Sugli insiemi di permutazioni strettamente k-transitivi (k ≥ 3)

Summary Let G be a sharply 3-transitive permutation set on a finite set E of even cardinality and let 1 be in G. The following theorems are proved. G is one of the known examples if and only if there exists a non-identity normal subgroup N of G and an element of E such that NG G.G is a group if and only if G for every G and for every G and for every G .By using the classification of finite single groups a result concerning sharply k-transitive permutation sets k>3 is also proved.

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Dedicato a Guido Zappa in occasione del suo 70° compleanno

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Lavoro eseguito nell'ambito dei progetti finanziati dal Ministero della Pubblica Istruzione.     

Nickel-Ruthenium Mixed-Metal Carbonyl Clusters Syntheses and Solid State Structures of the Two Tetrahedral Clusters [PPh4][NiRu3(μ3 H)(CO)9(μ-CO)3] and [NEt4]2[NiRu3(CO)8(μ-CO)4]

Redox condensation of [Ru₃H(CO)₁₁]- with Ni(CO)₄, in tetrahydrofuran solution, under a nitrogen atmosphere, yields the tetranuclear anion [NiRu_H(CO)₁₁)-. Subsequent deprotonation with Bu'OK in acetonitrile solution leads to the formation of the related dianion. Both anions have been characterized by spectroscopic techniques, elemental analysis and single crystal X-ray diffraction. [PPh₄][NiRu₃H(CO)₁₂] crystallizes in the triclinic space group PI with unit cell dimensionsof a = 11.842(2) Å,b = 12.335(3) Å, c = 13.3080) Å,a = 91.89(2)°, = 93.35(1)°,y = 96.41(2)°, Z = 2, V= 1926.9(7) Å'. The NiRu₃, metal core of the molecule defines a distorted tetrahedron with nine terminal and three edge bridging carbonyl groups. The hydrido ligand was located by difference Fourier techniques and was found to bridge the NiRu₂ basal triangle at a distance of 0.88(6) A from this plane. Selected average distances and angles are: Ru-Ru = 2.839 Å, Ru-Ni = 2.640 Å, Ru-C, = 1.910 A,Ru-C _b = 2.084 Å, Ni-C _b = 2.022 Å, Ru-H = 1.77 Å, C-0, = 1.135 Å, C-O _b = 1.159 Å, M-C-O, = 176.3°,M-C--O _b = 139.3°;other distances are: Ni-C₁ = l.758(7) Å, Ni-H= 1.85(7) Å. [NEt₄]₂[NiRu₃(CO)₁₂] crystallizes in the orthorhombic space group Pnma (no. 62) with unit cell dimensions ofa=20.247(5) Å,b = 15.038(4)Å,c = 12.079(3) Å, Z=4, V=3678(2) A'. The molecule contains a tetrahedral NiRu₃ core with eight terminal and four edge bridging carbon monoxide groups which bridge the three Ni-Ru and one Ru-Ru bond. Average distances and angles are: Ru -Ru =2.3050A Ru-Ni 2.648 Å, Ru-C _t = 1.878 Å, Ru-C _b 2.045 Å, Ni-C _b = 2.055 Å, C-O _t = 1.145 Å, C-01,=1.157 Å, M-C-O,= 176.9°, M-C-O _b = 138.6°; other distance is: Ni-C _t = 1.754(10) Å,t = terminal,b = bridging.     

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.     

Effect of the addition of a nonionic surfactant on the complex poly(asparagine)--cationic surfactant

Poly(asparagine) (pAsn) at 0.1wt % in the presence of dodecyltrimethylammonium bromide (DTAB) and pentaoxyethylene octyl ether (C(8)E(5)) at 1:1 molar ratio leads to the formation of mixed DTAB/C(8)E(5) micelle-like aggregates onto the polypeptide as a total surfactant critical association concentration (cac) is reached, as revealed by surface tension measurements and NMR chemical shifts. Two-dimensional nuclear Overhauser enhancement spectroscopy (NOESY) capable of revealing spatial relationships among proximal protons has been performed on the pAsn-DTAB-C(8)E(5)-water system to study structural details of the surfactant-polypeptide aggregates. NOESY cross-peaks at sample temperature of 298.15 K indicate that the polypeptide interacts with the DTAB/C(8)E(5) micelle-like aggregates. The NOE intermolecular effects also show direct interactions between surfactant and polypeptide in the pAsn-DTAB-water system, whereas no interaction has been revealed in the pAsn-C(8)E(5)-water system. Furthermore, the experimental evidence suggest that the DTAB-polypeptide complex is mainly driven by the polar attraction between the two molecules.     

