A facile approach toward multicomponent supramolecular structures: selective self-assembly via charge separation

A novel approach toward the construction of multicomponent two-dimensional (2-D) and three-dimensional (3-D) metallosupramolecules is reported. Simply by mixing carboxylate and pyridyl ligands with cis-Pt(PEt(3))(2)(OTf)(2) in a proper ratio, coordination-driven self-assembly occurs, allowing for the selective generation of discrete multicomponent structures via charge separation on the metal centers. Using this method, a variety of 2-D rectangles and 3-D prisms were prepared under mild conditions. Moreover, multicomponent self-assembly can also be achieved by supramolecule-to-supramolecule transformations. The products were characterized by (31)P and (1)H multinuclear NMR spectroscopy, electrospray ionization mass spectrometry, and pulsed-field-gradient spin echo NMR techniques together with computational simulations.     

Optimal Sequencing of Inspection of Dependent Characteristics

We address the problem of sequentially inspecting the dependent characteristics of a product, where the dependency is expressed in terms of the joint probabilities of the fitness of the characteristics. We show that, even when the inspection has classification errors, the joint probability mass function of the observed fitness of the characteristics is independent of the sequence of inspection. Using this result, a dynamic programming approach is presented for finding the optimal sequence that minimizes the expected total cost of inspection. Previously reported policies for independent characteristics are shown to be special cases of the results presented here.     

The spin density distribution in some phenyl substituted imidazyl and pyrryl radicals

ENDOR spectroscopy has been used to interpret the E.S.R. spectra of the 2,4,5-triphenylimidazyl, tetraphenylpyrryl, tetrakis (p-tolyl) pyrryl, tetrakis (p-anisyl) pyrryl radicals. Using the hyperfine coupling constants thus obtained in conjunction with a McLachlan-type HMO calculation the spin density distribution in these radicals is calculated. The configuration of the phenyl rings and the deviation of their bond lengths from hexagonal symmetry is inferred from the MO parameters required to fit the experimental couplings.     

Static dielectric properties of Stockmayer fluids

Dielectric constants for the Stockmayer fluid are computed both from the equilibrium fluctuations of the polarization and from the polarization response to an applied field in a molecular dynamics simulation with periodic boundary conditions and with the dipole interactions treated by the Ewald method. The dielectric constant at finite wavelength is obtained from a Kirkwood-like expression, while for uniform polarization fluctuations a different expression applies due to the absence of surface effects in the Ewald calculation. The results are nearly independent of the number (up to 500) of particles investigated, even at large values of the dipole moment. The dielectric constants obtained from the approximate solution of the hypernetted chain integral equation are considerably larger than the molecular dynamics results except at low dielectric constants. The external field simulation permits study of the non-linear dependence of the dielectric constant on the magnitude of the applied electric field.     

Toward a storage ring with no shear

One barrier to the attainment of a crystalline ordered state for a well-cooled beam in a storage ring will be the viscous heating by the shear induced in the bending fields of the ring. Shear will transfer some of the energy of coherent motion to thermal energy and may prevent reaching the very low temperatures required for formation of the ordered state. A concept for a ring is proposed in which shear within a monoenergetic beam of finite size is substantially reduced by means of combined electrostatic and magnetic fields within the bending elements.     

Multiplicity structure of proton and kaon diffractive dissociation in 10 and 16 GeV/c K-p interactions

A new method to calculate diffractive mass spectra has been developed. It is applied to K^-p interactions at 10 and 16 GeV/c. Cross sections and mass spectra are given for the difractive dissociation processes p→(N+iπ) and K^-p→(K+iπ) for i = 1 to 5 and also summed over all multiplicities. In addition to the diffractive peak at low mass coming from low multiplicities, a long tail extending to high masses and high multiplicities has been found. The multiplicity structure of diffraction dissociation can be understood in the context of the two-step dynamical picture of Pokorsky and Van Hove.     

Two‐Color Valence‐to‐Core X‐ray Emission Spectroscopy Tracks Cofactor Protonation State in a Class I Ribonucleotide Reductase

Proton transfer reactions are of central importance to a wide variety of biochemical processes, though determining proton location and monitoring proton transfers in biological systems is often extremely challenging. Herein, we use two‐color valence‐to‐core X‐ray emission spectroscopy (VtC XES) to identify protonation events across three oxidation states of the O₂‐activating, radical‐initiating manganese–iron heterodinuclear cofactor in a class I‐c ribonucleotide reductase. This is the first application of VtC XES to an enzyme intermediate and the first simultaneous measurement of two‐color VtC spectra. In contrast to more conventional methods of assessing protonation state, VtC XES is a more direct probe applicable to a wide range of metalloenzyme systems. These data, coupled to insight provided by DFT calculations, allow the inorganic cores of the Mn^IVFe^IV and Mn^IVFe^III states of the enzyme to be assigned as Mn^IV(μ‐O)₂Fe^IV and Mn^IV(μ‐O)(μ‐OH)Fe^III, respectively.     

Scaffold topologies. 2. Analysis of chemical databases

We have systematically enumerated graph representations of scaffold topologies for up to eight-ring molecules and four-valence atoms, thus providing coverage of the lower portion of the chemical space of small molecules (Pollock et al. J. Chem. Inf. Model., this issue). Here, we examine scaffold topology distributions for several databases: ChemNavigator and PubChem for commercially available chemicals, the Dictionary of Natural Products, a set of 2742 launched drugs, WOMBAT, a database of medicinal chemistry compounds, and two subsets of PubChem, "actives" and DSSTox comprising toxic substances. We also examined a virtual database of exhaustively enumerated small organic molecules, GDB (Fink et al. Angew. Chem., Int. Ed. 2005, 44, 1504-1508), and we contrast the scaffold topology distribution from these collections to the complete coverage of up to eight-ring molecules. For reasons related, perhaps, to synthetic accessibility and complexity, scaffolds exhibiting six rings or more are poorly represented. Among all collections examined, PubChem has the greatest scaffold topological diversity, whereas GDB is the most limited. More than 50% of all entries (13 000 000+ actual and 13 000 000+ virtual compounds) exhibit only eight distinct topologies, one of which is the nonscaffold topology that represents all treelike structures. However, most of the topologies are represented by a single or very small number of examples. Within topologies, we found that three-way scaffold connections (3-nodes) are much more frequent compared to four-way (4-node) connections. Fused rings have a slightly higher frequency in biologically oriented databases. Scaffold topologies can be the first step toward an efficient coarse-grained classification scheme of the molecules found in chemical databases.     

Convergence of goal‐oriented adaptive finite element methods for nonsymmetric problems

In this article, we develop convergence theory for a class of goal‐oriented adaptive finite element algorithms for second‐order nonsymmetric linear elliptic equations. In particular, we establish contraction results for a method of this type for Dirichlet problems involving the elliptic operator with A Lipschitz, symmetric positive definite, with b divergence‐free, and with . We first describe the problem class and review some standard facts concerning conforming finite element discretization and error‐estimate‐driven adaptive finite element methods (AFEM). We then describe a goal‐oriented variation of standard AFEM. Following the recent work of Mommer and Stevenson for symmetric problems, we establish contraction and convergence of the goal‐oriented method in the sense of the goal function. Our analysis approach is signficantly different from that of Mommer and Stevenson, combining the recent contraction frameworks developed by Cascon, Kreuzer, Nochetto, and Siebert; by Nochetto, Siebert, and Veeser; and by Holst, Tsogtgerel, and Zhu. We include numerical results, demonstrating performance of our method with standard goal‐oriented strategies on a convection problem. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 479–509, 2016