Guaranteed convergence for a class of coupled-cluster methods based on Arponen's extended theory

Abstract

A wide class of coupled-cluster methods is introduced, based on Arponen's extended coupled-cluster theory. This class of methods is formulated in terms of a coordinate transformation of the cluster operators. The mathematical framework for the error analysis of coupled-cluster methods based on Arponen's bivariational principle is presented, in which the concept of local strong monotonicity of the flipped gradient of the energy is central. A general mathematical result is presented, describing sufficient conditions for coordinate transformations to preserve the local strong monotonicity. The result is applied to the presented class of methods, which include the standard and quadratic coupled-cluster methods, and also Arponen's canonical version of extended coupled-cluster theory. Some numerical experiments are presented, and the use of canonical coordinates for diagnostics is discussed.

arXiv comment11 pages

References in corpus (6)

• Coupled-cluster computations of atomic nuclei
• Numerical and Theoretical Aspects of the DMRG-TCC Method Exemplified by the Nitrogen Dimer
• Coupled-Cluster Theory for Systems of Bosons in External Traps
• Analysis of The Tailored Coupled-Cluster Method in Quantum Chemistry
• Cost-effective description of strong correlation: efficient implementations of the perfect quadruples and perfect hextuples models
• The Coupled-Cluster Formalism - a Mathematical Perspective

Cited by in corpus (5)

• Dimensionality reduction of many-body problem using coupled-cluster sub-system flow equations: classical and quantum computing perspective
• The $S$-diagnostic -- an a posteriori error assessment for single-reference coupled-cluster methods
• Homotopy continuation methods for coupled-cluster theory in quantum chemistry
• A state-specific multireference coupled-cluster method based on the bivariational principle
• Configuration weights in coupled-cluster theory