Convergence of coupled cluster perturbation theory

TL;DR

This paper investigates the convergence properties of a coupled cluster perturbation series across different systems and basis sets, highlighting the influence of target state choice and basis set augmentation on convergence behavior.

Contribution

It provides a detailed analysis of the convergence of a CC perturbation series, emphasizing the role of target state selection and basis set augmentation in convergence and divergence.

Findings

Convergence depends mainly on the target state, not the parent state.

Augmented basis sets can induce divergence in the series.

Low-order corrections remain practically useful despite potential divergences.

Abstract

The convergence of a recently proposed coupled cluster (CC) family of perturbation series [Eriksen, J. J. et al., J. Chem. Phys. 140, 064108 (2014)], in which the energetic difference between two CC models - a low-level parent and a high-level target model - is expanded in orders of the M{\o}ller-Plesset (MP) fluctuation potential, is investigated for four prototypical closed-shell systems (Ne, singlet methylene, distorted HF, and the fluoride anion) in standard and augmented basis sets. In these investigations, energy corrections of the various series have been calculated to high orders and their convergence radii determined by probing for possible front- and back-door intruder states, the existence of which would make the series divergent. In summary, we conclude how it is primarily the choice of target state, and not the choice of parent state, which ultimately governs the convergence behavior of a given series. For example, restricting the target state to, say, triple or quadruple excitations might remove intruders present in series that target the full configuration interaction (FCI) limit, such as the standard MP series. Furthermore, we find that whereas a CC perturbation series might converge within standard correlation consistent basis sets, it may start to diverge whenever these become augmented by diffuse functions, similar to the MP case. However, unlike for the MP case, such potential divergences are not found to invalidate the practical use of the low-order corrections of the CC perturbation series.