Unusual magnetic properties of one-dimensional molecule-based magnets associated with a structural phase transition

Three ion-pair complexes, [RbzPy](+)[Ni(mnt)(2)](-) (mnt(2)(-) = maleonitriledithiolate; [RbzPy](+) = 4-R-benzylpyridinium; R = Br (1), Cl (2), and NO(2) (3)), with unusual magnetic properties have been synthesized and characterized. The crystal structures of 1 and 2 have been solved. The two complexes belong to the P2(1)/c space group with Z = 4 and C(20)H(11)BrN(5)NiS(4), a = 12.0744(17) A, b = 26.369(4) A, c = 7.440(3) A, and beta = 102.63(3) degrees for 1 and C(20)H(11)ClN(5)NiS(4), a = 12.105(2) A, b = 26.218(4) A, c = 7.374(2) A, and beta = 102.55(2) degrees for 2, respectively. The [Ni(mnt)(2)](-) anions in 1-3 form uniformly spaced one-dimensional (1-D) magnetic chains of s = 1/2 at room temperature. The temperature dependences of the susceptibility for 1-3 show that they undergo phase transitions. All three complexes are paramagnetic in their high-temperature (abbreviation HT) phase and diamagnetic in the low-temperature (abbreviation LT) phase because of strong dimerization along the stacking direction. The results of thermal analysis (DSC) further confirm that the phase transition for 1 and 2 is first-order but maybe second-order for 3. The phenomena observed in this study are similar to those of the 1-D radical systems.     

Proton-mediated electron configuration change in high-spin iron(II) porphyrinates

The synthesis, molecular structure, and electronic structure characterization of two five-coordinate high-spin imidazolate-ligated iron(II) porphyrinates are reported. Their electronic structure, as deduced from M?ssbauer spectra obtained in strong magnetic fields, is distinctly different from that of the analogous imidazole-ligated species. The resulting electronic structure models are consistent with all observed differing features in the two classes.     

Synthesis,structure and the e.s.r. spectrum of the mixed-valence molybdovandate Na2(NH4)4[(VIVVV8Mo)O28] · 10H2O

The mixed-valence molybdovanadate compound Na₂(NH₄)₄[V^IVV^V ₈Mo)O₂₈] · 10H₂O [Vanadata(6-)tetradeca--oxotetra-₃-oxodi-₆-oxoheptaoxo(oxomolybdate) nonatetrammonium disodium, decahydrate] has been synthesized from sodium molybdate(VI) dihydrate and sodium metavanadate dihydrate in aqueous solution by adding NH₂OH · HCl. The molecular structure has been determined by X-ray diffraction and is based on the isopolydecavanadate structure. The molybdate atom is crystallographically disordered over 6MO₆ octahedral sites. The e.s.r. spectrum clearly indicates that one vanadium atom has the oxidation number +4.     

Formation–containment control for networked Euler–Lagrange systems with input saturation

Nonlinear Dynamics - This paper studies the formation–containment control problem for networked nonlinear Euler–Lagrange systems with input saturation. To realize the concurrency of...     

Chemistry of constrained dioxocyclam ligands with Co(III): unusual examples of C-H and C-N bond cleavage

The reactions between H(2)dc3 and Co(acac)(3) have been studied in the presence and absence of base. In the presence of base, a complex with an intramolecular Co-C bond, Co(dc3-C-(8))(H(2)O), 1, is formed, presumably through heterolytic C-H bond activation. An X-ray crystallographic study demonstrates the presence of a Co-C bond and shows that the diazacyclooctane (daco) subunit adopts the chair-boat conformation with respect to the metal. The cobalt-carbon bond induces strain in the macrocycle as demonstrated by bond angles significantly deviating from tetrahedral. The (13)C NMR resonance of the carbon atom bound to cobalt (-10.5 ppm) suggests significant ionic character in the cobalt-carbon bond. However, we were unable to cleave this bond in the presence of strong acid. In the absence of base, the reaction of Co(acac)(3) with H(2)dc3 resulted in C-N cleavage of the ligand and the formation of a complex of dioxocyclam, Co(dc)(acac), 2. This complex has subsequently been prepared in high yield by the reaction of Co(acac)(3) with dioxocyclam. An X-ray crystallographic study demonstrates that dioxocyclam adopts the heretofore unreported cis configuration, having folded along a N-Co-N axis that is perpendicular to the Co-acac plane.     

