The equation-of-motion coupled-cluster (EOM-CC) approach is a versatile electronic-structure tool that allows one to describe a variety of multiconfigurational wave functions within single-reference formalism. This review provides a guide to established EOM methods illustrated by examples that demonstrate the types of target states currently accessible by EOM. It focuses on applications of EOM-CC to electronically excited and open-shell species. The examples emphasize EOM's advantages for selected situations often perceived as multireference cases [e.g., interacting states of different nature, Jahn-Teller (JT) and pseudo-JT states, dense manifolds of ionized states, diradicals, and triradicals]. I also discuss limitations and caveats and offer practical solutions to some problematic situations. The review also touches on some formal aspects of the theory and important current developments.

Equation-of-Motion Coupled-Cluster Methods for Open-Shell and Electronically Excited Species: The Hitchhiker's Guide to Fock Space

Multiconfiguration Self-Consistent Field and Multireference Configuration Interaction Methods and Applications

Multireference nature of chemistry: the coupled-cluster view.

In the past decade, coupled-cluster theory has seen a renaissance in nuclear physics, with computations of neutron-rich and medium-mass nuclei. The method is efficient for nuclei with product-state references, and it describes many aspects of weakly bound and unbound nuclei. This report reviews the technical and conceptual developments of this method in nuclear physics, and the results of coupled-cluster calculations for nucleonic matter, and for exotic isotopes of helium, oxygen, calcium, and some of their neighbors.

http://iopscience.iop.org/article/10.1088/0034-4885/77/9/096302/pdf

Coupled-cluster computations of atomic nuclei

An overview is presented of the notions of size-extensivity and size-consistency, which play an important role in the discussion of many-body methods in physics and chemistry. We also introduce the concept of generalized extensivity, which has been used before implicitly in the literature, and provide an operational definition, which can be tested numerically in a similar way as size-consistency. A numerical example illustrates the concept of generalized extensivity as applied to the EOM-CCSD, STEOM-CCSD and extended-STEOM-CCSD electronic structure methods for excited states. In another line of thought it is argued that algebraic proofs are often more easily constructed than diagrammatic proofs to demonstrate proper separation into non-interacting fragments. The algebraic line of reasoning is illustrated for single reference methods and applied to discuss separability properties for a variety of Hilbert space multi-reference coupled cluster methods.

Reflections on size-extensivity, size-consistency and generalized extensivity in many-body theory

The state-specific equation of motion coupled cluster method is applied to three systems of diradical character: automerization of cyclobutadiene, singlet-triplet gaps of trimethylmethylene, and Bergman reaction. The aim of the paper is to assess the performance of the method and test numerically the importance of orbital optimization, three-body terms in transformed Hamiltonian, and the choice of cluster equations.

Application of Double Ionization State-Specific Equation of Motion Coupled Cluster Method to Organic Diradicals

The state specific equation of motion coupled cluster (SS-EOMCC) method is an internally contracted multireference approach, applicable to both ground and excited states. Attractive features of the method are as follows: (1) the SS-EOMCC wave function is qualitatively correct and rigorously spin adapted, (2) both orbitals and dynamical correlation are optimized for the target state, (3) nondynamical correlation and differential orbital relaxation effects are taken care of by a diagonalization of the transformed Hamiltonian in the multireference configuration-interaction singles space, (4) only one- and two-particle density matrices of a complete-active-space self-consistent-field reference state are needed to define equations for the cluster amplitudes, and (5) the method is invariant with respect to orbital rotations in core, active, and virtual subspaces. Prior applications focused on biradical-like systems, in which only one extra orbital is needed to construct the active space, and similarly, single b...

State specific equation of motion coupled cluster method in general active space.

State-specific Brueckner equation-of-motion coupled-cluster theory (SS-B-EOMCC) is summarized, which can be considered an internally contracted version of a state-selective multireference coupled-cluster theory, which, however, is not entirely size-consistent. The method is applicable to general multireference problems, adheres to the space and spin symmetries of the molecular system, is straightforwardly extended to a state-averaged version, and has an associated perturbative variant which yields results close to the full coupled-cluster treatment. A key strength is that Brueckner orbitals are used, such that orbitals are optimized in the presence of dynamic correlation. A number of variations on the theme of SS-EOMCC is applied to study the ionic-covalent avoided crossing in LiF in a 6-311++G(3df,3pd) basis set. While reasonable results are obtained at the state-averaged level, the iterative solution process does not consistently converge for SS-EOMCC, due to the non-Hermiticity of the transformed Hamiltonian which may yield complex eigenvalues upon truncated diagonalization. This leads to an irrevocable breakdown of the state-specific EOMCC approach. We indicate some future directions that can resolve some of the problems with the SS-EOMCC methodology, as revealed by the demanding test case of the LiF potential energy curves.

A Case Study of State-Specific and State-Averaged Brueckner Equation-of-Motion Coupled-Cluster Theory: The Ionic-Covalent Avoided Crossing in Lithium Fluoride

We report matrix isolation infrared spectroscopic studies to characterize 3,6-didehydropyridazine 6, a heterocyclic analogue of para benzyne, combined with computations. In this regard, we have utilized 3,6-diiodopyridazine 11 as a photolytic precursor. The experiments toward the generation of the biradical are carried out in argon and nitrogen matrices at 4 K. Instead of the elusive biradical, we have observed a ring-opening product maleonitrile (Z)-7 upon irradiation at 254 nm. In contrast, prolonged irradiation at 254 nm leads only to Z-E isomerization, forming fumaronitrile (E)-7. The mechanistic aspects of ring-opening, product selectivity, and Z-E photoisomerization steps have been investigated in detail using high-level ab initio computations. These studies have found that 3,6-didehydropyridazine 6 is an untraceable intermediate, and the ring-opening step leading to maleonitrile is barrierless. In addition, we have proposed the involvement of the S1 (π-π*) state via conical intersection in the Z-E photoisomerization of maleonitrile.

K. R. Shamasundar

Papers

Reflections on size-extensivity, size-consistency and generalized extensivity in many-body theory

Application of Double Ionization State-Specific Equation of Motion Coupled Cluster Method to Organic Diradicals

State specific equation of motion coupled cluster method in general active space.

A Case Study of State-Specific and State-Averaged Brueckner Equation-of-Motion Coupled-Cluster Theory: The Ionic-Covalent Avoided Crossing in Lithium Fluoride

Photochemistry of 3,6-Didehydropyridazine Biradical─An Untraceable Para Benzyne Analogue.