(1R*,11R*)‐Bi­cyclo­[9.4.1]­hexa­decane‐12,16‐dione

The title compound, C₁₆H₂₆O₂, (I), prepared by oxidation of (1R*,11R*)‐12‐hydroxy­bi­cyclo­[9.4.1]­hexa­decan‐16‐one using pyridinium dichromate, has a trans configuration of the two fused rings and represents an interesting precursor for the synthesis of macrocyclic structures.     

Zwei Bemerkungen über transzendente Zahlen

In the first part theorems ofBaker are used to prove the transcendence of special values of power series whose coefficients are values of certain ordinary Dirichlet series with coefficients forming a periodic sequence of algebraic numbers. Especially the transcendence of (z)+C is shown for all rationalz which are not integers, denoting the logarithmic derivative of the gamma function andC Euler's constant. In the second part the intimate connection betweenSchanuel's conjecture and the arithmetic nature of ,s=3,4,5... is studied where (n) denotes the number of distinct representation ofn in the forma ^b with positive integersa, b. This function was recently introduced byGolomb.     

Die ersten Röntgenstrukturen kationischer Diorganylzinn(IV)‐Dichelate [R2Sn(L–L)2]2⊕ mit zweizähnigen Phosphanoxid‐Liganden: Di(methansulfonyl)amid als nichtkoordinierendes Gegenion

Polysulfonylamines. CXI. The First X‐Ray Structures of Cationic Diorganyltin(IV) Dichelates [R₂Sn(L–L)₂]^2⊕ Involving Bidentate Phosphine Oxide Ligands: Di(methanesulfonyl)amide as a Non‐Coordinating Counter‐Ion The reaction of Me₂Sn(A)₂, where A^⊖ = (MeSO₂)₂N^⊖, with DPPOE = ethane‐1,2‐diylbis(diphenylphosphine oxide) or CDPPOET = cis‐ethene‐1,2‐diylbis(diphenylphosphine oxide) yields the ionic dichelates [Me₂Sn(dppoe)₂]^2⊕ · 2 A^⊖ ( 1 ; monoclinic, space group P2₁/c) and [Me₂Sn(cdppoet)₂]^2⊕ · 2 A^⊖ ( 2 ; monoclinic, P2₁/n). A solvated variety of 2 , [Me₂Sn(cdppoet)₂]^2⊕ · 2 A^⊖ · Et₂O · 0.15 MeCN ( 4 ; triclinic, P 1), was serendipitously obtained by thermal degradation of the new compound [Me₂Sn(A)(μ‐OH)]₂ · 2 CDPPOET in an MeCN/Et₂O medium. The crystals of 1 , 2 and 4 consist of discrete formula units (one independent unit for 1 and 2 , two independent units for 4 ); in the structure of 4 , the solvent molecules are located in lattice cavities. All the tin atoms lie on crystallographic inversion centres and display moderately distorted octahedral C₂O₄ coordinations with short Sn–O bonds in the range 218–223 pm. Within the formula units, the anions are connected to the P–CH donor groups of the chelating ligands by C–H…O/N interactions, some of which are remarkably short (e.g. in 1 : H…O 220 pm, C–H…O 170°; H…N 242 pm, C–H…N 153°).     

Reversible transformations of gold nanoparticle morphology

Herein is reported a metamorphosis taking place in a gold nanosized system. The observed phenomenon of shape and size transformations was found to be completely reversible. Unlike most procedures in the literature where shape and size control occur in the synthetic step by adding growth- and shape-controlling agents such as surfactants or polymers, in this system postsynthetic changes in shape and size can be carried out simply by changing the ratio of reactive, competing reagents, more specifically, alkylthiols versus tetralkylammonium salts. Interestingly, the transfer of gold metal occurs (large prismatic particles to small particles and vice versa) under the influence of reagents that do not cause such interactions with bulk gold. All intermediate steps of the morphology change were observed using HRTEM and electron diffraction. The processes of breaking down and "welding back" solid metal nanoparticles occur under mild conditions and are remarkable examples of the unique chemical properties of nanomaterials. The described process is expected to be relevant to other nanoscale systems where similar structural circumstances could occur.     

