Accelerating the convergence of higher-order coupled-cluster methods II: coupled-cluster Λ equations and dynamic damping

Abstract

The method of sub-iteration, which was previously applied to the higher-order coupled-cluster amplitude equations, is extended to the case of the coupled-cluster Λ equations. The sub-iteration procedure for the Λ equations are found to be highly similar to that for the amplitude equations, and to exhibit a similar improvement in the rate of convergence relative to extrapolation of all $\hat{T}$ or $\hat{\mathrm{\Lambda }}$ amplitudes using DIIS. A method of dynamic damping is also presented which is found to effectively recover rapid convergence in the case of oscillatory behaviour in the amplitude or Λ equations. Together, these techniques allow for the convergence of both the amplitude and Λ equations necessary for the calculation of analytic gradients and properties of higher-order coupled-cluster methods without the high memory or disk I/O cost of full DIIS extrapolation.

GRAPHICAL ABSTRACT

Keywords:

• Coupled cluster
• analytic gradients
• convergence acceleration
• extrapolation

Acknowledgments

I would like to thank Prof. Jürgen Gauss for inspiring this work, and for his efforts on the CCSDT implementation in CFOUR on which this work is ultimately based. A preliminary version of the original work on sub-iteration in the CC amplitude equations was also presented at the 2015 workshop ‘New Developments in Coupled-Cluster Theory’ co-organised by Prof. Gauss. This work was supported by a start-up grant from Southern Methodist University, and all calculations were performed on the ManeFrame II computing system at SMU.

Disclosure statement

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

Additional information

Funding

This work was supported by a start-up grant from Southern Methodist University, and all calculations were performed on the ManeFrame II computing system at SMU.