Structures of ordered tungsten- or molybdenum-containing quaternary perovskite oxides

The room temperature crystal structures of six A₂MMoO₆ and A₂MWO₆ ordered double perovskites were determined from X-ray and neutron powder diffraction data. Ba₂MgWO₆ and Ba₂CaMoO₆ both adopt cubic symmetry (space group Fm3?m, tilt system a⁰a⁰a⁰). Ba₂CaWO₆ has nearly the same tolerance factor (t=0.972) as Ba₂CaMoO₆ (t=0.974), yet it surprisingly crystallizes with I4/m symmetry indicative of out-of-phase rotations of the MO₆ octahedra about the c-axis (a⁰a⁰c^?). Sr₂ZnMoO₆ (t=0.979) also adopts I4/m symmetry; whereas, Sr₂ZnWO₆ (t=0.976) crystallizes with monoclinic symmetry (P2₁/n) with out-of-phase octahedral tilting distortions about the a- and b-axes, and in-phase tilting about the c-axis (a^?a^?c⁺). Ca₂CaWO₆ (t=0.867) also has P2₁/n symmetry with large tilting distortions about all three crystallographic axes and distorted CaO₆ octahedra. Analysis of 93 double perovskites and their crystal structures showed that while the type and magnitude of the octahedral tilting distortions are controlled primarily by the tolerance factor, the identity of the A-cation acts as the secondary structure directing factor. When A=Ba²⁺ the boundary between cubic and tetragonal symmetries falls near t=0.97, whereas when A=Sr²⁺ this boundary falls somewhere between t=1.018 and t=0.992.     

Deformation mechanisms of constrained polymer chains. I. Geometrically induced correlations in the deformation response mechanisms of tie molecules

The geometrical constraints acting on sections of tie molecules in noncrystalline regions severely limit the number and type of available polymer chain conformations. It is shown that these constraints induce explicit correlations in the rotations about the backbone bonds. These correlated rotations, in turn, specify distinct structural conversion paths which define the molecular mechanisms underlying the deformation response of tie molecules. Application of these constraining relationships to highly oriented polyethylene shows that the kink and jog structures of tie molecules can be decomposed into combinations of three primary conformational building blocks. Each of the basic conformational subunits follow an explicit set of dihedral angle correlations and, consequently, imparts specific characteristics to the composite structure of tie molecules. It is proposed that the composite response characteristics of tie molecules can be described as linear combinations of the response characteristics of these three primary conformational subunits.     

Numerical Hartree-Fock and MCSCF calculations on diatomic copper: calibration of basis sets

NHF and NMCSCF results for Cu₂ are compared with calculations employing basis set expansions. We find that nearly all previous SCF calculations using Gaussian basis sets have underestimated the bond length by about the same amount (0.03 Å) as that attributed to the unlinked cluster and relativistic corrections. The error is shown to be due to deficiencies in the 3d primitive set which yield sizable basis set superposition errors.     

New approaches to the synthesis of spiro-peroxylactones

Ozonolysis of (alkenyldioxy)cyclododecyl hydroperoxides in trifluoroethanol gave a separable mixture of the corresponding alpha-hydroperoxy- and alpha-hydroxy-substituted spiro-tetraoxacycloalkanes with ring sizes in the range 7-12. Dehydration of the hydroperoxides or oxidation of the hydroxy-compounds afforded the corresponding peroxylactones. The solid-state structure of 1,2,6,7-tetraoxaspiro[7.11]nonadecan-3-one was determined by X-ray crystallographic analysis.     

Synthesis of cyclic peroxides by chemo- and regioselective peroxidation of dienes with Co(II)/O2/Et3SiH

In the competitive peroxidation of mixtures of two alkenes with Co(II)/O(2)/Et(3)SiH, it was found that the relative reactivities of the alkene substrates are influenced by three major factors:. (1) relative stability of the intermediate carbon-centered radical formed by the reaction of the alkene with HCo(III) complex, (2) steric effects around the C=C double bond, and (3) electronic factors associated with the C=C double bond. Consistent with results from simple alkenes, the chemo- and regioselective peroxidation of dienes was also realized. Depending on the diene structure, the product included not only the expected acyclic unsaturated triethylsilyl peroxides but also 1,2-dioxolane and 1,2-dioxane derivatives via intramolecular cyclization of the unsaturated peroxy radical intermediates.     

Determination of benzidines by gas chromatographic separation of derivatives with electron capture detection

Factors considered in the development of a method for the determination of toxic, water-soluble benzidines. involved providing a good technique for their adequate recovery, converting quantitatively the isolated amines to relatively stable derivatives suitable for measurement and storage, coupled with relative ease of preparation of the derivatives, and resolving the prepared compounds during their measurement. Benzidine and dichlorobenzidine are quantitatively extracted from wastewater and measured quantitatively through the preparation of their respective pentafluoropropionamides (PFP) by using PFP-imidazole. Overall recovery efficiency for benzidines from wastewater ranges from 91 to 103%. These derivatives are relatively stable compounds and have detection limits of 0.2 pg or less, when electron capture detection is used with gas chromatography. Derivatives of o-tolidine and dianisidine are also described.     

The 3-Isometric Lifting Theorem

An operator T on Hilbert space is a 3-isometry if \({T^{*n}T^{n}= I +n B_1 +n^{2} B_2}\) is quadratic in n. An operator J is a Jordan operator if J = U + N where U is unitary, N ² = 0 and U and N commute. If T is a 3-isometry and \({c > 0,}\) then \({I-c^{-2} B_{2} + sB_{1} + s^{2}B_2}\) is positive semidefinite for all real s if and only if it is the restriction of a Jordan operator J = U + N with the norm of N at most c. As a corollary, an analogous result for 3-symmetric operators, due to Helton and Agler, is recovered.