Chiral Interlocked Corrole Dimers Directly Linked at Inner Carbon Atoms of Confused Pyrrole Rings

A facile synthetic strategy towards conformationally stable chiral chromophores based on dimeric porphyrinoids has been established. A peculiar class of face-to-face intramolecularly interlocked corrole dimers were formed by the oxidative C−C coupling linked at the inner carbon sites upon simple treatment of copper(II) ions. Their intrinsic electronic structures were modulated by the peripheral corrole ring annulations, which lead to distinct optical properties and redox profiles. The stereogenic carbon centers implemented in the confused corrole skeleton provided a rationale for designing novel chiral materials.     

Computing centre conditions for certain cubic systems

We present necessary and sufficient conditions for a critical point of certain two-dimensional cubic differential systems to be a centre. Extensive use of the computer algebra system REDUCE is involved. The search for necessary and sufficient conditions for a centre has long been of considerable interest in the theory of nonlinear differential equations. It has proved to be a difficult problem, and full conditions are known for very few classes of systems. Such conditions are also required in the investigation of Hilbert's sixteenth problem concerning the number of limit cycles of polynomial systems.     

Non-Colliding Paths in the Honeycomb Dimer Model and the Dyson Process

In this paper we describe a natural family of random non-intersecting discrete paths in the dimer model on the honeycomb lattice. We show that when the dimer model is going to freeze, this family of paths, after a proper rescaling, converges to the extended sine process, obtained traditionally as the limit of the Dyson model when the number of particles goes to infinity.     

New two-color dimer models with critical ground states

We define two new models on the square lattice in which each allowed configuration is a superposition of a covering by white dimers and one by black dimers. Each model maps to a solid-on-solid (SOS) model in which the height field is two dimensional. Measuring the stiffness of the SOS fluctuations in the rough phase provides critical exponents of the dimer models. Using this height representation, we have performed Monte Carlo simulations. They confirm that each dimer model has critical correlations and belongs to a new universality class. In the dimer-loop model (which maps to a loop model) one height component is smooth, but has unusual correlated fluctuations; the other height component is rough. In the noncrossing-dimer model the heights are rough, having two different elastic constants; an unusual form of its elastic theory implies anisotropic critical correlations.     

Complexes of Cu2(μ‐OAc)4(H2O)2 with 1,10‐Phenanthroline and Comparison with those of 2,2′‐Bipyridine. Crystal Structure of the Dimer [Cu(OAc)2(phen)](μ‐H2O)

The two complexes of composition Cu₂(OAc)₄(phen)(H₂O)₂ ( 1 ) andCu₂(OAc)₄(phen)₂(H₂O) ( 2 ) have been synthesized and characterized by chemical analysis and IR and electronic spectroscopies. Compound 2 has the structure of a dimer with a phenanthroline molecule and two monodentate acetate groups coordinated to each copper atom and a water molecule as the only bridging ligand between them. Each copper atom has a distorted square‐planar pyramidal coordination, determined by two oxygen atoms at 1.94(3) and 1.959(3) Å, two nitrogen atoms at 2.023(4) Å and the oxygen atom of the bridging water molecule at 2.289(2) Å. The distance between the two copper atoms is of 4.29 Å and the angle Cu(1)‐O(3)‐Cu(1A) 139.2(2)°. The water molecule is involved in two intramolecular hydrogen bonds with non coordinated oxygen atoms. The distance between the molecules of phenanthroline is 3.75 Å. Magnetic and EPR results for Cu₂(OAc)₄(phen)(H₂O)₂ ( 1 ), Cu₂(OAc)₄(phen)₂(H₂O) ( 2 ), Cu₂(OAc)₄(bipy) ( 3 ) and Cu₂(OAc)₄(bipy)₂(H₂O)₂ ( 4 ) have been analysed and compared. For 1 and 3 an antiferromagnetic dimer unit [Cu₂(μ‐OAc)₄] with 2J = ?325 and ?292 cm^?1, respectively, and other two copper atoms without significant magnetic interaction are present. Triplet signals are detected in the EPR spectra. In 2 and 4 there is no practically magnetic exchange and the orthorhombic signals are observed in the EPR spectra.     

Radiation centre of institute of physical chemistry in Moscow

Radiation centre of the Institute of Physical Chemistry of Russian Academy of Sciences (Moscow) is described. It has four ⁶⁰Co γ-ray sources and four electron accelerators, three of them being linear ones. The brief consideration of researches and developments in radiation chemistry and radiation processing is conducted.     

Commutators and decompositions of orthomodular lattices

We show that in any complete OML (orthomodular lattice) there exists a commutatorc such that [0,c ] is a Boolean algebra. This fact allows us to prove that a complete OML satisfying the relative centre property is isomorphic to a direct product [0,a] × [0,a ] wherea is a join of two commutators, [0,a] is an OML without Boolean quotient and [0,a ] is a Boolean algebra. The proof uses a new characterization of the relative centre property in complete OMLs. In a final section, we specify the previous direct decomposition in the more particular case of locally modular OMLs.     

NO双分子在Cu2O(111)面吸附与解离的理论研究

采用广义梯度密度泛函理论结合周期平板模型方法, 在DNP基组下, 研究了NO双分子在三重态和单重态两种电子组态下在Cu2O(111)完整表面的吸附情况. 考虑了Cu+(NO)(NO)、Cu+(NO)(ON)及Cu+(ON)(ON)这三种构型, 计算了它们的吸附能和Mulliken电荷, 分析并预测了吸附后可能产生的物种. 结果表明, 当两个NO分子都以O端吸附在Cu2O(111)表面时即Cu+(ON)(ON)构型, N—N键长很短, 只有124.4 pm, 吸附的两个NO分子形成了二聚体形式, 这种吸附构型有利于进一步离解产生N2或N2O并形成Cu-O表面物种.     

Spirobicyclic diamines. Part 3: Synthesis and metal complexation of proline-derived [4.4]-spirodiamines

The syntheses of racemic and homochiral [4.4]-spirolactams, starting from l-proline, in good yields are described. Reduction of the lactam carbonyl group of spirolactams, containing chiral substituents on the lactam nitrogen, with lithium aluminium hydride, gives a series of homochiral [4.4]-spirodiamines. The crystal structure of one of these spirodiamines on complexation with zinc chloride was obtained. Interestingly it showed a hydrogen-bonded dimeric structure, where the monomers are diastereoisomeric diamines.     

A Fibonacci generalization and its dual

An interesting dual sequence for the Fibonacci sequence is presented in which the consecutive terms are constructed via multiplication of the preceding terms, instead of addition. Well-known results illustrating this duality are also generalized, showing how these relate to generalizations of the golden ratio.