Selection rules for Raman scattering from eigenmodes of spherical nanoparticles

The elastic vibrations of spherical nanoparticles have been widely studied by Raman scattering. However, there exist more than one set of selection rules for Raman scattering from these vibrations. For instance, Kanehisa has stated that only torsional modes with angular momentum l = 2 are Raman-active, while Tanaka et al. proposed that spheroidal modes of even l and torsional modes of odd l are Raman-active. These contradict selection rules of Duval which states that only spheroidal modes of l = 0 or 2 are Raman-active. Our present calculations based on a macroscopic model show that all torsional modes have vanishing intensity in the Raman spectrum.     

Ion-pair formation observed in a pulsed-field ionization photoelectron spectroscopic study of HF

The pulsed-field ionization (PFI) photoelectron (PE) spectrum of HF has been recorded at the chemical dynamics beamline of the advanced light source over the photon energy range 15.9-16.5 eV using a time-of-flight selection scheme at a resolution of 0.6 meV. Rotationally-resolved structure in the HF+(X 2 pi 3/2, 1/2, v+ = 0, 1) band systems are assigned. The spectral appearance of these systems agrees with a previous VUV laser PFI-PE study. Importantly, extensive rotationally-resolved structure between these two vibrational band systems is also observed. This is attributed to ion-pair formation via Rydberg states converging on the v+ = 1 vibrational levels of the HF+(X 2 pi 3/2, 1/2) spin-orbit states. These Rydberg states are assigned to the 1 sigma+ part of the nd-complexes (sigma, pi, and delta). Ion-pair formation is observed in this study by the detection of F- ions. Some partially rotationally-resolved structure in a previously published threshold photoelectron spectrum is similarly attributed to ion-pair formation (F- detection) through a combination of the v+ = 17 level of the (A 2 sigma+) 3s sigma Rydberg state and the (X 2 pi 3/2, 1/2, v+ = 1) 7d Rydberg states. On the basis of the present study, an accurate experimental value for the dissociation energy of the ground state of HF has been obtained, D0(HF) = 5.8650(5) eV.     

Preparation and chiral recognition of a novel chiral stationary phase for high-performance liquid chromatography, based on mono(6A-N-allylamino-6A-deoxy)-perfunctionalized beta-cyclodextrin and covalently bonded silica gel

A novel chiral stationary phase (CSP) was prepared by immobilizing mono(6A-N-allylamino-6A-deoxy)-perphenylcarbamoylated beta-cyclodextrin onto the surface of silica gel via hydrosilylation. The chromatographic properties of this column were tested with a wide range of structurally diverse racemic compounds and drugs under reverse phases. Separation mechanisms involved are also discussed.     

Gas chromatographic-mass spectrometric analysis of acids and phenols in distilled alcohol beverages. Application of anion-exchange disk extraction combined with in-vial elution and silylation

A GC-MS protocol for profiling spirits, based on 19 acids and phenolic compounds, has been proposed and evaluated. The method combined a simple preconcentration procedure based on solid-phase (anion-exchange) disk extraction, and in-vial elution and silylation of the analytes. The derivatized extract was directly injected into the GC-MS system. These analytes were: C6, C8, C10, C12 acids, pyruvic acid, 2-furoic acid, succinic acid, fumaric acid, glutaric acid, lactic acid, glycolic acid, malic acid, tartaric acid, citric acid, vanillin, syringaldehyde, coniferaldehyde, vanillic acid and gallic acid. The profiles of six different spirits were found reproducible from day-to-day with <20% RSD for measurements of most of the analytes at different concentrations. Recoveries of individual analytes appear to be affected by the level of tannins in the spirits, and they varied from sample to sample. The method of standard addition was used to quantify age-related analytes. Good linearity of response with correlation coefficients in the range of 0.992-0.999 was obtained. The results of the study indicate that for spirits of the same brand but of different ages, the amounts of these analytes appear to increase with the ageing period.     

Bis[bis­(methoxy­carbimido)amine‐κ2N,N′]bis­(perchlorato‐κO)copper(II) bis­[bis­(methoxy­carbimido)amine‐κ2N,N′]bis­(methanol‐κO)copper(II) bis­(perchlorate) methanol disolvate

The title compound, [Cu(ClO₄)₂(C₄H₉N₃O₂)₂][Cu(C₄H₉N₃O₂)₂(CH₄O)₂](ClO₄)₂·2CH₃OH, comprises two independent Cu^II species lying on different inversion sites. In the Cu complexes, a distorted octa­hedral geometry arises (from basic square‐planar N₄ coordination) from the weak coordination of two perchlorate ions (as Cu—O) in one species and two methanol mol­ecules in the other (also as Cu—O). Inter­actions between the O atoms of the perchlorate anions or methanol groups and the imide or amine NH groups afford an extensive inter­molecular hydrogen‐bonding network.     

Coordination compounds of indium : XIV. The insertion of indium(I) iodide into carbon-iodide bonds

Alkylindium(III) diiodides can be conveniently prepared in high yield by the insertion of indium(I) iodide into the CI bond of alkyl iodides. The products are halogen-bridged neutral dimers, except for the methyl compound, which is believed to be [(CH₃)₂In][InI₄ in the solid state. One of the intermediates isolated from the reaction mixture is (CH₃)₂InI₂INI(CH₃); the vibrational spectrum of this compound, and of (CH₃IInI₂INI₂, have been investigated. The mechanism of the initial reaction, and the subsequent rearrangement processes, are discussed.     

Fastiterative methods for least squares estimations

Least squares estimations have been used extensively in many applications, e.g. system identification and signal prediction. When the stochastic process is stationary, the least squares estimators can be found by solving a Toeplitz or near-Toeplitz matrix system depending on the knowledge of the data statistics. In this paper, we employ the preconditioned conjugate gradient method with circulant preconditioners to solve such systems. Our proposed circulant preconditioners are derived from the spectral property of the given stationary process. In the case where the spectral density functions() of the process is known, we prove that ifs() is a positive continuous function, then the spectrum of the preconditioned system will be clustered around 1 and the method converges superlinearly. However, if the statistics of the process is unknown, then we prove that with probability 1, the spectrum of the preconditioned system is still clustered around 1 provided that large data samples are taken. For finite impulse response (FIR) system identification problems, our numerical results show that annth order least squares estimator can usually be obtained inO(n logn) operations whenO(n) data samples are used. Finally, we remark that our algorithm can be modified to suit the applications of recursive least squares computations with the proper use of sliding window method arising in signal processing applications.Research supported in part by HKRGC grant no. 221600070, ONR contract no. N00014-90-J-1695 and DOE grant no. DE-FG03-87ER25037.