Vibrational spectroscopic studies and DFT calculations on tribromoacetate and tribromoacetic acid in aqueous solution

Aqueous solutions of sodium tribromoacetate (NaCBr3CO2) and its corresponding acid (CBr3COOH) have been studied using Raman and infrared spectroscopy. The spectra of the species in solution were assigned according to symmetry Cs. Characteristic bands of CBr3CO2-(aq) and the tribromoacetic acid, CBr3COOH(aq), are discussed. For the hydrated anion, the CO2 group, the symmetric CO2 stretching mode at 1332 cm(-1) and the asymmetric stretching mode at 1651 cm(-1) are characteristic while the CO mode at 1730 cm(-1) is characteristic for the spectra of the acid. The stretching mode, νC-C at 912cm(-1) for CBr3CO2-(aq) is 10 cm(-1) lower in the anion compared with that of the acid. These characteristic modes are compared to those in acetate, CH3CO2-(aq). Coupling of the modes are fairly extensive and therefore DFT calculations have been carried out in order to compare the measured spectra with the calculated ones. The geometrical parameters such as bond length and bond angles of the tribromoacetate, and tribromoacetic acid have been obtained and may be compared with the ones published for other acetates and their conjugated acids. CBr3COOH(aq) is a moderately strong acid and the pKa value derived from quantitative Raman measurements is equal to -0.23 at 23°C. The deuterated acid CBr3COOD in heavy water has been measured as well and the assignments were given.     

First fluorescence spectroscopic investigation of Am(III) complexation with an organic carboxylic ligand, pyromellitic acid

For the first time Am(III) complexation with a small organic ligand could be identified and characterized with time-resolved laser-induced fluorescence spectroscopy (TRLFS) at room temperature and trace metal concentration. With pyromellitic acid (1,2,4,5-benzene-tetracarboxylic acid, BTC) as ligand spectroscopic characteristics for the Am-BTC complex system were determined at pH 5.0, an ionic strength of 0.1 M (NaClO4) and room temperature. The fluorescence lifetimes were determined to be 23.2±2.2 ns for Am3+(aq) and 27.2±1.2 ns for the Am-BTC 1:1 complex; the emission maximum for the 5D1-(7)F1 transition is 691 nm for both species. The complex stability constant for the Am-BTC 1:1 complex was calculated to be logβ110=5.42±0.16.     

Approximation by Conic Splines

We show that the complexity of a parabolic or conic spline approximating a sufficiently smooth curve with non-vanishing curvature to within Hausdorff distance ɛ is c ₁ɛ^−1/4 + O(1), if the spline consists of parabolic arcs, and c ₂ɛ^−1/5 + O(1), if it is composed of general conic arcs of varying type. The constants c ₁ and c ₂ are expressed in the Euclidean and affine curvature of the curve. We also show that the Hausdorff distance between a curve and an optimal conic arc tangent at its endpoints is increasing with its arc length, provided the affine curvature along the arc is monotone. This property yields a simple bisection algorithm for the computation of an optimal parabolic or conic spline. The research of SG and GV was partially supported by grant 6413 of the European Commission to the IST-2002 FET-Open project Algorithms for Complex Shapes in the Sixth Framework Program.     

Interior barriers and dimer nucleation on islands

On (1 1 1) islands of platinum as well as iridium self-adsorbed on (1 1 1) planes, it is now established that there are interior barriers impeding the movement of adatoms from the inner region to the steps of the island. We have carried out Monte Carlo simulations of adatoms migrating on such islands to establish the effect of interior barriers on the rate at which adsorbed atoms nucleate to form dimers rather than incorporate into the steps of the island. It is found that interior barriers significantly increase the rate at which dimers are created by collisions of two adatoms, and that the presence of additional step-edge barriers further raises the rate of dimer nucleation.     

Balinski—Tucker simplex tableaus: Dimensions, degeneracy degrees, and interior points of optimal faces

This paper shows the relationship between degeneracy degrees and multiple solutions in linear programming (LP) models. The usual definition of degeneracy is restricted to vertices of a polyhedron. We introduce degeneracy for nonempty subsets of polyhedra and show that for LP-models for which the feasible region contains at least one vertex it holds that the dimension of the optimal face is equal to the degeneracy degree of the optimal face of the corresponding dual model. This result is obtained by means of the so-called Balinski—Tucker (B—T) Simplex Tableaus. Furthermore, we give a strong polynomial algorithm for constructing such a B—T Simplex Tableau when a solution in the relative interior of the optimal face is known. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.     

Isotopic Implicit Surface Meshing

This paper addresses the problem of piecewise linear approximation of implicit surfaces. We first give a criterion ensuring that the zero-set of a smooth function and the one of a piecewise linear approximation of it are isotopic. Then, we deduce from this criterion an implicit surface meshing algorithm certifying that the output mesh is isotopic to the actual implicit surface. This is the first algorithm achieving this goal in a provably correct way.     

Semi-classical calculations of rotational/vibrational transitions in Li+ − H2

Some semi-classical calculations of rot/vib transitions in Li⁺ ? H₂ at 0.869, 1.469 and 3.919 eV total energy are presented. Comparison with recent quantum mechanical and classical S-matrix calculations is made.     

Semiclassical calculation of VV and VT rate coeffecients in CO

We have calculated 66 rate constants for vibration-vibration (V-V) and vibration-translation/rotation (V-T/R) energy transfer in CO by using a semiclassical collision model. Extensive comparison with experimental data and more approximate theoretical predictions is carried out.