Volume 57, Number 2, March-April 2023
|Page(s)||545 - 583|
|Published online||27 March 2023|
Coupled-Cluster theory revisited
Part II: Analysis of the single-reference Coupled-Cluster equations
Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033, Blindern, N-0315 Oslo, Norway
2 Department of Computer Science, Oslo Metropolitan University, P.O. Box 4, St. Olavs plass, NO-0130 Oslo, Norway
* Corresponding author: email@example.com
Accepted: 30 November 2022
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.
Mathematics Subject Classification: 81V55 / 81-08 / 81-10 / 47H11
Key words: Quantum mechanics / many-body problem / quantum chemistry / electronic structure / coupled-cluster theory / nonlinear analysis / topological degree / Brouwer degree
© The authors. Published by EDP Sciences, SMAI 2023
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