Conformal regularization of the Kepler Problem

The manifoldM of null rays through the origin of ^2,n+1 is diffeomorphic toS ¹×S ⁿ , and it is a homogeneous space of SO(2,n+1). This group therefore acts onT*M, which we show to be the generating manifold of the extended phase space of the regularized Kepler Problem. A local canonical chart inT*M is found such that the restriction to the subbundle of the null nonvanishing covectors is given byp ₀+H(q,p)=0, whereH(q,p) is the Hamiltonian of the Kepler Problem. By means of this construction, we get some results that clarify and complete the previous approaches to the problem.     

Conversion electron and X-ray Mössbauer studies of boronized low-carbon steel under corrosion and oxidation conditions

Iron-boride layers on low-carbon steel were produced by thermochemical diffusion process. The surface interaction products: Fe₂B, FeB, FeB_x (x>1) and a solid solution of iron in boron were identified by surface Mössbauer spectroscopy (CEMS and XMS). Samples of original and boronized steel were subjected to corrosion process by immersion in HCl (0.1 N) solution for 150 h. While the steel sample was strongly corroded, none corrosion product was found on the boronized sample surface. However, significant changes in relative percentages of the various iron boride phases were detected. Also, samples of original and boronized steel were subjected to oxidation process by heat-treatment in air at 300°C for 8 h and 500°C for 4 h. At 300°C, while bulk Fe₃O₄ and -Fe₂O₃ were formed on the steel surface, none iron oxide was detected on the boronized surface. At 500° C, while only pure bulk -Fe₂O₃ was detected on the steel surface, a particle size distribution of-Fe₂O₃, with particle size of about 100 Å, was probably formed on the boronized surface, as evidenced by CEMS.     

Monolayers as models for supported catalysts: zirconium phosphonate films containing manganese(III) porphyrins

Organized monolayer films of a manganese tetraphenylporphyrin have been prepared and used as supported oxidation catalysts. Manganese 5,10,15,20-tetrakis(tetrafluorophenyl-4'-octadecyloxyphosphonic acid) porphyrin (1) has been immobilized as a monolayer film by a combination of Langmuir-Blodgett (LB) and self-assembled monolayer techniques that use zirconium phosphonate linkages to bind the molecule to the surface. Analysis by FTIR, XPS, UV-vis and polarized optical spectroscopy show that the films consist of noninteracting molecules effectively anchored and oriented nearly parallel to the surface. The monolayer films are stable to the solvent and temperature conditions needed to explore organic oxidations. The activity of films of 1 toward the epoxidation of cyclooctene using iodosylbenzene as the oxidant was compared to that of Manganese 5,10,15,20-tetrakis(pentafluorophenyl) porphyrin (2) and 1 under equivalent homogeneous conditions. The immobilized porphyrin 1 shows an enhanced activity relative to either homogeneous reaction. The main difference between 1 and 2 is the four alkyl phosphonate arms in 1 designed to incorporate the porphyrin within the films. The increased activity of immobilized 1 is a combination of the porphyrin structure, which prohibits the formation of mu-oxo dimers even in solution, and a change in conformation when anchored to the surface. The study demonstrates that careful monolayer studies can provide useful models for the design and study of supported molecular catalyst systems.     

Electrochemical Synthesis of MII Complexes with a Schiff Base containing an Amido Group. Crystal Structure of a Cobalt(II) Complex with a Reorganised Ligand

M(HL)(H₂O)_n complexes have been obtained by the electrochemical reaction of Fe, Co, Ni, Cu, Zn and Cd anodes with the potentially pentadentate and trianionic asymmetrical Schiff base 3‐aza‐N‐{2‐[1‐aza‐2‐(5‐nitro‐2‐hydroxylphenyl)‐vinyl]phenyl}‐4‐(5‐nitro‐2‐hydroxyphenyl)but‐3‐enamide (H₃L), containing a hard amido donor atom. The complexes have been characterized by elemental analysis, mass spectrometry, IR and ¹H NMR spectroscopies, magnetic measurements and molar conductivities. Co(HL)(H₂O) ( 2 ) has been found to rearrange in DMF solution into a crystallographically solved octahedral complex, CoL¹(H₂O)₂ ( 7 ) [where H₂L¹ is the symmetrical Schiff base ligand N,N′‐(1,2‐phenylene)‐bis(5‐nitro‐3‐hydroxysalicylidenimine)]. A hydrolysis mechanism is discussed to explain this rearrangement.     

Polymer-supported O-alkylisoureas: useful reagents for the O-alkylation of carboxylic acids

Polymer-supported O-alkylisoureas were prepared by reaction of an alcohol with a polymer-supported carbodiimide under copper(II) catalysis. These reagents were used to transform carboxylic acids into the corresponding methyl, benzyl, allyl, and p-nitrobenzyl esters in a highly chemoselective manner in high yields and in very high purity after simple resin filtration and solvent evaporation. The reactions could be carried out using both conventional or microwave heating, with reaction times as short as 3-5 min in the latter case, without compromising yield, purity, or chemoselectivity. Unfortunately, the corresponding solid-supported tert-butyl isoureas could not be prepared.     

