Abstract
Downfolding coupled cluster 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 parameterization 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.
Highlights
Over the last few decades, the coupled cluster (CC) theory[1–9] has evolved into one of the most accurate and dominant theories to describe various many-body systems across spatial scales and addressing fundamental problems in quantum chemistry,[10–17] material sciences,[18–25] and nuclear structure theory.[26–28] Many strengths of the single-reference CC formalism (SR-CC) originate in the exponential representation of the ground-state wave function ∣Ψ⟩, ∣Ψ⟩ = eT∣Φ⟩, (1)where T and ∣Φ⟩ correspond to the cluster operator and a reference function that provides an approximation to the exact ground-state wave function
The implementations of A(2)–A(7) formulations have been integrated with the Tensor Contraction Engine (TCE)[127] environment of NWChem,[128,129] which allows us to use a variety of formulations to extract the external cluster operator
In all approximations analyzed in this paper, we used a subset of coupled cluster single double (CCSD) cluster amplitudes to evaluate the so-called external part of the anti-Hermitian cluster operator σext
Summary
One can define a hierarchy of CC approximations by increasing the excitation level in the cluster operator. Another important feature of the CC formalism stems from the linked cluster theorem,[29,30] which allows one to build efficient algorithms for the inclusion of the higher-rank excitations. When these two features are combined, they give rise to efficient and accurate methodologies that account for higher-order correlation effects and that have been widely used in physics and quantum chemistry. The diverse manifold of higher-order approximations include, among others, categories of active-space, multi-reference, externally corrected, and adaptive approaches as well as noniterative corrections and approaches that combine stochastic techniques (for key reviews and papers, see Refs. 7, 9, and 31–39 and references therein)
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