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ABSTRACTThe 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. 相似文献
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Dr. Sabin Llona‐Minguez Dr. Matthieu Desroses Artin Ghassemian Dr. Sylvain A. Jacques Dr. Lars Eriksson Rebecka Isacksson Tobias Koolmeister Dr. Pål Stenmark Dr. Martin Scobie Prof. Thomas Helleday 《Chemistry (Weinheim an der Bergstrasse, Germany)》2015,21(20):7394-7398
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. 相似文献
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Nano palladium supported on high‐surface‐area metal–organic framework MIL‐101: an efficient catalyst for Sonogashira coupling of aryl and heteroaryl bromides with alkynes 下载免费PDF全文
Manne Annapurna T. Parsharamulu P. Vishnuvardhan Reddy M. Suresh Pravin R. Likhar Mannepalli Lakshmi Kantam 《应用有机金属化学》2015,29(4):234-239
Palladium nanoparticle‐incorporated metal–organic framework MIL‐101 (Pd/MIL‐101) was successfully synthesized and characterized using X‐ray diffraction, nitrogen physisorption, X‐ray photoelectron, UV–visible and infrared spectroscopies, and transmission electron microscopy. The characterization techniques confirmed high porosity and high surface area of MIL‐101 and high stability of nano‐size palladium particles. Pd/MIL‐101 nanocomposite was investigated for the Sonogashira cross‐coupling reaction of aryl and heteroaryl bromides with various alkynes under copper‐free conditions. The reusability of the catalyst was tested for up to four cycles without any significant loss in catalytic activity. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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Pd0‐Catalyzed Intramolecular α‐Arylation of Sulfones: Domino Reactions in the Synthesis of Functionalized Tetrahydroisoquinolines 下载免费PDF全文
Prof.Dr. Daniel Solé Ferran Pérez‐Janer Dr. Raffaella Mancuso 《Chemistry (Weinheim an der Bergstrasse, Germany)》2015,21(12):4580-4584
A new strategy for the synthesis of tetrahydroisoquinolines based on the Pd0‐catalyzed intramolecular α‐arylation of sulfones is reported. The combination of this Pd‐catalyzed reaction with intermolecular Michael and aza‐Michael reactions allows the development of two‐ and three‐step domino processes to synthesize diversely functionalized scaffolds from readily available starting materials. 相似文献