The synthesis, structural characterization, magnetochemistry and Mössbauer spectroscopy of [Fe3LnO2(CCl3COO)8H2O(THF)3] (Ln = Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Lu and Y)

The new tetranuclear complexes [Fe₃Ln(μ₃-O)₂(CCl₃COO)₈(H₂O)(THF)₃]·THF (Ln = Ce^III (1), Pr^III (2), Nd^III (3)) and [Fe₃Ln(μ₃-O)₂(CCl₃COO)₈(H₂O)(THF)₃]·THF·C₇H₁₆ (Ln = Sm^III (4), Eu^III (5), Gd^III (6), Tb^III (7), Dy^III (8), Ho^III (9), Lu^III (10) and Y^III (11)) have been prepared. All compounds were prepared by the reaction between [Fe₂BaO(CCl₃COO)₆(THF)₆] and the corresponding Ln^III nitrate salt. The crystal structures of 1–4, 8 and 9 have been determined; these isostructural molecules have a non-planar {Fe₃Ln(μ₃-O)₂} “butterfly” core. Magnetic susceptibility measurements show dominant intramolecular antiferromagnetic exchange interactions for all the complexes. ⁵⁷Fe Mössbauer spectroscopy shows three different environments for the Fe^III metal ions, all in their high-spin state S = 5/2 (confirming that no electron transfer from Ce^III to Fe^III occurs in 1). At the time scale of the Mössbauer spectroscopy (about 10⁻⁷ s), evidence of magnetization blocking, i.e. slow relaxation of the magnetization, is observed below 3 K for 7, which was confirmed by ac susceptibility measurements.     

New penta-nuclear and hepta-nuclear iron(II, III) complexes with ferrocenedicarboxylic acid

The reaction of [Fe₃EuO₂(O₂CCCl₃)₈(H₂O)(THF)₃] or [Fe₂CaO(O₂CCCl₃)₆(THF)₄] and [Fe₃O(O₂CCMe₃)₆(H₂O)₃]NO₃ with 1,1′-ferrocenedicarboxylic acid (fcdcH₂) yielded penta- and hepta-nuclear [Fe₄O₂(O₂CCCl₃)₆(fcdc)(THF)₂(H₂O)₂] and [Fe₆O₂(OH)₂(O₂CCMe₃)₁₀(fcdc)(H₂O)₂], respectively, which are the first X-ray structurally characterized clusters comprising Fe(III) and the ferrocenedicarboxylic organometallic ligand. Variable-temperature solid-state magnetic susceptibility measurements in the temperature range 1.8–300 K were carried out, and for both complexes a predominantly antiferromagnetic exchange interaction between the metal centres was observed. Mössbauer investigations show the presence of different environments for the Fe(III) atoms and confirm that no electron-transfer from Fe(II) of the ferrocene unit to Fe(III) of the central core occurs.     

Locally Anisotropic Kinetic Processes and Thermodynamics in Curved Spaces

The kinetic theory is formulated with respect to anholonomic frames of reference on curved spacetimes. By using the concept of nonlinear connection we develop an approach to modelling locally anisotropic kinetic processes and, in corresponding limits, the relativistic nonequilibrium thermodynamics with local anisotropy. This leads to a unified formulation of the kinetic equations on (pseudo) Riemannian spaces and in various higher dimensional models of Kaluza–Klein type and/or generalized Lagrange and Finsler spaces. The transition rate considered for the locally anisotropic transport equations is related to the differential cross section and spacetime parameters of anisotropy. The equations of states for pressure and energy in locally anisotropic thermodynamics are derived. The obtained general expressions for heat conductivity, shear, and volume viscosity coefficients are applied to determine the transport coefficients of cosmic fluids in spacetimes with generic local anisotropy. We emphasize that such local anisotropic structures are induced also in general relativity if we are modelling physical processes with respect to frames with mixed sets of holonomic and anholonomic basis vectors which naturally admits an associated nonlinear connection structure.     