Thermodynamic and Dynamic Properties of Micellar Aggregates of Nonionic Surfactants with Short Hydrophobic Tails

The densities and viscosities of binary aqueous mixtures of poly(ethylenoxide)hexanols [C₆H₁₃(OCH₂CH₂)_mOH, C₆E_m] (m= 3, 4, and 5) have been studied in the micellar composition range. For the same surfactants the self-diffusion coefficients in mixtures with heavy water have been determined by the spin-echo pulsed field gradient method. The volumetric data are interpreted by means of the phase separation model, and values of the CMC, volume change, and standard free energy change of micellization are obtained. From the viscosity data the hydration numbers of the surfactant hydrophilic head in the micellar state are computed; they are in agreement with those obtained from HDO self-diffusion data. The surfactant self-diffusion data are used to calculate the apparent micelle radius and the aggregation number. The micellization parameters obtained for the different surfactants are compared and discussed.     

Rank-1 approximation to the van der Waals interaction

We present and discuss a variational single-product approximation to the van der Waals dispersion interaction leading to a simple formula for C ₆ that seems capable to give more than 99% of the ‘exact’ value. The formula is derived from Hylleraas’ variational principle in the tensor product space of the interacting molecules and therefore enjoys bounding properties. The formula has been tested by computing the C ₆ dispersion constants of H–H, and, at Full CI level, of the following systems: He–He, He–Li, Li–Li, LiH–LiH, HF–HF. Connections with the London formula are discussed. Contribution to the Fernando Bernardi Memorial Issue.     

Enzymes Hosted in Reverse Micelles in Hydrocarbon Solution

Reverse micelles are spheroidal aggregates formed by certain surfactants in apolar media. In contrast to normal micelles in water, the polar head groups of the surfactant molecules are directed towards the interior of the aggregate and form a polar core which can solubilize water (the “water pool”); the lipophilic chains are exposed to the solvent. The water of the water pool exhibits properties that (depending on the mole ratio of water to surfactant) differ from those of bulk water. Surprisingly, these reverse micelles are able to solubilize in hydrocarbon solvents hydrophilic molecules, e.g., enzymes and even plasmids, that are much larger than the original water-pool diameter. These biopolymer-containing reverse micelles can be viewed as novel microreactors, whose physical properties can be controlled through the water content. Remarkable is the ability of enzyme-containing micelles to react with water-insoluble, hydrocarbon-soluble substrates, as in the example of lipoxygenase with linoleic acid.     

Substituent-controlled photoisomerization in retinal chromophore models: Fluorinated and methoxy-substituted protonated Schiff bases

The effect of substitution on the intrinsic (i.e. in vacuo) photoisomerization ability of retinal chromophore models has been explored using CASPT2//CASSCF minimum energy path computations to map the S₁ photoisomerization paths of two substituted minimal models of the retinal chromophore: the 2-cis-penta-2,4-dieniminium and the all-trans-epta-2,4,6-trieniminium cations, which have been modified using fluorine or methoxyl substituents as representative examples of electron-withdrawing and electron-releasing groups, respectively. A systematic analysis has been performed involving substitutions in all the possible positions along the chain. It is shown that the photochemical reactivity and photoisomerization efficiency of these systems may be tuned or indeed changed, although this effect strongly depends on the position of the substituent. In particular, we have shown that (i) most of the systems preserves qualitatively the reactivity of the parent (i.e. unsubstituted) compound; (ii) substitution at positions C4 or C6 leads to a different relaxed excited state structure of the chromophore and in general to a very flat photoisomerization path (or to a tiny S₁ energy barrier in some cases); (iii) the nature of the TICT state (i.e. the S₁ → S₀ decay funnel) may be turned from a conical intersection into an excited state minimum; (iv) for the C4 methoxy-substituted system the isomerization path as well as the S₁/S₀ decay funnel involve an unusual torsional angle. Thus, substitution turns out to be a good tool not only to tune the optical properties (i.e. the absorption and emission features) of the chromophore (as we have already shown in a previous work: I. Conti, F. Bernardi, G. Orlandi, M. Garavelli, Mol. Phys. 104 (2006) 915–924), but it may also play a crucial role in tuning and controlling photoisomerization selectivity and efficiency, affecting excited state lifetime and reaction rate. A rationale for these effects is presented, which provides a basis for understanding reactivity properties and the intrinsic photochemical behavior of substituted retinal chromophores.     

A new class of C1-symmetric monosulfoximine ligands for enantioselective hetero Diels-Alder reactions

Quinoline-based C1-symmetric sulfoximines have been used as chiral ligands in copper-catalyzed asymmetric hetero Diels-Alder reactions leading to cycloadducts with up to 96% ee.