Fourier transform infrared and Raman spectra, and AB initio calculations for cadmium(II)-cysteinate glycinate complex [Cd(Cys)(Gly)

The cysteinate glycinate cadmium(II) complex was synthesized and structural analysis was carried out using the following methods: determination of the C, H, N, S and O contents, thermogravimetry, infrared and Raman spectra. The most probable structure for the complex at a minimum of energy was calculated by the density functional theory (DFT):B3LYP/3-21G quantum mechanical method. The infrared and Raman spectra were analyzed and bands assigned through the DFT procedures, the stabilization energy being equal to: E(RB+HF-LYP)= -6442.67784a.u. Features of the infrared and Raman spectra confirm theoretical structural prediction with respect to the metal-ligand bonds: Cd-O, Cd-S and Cd-N. Full assignment of the vibrational spectra was also supported by a carefully analysis of the distorted geometries generated by the normal modes.     

Best Constants in Sobolev Inequalities on Riemannian Manifolds in the Presence of Symmetries

Let (M,g) be a smooth compact Riemannian manifold, and G a subgroup of the isometry group of (M,g). We compute the value of the best constant in Sobolev inequalities when the functions are G-invariant. Applications to non-linear PDEs of critical or upper critical Sobolev exponent are also presented.     

Optimal constants in the exceptional case of Sobolev inequalities on Riemannian manifolds

Let be a Riemannian compact -manifold. We know that for any , there exists such that for any , , being the smallest constant possible such that the inequality remains true for any . We call the ``first best constant'. We prove in this paper that it is possible to choose and keep a finite constant. In other words we prove the existence of a ``second best constant' in the exceptional case of Sobolev inequalities on compact Riemannian manifolds.

     

Optimal Constants in Critical Sobolev Inequalities on Riemannian Manifolds in the Presence of Symmetries

We prove a theorem on the existence of a `second best constant' incritical Sobolev inequalities on compact Riemannian manifolds underthe action of an isometry group. The theorem is then applied toseveral examples initially introduced by different authors.     

Fourier-transform infrared and Raman spectra of cysteine dichloride cadmium(II) anion DFT: B3LYP/3-21G(d) structural and vibrational calculations

The cysteine dichloride cadmium(II) potassium was synthesized and the structural analysis was carried out through the following methods: determination of the C, H, N, S and O contents, thermogravimetry, infrared and Raman spectra. Assuming Cd-S, Cd-O (O-carboxilate) and Cd-N bonds, several hypothetical structures were calculated by means DFT: B3LYP/3-21G(d) quantum mechanical method. The calculations shows that the Cd-S and Cd-N central bonds are favoured in the anion complex formation [Cd(Cys)Cl2]-, being the stabilization energy 55.52 kcal mol(-1) lower than isotopomers with Cd-S and Cd-O central bonds. Features of the infrared and Raman spectra confirm the theoretical structural prediction. Full assignment of the vibrational spectra is proposed based on the DFT procedure, and in order to confirm the C-H, N-H, C-C, C-N, Cd-N, Cd-S and Cd-Cl stretching and the HNH and HCH bending, a normal coordinate analysis based on local symmetry force field for -SC(H2)C-, -CdN(H2)C- and -SCd(Cl2)N- fragments was carried out.     

Best constants in the exceptional case of Sobolev inequalities

We prove the existence of a second best constant in the exceptional case of Sobolev inequalities on a compact Riemannian n-manifold locally conformally flat.