The Fourier space restricted Hartree-Fock method for the electronic structure calculation of linear poly(tetrafluoroethylene)

Building on the pioneering work of Jean-Marie André and working in the laboratory he founded, the authors have developed a code called FT-1D to make Hartree-Fock electronic structure computations for stereoregular polymers using Ewald-type convergence acceleration methods. That code also takes full advantage of all line-group symmetries to calculate only the minimal set of two-electron integrals and to optimize the computation of the Fock matrix. The present communication reports a benchmark study of the FT-1D code using polytetrafluoroethylene(PTFE) as a test case. Our results not only confirm the algorithmic correctness of the code through agreement with other studies where they are applicable, but also show that the use of convergence acceleration enables accurate results to be obtained in situations where other widely-used codes(e.g., PLH and Crystal) fail. It is also found that full attention to the line-group symmetry of the PTFE polymer leads to an increase of between one and two orders of magnitude in the speed of computation. The new code can therefore be viewed as extending the range of electronic-structure computations for stereoregular polymers beyond the present scope of the successful and valuable code Crystal.     

A Happy Get-Together – Probing Electrochemical Interfaces by Non-Linear Vibrational Spectroscopy

Electrochemical interfaces are key structures in energy storage and catalysis. Hence, a molecular understanding of the active sites at these interfaces, their solvation, the structure of adsorbates, and the formation of solid-electrolyte interfaces are crucial for an in-depth mechanistic understanding of their function. Vibrational sum-frequency generation (VSFG) spectroscopy has emerged as an operando spectroscopic technique to monitor complex electrochemical interfaces due to its intrinsic interface sensitivity and chemical specificity. Thus, this review discusses the happy get-together between VSFG spectroscopy and electrochemical interfaces. Methodological approaches for answering core issues associated with the behavior of adsorbates on electrodes, the structure of solvent adlayers, the transient formation of reaction intermediates, and the emergence of solid electrolyte interphase in battery research are assessed to provide a critical inventory of highly promising avenues to bring optical spectroscopy to use in modern material research in energy conversion and storage.     

Strichartz Estimates for Non-Elliptic Schrödinger Equations on Compact Manifolds

In this note we consider the Schrödinger equation on compact manifolds equipped with possibly degenerate metrics. We prove Strichartz estimates with a loss of derivatives. The rate of loss of derivatives depends on the degeneracy of metrics. For the non-degenerate case we obtain, as an application of the main result, the same Strichartz estimates as that in the elliptic case. This extends Strichartz estimates for Riemannian metrics proved by Burq-Gérard-Tzvetkov to the non-elliptic case and improves the result by Salort for the degenerate case. We also investigate the optimality of the result for the case on 𝕊³ × 𝕊³.     

Asymptotically optimal neighbour sum distinguishing colourings of graphs

Consider a simple graph G = (V,E) and its proper edge colouring c with the elements of the set {1,2,…,k}. The colouring c is said to be neighbour sum distinguishing if for every pair of vertices u, v adjacent in G, the sum of colours of the edges incident with u is distinct from the corresponding sum for v. The smallest integer k for which such colouring exists is known as the neighbour sum distinguishing index of a graph and denoted by . The definition of this parameter, which makes sense for graphs containing no isolated edges, immediately implies that , where Δ is the maximum degree of G. On the other hand, it was conjectured by Flandrin et al. that for all those graphs, except for C₅. We prove this bound to be asymptotically correct by showing that . The main idea of our argument relays on a random assignment of the colours, where the choice for every edge is biased by so called attractors, randomly assigned to the vertices. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 776–791, 2015     

The Phosphorus Bond,or the Phosphorus-Centered Pnictogen Bond: The Covalently Bound Phosphorus Atom in Molecular Entities and Crystals as a Pnictogen Bond Donor

The phosphorus bond in chemical systems, which is an inter- or intramolecular noncovalent interaction, occurs when there is evidence of a net attractive interaction between an electrophilic region associated with a covalently or coordinately bonded phosphorus atom in a molecular entity and a nucleophile in another, or the same, molecular entity. It is the second member of the family of pnictogen bonds, formed by the second member of the pnictogen family of the periodic table. In this overview, we provide the reader with a snapshot of the nature, and possible occurrences, of phosphorus-centered pnictogen bonding in illustrative chemical crystal systems drawn from the ICSD (Inorganic Crystal Structure Database) and CSD (Cambridge Structural Database) databases, some of which date back to the latter part of the last century. The illustrative systems discussed are expected to assist as a guide to researchers in rationalizing phosphorus-centered pnictogen bonding in the rational design of molecular complexes, crystals, and materials and their subsequent characterization.     

Maximal inequality and complete convergences of non-identically distributed negatively associated sequences

A maximal inequality for the partial sum of NA sequence is constructed.By using this inequality the complete convergence rates in the strong laws for a class of dependent random variables for weighted sums are discussed.The results obtained extend the results of Liang(1999, 2000).     

关于多元幂级数

引入了多元函数项级数的概念,给出了其收敛域及和函数的定义;通过详实的例子讨论了多元幂级数的收敛域、和函数及多元函数展开为多元幂级数的计算方法.     

NA序列部分和的矩完全收敛性

讨论了NA序列部分和的矩完全收敛性,在一定条件下获得了NA序列矩完全收敛的充要条件,显示了矩完全收敛和矩条件之间的关系,将独立同分布随机变量序列矩完全收敛的结果推广到NA序列,得到了与独立随机变量序列情形类似的结果.