millimeter wave spectra values of 152 cm(-1) and 23 degrees , which utilized different data and a different type of potential function for the calculations. The MP2/cc-pvtz ab initio values of 238 cm(-1) and 26.5 degrees agree more poorly. If the benzene ring is assumed to remain rigid, the calculated barrier drops to 204 cm(-1). The puckering potential functions for the ring-flapping and ring-twisting vibrationally excited states were also determined and the barriers were found to be 149 and 156 cm(-1), respectively.     

Oil-in-water emulsions stabilized by highly charged polyelectrolyte-grafted silica nanoparticles

Fully sulfonated poly(styrenesulfonate) brushes were grown from the surface of colloidal silica particles and used to prepare stable trichloroethylene-in-water and heptane-in-water Pickering emulsions. These particles were highly charged and colloidally stable in water but could not be dispersed in trichloroethylene or heptane. Both two-phase (emulsion plus neat water) and three-phase (emulsion separating neat oil and water phases) systems were observed, with water-continuous emulsion phases in all cases. Emulsion phases containing as much as 83% (v/v) oil were stable for over six months. Poly(styrenesulfonate)-grafted particles were very efficient emulsifiers; stable emulsion phases were prepared when using as little as 0.04 wt% particles. The emulsifying effectiveness of the poly(styrenesulfonate)-grafted silica particles can be attributed to the hydrophobicity of the vinylic polymer backbone that makes this highly charged polyelectrolyte unusually surface active at the oil/water interface.     

Pulsed EPR and NMR spectroscopy of paramagnetic iron porphyrinates and related iron macrocycles: how to understand patterns of spin delocalization and recognize macrocycle radicals

Pulsed EPR spectroscopic techniques, including ESEEM (electron spin echo envelope modulation) and pulsed ENDOR (electron-nuclear double resonance), are extremely useful for determining the magnitudes of the hyperfine couplings of macrocycle and axial ligand nuclei to the unpaired electron(s) on the metal as a function of magnetic field orientation relative to the complex. These data can frequently be used to determine the orientation of the g-tensor and the distribution of spin density over the macrocycle, and to determine the metal orbital(s) containing unpaired electrons and the macrocycle orbital(s) involved in spin delocalization. However, these studies cannot be carried out on metal complexes that do not have resolved EPR signals, as in the case of paramagnetic even-electron metal complexes. In addition, the signs of the hyperfine couplings, which are not determined directly in either ESEEM or pulsed ENDOR experiments, are often needed in order to translate hyperfine couplings into spin densities. In these cases, NMR isotropic (hyperfine) shifts are extremely useful in determining the amount and sign of the spin density at each nucleus probed. For metal complexes of aromatic macrocycles such as porphyrins, chlorins, or corroles, simple rules allow prediction of whether spin delocalization occurs through sigma or pi bonds, and whether spin density on the ligands is of the same or opposite sign as that on the metal. In cases where the amount of spin density on the macrocycle and axial ligands is found to be too large for simple metal-ligand spin delocalization, a macrocycle radical may be suspected. Large spin density on the macrocycle that is of the same sign as that on the metal provides clear evidence of either no coupling or weak ferromagnetic coupling of a macrocycle radical to the unpaired electron(s) on the metal, while large spin density on the macrocycle that is of opposite sign to that on the metal provides clear evidence of antiferromagnetic coupling. The latter is found in a few iron porphyrinates and in most iron corrolates that have been reported thus far. It is now clear that iron corrolates are remarkably noninnocent complexes, with both negative and positive spin density on the macrocycle: for all chloroiron corrolates reported thus far, the balance of positive and negative spin density yields -0.65 to -0.79 spin on the macrocycle. On the other hand, for phenyliron corrolates, the balance of spin density on the macrocycle is zero, to within the accuracy of the calculations (Zakharieva, O.; Schünemann, V.; Gerdan, M.; Licoccia, S.; Cai, S.; Walker, F. A.; Trautwein, A. X. J. Am. Chem. Soc. 2002, 124, 6636-6648), although both negative and positive spin densities are found on the individual atoms. DFT calculations are invaluable in providing calculated spin densities at positions that can be probed by (1)H NMR spectroscopy, and the good agreement between calculated spin densities and measured hyperfine shifts at these positions leads to increased confidence in the calculated spin densities at positions that cannot be directly probed by (1)H NMR spectroscopy. (13)C NMR spectroscopic investigations of these complexes should be carried out to probe experimentally the nonprotonated carbon spin densities.     

Models of the low-spin iron(III) hydroperoxide intermediate of heme oxygenase: magnetic resonance evidence for thermodynamic stabilization of the d(xy) electronic state at ambient temperatures

The (13)C pulsed ENDOR and NMR study of [meso-(13)C-TPPFe(OCH(3))(OO(t)Bu)](-) performed in this work shows that although the unpaired electron in low-spin ferrihemes containing a ROO(-) ligand resides in a d(pi) orbital at 8 K, the d(xy) electron configuration is favored at physiological temperatures. The variable temperature NMR spectra indicate a dynamic situation in which a heme with a d(pi) electron configuration and planar porphyrinate ring is in equilibrium with a d(xy) electron configuration that has a ruffled porphyrin ring. Because of the similarity in the EPR spectra of the hydroperoxide complexes of heme oxygenase, cytochrome P450, and the model heme complex reported herein, it is possible that these two electron configurations and ring conformations may also exist in equilibrium in the enzymatic systems. The ruffled porphyrinate ring would aid the attack of the terminal oxygen of the hydroperoxide intermediate of heme oxygenase (HO) on the meso-carbon, and the large spin density at the meso-carbons of a d(xy) electron configuration heme suggests the possibility of a radical mechanism for HO. The dynamic equilibrium between the ruffled (d(xy)) and planar (d(pi)) conformers observed in the model complexes also suggests that a flexible heme binding cavity may be an important structural motif for heme oxygenase activity.     

Self-selection in olefin cross-metathesis: the effect of remote functionality

Olefin cross-metathesis (CM) is potentially an attractive method for generating dynamic combinatorial libraries (DCLs). In order for the CM reaction to be useful for DCL production, the course of the reaction and product distribution must be relatively insensitive to functionality remote from the reacting centers. We report on the CM of a series of allyl- and homoallylamides that are strongly dependent on remote functionality. This includes an unusual example of a cis-selective CM. [Reaction: see text]