Exploring alternative approaches to improve the convergence pattern in solving the coupled-cluster equations

Abstract

The perturbational parameter λ formally appearing in the coupled-cluster (CC) and perturbation theory (PT) frameworks is included explicitly in the Hamiltonian and the CC formalism. Using the Møller–Plesset (MP) partitioning, properties of the resulting λ-dependent amplitude functions are discussed. Truncating the cluster expansion at singles and doubles (CCSD), we use these properties and knowledge of the CCSD amplitudes at $|\lambda |<1$ values to estimate the CCSD amplitudes without solving the relevant equations at $\lambda =1$ (corresponding to the original, physical problem). This extrapolation scheme is explored, with emphasis on convergence improvement of CC iterations. The approximate amplitudes generated by this procedure are used as the starting point for the CCSD iterations, an alternative to the first order MP (MP1) set. Numerical examples are presented which show that the technique combined with the direct inversion in the iterative subspace (DIIS) method is especially helpful in situations where the standard CCSD iterations converge slowly or not at all. We report cases where starting from MP1, the solution process has an unfavourable convergence pattern even with DIIS applied, while the amplitudes generated by our method provide a much better starting point, overcoming the divergence issues of the original sequence.

GRAPHICAL ABSTRACT

Keywords:

• Coupled-cluster equations
• amplitude function
• extrapolation
• convergence properties

Acknowledgments

J.N. greatly appreciates the long-lasting friendship of Prof. Péter Szalay, to whom this work is dedicated. Zs.É.M. is grateful to Prof. Péter Surján for discussions on the topic.

Disclosure statement

No conflict of interest was reported by the author(s).

Additional information

Funding

The project has received funding from the European Union's Horizon 2020 Research and Innovation Programme on the basis of the Grant Agreement under the Marie Skłodowska–Curie funding scheme No. 945478 - SASPRO2, MSCA-COFUND. This work has been also supported by the Slovak Research and Development Agency (Grant No. APVV-21-0497).