Instability of the paramagnetic state towards incommensurate magnetic order in the 2-d Hubbard model

We determine the instability line separating the paramagnetic phase in the phase diagram of the 2-d Hubbard Model from a phase with incommensurate magnetic order. A mean-field approximation of the Kotliar-Ruckenstein slave boson representation is used to calculate the wave-vector dependent magnetic susceptibility. For largeU/t the instability occurs at a densityn0.37, and a wave-vector close toq=(0,). The dependence ofq onU andn is also given.     

Reductive cleavage of axially disymmetric tertiary amines and quaternary ammonium salts by lithium aluminium hydride. Synthesis of new 1,1′-binaphthyl substituted amines

Axially disymmetric tertiary amines or quaternary ammonium salts $\text{A}$ are synthesized by double alkylation of primary or secondary amines with racemic or optically pure 2,2′-bis (bromomethyl)-1,1′-binaphthyl. Their reductive cleavage by lithium aluminium hydride in refluxing THF leads to chiral secondary or tertiary amines $\text{B}$, substituted by a binaphthyl unit, with high yields and absence of racemization.     

Formation and reactions of metal-metal bonded heterobimetallic (C5H4PR2)-bridged (Zr-Ir) and (Zr-Rh) complexes: evidence for the participation of metal hydride intermediates

Treatment of the complexes [(C(5)H(4)PR(2))(2)Zr(CH(3))(2)](b: R = isopropyl; c: R = cyclohexyl) with the reagent HIr(CO)(PPh(3))(3) (2b) yield the heterobimetallic complexes [mu-C(5)H(4)PR(2))(2)(H(3)C-Zr-Ir(CO)(PPh(3)))] (4b, 4c) with evolution of methane. The reaction of the -PPh(2) substituted analogue with initially yields an intermediate [(H(3)C)(2)Zr(mu-C(5)H(4)PPh(2))(2)Ir(H)(CO)(PPh(3))] 5a, that still contains both methyl groups at zirconium and does not contain a metal-metal bond. At room temperature, the intermediate reacts further with methane formation to eventually yield the (Zr-Ir) complex 4a. The corresponding [mu-C(5)H(4)PR(2))(2)(H(3)C-Zr-Rh(CO)(PPh(3)))] complexes 3a (R = Ph) and 3b (R = isopropyl) react cleanly with isopropyl alcohol to liberate methane and yield the corresponding [mu-C(5)H(4)PR(2))(2)(Me(2)CHO-Zr-Rh(CO)(PPh(3)))] products (7a, 7b). Carefully monitoring the reaction of with Me(2)CHOH by NMR revealed that the Zr-Rh functionality is attacked first to give the intermediate [Me(Me(2)CHO)Zr([micro sign]-C(5)H(4)PR(2))(2)Rh(H)(CO)(PPh(3))] (6b). This intermediate then reacts further to cleave off methane and re-form the (Zr-Rh) metal-metal bond to yield the product 7b. The tetrametallic mu-oxo-(Zr-Rh) metallocene derivate 11a was obtained starting from the (Zr-Rh) complex 3a and it was characterized by X-ray diffraction. It may be that this reaction is also initiated by H-OH addition to the [Zr-Rh] metal-metal bond.     

Borel summability of the 1/N expansion for theN-vector [O(N) non-linear σ] models

We construct an analytic interpolation in 1/N for theN-vector [O(N) non-linear ] models withN-component fields on a lattice. This interpolation, valid at sufficiently high temperatures, extends over a large domain in the complex plane containing the half plane Re(1/N)>0. We use this result to show that the 1/N expansion of the free energy density and of the correlation functions is Borel summable in the thermodynamic limit and at high temperature.On leave from C.P.T., Ecole Polytechnique, F-91128 Palaiseau Cédex, France     

Mono- and dinuclear molybdenum complexes with sterically demanding cycloheptatrienyl ligands

Sterically demanding cycloheptatrienylium (tropylium) salts of the type (1,3,5-C7H4R3)BF4 [R = t-Bu, (3a)BF4; R = SiMe3, (3b)BF4] have been prepared from the corresponding 1,3,5-trisubstituted benzene derivatives 1 by ring expansion with diazomethane followed by hydride abstraction with triphenylcarbenium tetrafluoroborate, (Ph3C)BF4. Complexation can be achieved by arene exchange and Mo(CO)3 group transfer employing [(eta6-p-xylene)Mo(CO)3] (4) to yield the cationic complexes (5)BF4. In refluxing mesitylene, [(eta7-C7H4t-Bu3)Mo(CO)3]BF4, (5a)BF4, undergoes CO substitution to furnish the mesitylene sandwich complex (6a)BF4. A cyclic voltammetric study reveals that this complex exhibits a reversible one-electron oxidation to the dicationic 17e complex 6a2+, which can also be accessed by chemical oxidation with AgBF4. On the contrary, the reduction of 6a+ is irreversible and does not yield a stable 19e complex 6a. To study the fate of the reduced 19e form, (5a)BF4 was treated with Na2Hg to diastereoselectively afford the C-C coupled bicycloheptatriene complex 7a. Paramagnetic, dinuclear complexes of the type [(eta7-C7H4R3)Mo(mu-Cl)3Mo(eta7-C7H4R3)] (8) have been obtained from the reaction of (5)BF4 with Me3SiCl. These can be regarded as mixed-valence Mo(0)/Mo(+I) compounds with a metal-metal bond order of 0.5. Cyclic voltammetric studies reveal that both complexes 8a and 8b undergo reversible one-electron oxidation as well as reduction. Treatment with one equivalent of ferrocenium hexafluorophosphate leads to removal of the unpaired electron and formation of the diamagnetic complexes (8)PF6. Theoretical DFT calculations have been carried out to further elucidate the bonding in these systems. In addition, the X-ray crystal structures of (5b)BF4, (6a)BF4 x CH2Cl2, (6a)(BF4)2 x (acetone)2, 7a x CH2Cl2, 8a x 0.5C6H14, and (8a)PF6 x Et2O are reported.     

Base-induced heterochiral dimerization of an oxiranyl carbaldimine: stereoselective synthesis of a highly functionalized aziridine

[reaction: see text] Treatment of the oxiranyl carbaldimine with base (LDA or LDA/KOtBu) leads in an one-step procedure to the polyfunctionalized aziridine. This highly diastereoselective reaction is explained by a new type of an Aza-Darzens reaction, in which one enantiomer of the starting material is deprotonated to form an oxiranyl anion, which attacks the imine carbon atom of the other enantiomer (mutual kinetic resolution by double diastereofacial selection).     

Dérivés de la dihydro-2,4 triazole-1,2,4 thione-3 et de l'amino-2 thiadiazole-1,3,4 à partir de nouvelles thiosemicarbazones d'esters

A new general synthesis of 4,5-disubstituted 2,4-dihydro-1,2,4-triazole-3-thiones is proposed. These heterocycles are obtained by the action of primary amines, arylhydrazines or aroylhydrazines on the thiosemicarbazones of eaters. These last compounds are prepared by action of chlorhydrates of iminoethers on thiosemicarbazide in dimethylformamide. These thiosemicarbazones react also with strong acids, acid anhydrides and chlorides; by thermolysis and they give 2-amino-1,3,4-thiadiazole derivatives. Also, two derivatives of 1,2,4-triazolo[3,4-b]-1,3,4-thiadiazole have been prepared.