Asymptotic properties of dynamic stochastic parameter estimates (III)

In this paper we establish three theorems concerning the asymptotic distributions of ordinary least-squares estimates of the parameters of a stochastic difference equation. We show that, if there is at least one root of the associated characteristic equation with modulus less than one and if all the roots have moduli different from one, the vector of least-squares estimates converges in distribution to a normally distributed vector. The distribution of the limiting vector is degenerate if there is at least one root with modulus greater than one. The results we obtain represent extensions of results proviously obtained by H. B. Mann and A. Wald, H. Rubin, J. S. White, T. W. Anderson, M. M. Rao, T. J. Muench, and the author.     

XAS spectroelectrochemistry: reliable measurement of X‐ray absorption spectra from redox manipulated solutions at room temperature

The design and operation of a low‐volume spectroelectrochemical cell for X‐ray absorption spectroscopy (XAS) of solutions at room temperature is described. Fluorescence XAS measurements are obtained from samples contained in the void space of a 50 µL reticulated vitreous carbon (sponge) working electrode. Both rapid electrosynthesis and control of the effects of photoreduction are achieved by control over the flow properties of the solution through the working electrode, where a good balance between the rate of consumption of sample and the minimization of decomposition was obtained by pulsing the flow of the solution by 1–2 µL with duty cycle of ～3 s while maintaining a small net flow rate (26–100 µL h^?1). The performance of the cell in terms of control of the redox state of the sample and minimization of the effects of photoreduction was demonstrated by XAS measurements of aqueous solutions of the photosensitive Fe^III species, [Fe(C₂O₄)₃]^3?, together with that of the electrogenerated [Fe(C₂O₄)₃]^4? product. The current response from the cell during the collection of XAS spectra provides an independent measure of the stability of the sample of the measurement. The suitability of the approach for the study of small volumes of mM concentrations of protein samples was demonstrated by the measurement of the oxidized and electrochemically reduced forms of cytochrome c.     

Reevaluation of the kinetics of polynuclear mimics for manganese catalases

Considerable effort has been expended in order to understand the mechanism of manganese catalases and to develop functional mimics for these enzymes. For many years, the most efficient reactivity mimic was [MnIVsalpn(mu-O)]2 [H2salpn = 1,3-bis(salicylideneiminato)propane], a compound that cycles between the MnIV2 and MnIII2 oxidation levels instead of the MnII2 and MnIII2 oxidation states used by the enzyme, with kcat = 250 s(-1) and kcat/KM = 1000 M(-1) s(-1). Recently, a truly exceptional high value of kcat was reported for the complex [Mn(bpia)(mu-OAc)]22+ [bpia = bis(picolyl)(N-methylimidazol-2-yl)amine]. On the basis of a calculated kcat value of 1100 s(-1) and an efficiency kcat/KM of 34 000 M(-1) s(-1), this complex has been suggested to represent a significant breakthrough in catalytic efficiencies of manganese catalase mimics. However, a plot of ri/[cat]T vs [H2O2]0, where the saturation value approaches 1.5 s(-1), is inconsistent with the 1100 s(-1) value tabulated for kcat. Similar discrepancies are observed for two other families of manganese complexes containing either a Mn2(mu-OPh)22+ core and different substituted tripodal ligands or complexes of methyl and ethyl salicylimidate, with an Mn2(mu-OPh)24+ core. Reevaluation of the kinetic parameters for these three systems reveals that the originally reported values were overestimated by a factor of approximately 1000 for both kcat and kcat/KM. We discuss the origin of the discrepancy between the previously published kinetic parameters and the newly derived values. Furthermore, we provide a short analysis of the existing manganese catalase mimics in an effort to provide sound directions for future investigations in this field.     

Na2B2S5 and Li2B2S5: Two Novel Perthioborates with Planar 1,2,4-Trithia-3,5-Diborolane Rings

For the first time perthioborates with trigonal planar coordination of boron were prepared. Na₂B₂S₅ (Pnma, a = 12.545(2) Å, b = 7.441(1) Å, c = 8.271(1) Å, Z = 4) and Li₂B₂S₅ (Cmcm, a = 15.864(1) Å, b = 6.433(1) Å, c = 6.862(1) Å, Z = 4) were obtained by reaction of the metal sulfides with stoichiometric amounts of boron and an excess of sulfur (effective molar ratio M:B:S = 1:1:4) at 600°C (650°C) and subsequent annealing. The non-isotypic structures contain exactly planar [B₂S₅]^2? groups consisting of five-membered B₂S₃ rings with one additional exocyclic sulfur on each of the boron atoms. The alkaline metal cations are four-coordinate (lithium) and (four + four)-coordinate (sodium) respectively.