Victor M. S. Gil

Relativistic particle in a box

The problem of a relativistic spin 1/2 particle confined to a one-dimensional box is solved in a way that resembles closely the solution of the well known quantum-mechanical textbook problem of a non-relativistic particle in a box. The energy levels and probability density are computed and compared with the non-relativistic case. Resumo. O problema de uma particula de spin 1/2 confinada por uma caixa a uma dimensao e resolvido de uma maneira muito semelhante a da resolucao do problema de uma particula no-relativista numa caixa referido em muitos livros introdutorios de Mecânica Quntâica. Os niveis de energia e a densidade de probabilidade sao calculados e comparados com os valores nao-relativistas.

The conformation of benzalanilines studied by NMR

Abstract Proton chemical shifts for benzalaniline and some p , p ′-derivatives in dilute solutions in cyclohexane were obtained and compared with those for the corresponding parent benzaldehydes and anilines. Discussion of these chemical shifts showed that there is rapid rotation of the phenyl rings about the CC and CN bonds at room temperature, and provided evidence of the averaged (effective) dihedral angles between the HCN nuclear plane and the ring planes; in particular, this was shown to be 45° at most for the aniline ring. Solvent effects, especially the effect of protonation, are also briefly investigated.

NMR Study of uronic acids and their complexation with molybdenum(VI) and tungsten(VI) oxoions

Abstract A multinuclear 1D and 2D NMR study of d -galacturonic and d -glucuronic acids in aqueous solution and their complexation with tungstate and molybdate ions for variable concentration and pH conditions has been undertaken. The acids exist mainly in the pyranose forms, but complexes were detected involving the less stable α- and β-furanose anomers as well as the α-pyranose form. Thus, NMR evidence was gathered for the formation of two 1:2 (metal-ligand) complexes of W(VI) with the furanose forms. These are stronger with d -galacturonic acid and when the β forms are involved. The same was found with Mo(VI), but, in addition, 2:1 complexes also form. In the case of d -galacturonic acid, three such complexes were detected, two involving the α-pyranose form, in an approximately 4 C 1 , and a 1 C 4 conformation, respectively, and the other presumably involving the β-furanose isomer. With d -glucuronic acid, only one such complex could be characterized, involving the α-pyranose isomer in a distorted 1 C 4 conformation. More detailed information on the structure of the various complexes was obtained from 1 H, 13 C, 17 O, 95 Mo, and 183 W NMR data. The 2:1 complexes with the α-pyranose forms, insofar as they involve metal binding to the ring oxygen atom, are considered to play an important role in the oxidation of the acids especially by Mo(VI).

New NMR evidence on the uranylcitrate complexes

Abstract A 1 H and 13 C NMR study of the complexation of citric acid to uranyl ion is reported over a wide pH range (1.3–10.3). At least six complexes are formed. Structures are proposed for four of them; in particular one of the complexes dominant at high pH values seems to be a cyclic trimer (3:2).

Complexes of Mo(VI) with lactic, thiolactic and thiomalic acids studied by NMR spectroscopy

Proton and 13C evidence is presented on the number, stoichiometry, geometry and relative stability of the complexes formed in the systems Mo(VI) + L-lactic acid, Mo(VI) + D,L-thiolactic acid and Mo(VI) + D,L-thiomalic acid in aqueous solutions at pH values in the range 3–8. In particular, 1:2 complexes are always formed and, in addition, complexes of higher metal content are detected in the case of thiolactic and thiomalic acids.

Peroxovanadium(V) complexes of glycolic acid as studied by NMR spectroscopy

Multinuclear ( 1 H, 13 C, 17 O, 51 V) 1D and 2D NMR spectroscopy has been used to characterize the peroxovanadium(V) complexes of glycolic acid in aqueous solution. One 2:2:2 (metal:ligand:peroxo) complex, together with a 1:1:1 and a 2:2:1 species, are found in the pH range 1‐7. The 2:2:2 complex is a monoperoxo (one peroxide unit per vanadium atom) dinuclear species having a V2O3 4 seven-coordinated metal centre. In this structure, the two vanadium atoms are triple bridged, two of those bridges being formed by oxygen atoms of the hydroxyl group of the acid. The 1:1:1 species has a seven-coordinated VO 3 metal centre. Glycolic acid bonds to the vanadium atoms in a bidentate way, through both the carboxylic and the hydroxyl groups. The peroxo groups are bound in the equatorial plane relative to the apical VO and the geometry around each vanadium atom is close to pentagonal bipyramidal. The 2:2:1 complex is similar to the 2:2:2 species, except for one of the vanadium centres, which is now a five-coordinated oxovanadium centre. Three additional complexes are found in very small amounts for some pH and concentration conditions. Further support for the proposal of monoperoxovanadium species is given by UV‐visible spectroscopy results.

