Singular analysis and coupled cluster theory

  • 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 theThe 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.show moreshow less

Export metadata

Additional Services

Share in Twitter Search Google Scholar Statistics
Metadaten
Author:Heinz-Jürgen Flad, Gohar Harutyunyan, Bert-Wolfgang SchulzeGND
DOI:https://doi.org/10.1039/c5cp01183c
ISSN:1463-9076 (print)
ISSN:1463-9084 (online)
Pubmed Id:http://www.ncbi.nlm.nih.gov/pubmed?term=26094979
Parent Title (English):Physical chemistry, chemical physics : a journal of European Chemical Societies
Publisher:Royal Society of Chemistry
Place of publication:Cambridge
Document Type:Article
Language:English
Year of first Publication:2015
Year of Completion:2015
Release Date:2017/03/27
Volume:17
Issue:47
Pagenumber:12
First Page:31530
Last Page:31541
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Peer Review:Referiert