Symmetric solutions of some production economies

A symmetricn-person game (n, k) (for positive integerk) is defined in its characteristic function form byv(S)=[¦S¦/k], where ¦S¦ is the number of players in the coalitionS and [x] denotes the largest integer not greater thanx, (i.e., anyk players, but not less, can “produce” one unit). It is proved that in any imputation in any symmetric von Neumann-Morgenstern solution of such a game, a blocking coalition ofp=n?k+1 players who receive the largest payoffs is formed, and their payoffs are always equal. Conditions for existence and uniqueness of such symmetric solutions with the otherk?1 payoffs equal too are proved; other cases are discussed thereafter.     

Convergence theorems for continuous descent methods

We examine continuous descent methods for the minimization of Lipschitzian functions defined on a general Banach space. We establish several convergence theorems for those methods which are generated by regular vector fields. Since the complement of the set of regular vector fields is -porous, we conclude that our results apply to most vector fields in the sense of Baires categories.     

Structure of ions [ZnNCR]+ and [Zn(NCR)2]+ (R = H,CH3) in the gas phase

Structures of [ZnNCR]⁺ and [Zn(NCR)₂]⁺ ions (R = H, Me), which are abundant in the mass spectra of many types of coordination compounds, were studied by the MNDO method. In all cases the most stable isomers correspond to the zinc ion coordinated with the nitrogen(s) of the nitrile ligand. For [Zn(NCR)₂]⁺, the N-Zn-N angles are ～108°.     

Alkylperoxyl spin adducts of pyrroline‐N‐oxide spin traps: Experimental and theoretical CASSCF study of the unimolecular decomposition in organic solvent,potential applications in water

Spin trapping coupled with electron paramagnetic resonance spectroscopy is the most direct method for detection of very low concentrations of free radicals, and it has been intensively used to detect superoxide or alkylperoxyl radicals in biological systems, using cyclic nitrones as spin traps. The half‐life time of the ensuing spin adducts depends dramatically on the spin trap structure; however, their mechanism of decay has never been definitely established. We investigated at the MRMP2/CASSCF (MultiReference second‐order Møller‐Plesset perturbation theory/Complete Active Set Self Consistent Field) level of theory the mechanism of decay of methylperoxyl and tert‐butylperoxyl spin adducts formed with various cyclic nitrones. We showed that no transition state can be located for the O─O homolytic cleavage, which yields an intermediate biradical with the following sequence ^?O─N─C─O^?. Then, homolytic cleavage of the N─C bond yields a nitrosoaldehyde, through an early transition state with a very low activation energy. For each nitrone used as spin trap, electrospray ionization mass spectrometry analysis of the spin trapping mixture allowed to detect the presence of the expected nitrosoaldehyde. We generated tert‐butylperoxyl spin adducts in toluene, and we found a good correlation between their half‐life time and the bond dissociation energy of their peroxidic O─O bond. The theoretical method was then extended to hydroperoxyl spin adducts in water and provided promising results.     

Synthesis and Toxicity Evaluation of New Pyrroles Obtained by the Reaction of Activated Alkynes with 1-Methyl-3-(cyanomethyl)benzimidazolium Bromide

A series of new pyrrole derivatives were designed as chemical analogs of the 1,4-dihydropyridines drugs in order to develop future new calcium channel blockers. The new tri- and tetra-substituted N-arylpyrroles were synthesized by the one-pot reaction of 1-methyl-3-cyanomethyl benzimidazolium bromide with substituted alkynes having at least one electron-withdrawing substituent, in 1,2-epoxybutane, acting both as the solvent and reagent to generate the corresponding benzimidazolium N3-ylide. The structural characterization of the new substituted pyrroles was based on IR, NMR spectroscopy as well as on single crystal X-ray analysis. The toxicity of the new compounds was assessed on the plant cell using Triticum aestivum L. species and on the animal cell using Artemia franciscana Kellogg and Daphnia magna Straus crustaceans. The compounds showed minimal phytotoxicity on Triticum rootlets and virtually no acute toxicity on Artemia nauplii, while on Daphnia magna, it induced moderate to high toxicity, similar to nifedipine. Our research indicates that the newly synthetized pyrrole derivatives are promising molecules with biological activity and low acute toxicity.