Nonlinear dynamics of the infinite classical Heisenberg model: Existence proof and classical limit of the corresponding quantum time evolution

For any initial spin configuration we prove the existence, unicity and regularity properties of the solution of Hamilton's equations for the infinite classical Heisenberg model with stable interactions, along with the essential selfadjointness of the associated Liouville operator. We also prove new properties of SU (2)-coherent states which, together with the concept of Trotter approximations for one-parameter (semi-) groups, are used to show that this dynamics is nothing but the classical limit of the time evolution generated by the infinite quantum (suitably normalized) Heisenberg Hamiltonian. The classical limit emerges when the spin magnitude S goes to infinity while Plank's constant goes to zero, their product S remaining fixed. The main results are stated in the form of intertwining relations between the classical and the quantum unitary group.Work supported in part by the Swiss National Science Foundation under Grant 820-436-76 and in part by the U.S. Department of Energy under contract EG-77-C-03-1538.     

Strictly heterodinuclear compounds containing U and Cu or Ni ions

Treatment of [M(H₂Lⁱ)] with UCl₄ in pyridine led to the formation of the dinuclear complexes [MLⁱ(py)UCl₂(py)₂] and/or [Hpy][MLⁱ(py)UCl₃] [Lⁱ = N,N′-bis(3-hydroxysalicylidene)-R, R = 1,2-phenylenediamine (i = 1), R = trans-1,2-cyclohexanediamine (i = 2), R = 2-amino-benzylamine (i = 3), R = 1,3-propanediamine (i = 4), R = 2,2-dimethyl-1,3-propanediamine (i = 5); M = Cu or Ni]. The crystal structures show that the 3d and 5f ions occupy, respectively, the N₂O₂ and O₄ cavities of the Schiff base ligand, the U⁴⁺ ion adopting a dodecahedral or pentagonal bipyramidal configuration in the neutral and anionic complexes, respectively.     

Evaluation of capillary isoelectric focusing in glycerol-water media with a view to hydrophobic protein applications

Capillary isoelectric focusing (CIEF) separations are usually performed with neutral coated fused-silica capillaries in aqueous anticonvective media. Glycerol, a very viscous solvent (eta = 945 mPa x s at 25 degrees C), known to help stabilize any kind of proteins and solubilize hydrophobic ones, was tested as an alternative to using commercial gels. Viscosity and electroosmotic mobility were measured as a function of gel or glycerol content in water, and a 30:70 v/v glycerol-water medium appeared as a good compromise for performing CIEF in a bare fused-silica capillary without imposing too high a viscosity. To demonstrate the feasibility of this new CIEF system, a standard mixture of nine model proteins was separated according to their pI with a good agreement between experimental and literature aqueous pIs. Moreover, better resolution was achieved with this system than with the conventional aqueous CIEF system, as two of the model proteins could not be separated in the latter system. Glycerol-water CIEF in bare silica capillary was next applied to the separation of horse radish peroxidase, a complex mixture of protein isoforms. The good concordance with the separation obtained by the conventional CIEF system indicated the adequacy of this new system. Finally, as anticipated from the results obtained for the separation of bacteriorhodopsin, a membrane protein, glycerol-water CIEF performed in bare silica capillary appears to be a promising alternative to conventional aqueous CIEF for hydrophobic protein characterization, under their native form.     

Tunable N-substitution in zwitterionic benzoquinonemonoimine derivatives: metal coordination, tandemlike synthesis of zwitterionic metal complexes, and supramolecular structures