Poly[[(μ2‐biphenyl‐2,4′‐dicarboxylato)[μ2‐1,4‐bis(imidazol‐1‐ylmethyl)benzene]cadmium(II)] 0.15‐hydrate]

The asymmetric unit of the title two‐dimensional coordination polymer, {[Cd(C₁₄H₈O₄)(C₁₄H₁₄N₄)]·0.15H₂O}_n, is composed of one Cd^II cation, one biphenyl‐2,4′‐dicarboxylate (bpdc) anion, one 1,4‐bis(imidazol‐1‐ylmethyl)benzene (bix) ligand and 0.15 solvent water molecules. The coordination environment of the Cd^II cation is defined by four carboxylate O atoms from two different bpdc anions in a chelating mode and two N atoms from two distinct bix ligands, constructing a distorted trigonal prism polyhedron. Two inversion‐related Cd^II cations are bridged together by two positionally disordered bpdc anions, forming a 22‐membered ring with a Cd...Cd distance of 9.1966 (9) Å. These rings are then further linked by two bix ligands, extending into a two‐dimensional layer along (102) with 6³ topology.     

Sulfoxide as a ligand in iron(II) porphyrinates: S- or O-bound?

In order to study the bonding of sulfoxides to iron(II) porphyrinates, an equilibrium study of Fe(TPP) with tetramethylenesulfoxide (TMSO) has been performed. UV-vis spectra at different concentrations of TMSO have shown distinct character belonging to three species: four-coordinate Fe(II)(TPP), five-coordinate [Fe(II)(TPP)(TMSO)], and six-coordinate [Fe(II)(TPP)(TMSO)2]. The isosbestic points for the low TMSO concentrations suggest that the equilibrium constant K1 is much larger than K2. Analysis of spectral data by the nonlinear least-squares program SQUAD gives K1 = 267 and K2 approximately 1. Even though the five-coordinate species is the dominant species under the synthetic conditions, only the six-coordinate species was crystallized and characterized by an X-ray diffraction study. [Fe(TPP)(TMSO)2] (C52H44Fe-N4O2S2): monoclinic, P2(1)/c, a = 11.2580(3) A, b = 15.9262(5) A, c = 12.3930(4) A, beta = 116.246(1) degrees , V = 1992.95(10) A3, Z = 2. X-ray crystallography demonstrates the complex is a low-spin bis-TMSO ligated species. The average Fe-Np distance is 1.999(4) A. The most important feature is that TMSO is coordinated to iron(II) by the sulfur donors, not oxygen. The Fe-S distance is 2.2220(3) A.     

基于分形分布的股票期权VaR计算

本文提出一种运用分形分布计算股票期权VaR的方法.首先对股票价格行为进行了理论总结和实证分析,表明采用分形分布来拟合股票的对数收益率是合理的,然后在此基础上推导股票期权VaR的计算公式,最后给出若干算例.     

Electronic configuration of high-spin imidazole-ligated iron(II) octaethylporphyrinates

The preparation and characterization of two new five-coordinate, imidazole-ligated, high-spin iron(II) octaethylporphyrinates is described. [Fe(OEP)(1,2-Me2Im)] and [Fe(OEP)(2-MeHIm)] have been characterized by X-ray structure determinations and temperature-dependent M?ssbauer spectroscopy in zero and applied magnetic fields. The distinction between imidazole-ligated and other ligands in high-spin iron(II) porphyrinates, noted for a series of tetraarylporphyrinate derivatives (Hu, C.; Roth, A.; Ellison, M. K.; An, J.; Ellis, C. M.; Schiltz, C. E.; Scheidt, W. R. J. Am. Chem. Soc. 2005, 127, 5675), is seen here as well. The sign of the quadrupole-splitting constant is again negative, which is unique to the imidazole-ligated derivatives and suggests a distinct electronic structure. The derivatives again display a remarkable temperature dependence in the quadrupole splitting, which is also seen for deoxymyoglobin and -hemoglobin. Structural features for the two new derivatives are similar to those seen earlier, although the core conformations show somewhat more doming character.     

On some inequalities for unitarily invariant norms and singular values

In this note, we improve and generalize some existing inequalities for unitarily invariant norms and singular values, and present some other inequalities for unitarily invariant norms.