Synthesis, characterisation and molecular structure of Re(III) 2-oxacyclocarbenes stabilised by a benzoyldiazenido ligand

A family of new Fischer-type rhenium(III) benzoyldiazenido-2-oxacyclocarbenes of formula [(ReCl2[eta1-N2C(O)Ph][=C(CH2)nCH(R)O](PPh3)2][n = 2, R = H (2), R = Me (3); n = 3, R = H (4), R = Me (5)] have been prepared by reaction of [ReCl2[eta2-N2C(Ph)O](PPh3)2] (1) with omega-alkynols, such as 3-butyn-1-ol, 4-pentyn-1-ol, 4-pentyn-2-ol, 5-hexyn-2-ol in refluxing THF. The correct formulation of the carbene derivatives 2-5 has been unambiguously determined in solution by NMR analysis and confirmed for compounds 2-4 by X-ray diffraction methods in the solid state. All complexes are octahedral with the benzoyldiazenido ligand, Re[N2C(O)Ph], adopting a "single bent" conformation. The coordination basal plane is completed by an oxacyclocarbene ligand and two chlorine atoms. Two triphenylphosphines in trans positions with respect to each other complete the octahedral geometry around rhenium. The reactivity of 1 towards different alkynes and alkenes including propargyl- and allylamine has been also studied. With propargyl amine, monosubstituted or bisubstituted complexes, [(ReCl2[eta1-N2C(O)Ph][eta1-NH2CH2C triple bond CH]n(PPh3)(3-n)][n= 1 (6); n = 2 (7)], have been isolated depending on the reaction conditions. In contrast, the reaction with allylamine gave only the disubstituted complex [(ReCl2[eta1-N2C(O)Ph][eta1-NH2CH2CH=CH2]2(PPh3)] (8). The molecular structure of the monosubstituted adduct has been confirmed by X-ray analysis in the solid state.     

X-ray crystal structures of two polymorphic forms,monoclinic and triclinic,of: 1-[(<Emphasis Type="Italic">E</Emphasis>)-2-(4-bromophenyl)1-diazenyl]-3-({3-[(<Emphasis Type="Italic">E</Emphasis>)-2-(4-bromophenyl)-1-diazenyl]-6-ethylhexahydro-1-pyrimidinyl}methyl)-4-ethylhexahydropyrimidine

1-[(E)-2-(4-bromophenyl)-1-diazenyl]-3-({3-[(E)-2-(4-bromophenyl)-1-diazenyl]-6-ethylhexahydro-1-pyrimidinyl}methyl)-4-ethylhexahydropyrimidine (1) has been synthesized by reaction of a mixture of formaldehyde and 1,3-pentanediamine{DYTEK^®EPdiamine} with p-bromobenzenediazonium chloride. This compound crystallizes in two polymorphic forms 1-α and 1-β whose crystal structures have been determined by single crystal X-ray diffraction analysis. Both polymorphs 1-α and 1-β display crystallographic disorder within the hexahydropyrimidine rings. The molecule of 1 is built up of two equivalent 3-(aryldiazenyl)-6-ethylhexahydro-1-pyrimidinyl groups in the s-trans orientation around the central methylene group (C13). In both structures the triazene moieties adopt the anti configuration around the N=N bonds, displaying significant π-conjugation. The crystal packings are determined only by van der Waals interactions. The crystal structures of 1-α and 1-β are compared with the previously reported structure of the 5,5-dimethylhexahydropyrimidine analogue 3. Compounds 1 and 3 are isomeric with respect to the hexahydropyrimidine moiety. The structures of 1 and 3 are very different in one respect; in 1 the aryldiazenyl-hexahydropyrimidinyl groups are in the s-trans orientation around the central methylene group, whereas in 3 the arrangement of the aryldiazenylhexahydropyrimidinyl groups is the s-cis orientation. Crystal data: 1-α C₂₅H₃₄N₈Br₂, monoclinic, space group P2(1)/c, a = 9.2150(3), b = 19.4059(6), c = 15.4324(5) Å, β = 98.738(1)^°, V = 2727.7(2) ų, for Z = 4; 1-β C₂₅H₃₄N₈Br₂, triclinic, space group P-1, a = 9.6009(3), b = 10.7509(4), c = 14.2169(5) Å, α = 99.830(2), β = 105.973(3), γ = 95.578(1)^°, V = 1373.9(1) ų, for Z = 2.     