Full details on a very efficient transamination reaction for the synthesis of zwitterionic N,N-dialkyl-2-amino-5-alcoholate-1,4-benzoquinonemonoiminium derivatives [C6H2(=NHR)2(=O)2] 5-16 are reported. The molecular structures of zwitterions 5 (R=CH3) in 5.H2O, 13 (R=CH2CH2OMe), 15 (R=CH2CH2NMe2), and of the parent, unsubstituted system [C6H2(=NH2)2(=O)2] 4 in 4.H2O have been established by single-crystal X-ray diffraction. This one-pot preparation can be carried out in water, MeOH, or EtOH and allows access to new zwitterions with N-substituents bearing functionalities such as -OMe (13), -OH (9-12), NR1R2 with R1 = or not equal R2 (14-16) or an alkene (8), leading to a rich coordination chemistry and allowing fine-tuning of the supramolecular arrangements in the solid state. As previously described for 15, which reacted with Zn(acac)2 to afford the octahedral Zn(II) complex [Zn[C6H2(NCH2CH2NMe2)O(O)(NHCH2CH2NMe2)]2] (20), ligands 13 and 16 with coordinating "arms" afforded with Zn(acac)2 the 2:1 adducts [Zn[C6H2(NCH2CH2X)O(=O)(NHCH2CH2NX)]2] 19 (X=OMe) and 21 (X=NHEt), with N2O4 and N4O2 donor sets around the octahedral Zn(II) center, respectively. Furthermore, zwitterions 15 and 16 reacted with ZnCl2 to give the stable, crystallographically characterized Zn(II) zwitterionic complexes [ZnCl2[C6H2(NCH2CH2NR1R2)O(=O)(NHCH2CH2NHR1R2)]] 22 (R1=R2=Me) and 23 (R1=Et, R2=H) by means of an unprecedented, tandemlike synthesis in which 1) the two pendant amino groups of the organic benzoquinonemonoimine zwitterionic precursor favor metal coordination and proton transfer and 2) the saturated linker prevents pi-conjugation between the charges. The nature of the structural arrangements in the solid state for both inorganic (20, 22, 23) and organic (5, 9, 13, and 15) molecules is determined by subtle variations in the nature of the N-substituent on the zwitterion precursor.     

Non-aqueous capillary electrophoresis of the positional isomers of a sulfated monosaccharide

A non-aqueous capillary electrophoresis (NACE) method coupled to indirect absorbance detection has been developed for the separation of the three positional isomers of monosulfated fucose. The optimized electrolyte was composed of 12 mM ethanolamine, 2 mM trimesic acid buffer in a methanol-ethanol (1:1, v/v) mixture. As the retained electrolyte entails no separating agent other than the pH buffer, the NACE separation of the positional isomers has been ascribed mainly to selective ion-pairing with the electrolyte counter-ion and the possibility of a selective solvation effect in the alcohol mixture. In the absence of pure isomeric standards, peak identification was completed by MS and NMR spectroscopy and selective enzymatic desulfation. This method should be of interest for the structure elucidation of monosulfated fucose-based polysaccharides and for the screening of sulfoesterase of unknown activity.     

(18‐Crown‐6)‐μ‐oxo‐hexa­kis(tetra­hydro­borato)diuranium(IV): an unprecedented asymmetric dinuclear complex

In the title compound, (1,4,7,10,13,16‐hexa­oxacyclo­octa­decane‐1κ⁶O)‐μ‐oxo‐1:2κ²O:O‐hexa­kis(tetra­hydro­borato)‐1κ³H;2κ²H;2κ²H;2κ³H;2κ³H;2κ³H‐diuranium(IV), [U₂(BH₄)₆O(C₁₂H₂₄O₆)], one of the U atoms (U1), located at the centre of the crown ether moiety, is bound to the six ether O atoms, and also to a tridentate tetra­hydro­borate group and a μ‐oxo atom in axial positions. The other U atom (U2) is bound to the same oxo group and to five tetra­hydro­borate moieties, three of them tridentate and the other two bidentate. The two metal centres are bridged by the μ‐oxo atom in an asymmetric fashion, thus giving the species (18‐crown‐6)(κ³‐BH₄)U=(μ‐O)—U(κ³‐BH₄)₃(κ²‐BH₄)₂, in which the U1=O and U2—O bond lengths to the μ‐O atom [1.979 (5) and 2.187 (5) Å, respectively] are indicative of the presence of positive and negative partial charges on U1 and U2, respectively.     

