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.     

Amphiphilic cyclodextrin carriers embedding porphyrins: charge and size modulation of colloidal stability in heterotopic aggregates

The interaction between the anionic 5,10,15,20-tetrakis(4-sulfonatophenyl)-21H,23H-porphyrin (TPPS) and cationic vesicles formed by heptakis(2-omega-amino-O-oligo(ethylene oxide)-6-hexylthio)-beta-cyclodextrin (SC6CDNH2) has been investigated in detail through a combination of elastic light scattering (ELS), quasi-elastic light scattering (QELS), zeta potential measurements, and time-resolved fluorescence anisotropy. ELS experiments provided the first structural characterization of these cationic vesicles both in the absence and in the presence of TPPS porphyrin, modeling the system as a spherical particle described by a single thin shell form factor. The structure of mixed hetero-aggregates is modulated by charge and size of the two components as function of different porphyrin/cyclodextrin (CD) molar ratios. At the limiting molar ratio studied, the absolute value of zeta potential (/zeta/ = 12.5 mV) seems to be a reference value for the formation of stable colloidal CD vesicular aggregates at thermodynamic equilibrium. New insights on the structure of these heterotopic colloids have been obtained by analysis of rotational correlation times at different molar ratios exploiting time-resolved fluorescence anisotropy experiments. At high porphyrin loads, the anisotropy decays behave as monoexponentials and the rotational correlation times (1-2 ns) together with the r(0) values close to zero suggest the presence of small amounts of TPPS embedded in a hydrophobic environment either in monomeric or in aggregated form. At the lower porphyrin/CD molar ratios, the anisotropy decays exhibit a double-exponential behavior showing a predominant component with a slow rotational correlation time (20-25 ns) and limiting anisotropy values of approximately 0.15. This component has been assigned to molecules that are more stabilized onto the CD vesicles, that is, porphyrins embedded into the oligo-ethylene "wall" of the CD vesicles. Scanning near-field optical microscopy of the samples evaporated on glass surfaces gave further insights on the morphology and optical properties of these systems, confirming the embedding of TPPS on the vesicles and evidencing the role of the solvent.     

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 boxmodel development to study the relationships between the photo-oxidants and the particles formation in the troposphere

The model BAGS (Boxmodel for Aerosol and Gasphase Simulations) has been developed. It is composed of two major modules: the first one describes the system of the chemical reactions in the gaseous phase, the second one calculates the aerosol chemical composition and the dimensional distribution of the particles. The boxmodel has been developed with the introduction of new chemical and physical processes, not previously included, in particular the formation of Secondary Organic Aerosol. The other implemented processes are a module for the dynamic of the particle population, nucleation, coagulation and dry deposition. The last phase of the work has been a check of the BAGS capabilities by a series of tests, that have permitted to compare it with other models (MAPS and MADM). The tests in particular have concerned the aerosol water content prediction, the photochemistry, the condensation of the inorganic compounds and the formation of Secondary Organic Aerosol.