Experimental Charge Density Evidence for Pnicogen Bonding in a Crystal of Ammonium Chloride

Chemical binding in crystalline ammonium chloride, a simple inorganic salt with an unexpectedly complex bonding pattern, was studied by using a topological analysis of electron density function derived from high‐resolution X‐ray diffraction. Supported by periodic quantum chemical calculations, it provided experimental evidence for weak σ‐hole bonds (1.5 kcal mol^?1) that involve ammonium cations in a crystal. Our results show this type of supramolecular interaction to be more numerous than has been found to date by using gas‐phase calculations or statistical analysis of CSD.     

Electron Density Analysis of Hyperconjugation

Hyperconjugation is analyzed through the electron density of orbitals responsible for hyperconjugative interactions, which cannot be detected by means of conventional electron‐density‐based calculations. This interaction is detected through the π electron density topology, by excluding σ electron density from the total. As the presence of the hyperconjugation phenomenon in carbocation systems is well understood, several carbocations are benchmarked, and the results show that the positive carbon atom establishes a hyperconjugative critical point with the adjacent methyl group(s). Also, π localization and delocalization indices are employed to support the conclusions made by the topological analysis.     

Symmetry calculation for molecules and transition states

The symmetry of molecules and transition states of elementary reactions is an essential property with important implications for computational chemistry. The automated identification of symmetry by computers is a very useful tool for many applications, but often relies on the availability of three‐dimensional coordinates of the atoms in the molecule and hence becomes less useful when these coordinates are a priori unavailable. This article presents a new algorithm that identifies symmetry of molecules and transition states based on an augmented graph representation of the corresponding structures, in which both topology and the presence of stereocenters are accounted for. The automorphism group order of the graph associated with the molecule or transition state is used as a starting point. A novel concept of label‐stereoisomers, that is, stereoisomers that arise after labeling homomorph substituents in the original molecule so that they become distinguishable, is introduced and used to obtain the symmetry number. The algorithm is characterized by its generic nature and avoids the use of heuristic rules that would limit the applicability. The calculated symmetry numbers are in agreement with expected values for a large and diverse set of structures, ranging from asymmetric, small molecules such as fluorochlorobromomethane to highly symmetric structures found in drug discovery assays. The new algorithm opens up new possibilities for the fast screening of the degree of symmetry of large sets of molecules. © 2014 Wiley Periodicals, Inc.     

Multidimensional persistence in biomolecular data

Persistent homology has emerged as a popular technique for the topological simplification of big data, including biomolecular data. Multidimensional persistence bears considerable promise to bridge the gap between geometry and topology. However, its practical and robust construction has been a challenge. We introduce two families of multidimensional persistence, namely pseudomultidimensional persistence and multiscale multidimensional persistence. The former is generated via the repeated applications of persistent homology filtration to high‐dimensional data, such as results from molecular dynamics or partial differential equations. The latter is constructed via isotropic and anisotropic scales that create new simiplicial complexes and associated topological spaces. The utility, robustness, and efficiency of the proposed topological methods are demonstrated via protein folding, protein flexibility analysis, the topological denoising of cryoelectron microscopy data, and the scale dependence of nanoparticles. Topological transition between partial folded and unfolded proteins has been observed in multidimensional persistence. The separation between noise topological signatures and molecular topological fingerprints is achieved by the Laplace–Beltrami flow. The multiscale multidimensional persistent homology reveals relative local features in Betti‐0 invariants and the relatively global characteristics of Betti‐1 and Betti‐2 invariants. © 2015 Wiley Periodicals, Inc.     

Topological Effect on the Structure of Self‐Assembled Aggregates from Amphiphilic Macromolecules in Solution

The self‐assembled morphologies of cyclic amphiphiles, which are composed of a long hydrophobic block and a short hydrophilic block, in selective solutions are studied by using a simulated annealing method. The morphological dependence of the aggregates on solvent quality is investigated. The topology effects are studied by comparing results from linear counterparts of the amphiphiles. It is observed that, in addition to spherical micelles, cylindrical micelles, disklike micelles, vesicles, and large compound micelles, muticompartment vesicles with several fluidic cores can be formed by the cyclic systems. The morphologies are regulated by the interaction parameter ε_AS between the hydrophobic block and solvents. Furthermore, it is revealed that the differences of characteristics of the self‐assembled aggregates originate from the difference in architectural constraint. The wide region of forming multicompartment vesicles suggests that cyclic amphiphilic macromolecules could be a suitable candidate for applications to deliver multiple functional components by compartmentalizing different components in different confined space of vesicles.     

On the vanishing of homology in random Čech complexes

We compute the homology of random ?ech complexes over a homogeneous Poisson process on the d‐dimensional torus, and show that there are, coarsely, two phase transitions. The first transition is analogous to the Erd?s ‐Rényi phase transition, where the ?ech complex becomes connected. The second transition is where all the other homology groups are computed correctly (almost simultaneously). Our calculations also suggest a finer measurement of scales, where there is a further refinement to this picture and separation between different homology groups. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 51, 14–51, 2017     

Wedge Operations and Doubling Operations of Real Toric Manifolds

This paper deals with two things.First,the cohomology of canonical extensions of real topological toric manifolds is computed when coefficient ring G is a commutative ring in which 2 is unit in G.Second,the author focuses on a specific canonical extensions called doublings and presents their various properties.They include existence of infinitely many real topological toric manifolds admitting complex structures,and a way to construct infinitely many real toric manifolds which have an odd torsion in their cohomology groups.Moreover,some questions about real topological toric manifolds related to Halperin's toral rank conjecture are presented.     

Neumann problems with resonance in the first eigenvalue

The aim of this work is to present results of existence of solutions for a class of superlinear asymmetric elliptic systems with resonance in the first eigenvalue. The asymmetry that we consider has linear behavior on and superlinear on . To obtain these results we apply topological degree theory.     

内部算子生成的直觉I-Fuzzy拓扑空间

在直觉I-fuzzy拓扑空间中定义了内部度,并研究了它的一些性质,接着给出了直觉I-fuzzy拓扑空间内部算子的概念,最后得到了从拓扑的直觉I-Fuzzy内部算子I出发,得到一个直觉I-fuzzy拓扑r,再利用r定义的内部算子恰好回到了I等结论.