A Unified Treatment of the Relationship Between Ligand Substituents and Spin State in a Family of Iron(II) Complexes

The influence of ligands on the spin state of a metal ion is of central importance for bioinorganic chemistry, and the production of base‐metal catalysts for synthesis applications. Complexes derived from [Fe(bpp)₂]²⁺ (bpp=2,6‐di{pyrazol‐1‐yl}pyridine) can be high‐spin, low‐spin, or spin‐crossover (SCO) active depending on the ligand substituents. Plots of the SCO midpoint temperature (T ) in solution vs. the relevant Hammett parameter show that the low‐spin state of the complex is stabilized by electron‐withdrawing pyridyl (“X”) substituents, but also by electron‐donating pyrazolyl (“Y”) substituents. Moreover, when a subset of complexes with halogeno X or Y substituents is considered, the two sets of compounds instead show identical trends of a small reduction in T for increasing substituent electronegativity. DFT calculations reproduce these disparate trends, which arise from competing influences of pyridyl and pyrazolyl ligand substituents on Fe‐L σ and π bonding.     

Cooperative AND ion-pair recognition by heteroditopic calix[4]diquinone receptors

A new family of heteroditopic calix[4]diquinone receptors capable of the cooperative recognition of ion-pair species through a contact binding mechanism has been developed. The receptors bind contact ion pairs cooperatively, with an unprecedented AND recognition phenomenon being observed to operate in certain cases, in which receptors display no affinity for either of the individual "free" cation or anion, but bind the cation and anion ion-pair strongly. X-ray crystallographic, solution-state, and computational methods rationalize the observed recognition behavior of the receptors. It is shown that the contact ion-pair interaction occurs through a pi-stacking-mediated folding of the receptors such that the anion and cation binding sites are arranged in close proximity, while in the solid state an unusual ion-mediated receptor dimerization is observed. Molecular dynamics simulations are further used to explain the observed trends in the association constants of different ion-pair species and the mechanism of interaction.     

Meinardus' theorem on weighted partitions: Extensions and a probabilistic proof

The number c_n of weighted partitions of an integer n, with parameters (weights) b_k, k1, is given by the generating function relationship . Meinardus (1954) established his famous asymptotic formula for c_n, as n→∞, under three conditions on power and Dirichlet generating functions for the sequence b_k. We give a probabilistic proof of Meinardus' theorem with weakened third condition and extend the resulting version of the theorem from weighted partitions to other two classic types of decomposable combinatorial structures, which are called assemblies and selections.     

Theoretical evidence for the nucleophilic addition of sulfur dioxide to 1,2-bridged chloronium and bromonium ions

The nucleophilic addition of SO2, SO2ClF, and SO2F2 to carbenium ions and the nucleophilic addition of SO2 to 1,2-bridged halonium ions are theoretically investigated by using B3LYP/6-311+G(d,p). On the basis of geometric changes in ion-solvent complexes compared to isolated molecules, the theoretical data for the addition of solvent to carbenium ions uniformly agree with experiments by Olah and Donovan. The relative reactivity of carbenium ions (methyl > ethyl > iso-propyl > tert-butyl) follows the familiar trend based on electron demand at the carbenium center. The theoretical data for the addition of SO2 to 1,2-bridged halonium ions with use of similar methods indicate that this addition exhibits a reversed trend on the basis of the electron demand; SO2 adds to 2,2-dimethylethylene chloronium and bromonium ions but does not add to the fluoronium analogue. Furthermore, the addition depends on the stereochemistry of the approaching SO2. When SO2 approaches syn to the halogen atom on the halonium ion, addition is observed. When SO2 is anti, addition is not observed. The reversed reactivity and stereochemistry of the addition of SO2 to halonium ions can be explained by electron donation from the halogen atom to the sulfur atom of the approaching SO2. This sulfur-halogen interaction activates the nucleophilicity of the approaching SO2 and makes a normally unreactive tertiary carbenium carbon susceptible to addition. The theoretical evidence for covalently bound halonium ion-SO2 complexes is discussed in the context of previously reported experimental evidence for the existence of equilibria involving beta-halocarbenium ions.     

Investigation of the effects of the local environment on the surface-enhanced Raman spectra of striped gold/silver nanorod arrays

The effects of the local environment on surface-enhanced Raman scattering (SERS) spectra utilizing gold, silver, and gold/silver striped nanorod array substrates was investigated. The arrays were fabricated using an electrochemical metal deposition into an anodic aluminum oxide template. The analyte chosen for this study was p-nitroso-N,N-dimethylaniline (p-NDMA), which has an electronic structure that is highly sensitive to its surrounding environment. Changes in the peak positions and peak ratios were used to probe the influence of water and the striping pattern on the SERS signal of p-NDMA. We present the results of the fabrication and characterization of the nanorod array substrates, as well as SERS spectra of p-NDMA in both polar and nonpolar environments and SERS spectra on a variety of striped nanorod arrays. The Raman data suggests that the p-NDMA molecule exists in a more polarized state when bound to the gold as compared to the silver rods. We have attempted to use these differences to determine whether the SERS signal predominantly arises from the tips of the rods or from the interior of the array.     

