A review of forecast error covariance statistics in atmospheric variational data assimilation. I: Characteristics and measurements of forecast error covariances

Notations and conventions in molecular spectroscopy: part 3. Permutation and permutation-inversion symmetry notation

The field of Molecular Spectroscopy was surveyed in order to determine a set of conventions and symbols which are in common use in the spectroscopic literature. This document, which is Part 3 in a series, deals with symmetry notation referring to groups that involve nuclear permutations and the inversion operation. Further parts will follow, dealing inter alia with vibration-rotation spectroscopy and electronic spectroscopy.

Coriolis interactions about x-y axes in symmetric tops

Selection rules and matrix elements are derived for Coriolis interactions between vibrational levels due to rotation about (x, y) axes in symmetric top molecules. The theory is developed in detail for the case of interaction between an A1 and an E species vibrational level in a C3v molecule; perturbations to both the positions and the intensities of the rovibration transitions in the spectrum are considered. A computer program has been written which calculates exactly the perturbed spectrum of two interacting rovibration bands according to this model, the results being presented directly by a graph plotter connected to the computer. This has been used to interpret perturbations observed in two pairs of interacting fundamentals in the spectrum of CH3F (ν2 - ν5 and ν3 - ν6) and one pair in CD3Cl (ν2 - ν5). The resulting analysis of the observed spectrum leads to new values for some vibration-rotation interaction constants and also leads to a unique determination of the sign relationship between the dipole moment derivatives in each pair of interacting normal vibrations. These sign relations are summarized in Figs. 8, 12, and 15.

Selection rules for rovibronic transitions in symmetric top molecules

A simple diagrammatic rule is presented for determining the rotational selection rules governing transitions between any pair of vibronic states in electric dipole spectra of symmetric top molecules. The rule is useful in cases where degenerate vibronic levels with first-order Coriolis splittings occur, because it gives immediately the selection rule for the (+l) and (-l) components in any degenerate state. The rule is also helpful in determining the symmetry species and the effective zeta constants in overtone and combination levels involving degenerate vibrations. Particular attention is devoted to the conventions concerning the signs of zeta constants.

Raman selection rules for vibration-rotation transitions in symmetric top molecules

Symmetry restrictions on Raman selection rules can be obtained, quite generally, by considering a Raman allowed transition as the result of two successive dipole allowed transitions, and imposing the usual symmetry restrictions on the dipole transitions. This leads to the same results as the more familiar polarizability theory, but the vibration-rotation selection rules are easier to obtain by this argument. The selection rules for symmetric top molecules involving the (+l) and (-l) components of a degenerate vibrational level with first-order Coriolis splitting are derived in this paper. It is shown that these selection rules depend on the order of the highest-fold symmetry axis Cn, being different for molecules with n=3, n=4, or n ≧ 5; moreover the selection rules are different again for molecules belonging to the point groups Dnd with n even, and Sm with 1/2m even, for which the highest-fold symmetry axes Cn and Sm are related by m=2n. Finally it is shown that an apparent anomaly between the observed Raman and infra-red vibration-rotation spectra of the allene molecule is resolved when the correct selection rules are used, and a value for the A rotational constant of allene is derived without making use of the zeta sum rule.

Synthesis of a novel class of chiral polyaromatic amide dendrimers bearing an amino acid derived C-3-symmetric core

Chiral polyaromatic amide dendrimers incorporating a C-3-core have been prepared as potential catalysts for asymmetric reactions. (C) 2002 Elsevier Science Ltd. All rights reserved.

Chiral poly(aromatic amide ester) dendrimers bearing an amino acid derived C-3-symmetric core: synthesis and properties

The effect of hyperbranched macromolecular architectures (dendrimers) upon chirality has received significant attention in recent years in the light of the proposal of amplification of chirality. In particular, several studies have been carried out on the chiroptical properties of dendrimers that contain a chiral core and achiral branches in order to determine if the chirality of the central core can be transmitted to the distal. region of the macromolecule. In addition to interest of a pure academic nature, the presence of such chiral conformational order would be extremely useful in the development of asymmetric catalysts. In this paper, a novel class of chiral dendrimers is described - these perfect hyperbranched macromolecules have been prepared by a convergent route by the coupling of a chiral central core based upon tris(2-aminoethyl)amine and poly(aromatic amide ester) dendritic branches. The chiral properties of these dendrimers have been investigated by detailed optical rotation studies and circular dichroism analysis; the results of these studies are described herein. (C) Wiley-VCH Verlag GmbH Co.

Cylindrically symmetric flows in a Lagrangian frame

An approximate Riemann solver, in a Lagrangian frame of reference, is presented for the compressible flow equations with cylindrical and spherical symmetry, including flow in a duct of variable cross section. The scheme is applied to a cylindrically symmetric problem involving the interaction of shocks.