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WIREs Comput Mol Sci
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Single‐reference coupled cluster methods for computing excitation energies in large molecules: The efficiency and accuracy of approximations

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Abstract While methodological developments in the last decade made it possible to compute coupled cluster (CC) energies including excitations up to a perturbative triples correction for molecules containing several hundred atoms, a similar breakthrough has not yet been reported for excited state computations. Accurate CC methods for excited states are still expensive, although some promising candidates for an efficient and accurate excited state CC method have emerged recently. This review examines the various approximation schemes with particular emphasis on their performance for excitation energies and summarizes the best state‐of‐the‐art results which may pave the way for a robust excited state method applicable to molecules of hundreds of atoms. Among these, special attention will be given to exploiting the techniques of similarity transformation, perturbative approximations as well as integral decomposition, local and embedding techniques within the equation of motion CC framework. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Structure and Mechanism > Molecular Structures
The structure of the Jacobian A for second‐order‐coupled cluster methods for excited states. The methods that derive from equation of motion (EOM)–CC singles doubles, CCSD(2), require an MP2 ground state (blue color). CC2 has a corresponding ground state CC2 solution (red color). The remaining methods use the CCSD ground state amplitudes (black color). CIS(D) is noniterative, the other methods are iterative. The doubles part of the CIS(D) energy is denoted as ωD. The notation is used if the amplitudes are present
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Embedding approaches for solvents and solid states. Subfigure (a) (Reprinted with permission from Reference. Copyright 2015 American Chemical Society). (a) PDE–RICC2 QM/QM/MM embedding solvent model (b) bt–PNO–STEOM–CCSD with Gaussian embedding potentials and point charges
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Test systems for DLPNO‐based approaches for ionization and excitation energies. (a) DLPNO–IP, (b) DLPNO–EA, (c) DLPNO–STEOM
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A local ππ* excitation of the PNP anion surrounded by water molecules using pair natural orbital (PNO)–CC2. (Reprinted with permission from Reference . Copyright XXX Benjamin Helmich‐Paris)
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Error distributions for the various second‐order methods for valence and Rydberg states based on the data of Tajti and Szalay. CC singles doubles, CCSD(2), and P–CCSD(2) stand for equation of motion (EOM)–CCSD(2) and P–EOM–CCSD(2). The Gaussian curves are illustrative, since error distributions of quantum chemical methods are not guaranteed to be Gaussian
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The process of successive similarity transformation used in similarity transformed EOM (STEOM)‐coupled cluster (CC). EHF is the RHF energy, while E0 denotes the ground state CC energy
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Structure and Mechanism > Molecular Structures
Electronic Structure Theory > Ab Initio Electronic Structure Methods

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