Synthesis of the tricyclic core of aldingenin B by oxidative cyclo-ketalization of an alkyne-diol

The preparation and selenium-mediated cyclo-ketalization of an alkyne-diol is described as a model study for the synthesis of aldingenin B. The oxidative cyclization is a simplifying transformation for aldingenin B, as it provides a convenient method for generating the tricylic core of the natural product from a functionalized cyclohexane.     

A new approach to a practical subwavelength resolving microscope

Superresolution depends on near-field capture and transfer of high spatial frequencies from the scattering object. These evanescent waves are transferred to a near-field image domain using a negative index material. Measuring images with subwavelength scale resolution in the near field by scanning is not practical and ignores inevitable object–lens–image coupling phenomena as well as the need to employ inverse scattering algorithms. An alternative approach based on compressive sampling permits the use of a single fixed detector. Traditionally, in such a system, an image-bearing wavefront is projected onto a series of patterns (= basis functions) and the transmitted light integrated by a lens onto a single-point detector. Image reconstruction is possible by weighting each basis function with its measured coefficient and summing, including basis functions representing evanescent waves. We employ a single fixed detector in the back focal plane of a negative index concave lens and basis functions realized by structured illumination from combinations of a set of discrete sources. We have investigated this as an approach to recover subwavelength scale details about a scattering object and report our results.     

Passively controlled supersonic cavity flow using a spanwise cylinder

An experimental investigation of a passively controlled open cavity with a length to depth ratio of six and freestream Mach number of 1.4 was conducted to investigate the mechanisms responsible for the observed surface pressure reductions. The passive control comes from placing a spanwise aligned cylinder in the boundary layer near the leading edge of the cavity. The two control configurations were isolated from previous experiments of the fluctuating surface pressure and correspond to a larger diameter rod near the top of the boundary layer and a smaller diameter rod placed near the wall. These were further analyzed using particle image velocimetry in an attempt to elicit the responsible mechanism for the flow control. The use of two-point statistics revealed the wall normal turbulent velocity correlation’s evolution became elongated in the wall normal direction. This suggests that the shear layer may be less-organized and consists of smaller-scale structures. The disturbance of the feedback receptivity loop is clearly demonstrated for the controlled configurations evidenced by weakened correlation signals between the aft wall sensor and positions on the cavity floor. The presence of the rod is shown to decrease the mean shear gradient, more effectively for the large rod placed at the top of the boundary layer, throughout the shear layer. The efficacy of the control leads to an initially thicker shear layer which spreads more rapidly and is clearly demonstrated by vorticity growth rates, mean, and turbulent flowfield statistics.     

Sorting dinosaurs: an opportunity to teach mathematics with biology

With the growing desire for increased communication between mathematics teachers and science teachers there is a need for materials specifically written to help bring about communication at that level which also have potential in class. This paper is concerned with one example, a study of dinosaurs through the algebra of sets, simultaneously exploring and developing a topic in biology and a topic in mathematics by raising a series of questions about dinosaurs which are most effectively answered by means of mathematics.

Initially the questions asked can be answered by means of Venn diagrams, and set notation is no more than an alternative, brief way of expressing the same answer. But systematically the Venn diagrams become more involved and there is a growing dependence upon the algebra of sets so that ultimately answers are sought by that means and Venn diagrams are used (if at all) to reinforce the findings. Very many aspects of set notation and algebra are incorporated into the study and a number of set theories illustrated.

Some aspects of its possible use in class are considered.     

Growth mechanisms and defect structures of B12As2 epilayers grown on 4 H-SiC substrates

Epitaxial growth of icosahedral B₁₂As₂ on c-plane 4 H-SiC substrates has been analyzed. On on-axis c-plane 4 H-SiC substrates, Synchrotron white beam x-ray topography (SWBXT) revealed the presence of a homogenous solid solution of twin and matrix B₁₂As₂ epilayer domains. High resolution transmission electron microscopy (HRTEM) and scanning transmission electron microscopy (STEM) both revealed the presence of an ～20 nm thick, disordered transition layer at the interface. (0003) twin boundaries are shown to possess fault vectors such as 1/3[1–100]_B12As2, which originate from the mutual shift between the nucleation sites. On the contrary, B₁₂As₂ epilayers grown on c-plane 4 H-SiC substrates intentionally misoriented from (0001) towards [1–100] is shown to be free of rotational twinning. SWBXT, HRTEM and STEM all confirmed the single crystalline nature and much higher quality of the films. In addition, no intermediate layer between the epilayer and the substrate was observed. It is proposed that the vicinal steps formed by hydrogen etching on the off-axis 4 H-SiC substrate surface before deposition cause the film to adopt a single orientation during nucleation process. This work also demonstrates that c-plane 4 H-SiC with offcut toward [1–100] is potentially a good substrate choice for the growth of high-quality, single crystalline B₁₂As₂ epilayers for future device applications.