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.

GRAPHICAL ABSTRACT

Keywords:

• Coupled-cluster method
• extended coupled-cluster method
• error analysis
• electronic-structure theory

Acknowledgments

The authors are thankful to M. A. Csirik for useful comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work has received funding from the Research Council of Norway (RCN) [CoE grant numbers 287906 and 262695] (Hylleraas Centre for Quantum Molecular Sciences), and from ERC-STG-2014 [grant number 639508].