Synthesis and Crystal Structure of a Novel Manganese Coordination Polymer： 2,5-Bis（4-pyridyl）-3,4-diaza-2,4-hexadiene

A new manganese coordination polymer 1, [Mn(H2O)4(L)]n(ClO4)2n·2nH2O·3nL (L = 2,5-bis(4-pyridyl)-3,4-diaza-2,4-hexadiene), has been synthesized and structurally characterized. The crystal structure was determined by single-crystal X-ray diffraction. The crystal is of monoclinic, space group Pn with a = 13.9176(8), b = 15.4754(9), c = 15.9670(9) , β = 99.5010(10)o, V = 3391.8(3) 3, Z = 2, C56H68Cl2MnN16O14 , Mr = 1315.10, Dc = 1.288 g/cm3, μ = 0.344 mm-1, F(000) = 1374, R = 0.0733 and wR = 0.2035. In the crystal the manganese atom is six-coordinated by two nitrogen atoms from 2,5-bis(4-pyridyl)-3,4-diaza-2,4-hexadiene and four oxygen atoms from water molecules, completing an octahedral geometry. The title complex exhibits a novel supramolecular layer architecture sustained by the concurrence of coordination bonds, hydrogen bonds, and π-π stacking interactions.     

Molecular conformation search by distance matrix perturbations

Three-dimensional molecular structure is fundamental in chemical function identification and computer-aided drug design. The enumeration of a small number of feasible conformations provides a rigorous way to determine the optimal or a few acceptable conformations. Our contribution concerns a heuristic enhancement of a method based on distance geometry, typically in relation with experiments of the NMR type. Distance geometry has been approached by different viewpoints; ours is expected to help in several subtasks arising in the process that determines 3D structure from distance information. More precisely, the input to our algorithm consists of a set of approximate distances of varying precision; some are specified by the covalent structure and others by Nuclear Magnetic Resonance (NMR) experiments (or X-ray crystallography which, however, requires crystallization). The output is a valid tertiary structure in a specified neighborhood of the input. Our approach should help in detecting outliers of the NMR experiments, and handles inputs with partial information. Moreover, our technique is able to bound the number of degrees of freedom of the conformation manifold. We have used numerical linear algebra algorithms for reasons of speed, and because they are well-implemented, fully documented and widely available. Our main tools include, besides distance matrices, structure-preserving matrix perturbations for minimizing singular values. Our MATLAB (or SCILAB) implementation is described and illustrated.AMS subject Classification: 92E10 Molecular structure, 92C40 Biochemistry, molecular biology, 65F15 Eigenvalues, eigenvectors, 15A18 Eigenvalues, singular values, and eigenvectors     

烷基吡啶及氯化铝正负离子结构的密度泛函研究

采用量子化学密度泛函方法对N-烷基吡啶阳离子和阴离子AlCl4-,Al2Cl7-和Al3Cl10-进行了全优化计算,得到了阴阳离子的几何构型和净电荷分布.计算发现,吡啶环上的电子数符合4n 2规则,具有芳香性.吡啶阳离子的LUMO轨道主要由环上原子的2pz所贡献,是反键π分子轨道.AlCl4-,Al2Cl7-和Al3Cl10-的HOMO轨道主要由Cl原子的2px所贡献.推测吡啶阳离子的LUMO与阴离子的HOMO相互作用形成离子液体分子.     

Isomers of C20: an energy profile III

Semiempirical calculations, at the PM3 level provided within the Winmopac v2.0 software package, are used to geometrically optimize and determine the absolute energies (heats of formation) of a variety of C(20) isomers that are predicted to exist in and around the ring and cage isomers. Using the optimized Cartesian coordinates for the ring and the cage isomers, a saddle-point calculation was performed. The resulting energy profile, consisting of a series of peaks and valleys, is used as a starting point for the identification and location of fifteen additional isomers of C(20) that are predicted to be energetically stable, both via geometry optimizations and force constant analysis. These additional isomers were subsequently determined to lie adjacent to one another on the potential surface and establish a step-wise transformation between the ring and the cage. Transition-state optimization of the Cartesian coordinates at the saddle point between adjacent isomers was performed to quantify the energy of the transition state. The step-wise process from one isomer to another, which extends out over the three-dimensional surface, is predicted to require approximately 15% less energy than that of the direct, two-dimensional transformation predicted in the bowl-cage profile. However, the net atomic rearrangement for the step-wise process is about four times greater than that of the direct process. Although less in energy, the amount of atomic rearrangement in the step-wise process would make the occurrence of such a route prohibitive. Utilizing the direct distance separating the three primary isomers (ring, bowl, cage), the method of triangulation is performed to quantitatively position other C(20) structures on the potential surface, relative to the ring, bowl, and cage isomers.     