MULTINUCLEAR NMR STUDY OF THE COMPLEXATION OF D-GLUCARIC ACID WITH MOLYBDENUM(VI) AND TUNGSTEN(VI)

Abstract Proton and 13 C NMR spectra of aqueous solutions of sodium molybdate and D -glucaric acid for variable molar ratios and pH values (range 1–9) clearly show the existence of five complexes dominating for specific concentration and pH conditions: a 2:1 metal to ligand complex, a , dominant at low pH (pH ≈ 2) for dilute solutions; two other complexes, b and c , which seem to have 2:2 and 1:1 composition, respectively, and which dominate at low pH for higher concentrations; another 2:1 complex, d , formed at intermediate pH (pH ≈ 4.5–6); still another 2:1 complex, e , formed at higher pH (pH ≈ 6–8.5). From the 1 H and 13 C chemical shifts observed on complexation, the binding sites of D -glucaric acid to the metal are established. From the proton-proton coupling constants the approximate conformation of the bound ligand is determined. The structures proposed on this basis are partially supported by 95 Mo chemical shifts, and the structure changes for the 2:1 complexation with pH are rationalized. Similar results are expected with W(VI) but due to close chemical shifts and exchange phenomena, only a 2:1 complex at low pH is adequately characterized.

MULTINUCLEAR NMR STUDY OF COMPLEXATION OF D-GALACTARIC AND D-MANNARIC ACIDS WITH TUNGSTEN(VI) OXOIONS

Abstract The coordination compounds formed between W(VI) and D-galactaric and D-mannaric acids, in aqueous solution, have been studied by 1H, 13C, 17O and 183W NMR spectroscopy. In the pH range 3–8 for D-galactaric acid and 2–10 for D-mannaric acid, the acids are found to form n:n species (mainly 2:2) with tungstate, in which the ligands are bound to the metal by the two carboxylate groups and their adjacent OH groups. Above pH 6.5, a 2:1 species is also formed, in which all the OH functions are coordinated to the metal, the two carboxylate groups remaining free. The formation of symmetrical or asymmetrical species is discussed, taking into account the configuration of the ligands. Structures for the various complexes are formulated.

Density functional theory study of the oxoperoxo vanadium(V) complexes of glycolic acid. Structural correlations with NMR chemical shifts

The DFT B3LYP/SBKJC method has been used to calculate the gas-phase optimized geometries of the glycolate oxoperoxo vanadium(V) complexes [V(2)O(2)(OO)(2)(gly)(2)](2-), [V(2)O(3)(OO)(gly)(2)](2-) and [VO(OO)(gly)(H(2)O)](-). The (51)V, (17)O, (13)C and (1)H chemical shifts have been calculated for the theoretical geometries in all-electron DFT calculations at the UDFT-IGLO-PW91 level and have been subsequently compared with the experimental chemical shifts in solution. In spite of being applied to the isolated molecules, the calculations allowed satisfactory reproduction of the multinuclear NMR solution chemical shifts of the complexes, suggesting that the theoretical structures are probably close to those in solution. The effects of structural changes on the (51)V and (17)O NMR chemical shifts have been analysed using the referred computational methodologies for one of the glycolate complexes and for several small molecules taken as models. These calculations showed that structural modifications far from the metal nucleus do not significantly affect the metal chemical shift. This finding explains why it is possible to establish reference scales that correlate the type of complex (type of metal centre associated with a certain type of ligand) with its typical region of metal chemical shifts. It has also been found that the V[double bond, length as m-dash]O bond length is the dominant geometrical parameter determining both delta(51)V and the oxo delta(17)O in this kind of complex.

Oxoperoxo vanadium(V) complexes of L-lactic acid: density functional theory study of structure and NMR chemical shifts.

Various combinations of density functionals and pseudopotentials with associated valence basis-sets are compared for reproducing the known solid-state structure of [V 2O 2(OO) 2 l-lact 2] (2-) cis . Gas-phase optimizations at the B3LYP/SBKJC level have been found to provide a structure that is close to that seen in the solid state by X-ray diffraction. Although this may result in part from error compensation, this optimized structure allowed satisfactory reproduction of solution multinuclear NMR chemical shifts of the complex in all-electron DFT-IGLO calculations (UDFT-IGLO-PW91 level), suggesting that it is probably close to that found in solution. This combination of approaches has subsequently been used to optimize the structures of the vanadium oxoperoxo complexes [V 2O 3(OO) l-lact 2] (2-) cis , [V 2O 3(OO) l-lact 2] (2-) trans , and [VO(OO)( l-lact)(H 2O)] (-) cis . The (1)H, (13)C, (51)V, and (17)O NMR chemical shifts for these complexes have been calculated and compared with the experimental solution chemical shifts. Excellent agreement is seen with the (13)C chemical shifts, while somewhat inferior agreement is found for (1)H shifts. The (51)V and (17)O chemical shifts of the dioxo vanadium centers are well reproduced, with differences between theoretical and experimental shifts ranging from 22.9 to 35.6 ppm and from 25.1 to 43.7 ppm, respectively. Inferior agreement is found for oxoperoxo vanadium centers, with differences varying from 137.3 to 175.0 ppm for (51)V shifts and from 148.7 to 167.0 ppm for (17)O(oxo) shifts. The larger errors are likely to be due to overestimated peroxo O-O distances. The chosen methodology is able to predict and analyze a number of interesting structural features for vanadium(V) oxoperoxocomplexes of alpha-hydroxycarboxylic acids.