The coupled-cluster formalism – a mathematical perspective

ABSTRACT

The Coupled-Cluster (CC) theory is one of the most successful high precision methods used to solve the stationary Schrödinger equation. In this article, we address the mathematical foundation of this theory with focus on the advances made in the past decade. Rather than solely relying on spectral gap assumptions (non-degeneracy of the ground state), we highlight the importance of coercivity assumptions – Gårding type inequalities – for the local uniqueness of the CC solution. Based on local strong monotonicity, different sufficient conditions for a local unique solution are suggested. One of the criteria assumes the relative smallness of the total cluster amplitudes (after possibly removing the single amplitudes) compared to the Gårding constants. In the extended CC theory the Lagrange multipliers are wave function parameters and, by means of the bivariational principle, we here derive a connection between the exact cluster amplitudes and the Lagrange multipliers. This relation might prove useful when determining the quality of a CC solution. Furthermore, the use of an Aubin–Nitsche duality type method in different CC approaches is discussed and contrasted with the bivariational principle.     

Highly Proton-Conductive Zinc Metal-Organic Framework Based On Nickel(II) Porphyrinylphosphonate

The design of new solid-state proton-conducting materials is a great challenge for chemistry and materials science. Herein, a new anionic porphyrinylphosphonate-based MOF ( IPCE-1Ni ), which involves dimethylammonium (DMA) cations for charge compensation, is reported. As a result of its unique structure, IPCE-1Ni exhibits one of the highest value of the proton conductivity among reported proton-conducting MOF materials based on porphyrins (1.55×10⁻³ S cm⁻¹ at 75 °C and 80 % relative humidity).     

Chemical versus Electrochemical Synthesis of Carbon Nano‐onion/Polypyrrole Composites for Supercapacitor Electrodes

The development of high‐surface‐area carbon electrodes with a defined pore size distribution and the incorporation of pseudo‐active materials to optimize the overall capacitance and conductivity without destroying the stability are at present important research areas. Composite electrodes of carbon nano‐onions (CNOs) and polypyrrole (Ppy) were fabricated to improve the specific capacitance of a supercapacitor. The carbon nanostructures were uniformly coated with Ppy by chemical polymerization or by electrochemical potentiostatic deposition to form homogenous composites or bilayers. The materials were characterized by transmission‐ and scanning electron microscopy, differential thermogravimetric analyses, FTIR spectroscopy, piezoelectric microgravimetry, and cyclic voltammetry. The composites show higher mechanical and electrochemical stabilities, with high specific capacitances of up to about 800 F g^?1 for the CNOs/SDS/Ppy composites (chemical synthesis) and about 1300 F g^?1 for the CNOs/Ppy bilayer (electrochemical deposition).     

Vinylic MIDA Boronates: New Building Blocks for the Synthesis of Aza‐Heterocycles

A two‐step synthesis of structurally diverse pyrrole‐containing bicyclic systems is reported. ortho‐Nitro‐haloarenes coupled with vinylic N‐methyliminodiacetic acid (MIDA) boronates generate ortho‐vinyl‐nitroarenes, which undergo a “metal‐free” nitrene insertion, resulting in a new pyrrole ring. This novel synthetic approach has a wide substrate tolerance and it is applicable in the preparation of more complex “drug‐like” molecules. Interestingly, an ortho‐nitro‐allylarene derivative furnished a cyclic β‐aminophosphonate motif.     

SDN中基于KMOBPSO的高可靠性控制器部署算法

针对SDN中控制器系统的单节点故障问题,兼顾系统成本和系统时延,应用N+1冗余备份模型来提高SDN控制器部署的可靠性,并将其抽象为多目标优化问题.同时,提出了一种融合K-means聚类算法和遗传算子的多目标二进制粒子群算法——KMOBPSO算法,以求解SDN控制器高可靠性部署问题的解.仿真结果表明,所提算法具有求解精度高、分布均匀、沿Pareto前沿面覆盖广的特点,能够显著提高SDN中控制器部署的可靠性.