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Main Title: Singular analysis and coupled cluster theory
Author(s): Flad, Heinz-Jürgen
Harutyunyan, Gohar
Schulze, Bert-Wolfgang
Type: Article
Language Code: en
Abstract: The primary motivation for systematic bases in first principles electronic structure simulations is to derive physical and chemical properties of molecules and solids with predetermined accuracy. This requires a detailed understanding of the asymptotic behaviour of many-particle Coulomb systems near coalescence points of particles. Singular analysis provides a convenient framework to study the asymptotic behaviour of wavefunctions near these singularities. In the present work, we want to introduce the mathematical framework of singular analysis and discuss a novel asymptotic parametrix construction for Hamiltonians of many-particle Coulomb systems. This corresponds to the construction of an approximate inverse of a Hamiltonian operator with remainder given by a so-called Green operator. The Green operator encodes essential asymptotic information and we present as our main result an explicit asymptotic formula for this operator. First applications to many-particle models in quantum chemistry are presented in order to demonstrate the feasibility of our approach. The focus is on the asymptotic behaviour of ladder diagrams, which provide the dominant contribution to short-range correlation in coupled cluster theory. Furthermore, we discuss possible consequences of our asymptotic analysis with respect to adaptive wavelet approximation.
Issue Date: 2015
Date Available: 24-Oct-2017
DDC Class: 540 Chemie und zugeordnete Wissenschaften
Journal Title: Physical chemistry, chemical physics
Publisher: Royal Society of Chemistry
Publisher Place: Cambridge
Volume: 17
Issue: 47
Publisher DOI: 10.1039/c5cp01183c
Page Start: 31530
Page End: 31541
EISSN: 1463-9084
ISSN: 1463-9076
Notes: Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.
This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.
Appears in Collections:FG Modellierung, Simulation und Optimierung in Natur- und Ingenieurwissenschaften » Publications

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