Matrix elements of the Coulomb Green function between Slater orbitals

Analytic expressions are given for integrals of the Coulomb Green function with Slater type atomic orbitals. The results involve hypergeometric functions.Supported by the National Institutes of Health, Grant No. GM23223.     

Electrochemical investigations of cationictrans-haloarylisocyanidebis(tertiaryphosphino)platinum (II) complexes

Summary The electrochemical behaviour of a series of cationic platinum(II) isocyanide complexes has been studied in acetonitrile. All the tested compounds are oxidized at a platinum electrode via a two-electron process and reduced at a platinum or mercury electrode via two successive one-electron steps. The anodic step involves the formation of platinum(IV) complexes. The main reduction product formed in correspondence to the first cathodic process is a stable dimer platinum(I) containing bridging isocyanide ligands. Platinum(0) species are formed in the subsequent reduction step.     

The replacement of five-membered N-donor heterocycles from aminotrichlorogold(III) complexes. A comparison with pyridines

The kinetics of the process AuCl₃(nu) + Cl⁻→ AuCl ₄ ⁻ + nu (nu = one of a number of five-membered N-donor heterocycles covering a wide range of basicity, namely: oxazole, 2,4,5-trimethyloxazole, thiazole, 5-methylthiazole, 4-methylthiazole, 4,5-dimethylthiazole, 2,4-dimethylthiazole, 2,4,5-trimethylthiazole, imidazole and 2-methylimidazole) have been studied in methanol at 25 °C. The reactions follow the usual two-term rate law, rate = (k ₁ + k ₂[Cl⁻])[complex], observed in a square-planar substitution associative-mechanism. The second-order rate constants, k ₂, indicate that the discriminating ability of Au^(III) in these complexes is good and markedly influenced by the nature of the leaving group. A linear-free-energy relationship, logk ₂ = 0.53pK _a + constant, is observed between the rate constant and the basicity of the leaving group for its replacement by chloride. The results are compared with data from the literature regarding a series of complexes of the type AuCl₃(py) (py = one of a number of pyridines) reacting with the Cl⁻ anion under the same experimental conditions. The reactivity depends not only upon ligand basicity but also upon the nature of the ligand in the order: pyridines> five-membered heterocycles. Steric factor due to the presence of a single methyl group ortho to the sp² nitrogen atom in the ring has no influence on the rate of substitution while, surprisingly, when there are two ortho methyl groups a remarkable steric retardation effect is observable. The results are discussed in terms of reaction-profile in the associative-substitution reaction and bonding interactions in the ground and transition states.     

Anionic copper complex fragmentations from enkephalins under low-energy collision-induced dissociation in an ion trap mass spectrometer

Peptide metallation with Cu2+ was explored in the negative ESI mode using an ion trap mass spectrometer. Under these conditions, the [(M-3H) + CuII]- species formed were investigated under low-energy collision-induced dissociation conditions. MS2 experiments indicate a very different behavior of CuII metallated complexes compared with [M-H]- species. CuII induces an easy loss of CO2 and specific side-chain cleavages (by radical losses) at the C-terminal residue, as observed previously by prompt 'in source' dissociation experiments. The loss of CO2 yields an unstable carbylide that leads to further dissociations involving the migration of a proton or a hydrogen radical (through the reduction of CuII). Multistage MS3 experiments were carried out to rationalize this behavior. Fragmentation pathways are proposed in order to explain the product ions observed. The side-chain radical loss at the C-terminus was demonstrated to be a consecutive process. Finally, evidence is provided that the specific side-chain cleavages can be used for the differentiation of Leu/Ile and Gln/Lys residues when they are located at the C-terminus. The existence of a zwitterionic form in the case of the anionic YGGFK-CuII complex is proposed.     

A thermodynamic analysis on the coincidence of extrema conditions in the sorption equilibrium for ternary polymer systems

Flory-Huggins theory of polymer solutions has been used to express the condition of extrema values in the total sorption, as well as the inversion point in the preferential adsorption parameters for termary polymer systems. Two approaches have been followed, the first considers the binary and ternary interaction parameters independent of polymer concentration and solvent composition. In the second one, this dependence has been introduced. Our attention is focused on the volume fraction of solvent mixture dependence of the above parameters, in order to confirm or not the coincidence between the extrema values and the inversion point. Several cosolvent and cononsolvent ternary polymer systems, have been used to test the validity of the equations obtained. Also, it has been verified, from an experimental point of view, that in cosolvent ternary polymer systems there is coincidence in both compositions while in cononsolvent ternary polymer systems, such coincidence does not appear.