Casting a new light on azide photochemistry: photolytic production of cyclic-N3

The first postulated structure of the N(3) moiety appeared in a scientific journal in 1890 and was reported as a cyclic triangle with one N,N double bond and two N,N single bonds. Only in the last several years has our understanding of azides advanced to the point that we can now claim to know how to synthesize this prototypical bonding motif. This article examines the experiments and theory that were essential in reaching this point and suggests future directions of research on cyclic-N(3).     

The simplest all-nitrogen ring: photolytically filling the cyclic-N3 well

We report evidence that cyclic-N(3) is exclusively produced in the 157-nm photolysis of ClN(3). Photoproduct translational energy measurements reveal a single-peaked distribution for an N(3)-formation channel with maximum and minimum translational energies matching the theoretically predicted minimum and maximum binding energies of cyclic-N(3), respectively. The absence of linear-N(3) greatly simplifies the data analysis. The zero-Kelvin heat of formation of cyclic-N(3) is derived experimentally (142+/-3.5 kcal/mol) and is in excellent agreement with the best existing determinations from other studies.     

About the limits of regularization and the ansatz method

The well-known adsorption integral equation (AIE) for calculating pore size and adsorption energy distributions from adsorption isotherms on porous solids is, from the mathematical point of view, a linear Fredholm integral equation of the first kind and therefore an ill-posed problem. What can we realistically expect from the solution of such an ill-posed problem by regularization? Does it make sense to restrict the number of possible solutions by the so-called ansatz method? In this paper, the two methods for solving ill-posed problems are from scratch explained and illuminated by concrete examples. Their relevance and fundamental limitations are discussed.     

Interaction of diatomic germanium with lithium atoms: electronic structure and stability

Quantum chemical calculations were applied to investigate the electronic structure of mono-, di-, and trilithiated digermanium (Ge2Lin) and their cations (n=0-3). Computations using a multiconfigurational quasidegenerate perturbation approach based on complete active space self-consistent-field wave functions, and density functional theory reveal that Ge2Li has a 2B1 ground state with a doublet-quartet energy gap of 33 kcal/mol. Ge2Li2 has a singlet ground state with a 3Au-1A1 gap of 29 kcal/mol, and Ge2Li3 a doublet ground state with a 4B2-2A2 separation of 22 kcal/mol. The cation Ge2Li+ has a 3B1 ground state, being 13 kcal/mol below the open-shell 1B1 state. The computed electron affinities for diatomic germanium are EA(1)=1.9 eV, EA(2)=-2.5 eV, and EA(3)=-6.0 eV, for Ge2-, Ge2 (2-), and Ge2 (3-), respectively, indicating that only the monoanion is stable with respect to electron detachment, in such a way that Ge2Li is composed by Ge2-Li+ ions. An "atoms-in-molecules" analysis shows the absence of a ring critical point in Ge(2)Li. An electron localization function analysis on Ge2Li supports the view that the Ge-Li bond is predominantly ionic; however, a small covalent character could be anticipated from the analysis of the Laplacian at the Ge-Li bond critical point. The ionic picture of the Ge-Li bond is further supported by a natural-bond-order analysis and the Laplacian of the electron density. The calculated Li affinity value for Ge2 is 2.08 eV, while the Li+ cation affinity value for Ge2- is 5.7 eV. The larger Li+ cation affinity value of Ge2- suggests a Ge2-Li+ interaction and thus supports the ionic nature of Ge-Li bond. In GeLi4 and Ge2Li, the presence of trisynaptic basins indicates a three-center bond connecting the germanium and lithium atoms.     

Electronic structure of amorphous transition metal alloys

The electrical resistivity, the Hall coefficient and the magnetic susceptibility of amorphous alloys (Metglass 2826A, Allied Chemical) have been measured above room temperature. The experimental data show strong similarities with liquid alloys.     

Extended resolution wide-field optical imaging: objective-launched standing-wave total internal reflection fluorescence microscopy

Standing-wave total-internal-reflection fluorescence (SW-TIRF) microscopy uses a super-diffraction-limited standing evanescent wave to extract the high-spatial-frequency content of an object through a diffraction-limited optical imaging system. The effective point-spread function is better than a quarter of the emission wavelength. With a 1.45 numerical aperture objective and 532 nm excitation wavelength, a Rayleigh resolution of approximately 100 nm can be achieved, which is better than twice the resolution of conventional TIRF microscopy. This first experimental realization of SW-TIRF in an objective-launched geometry demonstrates the potential for extended resolution imaging at high speed by using wide-field microscopy.