Limitations of coupled cluster approximations for highlyaccurate investigations of Rb$_2^+$

TL;DR

This paper investigates the limitations of standard coupled-cluster methods in accurately modeling the potential energy curves of Rb$_2^+$ and similar systems, revealing unphysical barriers caused by symmetry instabilities.

Contribution

It introduces a new framework for perturbative triples corrections and identifies the root cause of unphysical barriers as symmetry instability in Hartree-Fock solutions.

Findings

Standard CC methods produce unphysical long-range barriers in Rb$_2^+$.

The barrier issue is linked to symmetry instability of the Hartree-Fock reference.

Using symmetry-broken references can yield physically meaningful PECs.

Abstract

We reveal limitations of several standard coupled-cluster (CC) methods with perturbation-theorybased noniterative or approximate iterative treatments of triple excitations when applied to thedetermination of highly accurate potential energy curves (PECs) of ionic dimers, such as the X $^2\Sigma^+_g$ electronic ground state of Rb$_2^+$. Such computations are of current interest for the understanding ofion-atom interactions in the ultracold regime. We demonstrate that these coupled-cluster methodslead to an unphysical long-range barrier for the Rb$_2^+$ system. The barrier is small but clearly spoilsthe entire long-range behavior of the PEC. The effect is also found for other X$_2^+$ systems, like X = Li, Na, and K. Calculations using a new flexible framework for obtaining leading perturbativetriples corrections derived using an analytic CC singles and doubles (CCSD) energy derivativeformulation demonstrate that the origin of this problem lies in the use of $T_3$ amplitudes obtained from approximate CC singles, doubles and triples (CCSDT) amplitude equations. It is shown thatthe unphysical barrier is related to a symmetry instability of the underlying Hartree-Fock mean-fieldsolution. Physically meaningful perturbative corrections in the long-range tail of the PEC mayinstead be obtained using symmetry-broken reference determinants.