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arXiv:2301.12228 · The Journal of Chemical Physics

Entanglement coupled cluster theory: Exact spin-adaptation

Sarai Dery Folkestad, Bendik Støa Sannes, Henrik Koch A

Published Jun 12, 2023• 6 citations
arXivHTMLPDF

Abstract

We present a novel framework for spin-adapted coupled cluster theory. The approach exploits the entanglement of an open-shell molecule with electrons in a non-interacting bath. Together, the molecule and the bath form a closed-shell system, and electron correlation can be included using the standard spin-adapted closed-shell coupled cluster formalism. A projection operator, which enforces conditions on the electrons in the bath, is used to obtain the desired state of the molecule. This entanglement coupled cluster theory is outlined, and proof-of-concept calculations for doublet states are reported. The approach is further extendable to open-shell systems with other values of the total spin.

DOI
10.1063/5.0144694

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We present a novel framework for spin-adapted coupled cluster theory. The approach exploits the entanglement of an open-shell molecule with electrons in a non-interacting bath. Together, the molecule and the bath form a closed-shell system, and electron correlation can be included using the standard spin-adapted closed-shell coupled cluster formalism. A projection operator, which enforces conditions on the electrons in the bath, is used to obtain the desired state of the molecule. This entanglement coupled cluster theory is outlined, and proof-of-concept calculations for doublet states are reported. The approach is further extendable to open-shell systems with other values of the total spin.
We present a spin-adapted coupled cluster singles and doubles model for the excitation energies of molecular doublets. The entanglement coupled cluster approach represents an unconventional take on the notorious problem of spin adaptation for open-shell species. In this approach, the high-spin open-shell molecular system is coupled to non-interacting bath orbitals to form a total closed-shell system. In entanglement coupled cluster theory, many of the attractive features of the spin-adapted closed-shell coupled cluster are retained: an unambiguous definition of the cluster operator and a terminating Baker-Campbell-Hausdorff expansion. The model produces excitation energies of a quality comparable to that of the closed-shell counterpart. Additionally, some ionized states that cannot be modeled accurately with the alternative equation-of-motion approach for ionized states can be described with the entanglement coupled cluster singles and doubles model.
The graphical techniques of spin algebras are combined with a diagrammatic approach based on the time independent Wick theorem to yield the spin-adapted form of the coupled cluster theory. The general rules for the implementation of this formalism are formulated and illustrated on the basic coupled-pair many-electron theory pertaining to closed shell ground states, for which case the explicit spin-adapted equations are derived. The advantages of the spin-adapted form of the theory are discussed along with the new insights it affords.
We introduce a simple coupled cluster approach for multireference and open-shell systems. In the restricted active space coupled cluster framework, the cluster operator only includes excitations from doubly occupied to virtual orbitals, and this ensures the individual operators commute among each other. The ground and excited states are obtained by diagonalisation of the coupled cluster similarity transformed Hamiltonian in a restricted active space. We demonstrate the framework for the RAS-CCSD model, where single and double excitations are included in the cluster operator, and likewise for a complete active space. We consider systems with multireference character and open-shell systems in a spin-adapted manner. The approach captures significantly more dynamical correlation than without the coupled cluster similarity transformation.
The orthogonally spin- and orbital-symmetry-adapted (LS\mathrm{LS}LS-coupled) coupled-pair many-electron theory and its extended version involving monoexcited and biexcited cluster coefficients is derived in a form suitable for application to closed-shell atomic systems. A diagrammatic approach, based on second quantization, the time-independent Wick theorem, and the graphical methods of spin algebras, is employed.
The orthogonally-spin-adapted form of the nonlinear system of equations for the extended coupled-pair many-electron theory, which involves the monoexcited, biexcited, and triexcited states and cluster components, is derived. A diagrammatic approach, based on second quantization, the time-independent Wick theorem, and the graphical methods of spin algebras, is employed. The advantages of using the orthogonally-spin-adapted states and cluster components, rather than the nonorthogonally-spin-adapted ones which have been previously employed, particularly in the triexcited case, are also discussed. It is also shown that the formulas for the direct configuration-interaction method can easily be obtained in compact form from the linear part of the system of extended coupled-pair equations.
We extend coupled-cluster (CC) theory performed on top of a Slater determinant breaking rotational symmetry to allow for the exact restoration of the angular momentum at any truncation order. The main objective relates to the description of near-degenerate finite quantum systems with an open-shell character. As such, the newly developed many-body formalism offers a wealth of potential applications and further extensions dedicated to the ab initio description of, e.g., doubly open-shell atomic nuclei and molecule dissociation. The formalism, which encompasses both single-reference CC theory and projected Hartree–Fock theory as particular cases, permits the computation of usual sets of connected diagrams while consistently incorporating static correlations through the highly non-perturbative restoration of rotational symmetry. Interestingly, the yrast spectroscopy of the system, i.e. the lowest energy associated with each angular momentum, is accessed within a single calculation. A key difficulty presently overcome relates to the necessity to handle generalized energy and norm kernels for which naturally terminating CC expansions could be eventually obtained. The present work focuses on SU (2) but can be extended to any (locally) compact Lie group and to discrete groups, such as most point groups. In particular, the formalism will be soon generalized to U (1) symmetry associated with particle number conservation. This is relevant to Bogoliubov CC theory that was recently applied to singly open-shell nuclei.