Polygermoxanes suitable for biochemical purposes: II Linear trigermoxanes (high-viscosity oils)

Linear trigermoxanes, R¹ RGeOGe(R³)₂OGeRR¹, a new series of organogermanium compounds, were synthesized by reaction of a lithium organogermanolate with a suitable organogermanium dihalide. With alkyl or phenyl substituents, these trigermoxanes are structurally unstable viscous oils, due to redistribution reactions. When R³ substituents are bulky groups, such as mesityl, trigermoxanes are thermally and structurally stable oils; depending on the R¹ and R² substituents their viscosities lie in the range 240 to more than 1500 cPo (mPa s) at 20°C. When both terminal germanium atoms are substituted with two mesityl groups, trigermoxanes are stable glassy solids.     

Face Selectivity of the Diels-Alder Additions of 2-Substituted 5,6-bis((E)-chloromethylidene)bicyclo[2.2.2]octanes

The preparation of 5,6-bis((E)-chlorommethylidene)bicyclo[2.2.2]oct-2-ene ( 13 ), 2,3-bis((E)-chloromethyl idene)-5exo,6exo- and -5endo,6endo-epoxybicyclo[2.2.2] octane ( 14 and 15 ), 5,6-bis((E)-chloromethylidene)-2exo- and -2endo-bicyclo[2.2.2] octanol ( 16 and 17 ) and 5,6-bis((E)-chloromethylidene)-2-bicyclo[2.2.2]octanone ( 18 ) are described. The face selectivity (endo-face vs. exo-face attack onto the exo-cyclic diene) of their cycloadditions to tetracyanoethylene has been determined in benzene at 20°. It is 78/22, 80/20, 60/40, 68/32, 3/97 and 30/70 for 13 , 14 , 15 , 16 , 17 and 18 , respectively.     

Chemo- and Stereoselective Coordination of 5,6-Dimethylidene-7-oxabicyclo[2.2.1]hept-2-ene by d8- and d6-Metal Carbonyls. Diels-Alder reactivity of Dienes Perturbed by Remote Olefin Complexation

The endocyclic double bond C(2), C(3) in 5,6-dimethylidene-7-oxabicyclo[2.2.1]-hept-2-ene ( 1 ) can he coordinated selectively on its exo-face before complexation of the exocyclic s-cis-butadiene moiety. Irradiation of Ru₃(CO)₁₂ or Os₃(CO)₁₂ in the presence of 1 gave tetracarbonyl [(1R,2R, 3S,4S)-2,3-η-(5,6-dimethylidene-7-oxabicyclo[2.2.1]-hept-2-ene)]ruthenium ( 6 ) or -osmium ( 8 ). Similarly, irradiation of Cr(CO)₆ or W(CO)₆ in the presence of 1 gave pentacarbonyl[(1R, 2R, 3S,4S)-2,3-η-(5,6-dimethylidene-7-oxabicyclo[2.2.1]hept-2-ene)]chromium (10) or -tungsten (11) . Irradiation of complexes 6 and 11 in the presence of 1 led to further CO substitution giving bed-tricarbonyl-ae-bis[(1R,2R,3S,4S)-2,3-η-(5,6-dimethylidene-7-oxabicyclo[2.2.1]hept-2-ene)]ruthenium ( 7 ) and trans-tetracarbonyl[(1R,2R,3S,4S)-2,3-η-(5,6-dimethylidene-7-oxabicyclo-[2.2.1]hept-2-ene)]tungsten (12) , respectively. The diosmacyclobutane derivative cis-m?-[(1R,3R,3S,4S)-(5,6-dimethylidene-7-oxabicyclo[2.2.1]hepta-2,3-diyl)]bis(tetracarbonyl-osmium) (Os-Os) (9) wa also obtained. The Diels-Alder reactivity of the exocyclic s-cis-butadiene moiety in complexs 7 and 8 was found to be significantly higher than that of the free triene 1 .     

Stereochimie de l'action des organomagnesiens et des organolithiens sur les dimethyl-1,2 alcoxy-1 silacyclobutanes

The reaction of organomagnesium organolithium compounds (alkyl, aryl, allyl and benzyl derivatives) with 1,2-dimethyl-1-alkoxy-l-silacyclobutanes proceeds with retention of configuration at the silicon atom. Stereochemical results are discussed in terms of the S_N2Si mechanism. The proposed configurations are supported by ¹H and ¹³C NMR data.