Expanded Prussian Blue Analogue Based on Octahedral {Nb<Subscript>6</Subscript>} Clusters and {K<Subscript>2</Subscript>} Dimers as Nodes

Abstract  The preparation, structures, and characterization of two new compounds containing octahedral niobium cyanochloride clusters as building units and (Et₄N)⁺ as cation are reported. The reaction between Nb₆Cl₁₄ · 8H₂O, KCN and (Et₄N)Cl led to the formation of (Et₄N)₄[Nb₆Cl₁₂(CN)₆] · 2.67H₂O (1) which crystallizes in triclinic P-1 space group (No. 2) with a = 12.552(2), b = 12.818(2), c = 12.919(2) ?, α = 105.157(3)°, β = 104.188(3)°, γ = 117.390(2)°, V = 1611.7(5) ?³ and Z = 1. 1 has a 2D hydrogen-bonded layer structure based on [Nb₆Cl₁₂(CN)₆]⁴⁻ units connected through hydrogen bonding between cyanide ligands and solvent water molecules. In the presence of large excess of K⁺ ions, similar reaction leads to formation of K₂(Et₄N)₂[Nb₆Cl₁₂(CN)₆] (2) which crystallizes in the tetragonal I4/m space group (No. 87) with a = b = 10.9597(3), c = 19.178(1) ?, V = 2303.6(2) ?³ and Z = 2. Its 3D structure is based on [Nb₆Cl₁₂]²⁺ and [K₂]²⁺ nodes bridged by cyanide ligands to form an expanded Prussian blue type framework with (Et₄N)⁺ acting as charge compensating ions. Index Abstract  An expanded Prussian blue type 3D framework based on hexanuclear {Nb₆} and dinuclear {K₂} units which are bridged by cyanide linker was synthesized and characterized. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

On the effect of a radiation field in modifying the intermolecular interaction between two chiral molecules

The change in the mutual energy of interaction between a pair of chiral molecules coupled via the exchange of a single virtual photon and in the presence of an electromagnetic field is calculated using nonrelativistic quantum electrodynamics. The particular viewpoint adopted is one that has an intuitive physical appeal and resembles a classical treatment. It involves the coupling of electric and magnetic dipole moments induced at each center by the incident radiation field to the resonant dipole-dipole interaction tensor. The energy shift is evaluated for fixed as well as random orientations of the molecular pair with respect to the direction of propagation of the field. A complete polarization analysis is carried out for the former situation by examining the effect of incident radiation that is linearly or circularly polarized and traveling in a direction that is parallel or perpendicular to the intermolecular distance vector. After tumble averaging, all polarization dependence of the energy shift vanishes. In both cases the interaction energy is directly proportional to the irradiance of the applied field, and is discriminatory, changing sign when one optically active species is replaced by its enantiomer. The asymptotic behavior of the energy shift at the limits of large and small separations is also studied.     

Generalizations of a result of Christensen on renewal sequences and linear recurrences

This note extends some recent work of Christensen on simple closed form solutions for linear recurrences, employing connections with renewal sequences. We obtain results for linear recursive sequences defined via monotone coefficients, and provide a broader result in the third-order case. A related open question is posed.     

The isomorphism problem for quantum affine spaces,homogenized quantized Weyl algebras,and quantum matrix algebras

Bell and Zhang have shown that if A and B are two connected graded algebras finitely generated in degree one that are isomorphic as ungraded algebras, then they are isomorphic as graded algebras. We exploit this result to solve the isomorphism problem in the cases of quantum affine spaces, quantum matrix algebras, and homogenized multiparameter quantized Weyl algebras. Our result involves determining the degree one normal elements, factoring out, and then repeating. This creates an iterative process that allows one to determine relationships between relative parameters.     

Generation of Acyl Nitroso Compounds by the Oxidation of N-Acyl Hydroxylamines with the Dessmartin Periodinane

The oxidation of hydroxamic acids, N-hydroxyureas and N-hydroxycarbamates with the Dess-Martin periodinane generates the corresponding acyl nitroso compounds that react with conjugated dienes to produce the corresponding cycloadducts.     

Diazotransfer Reactions with p-Acetamidobenzenesulfonyl Azide

The utility of p-acetamidobenzenesulfonyl azide in diazotransfer reactions is described. This practical, cost effective reagent offers advantages over existing alternatives.     

Measuring the Limping of Processive Motor Proteins

The cells of all living creatures rely on a host of molecular scale machines to perform vital tasks. In the spirit of this special issue of J. Stat. Phys., we describe briefly the background concerning one class of these machines, namely, processive motor proteins such as, specifically, conventional kinesin, myosin V, and cytoplasmic dynein. These single-molecule motors tow cellular cargoes under load along oriented linear molecular tracks within the cell taking many hundreds of consecutive discrete steps. Experiments aimed at understanding the mechanism of the stepping process have recently led to observations of ‘‘limping” in which alternate steps are found to be slow or fast, respectively. Reliable experimental measurements of the ‘‘true” or intrinsic limping factor, L ₀, understood as the ideal overall ratio of the longer dwell times prior to one set of steps to the shorter times for the interlaced steps, provide a route to improving appropriate biomechanochemical models. These, in turn, may help reveal and quantify details of the underlying asymmetric walking mechanisms. However, a difficulty is posed in measuring L ₀ by the inescapable thermal fluctuations that act on an individual motor molecule that takes only a finite number, say, n odd and n even steps under fixed load, etc. Accordingly, we treat the stochastic issues theoretically for some basic kinetic motor models and experimental procedures, obtaining various exact bounds and explicit results for distributions and their moments. Typically for n?10 the observed mean values, 〈L _n 〉, significantly overestimate L ₀. However, the medians and rescaled means, \({\overline{L}}_{n}^{\, *}=\langle L_{n}\rangle(n-1)/n\), provide better guides to the value of L ₀ provided it is not too close to unity. Separately, we present figures, a table, and approximate formulas intended to assist practically those designing, undertaking, and assessing experiments on limping.     

Experimental and theoretical studies of polaron optical properties in KNbO3 perovskite

Time-resolved absorption and luminescence spectra have been measured in KNbO₃ perovskite crystals after pulsed band-gap excitation by 200 fs laser pulses and 10 ns electron pulses. Quantum chemical calculations using the large unit cell periodic model support the interpretation of the observed transient absorption bands at 0.8 and 1.1 eV as the self-trapped electron polarons and bound hole polarons, respectively. The activation energy for the 2.2 eV green luminescence quenching is 0.05 eV. We suggest that the short lifetime (<15 ns) of the luminescence at RT is caused by the radiative recombination of nearest electron and hole polarons.