Today, coupled-cluster theory offers the most accurate results among the practical ab initio electronic-structure theories applicable to moderate-sized molecules. Though it was originally proposed for problems in physics, it has seen its greatest development in chemistry, enabling an extensive range of applications to molecular structure, excited states, properties, and all kinds of spectroscopy. In this review, the essential aspects of the theory are explained and illustrated with informative numerical results.

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Coupled-cluster theory in quantum chemistry

A new, noniterative triples correction to the coupled‐cluster singles and doubles (CCSD), method, for general single determinant reference functions is proposed and investigated numerically for various cases, including non‐Hartree–Fock (non‐HF) reference functions. It is correct through fourth‐order of perturbation theory for non‐HF references, and unlike other such methods, retains the usual invariance properties common to CC methods, while requiring only a single N7 step. In the canonical Hartree–Fock case, the method is equivalent to the usual CCSD(T) method, but now permits the use of restricted open‐shell Hartree‐Fock (ROHF) and quasirestricted Hartree–Fock (QRHF) reference determinants, along with many others. Comparisons with full configuration interaction (FCI) results are presented for CH2, CH2+, CH3, NH2, and SiH2. The paper also reports the derivation and initial computational implementation of analytical gradients for the ROHF‐CCSD(T) method, which includes unrestricted Hartree–Fock (UHF) CCSD...

Coupled‐cluster methods with noniterative triple excitations for restricted open‐shell Hartree–Fock and other general single determinant reference functions. Energies and analytical gradients

Prediction of molecular properties and molecular spectroscopy with density functional theory: From fundamental theory to exchange-coupling

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

The electron attachment equation of motion coupled cluster (EA‐EOMCC) method is derived which enables determination of the various bound states of an (N+1)‐electron system and the corresponding energy eigenvalues relative to the energy of an N‐electron CCSD reference state Detailed working equations for the EA‐EOMCC method are derived using diagrammatic techniques for both closed‐shell and open‐shell CCSD reference states based upon a single determinant The EA‐EOMCC method is applied to a variety of different problems, the main purpose being to establish its prospects and limitations The results from EA‐EOMCC calculations are compared to other EOMCC approaches, starting from different reference states, as well as other theoretical methods and experimental values, where available We have investigated electron affinities for a wide selection of both closed‐shell and open‐shell systems Excitation spectra of atoms and molecules with an odd number of electrons are obtained, taking the closed‐shell ground state of the ion as a reference in the EA‐EOMCC calculation Finally we consider excitation spectra of some closed‐shell systems, and find in particular that the electron attachment approach is capable of yielding accurate triplet excitation energies in an efficient way

Equation of motion coupled cluster method for electron attachment

Multireference coupled-cluster methods using an incomplete model space: Application to ionization potentials and excitation energies of formaldehyde

Multi-reference coupled-cluster methods for ionization potentials with partial inclusion of triple excitations

A fully linked multi-reference coupled-cluster (MRCC) method is used for the calculation of ionization potentials (IP), electron affinities (EA) and excitation energies (EE) of CH+. The model space for the IP/EA calculations consists of determinants where an electron out of an active set of orbitals has been removed/added to an RHF determinant. For the EE calculation the model space is constructed from all particle-hole excitations obtained from the IP/EA active orbitals. Results using the MRCCSD approximation are presented and compared to results obtained from CI, MCSCF, GF, single-reference CC calculations, and experiment.

Sourav Pal

Papers

Multireference coupled-cluster methods using an incomplete model space: Application to ionization potentials and excitation energies of formaldehyde

Multi-reference coupled-cluster methods for ionization potentials with partial inclusion of triple excitations

Applications of Multi-Reference Coupled-Cluster Theory