Metal–dielectric photonic crystal superlattice: 1D and 2D models and empty lattice approximation

Periodic nanostructures are one of the main building blocks in modern nanooptics. They are used for constructing photonic crystals and metamaterials and provide optical properties that can be changed by adjusting the geometrical parameters of the structures. In this paper the optical properties of a photonic crystal slab with a 2D superlattice are discussed. The structure consists of a gold layer with a finite periodic pattern of air holes that is itself repeated periodically with a larger superperiod. We propose simplified 1D and 2D models to understand the physical nature of Wood's anomalies in the optical spectra of the investigated structure. The latter are attributed to the Rayleigh anomalies, surface plasmon Bragg resonances and the hole-localized plasmons.     

Suitability of linear quadrupole ion traps for large Coulomb crystals

Growing and studying large Coulomb crystals, composed of tens to hundreds of thousands of ions, in linear quadrupole ion traps presents new challenges for trap implementation. We consider several trap designs, first comparing the total driven micromotion amplitude as a function of location within the trapping volume; total micromotion is an important point of comparison since it can limit crystal size by transfer of radiofrequency drive energy into thermal energy. We also compare the axial component of micromotion, which leads to first-order Doppler shifts along the preferred spectroscopy axis in precision measurements on large Coulomb crystals. Finally, we compare trapping potential anharmonicity, which can induce nonlinear resonance heating by shifting normal mode frequencies onto resonance as a crystal grows. We apply a non-deforming crystal approximation for simple calculation of these anharmonicity-induced shifts, allowing a straightforward estimation of when crystal growth can lead to excitation of different nonlinear heating resonances. In the anharmonicity point of comparison, we find significant differences between the trap designs, with an original rotated-endcap trap performing better than the conventional in-line endcap trap.     

Vibrational spectra and structure of gaseous and solid dimethylboric anhydride

The Raman spectra of gaseous, liquid and solid dimethylboric anhydride (CH₃)₂BOB(CH₃)₂ have been recorded from 10–3500 cm^?1. The IR spectra from 4000–30 cm^?1 have also been recorded. The spectra of the gaseous phase have been interpreted in terms of C₂ symmetry implying a bent B-O-B skeleton with the B(CH₃)₂ groups twisted and consistent with a rather larger barrier to internal rotation about the B-O bonds. The spectra of the crystalline state, however, suggest that the molecular symmetry is altered upon solidification. Isotopic substitution of the oxygen atom by ¹⁸O confirmed that the B-O-B skeleton is linear in the solid state, and the spectra have been interpreted in terms of D_2h molecular symmetry.     

New C-N and C-C bond forming reactions catalyzed by titanium complexes

Titanium(IV) complexes with two basic dimethylamido ligands can be efficient catalysts for alkyne hydroamination by primary amines. Readily prepared pyrrolyl ligands have proven to be especially useful in generating active catalysts for hydroamination and hydrohydrazination. From these reactions, new methodologies for the synthesis of imines, hydrazones, alpha,beta-unsaturated imines, pyridines, indoles, and pyrroles have developed. In addition, a new reaction that is mechanistically related to hydroamination, alkyne iminoamination, has been discovered. Iminoamination, which is a multicomponent coupling between an amine, alkyne, and isonitrile, provides unsymmetrical alpha, beta-unsaturated beta-iminoamines in a single, titanium-catalyzed step.     

Stabilisation of a heptamethine cyanine dye by rotaxane encapsulation

The crystal structure of a cyanine dye rotaxane shows that the cyclodextrin is tightly threaded round the polymethine bridge of the dye; encapsulation dramatically increases the kinetic chemical stability of the radicals formed on oxidation and reduction of the dye, making it possible to observe the rotaxane radical dication by ESR and UV-vis-NIR spectroscopy.     

Derivations, isomorphisms, and second cohomology of generalized Witt algebras

Generalized Witt algebras, over a field of characteristic , were defined by Kawamoto about 12 years ago. Using different notations from Kawamoto's, we give an essentially equivalent definition of generalized Witt algebras over , where the ingredients are an abelian group , a vector space over , and a map which is linear in the first variable and additive in the second one. In this paper, the derivations of any generalized Witt algebra
, with the right kernel of being , are explicitly described; the isomorphisms between any two simple generalized Witt algebras are completely determined; and the second cohomology group for any simple generalized Witt algebra is computed. The derivations, the automorphisms and the second cohomology groups of some special generalized Witt algebras have been studied by several other authors as indicated in the references.

     

Spectra and structure of phosphorus-boron compounds,XII1 Vibrational spectra and molecular symmetry of tetramethylbiphosphine-bisborane

The infrared (200–3500 cm^–1) and Raman (50–3500 cm^–1) spectra of two isotopic species of tetramethylbiphosphine-bisborane, (CH₃)₄P₂·2BH₃ and (CH₃)₄P₂·2BD₃, in the solid state at low temperatures have been recorded. The spectra have been interpreted in detail on the basis ofC _2h molecular symmetry. The P-B stretching modes were assigned to bands at 599 and 567 cm^–1 in the Raman and infrared spectra of the light compound, respectively. Only one P-P stretching mode was observed in the Raman spectra. The vibrational data appear to be consistent with the presence of only one conformer in the solid state, which is at variance with the conclusions from an X-ray study. Considerable splitting of the low-frequency bending modes was observed for both compounds; this splitting has been attributed to the factor group.For part XI, see J. D. Odom, V. F. Kalaskinsky, and J. R. Durig,Inorg. Chem. 14, 2837 (1975).Taken in part from the thesis of R. W. MacNamee which was submitted to the Department of Chemistry in partial fulfillment of the Ph.D. degree (1974).