Thermoluminescence mechanism of Mn, Mg and Sr doped calcite

In this work, the thermoluminescence properties of synthetic crystals of doped calcite were studied. Samples were doped with Mn²⁺, Mg²⁺ or Sr²⁺, either individually or simultaneously with more than one of these impurities. TL glow curves, partial heating measurements, isometric curves, emission spectra and thermal treatment were performed, in order to investigate the role played by the impurities in the TL glow peaks of calcite. We conclude that the crystals doped with Mn²⁺ show five TL peaks with emission spectra due only to the Mn²⁺. The relative intensity of these peaks is closely related to the other divalent dopant added in the solution (Sr²⁺ or Mg²⁺). These results suggest that although Sr²⁺ and Mg²⁺ act as TL activators stabilising slightly different electron traps, they are not directly connected to the Mn²⁺ luminescence centre.     

Linear response theory of the dipole–dipole dispersion interaction between H(1s) atoms

A self-consistent theory of the linear response previously developed by one of us is applied to the dipole–dipole dispersion interaction of two ground state H atoms in the united atom (He) limit, using a Sellmeier representation of the polarizability in terms of pseudostates. Numerical calculations show that a truncated 12-term expansion out of the N = 22 H(1s) dipole pseudospectrum built from STOs with orbital exponent c = 0.985 gives a result exceeding by no more than 5% the variational result for the He dispersion energy.     

Parametric smoothness and self-scaling of the statistical properties of a minimal climate model: What beyond the mean field theories?

A quasi-geostrophic intermediate complexity model of the mid-latitude atmospheric circulation is considered, featuring simplified baroclinic conversion and barotropic convergence processes. The model undergoes baroclinic forcing towards a given latitudinal temperature profile controlled by the forced equator-to-pole temperature difference T_E. As T_E increases, a transition takes place from a stationary regime-Hadley equilibrium-to a periodic regime, and eventually to a chaotic regime where evolution takes place on a strange attractor. The attractor dimension, metric entropy, and bounding box volume in phase space have a smooth dependence on T_E, which results in power-law scaling properties. Power-law scalings with respect to T_E are detected also for the statistical properties of global physical observables — the total energy of the system and the averaged zonal wind. The scaling laws, which constitute the main novel result of the present work, can be thought to result from the presence of a statistical process of baroclinic adjustment, which tends to decrease the equator-to-pole temperature difference and determines the properties of the attractor of the system. The self-similarity could be of great help in setting up a theory for the overall statistical properties of the general circulation of the atmosphere and in guiding-on a heuristic basis-both data analysis and realistic simulations, going beyond the unsatisfactory mean field theories and brute force approaches. A leading example for this would be the possibility of estimating the sensitivity of the output of the system with respect to changes in the parameters.     

Quantum cryptography protocols robust against photon number splitting attacks for weak laser pulse implementations

We introduce a new class of quantum key distribution protocols, tailored to be robust against photon number splitting (PNS) attacks. We study one of these protocols, which differs from the original protocol by Bennett and Brassard (BB84) only in the classical sifting procedure. This protocol is provably better than BB84 against PNS attacks at zero error.     

Parameter-free calculation of response functions in time-dependent density-functional theory

We have established and implemented a fully ab initio method which allows one to calculate optical absorption spectra, including excitonic effects, without solving the cumbersome Bethe-Salpeter equation, but obtaining results of the same precision. This breakthrough has been achieved in the framework of time-dependent density-functional theory, using new exchange-correlation kernels f(xc) that are free of any empirical parameter. We show that the same excitonic effects in the optical spectra can be reproduced through different f(xc)'s, ranging from frequency-dependent ones to a static one, by varying the kernel's spatial degrees of freedom. This indicates that the key quantity is not f(xc), but f(xc) combined with a response function. We present results for the optical absorption of bulk Si and SiC in good agreement with experiment, almost indistinguishable from those of the Bethe-Salpeter approach.     

Singly Periodic Costa Surfaces

Global Weierstrass representations are derived for completeminimal surfaces obtained by substituting the planar end ofthe Costa surface by Scherk ends. This gives rise to singlyperiodic examples, of which the fundamental piece is provedto be embedded by a simple geometric technique. This techniquecan be generalised for embeddedness proof of future examplesof the same nature.