Variational coupled cluster for ground and excited states

TL;DR

This paper investigates the energy landscape of variational coupled-cluster methods for ground and excited states, comparing it with traditional approaches using model systems and various orbital configurations.

Contribution

It provides a detailed comparison of variational and traditional coupled-cluster methods for excited states, highlighting their structural differences and performance in model systems.

Findings

Variational CC can access higher-energy solutions beyond the ground state.

Performance varies with symmetry breaking and orbital choices.

Comparison with CI methods shows strengths and limitations of VCC approaches.

Abstract

In single-reference coupled-cluster (CC) methods, one has to solve a set of non-linear polynomial equations in order to determine the so-called amplitudes which are then used to compute the energy and other properties. Although it is of common practice to converge to the (lowest-energy) ground-state solution, it is also possible, thanks to tailored algorithms, to access higher-energy roots of these equations which may or may not correspond to genuine excited states. Here, we explore the structure of the energy landscape of variational CC (VCC) and we compare it with its (projected) traditional version (TCC) in the case where the excitation operator is restricted to paired double excitations (pCCD). By investigating two model systems (the symmetric stretching of the linear \ce{H4} molecule and the continuous deformation of the square \ce{H4} molecule into a rectangular arrangement) in the presence of weak and strong correlations, the performance of VpCCD and TpCCD are gauged against their configuration interaction (CI) equivalent, known as doubly-occupied CI (DOCI), for reference Slater determinants made of ground- or excited-state Hartree-Fock orbitals or state-specific orbitals optimized directly at the VpCCD level. The influence of spatial symmetry breaking is also investigated.