Coupled Cluster Downfolding Methods: the effect of double commutator terms on the accuracy of ground-state energies

TL;DR

This paper investigates how including double commutator terms affects the accuracy of ground-state energy calculations in downfolded coupled cluster methods, demonstrating improved results for atomic and molecular systems.

Contribution

It introduces the impact of double commutator terms in downfolded coupled cluster Hamiltonians and evaluates their effect on ground-state energy accuracy.

Findings

Double commutator terms improve energy accuracy.

Efficient many-body expansions with single and double commutators.

Analysis of active space size effects on water energies.

Abstract

Downfolding coupled cluster (CC) techniques have recently been introduced into quantum chemistry as a tool for the dimensionality reduction of the many-body quantum problem. As opposed to earlier formulations in physics and chemistry based on the concept of effective Hamiltonians, the appearance of the downfolded Hamiltonians is a natural consequence of the single-reference exponential parametrization of the wave function. In this paper, we discuss the impact of higher-order terms originating in double commutators. In analogy to previous studies, we consider the case when only one- and two-body interactions are included in the downfolded Hamiltonians. We demonstrate the efficiency of the many-body expansions involving single and double commutators for the unitary extension of the downfolded Hamiltonians on the example of the beryllium atom, and bond-breaking processes in the Li2 and H2O molecules. For the H2O system, we also analyze energies obtained with downfolding procedures as functions of the active space size.