杂合型全局优化法优化水分子团簇结构

基于遗传算法、快速模拟退火及共轭梯度方法提出了一种快速的杂合型全局优化方法(fast hybrid global optimization algorithm, FHGOA),并将这一方法应用于TIP3P和TIPS2模型水分子团簇(H2O)n结构的优化.在进行TIP3P模型水分子团簇结构的优化过程中,发现了能量比文献值更低的团簇结构,且执行效率有较大提高.把该方法应用到优化TIPS2模型的水分子团簇,发现最优结构和采用TTM2-F模型优化的水分子团簇结构在n < 17时完全相同,为全表面结构;而在n=17、19、22时为单中心水分子笼状结构;在n=25、27时为双中心水分子笼状结构.说明随着团簇中水分子个数的增加,采用TIPS2和TTM2-F势能函数优化的团簇最优结构有相同的变化趋势.     

Three-dimensional hydrogen-bond geometry and probability information from a crystal survey

Summary An extensive crystal survey of the Cambridge Structural Database has been carried out to provide hydrogen-bond data for use in drug-design strategies. Previous crystal surveys have generated 1D frequency distributions of hydrogen-bond distances and angles, which are not sufficient to model the hydrogen bond as a ligand-receptor interaction. For each hydrogen-bonding group of interest to the drug designer, geometric hydrogen-bond criteria have been derived. The 3D distribution of complementary atoms about each hydrogen-bonding group has been ascertained by dividing the space about each group into bins of equal volume and counting the number of observed hydrogen-bonding contacts in each bin. Finally, the propensity of each group to form a hydrogen bond has been calculated. Together, these data can be used to predict the potential site points with which a ligand could interact and there-fore could be used in molecular-similarity studies, pharmacophore query searching of databases, or de novo design algorithms.     

Geometry prediction of hafnocenes by quantum chemical methods

The performance of quantum chemical methods for geometry prediction of hafnocenes was evaluated. HF, B3LYP and MP2 in combination with nonrelativistic (MHF) and relativistic (MWB and LANL2DZ) basis sets for hafnium together with standard basis sets 3-21G*, 6-31G* and 6-311G** for other elements were applied. Five basic structural parameters of the optimized structures of the hafnocenes were compared with experimental crystal structures obtained from the Cambridge structural database. Altogether 80 hafnocenes were included in the analysis. The results show that relativistic corrections are necessary for Hf atom. However, even the Hartree–Fock (HF) method, when combined with relativistic pseudopotentials, reproduces the experimental crystal structures with significant accuracy. The good performance of the HF method can be understood to originate from the absence of significant near-degeneracy correlations for hafnium. On average, the B3LYP and MP2 methods provide structural parameters somewhat closer to the experimental ones.     

Equivariant Chern Classes of Orientable Toric Origami Manifolds∗

A toric origami manifold, introduced by Cannas da Silva, Guillemin and Pires, is a generalization of a toric symplectic manifold. For a toric symplectic manifold, its equivariant Chern classes can be described in terms of the corresponding Delzant polytope and the stabilization of its tangent bundle splits as a direct sum of complex line bundles. But in general a toric origami manifold is not simply connected, so the algebraic topology of a toric origami manifold is more difficult than a toric symplectic manifold. In this paper they give an explicit formula of the equivariant Chern classes of an oriented toric origami manifold in terms of the corresponding origami template. Furthermore, they prove the stabilization of the tangent bundle of an oriented toric origami manifold also splits as a direct sum of complex line bundles.     