LaCO几何、电子结构和化学键的研究

长期以来 ,人们对希土羰基化合物的存在一直持怀疑态度[1 ] ,尽管 Slater[2 ] 等用基质隔离法合成部分希土羰基化合物的成功消除了这种疑问 ,但由于此类化合物高度的不稳定性 ,其几何结构至今尚未确定 ,希土羰基化合物的电子结构和化学键更是困扰人们的重要课题。希土羰基化合物是具有 L n- C键的最简单希土有机金属化合物 ,其结构和性能具有一定的代表性 ,探讨其化学键合本质及其不稳定的原因对深入了解希土金属有机化合物结构和性能的关系具有十分重要的意义。一 .研究方法本文采用洪功义、黎乐民等[3 ] 改进的高精度求解密度泛函理论方…     

Geometries and electronic structures of W4 and W clusters

Geometries and electronic structures of W₄ and W clusters were studied by use of density functional methods B3LYP, B3P86, B3PW91, BHLYP, BLYP, and MPW1PW91. The calculated results indicate that the three‐dimensional structure of singlet state with either D_2d symmetry (B3LYP, B3P86, B3PW91, BLYP, and MPW1PW91) or C_2v symmetry (BHLYP) is the ground state for the W₄ cluster. For the W cluster, the doublet state is preferred, and the most stable structure is also 3D with either D_2d symmetry (B3LYP, B3PW91, BHLYP, BLYP) or C_2v symmetry (B3P86 and MPW1PW91). The calculated electron affinity at B3P86 gives the best performance compared with experiment. For the dissociation channel, W + W₃ is suggested to be the possible route for the W₄ cluster. For the W cluster, W + W is the most likely route for dissociation, in agreement with experiment. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Rotational Hypersurfaces with Constant Gauss-Kronecker Curvature

The authors study rotational hypersurfaces with constant Gauss-Kronecker curvature in Rⁿ. They solve the ODE associated with the generating curve of such hypersurface using integral expressions and obtain several geometric properties of such hypersurfaces. In particular, they discover a class of non-compact rotational hypersurfaces with constant and negative Gauss-Kronecker curvature and finite volume, which can be seen as the higher-dimensional generalization of the pseudo-sphere.     

Lack of dissipativity is not symplecticness

We show that, when numerically integrating Hamiltonian problems, nondissipative numerical methods do not in general share the advantages possessed by symplectic integrators. Here a numerical method is called nondissipative if, when applied with a small stepsize to the test equationdy/dt = iy, real, has amplification factors of unit modulus. We construct a fourth order, nondissipative, explicit Runge-Kutta-Nyström procedure with small error constants. Numerical experiments show that this scheme does not perform efficiently in the numerical integration of Hamiltonian problems.This research has been supported by project DGICYT PB92-254.     

On the classification of geometric codes by polynomial functions

It is shown how to represent algebraically all functions that have a zero sum on all -dimensional subspaces ofPG(n,q) or ofAG(n,q). In this way one can calculate the dimensions of related codes, or one can represent interesting sets of points by functions.     

Multiple separatrix crossing in multi-degree-of-freedom Hamiltonian flows

Summary We study separatrix crossing in near-integrablek-degree-of-freedom Hamiltonian flows, 2 <k < , whose unperturbed phase portraits contain separatrices inn degrees of freedom, 1 <n <k. Each of the unperturbed separatrices can be recast as a codimension-one separatrix in the 2k-dimensional phase space, and the collection of these separatrices takes on a variety of geometrical possibilities in the reduced representation of a Poincaré section on the energy surface. In general 0 l n of the separatrices will be available to the Poincaré section, and each separatrix may be completely isolated from all other separatrices or intersect transversely with one or more of the other available separatrices. For completely isolated separatrices, transitions across broken separatrices are described for each separatrix by the single-separatrix crossing theory of Wiggins, as modified by Beigie. For intersecting separatrices, a possible violation of a normal hyperbolicity condition complicates the analysis by preventing the use of a persistence and smoothness theory for compact normally hyperbolic invariant manifolds and their local stable and unstable manifolds. For certain classes of multi-degree-of-freedom flows, however, a local persistence and smoothness result is straightforward, and we study the global implications of such a local result. In particular, we find codimension-one partial barriers and turnstile boundaries associated with each partially destroyed separatrix. From the collection of partial barriers and turnstiles follows a rich phase space partitioning and transport formalism to describe the dynamics amongst the various degrees of freedom. A generalization of Wiggins' higher-dimensional Melnikov theory to codimension-one surfaces in the multi-separatrix case allows one to uncover invariant manifold geometry. In the context of this perturbative analysis and detailed numerical computations, we study invariant manifold geometry, phase space partitioning, and phase space transport, with particular attention payed to the role of a vanishing frequency in the limit approaching the intersection of the partially destroyed separatrices. The class of flows under consideration includes flows of basic physical relevance, such as those describing scattering phenomena. The analysis is illustrated in the context of a detailed study of a 3-degree-of-freedom scattering problem.