Variational coupled cluster for ground and excited states

Antoine Marie,Fábris Kossoski,Pierre-François Loos

doi:10.1063/5.0060698

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 that 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 that may or may not correspond to genuine excited states. Here, we explore the structure of the energy landscape of variational CC and we compare it with its (projected) traditional version 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 H4 molecule and the continuous deformation of the square H4 molecule into a rectangular arrangement) in the presence of weak and strong correlations, the performance of variational pCCD (VpCCD) and traditional pCCD is gauged against their configuration interaction (CI) equivalent, known as doubly occupied CI, 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.

Highlights

Because SRCC works so well for weak correlation, it would be convenient to be able to treat strong correlation within the very same framework
We have shown that the agreement between pCCD and doubly occupied configuration interaction (DOCI) holds for excited states on the condition that state-specific optimized orbitals are employed.[126]
The first stage of this study consists in investigating the quality of the traditional pCCD (TpCCD) and variational pCCD (VpCCD) ground- and excited-state energies in the case where the reference wave function is chosen as the ground-state restricted HF (RHF) determinant, a choice that obviously induces a bias toward the ground state

Summary

Introduction

Because SRCC works so well for weak correlation, it would be convenient to be able to treat strong correlation within the very same framework This is further motivated by the fact that one can compensate for the poor quality of the reference wave function by increasing the maximum excitation degree of the CC expansion. A non-exhaustive list includes pair coupled-cluster doubles,[13,14,15,16,17,18,19,20,21,22] singlet-paired CCD,[23,24] the distinguishable cluster methods,[25–34] CCD-based variants involving a well-defined subset of diagrams,[35–39] the nCC hierarchy,[40,41] and parametrized CCSD.[42] Each of these methods sheds new light on the failures of SRCC to treat static correlation.

Objectives

Results

Conclusion