Spectroscopic and Quantum Mechanical Studies of Substituted Anilines and their Charge-Transfer Complexes with Iodine in Different Solvents

Summary. Equilibrium constants and molar extinction coefficients for 1:1 charge-transfer complexes between 2-hydroxyaniline (HA), 5-chloro-2-hydroxyaniline (CHA), and 4-bromo-2,6-dimethylaniline (BMA) as donors and iodine, as a typical σ-acceptor were determined spectrophotometrically in chloroform, dichloromethane, and carbontetrachloride solutions. Spectral characteristics and formation constants are discussed in terms of donor molecular structure and solvent polarity. The stoichiometry of the complexes was established to be 1:1. For this purpose, optical data were subjected to the form of the Rose-Drago equation for 1:1 equilibria. Electronic absorption spectra of the studied anilines were measured in different solvents. Spectral data were reported and band maxima were assigned to the appropriate molecular orbital transitions (π–π^* and n–π^* electronic transition). Solvent effects on the electronic transitions were discussed. Optimized geometry of the studied anilines was obtained at B3LYP/6-31 + G(d). The effect of the electronic factors of the substituents on the geometrical parameters of the ring has been explored. Geometrical values of the ring deviate from the regular hexagonal ring. Intramolecular H-bonds in HA and CHA have been computed at B3LYP/6-31 + G(d) and MP2/6-31 + G(d) levels. The H-bonding distance was calculated to be 2.105 ? in HA and 2.127 ? in CHA. Abstracted from her M.Sc. thesis     

Representation invariant Geometrothermodynamics: Applications to ordinary thermodynamic systems

In this work we employ a recently devised metric within the Geometrothermodynamics program to study ordinary thermodynamic systems. The new feature of this metric is that, in addition to Legendre symmetry, it exhibits invariance under a change of representation. This metric was derived in a previous work by the authors while addressing the problem of the conformal structure of the thermodynamic metrics for different representations. Here, we present a thorough analysis for the ideal gas, the van der Waals fluid, the one dimensional Ising model and some other systems of cosmological interest.     

Noether's Theorem on Surfaces

In this article we prove a version of Noether's Theorem (of Calculus of Variations) which is valid for a general regular (compact) surface. As a special feature, the Lie group of transformations is allowed to act on the Cartesian product of the surface and the functional space. Additionally, we apply the Theorem to a problem in Classical Differential Geometry of surfaces. The given application is actually an example showing how Noether's Theorem can be used to construct invariant properties of the solutions to variational problems defined on surfaces, or equivalently, of the solutions to the associated Euler-Lagrange equations resulting from them.     

The role of multiple solution tasks in developing knowledge and creativity in geometry

This paper describes changes in students’ geometrical knowledge and their creativity associated with implementation of Multiple Solution Tasks (MSTs) in school geometry courses. Three hundred and three students from 14 geometry classes participated in the study, of whom 229 students from 11 classes learned in an experimental environment that employed MSTs while the rest learned without any special intervention in the course of one school year. This longitudinal study compares the development of knowledge and creativity between the experimental and control groups as reflected in students’ written tests. Geometry knowledge was measured by the correctness and connectedness of the solutions presented. The criteria for creativity were: fluency, flexibility, and originality. The findings show that students’ connectedness as well as their fluency and flexibility benefited from implementation of MSTs. The study supports the idea that originality is a more internal characteristic than fluency and flexibility, and therefore more related with creativity and less dynamic. Nevertheless, the MSTs approach provides greater opportunity for potentially creative students to present their creative products than conventional learning environment. Cluster analysis of the experimental group identified three clusters that correspond to three levels of student performance, according to the five measured criteria in pre- and post-tests, and showed that, with the exception of originality, performance in all three clusters generally improved on the various criteria.     

Infinitely many singular interactions on noncompact manifolds

We show that the ground state energy is bounded from below when there are infinitely many attractive delta function potentials placed in arbitrary locations, while all being separated at least by a minimum distance, on two dimensional non-compact manifold. To facilitate the reading of the paper, we first present the arguments in the setting of Cartan–Hadamard manifolds and then subsequently discuss the general case. For this purpose, we employ the heat kernel techniques as well as some comparison theorems of Riemannian geometry, thus generalizing the arguments in the flat case following the approach presented in Albeverio et al. (2004).