Magnetic single-component molecular conductors exhibiting strong π-d interactions

Single-component molecular conductors [M(tmdt)₂] (tmdt = trimethylenetetrathiafulvalenedithiolate; M = Ni, Au, Pt, Cu), exhibit a variety of electromagnetic properties, which originate from the differences of the metal’s d-orbitals role in the band structure formation. The [Au(tmdt)₂] crystal undergoes an antiferromagnetic transition at 110 K, while maintaining a metallic state at lower temperatures. The Au analog has a high magnetic transition temperature as compared to traditional magnetic molecular conductors due to the strong three-dimensional (3-D) structure and the contribution of the metal d-orbitals. The single-component molecular conductor, [Cu(tmdt)₂], with π- and d-like frontier orbitals is isostructural with other metallic [M(tmdt)₂] systems (M = Ni, Pt, Au). The Cu(tmdt)₂ molecule is planar, which strikingly contrasts the tetrahedral coordination of Cu(dmdt)₂ (dmdt = dimethyltetrathiafulvalenedithiolate) with similarly extended TTF type ligands. Interestingly, unlike other [M(tmdt)₂] with metallic behavior, [Cu(tmdt)₂] shows semiconducting behavior at room temperature (σ(RT) = ∼7 S cm⁻¹). The RT conductivity increased linearly with increased pressure to 110 S cm⁻¹ at 15 kbar despite the compressed pellet sample. The magnetic susceptibility indicates one-dimensional (1-D) Heisenberg behavior with J = 117 cm⁻¹ and shows antiferromagnetic ordering at 13 K. The [Cu(tmdt)₂] is a new multi-frontier π-d system, which introduces a d(σ)-type frontier orbital around the Fermi level of the π-like metal bands.     

基于1-(1′，3′-苯并噁唑-2′-甲基)苯并咪唑的钴(Ⅱ)配合物：晶体结构、弱相互作用和荧光发射光谱

配体1-(1′,3′-苯并恶唑-2′-甲基)苯并咪唑(L)是通过苯并咪唑与2-(氯甲基)-1,3-苯并恶唑烷基化制备而来。配体L与CoCl2.2H2O反应得到了配合物[CoCl2L2](1)。配合物1通过π-π堆积作用和C-H…Cl氢键形成了三维超分子框架结构。测定了L和1的荧光发射光谱。     

Crystal structure of β-cyclodextrin-4-chlorobenzoic acid complex:Unusual C-Cl…π interaction between 4-chlorobenzoic acids in β-cyclodextrin dimer

The inclusion complex ofβ-cyclodextrin（β-CD） with 4-chlorobenzoic acid was synthesized and its crystal structure was determined by single crystal X-ray diffraction under cryogenic condition.The complex contains twoβ-CDs,two 4-chlorobenzoic acids and twenty-nine water molecules in the asymmetric unit,and can be formulated as 2(C₄₂H₇₀O₃₅)·2（C₇H₅O₂Cl）·29（H₂O）.In the crystal lattice,twoβ-CDs form a face-to-face dimer jointed together through hydrogen bonding between the secondary hydroxyl groups ofβ-CDs.Two 4-chlorobenzoic acid molecules which contact by C-Cl…πinteractions are included in theβ-CD dimer cavity.Theβ-CD dimers are arranged in brickwork-like pattern along the crystallographic a-axis.The effect of guest molecule length on the inclusion geometry was discussed by comparative study of someβ-CD complexes containing similar guests.     

Hopf π-代数与π-子代数

主要讨论局部有限维的Hopf π-代数的π-子代数与Hopf π-子代数,分别得到了Hopf π-代数的π-子代数和Hopf π-子代数的一些充分必要条件.     

Hopf π-子模

设H为有限型Hopfπ-代数,研究Hopfπ-代数H上的Hopfπ-模与Hopf π-余代数H *上的Hopfπ-余模之间的对偶关系,得出了Hopfπ-子模与Hopfπ-子 余模之间的充分必要条件,推广了Hopf代数中的相关结论.     

Upper and Lower Bounds of Table Sums

For a group G,we produce upper and lower bounds for the sum of the entries of the Brauer character table of G and the projective indecomposable character table of G.When G is a π-separable group,we show that the sum of the entries in the table of Isaacs' partial characters is a real number,and we obtain upper and lower bounds for this sum.     

Synthesis and Crystal Structure of [Zn(FcCOO)2(2,2′-bipy)(H2O)]2·H2O

A novel complex [Zn(FcCOO)2(2,2′-bipy)(H2O)]2·H2O (Fc = (η5-C5H5)Fe(η5-C5H4), 2,2′-bipy = 2,2′-bipyridine) has been synthesized and characterized by elemental analysis, IR and X-ray diffraction. It crystallizes in monoclinic system, space group P21/c with a = 6.8187(4), b = 21.7155(13), c = 19.7411(12) (A), α = 90, β = 97.7420(10), γ = 90°, C64H58Fe4Zn2N4O11, Mr = 1413.28, V = 2896.4(3) (A)3, Dc = 1.620 g/cm3, Z = 2, F(000) = 1444, μ(MoKα) = 1.857 mm-1, R = 0.0523 and wR = 0.0982 for 3219 observed reflections (I ＞ 2σ(I)). Structural analysis shows that the zinc atom is coordinated with three oxygen atoms from two ferrocenemonocarboxylates and one water molecule together with two nitrogen atoms from 2,2′-bipyridine, giving a distorted square-pyramidal coordination geometry. The complex molecules are linked to form an infinite one-dimensional chain by both intermolecular hydrogen bonds and π-π stacking interactions of the bipyridine rings.     

Inner invariant means and conjugation operators

It is shown that Paschke's result cannot be generalized to the [IN]-group setting given by Lau and Paterson. This resolves negatively a problem raised by Lau and Paterson.

     

The p-chain Spectral Sequence

We introduce a new spectral sequence called the p-chain spectral sequence which converges to the (co-)homology of a contravariant C-space with coefficients in a covariant C-spectrum for a small category C. It is different from the corresponding Atiyah–Hirzebruch-type spectral sequence. It can be used in combination with the Isomorphism Conjectures of Baum and Connes and Farrell and Jones to compute algebraic K- and L-groups of group rings and topological K-groups of reduced group C*-algebras.