Coupled-Cluster theory revisited Part II: Analysis of the single-reference Coupled-Cluster equations

In a series of two articles, we propose a comprehensive mathematical framework for Coupled-Cluster-type methods. In this second part, we analyze the nonlinear equations of the single-reference Coupled-Cluster method using topological degree theory. We establish existence results and qualitative info...

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Bibliographic Details
Published inESAIM: Mathematical Modelling and Numerical Analysis Vol. 57; no. 2; pp. 545 - 583
Main Authors Csirik, Mihály A., Laestadius, Andre
Format Journal Article
LanguageEnglish
Published 01.03.2023
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Summary:In a series of two articles, we propose a comprehensive mathematical framework for Coupled-Cluster-type methods. In this second part, we analyze the nonlinear equations of the single-reference Coupled-Cluster method using topological degree theory. We establish existence results and qualitative information about the solutions of these equations that also sheds light of the numerically observed behavior. In particular, we compute the topological index of the zeros of the single-reference Coupled-Cluster mapping. For the truncated Coupled-Cluster method, we derive an energy error bound for approximate eigenstates of the Schrödinger equation.
Bibliography:NFR/287906
ISSN:2822-7840
2804-7214
DOI:10.1051/m2an/2022099