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WIREs Comput Mol Sci
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State‐specific multireference coupled‐cluster theory

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Abstract The multireference problem is considered one of the great challenges in coupled‐cluster (CC) theory. Most recent developments are based on state‐specific approaches, which focus on a single state and avoid some of the numerical problems of more general approaches. We review various state‐of‐the‐art methods, including Mukherjee's state‐specific multireference coupled‐cluster (Mk‐MRCC) theory, multireference Brillouin–Wigner coupled‐cluster (MR‐BWCC) theory, the MRexpT method, and internally contracted multireference coupled‐cluster (ic‐MRCC) theory. Related methods such as extended single‐reference schemes [e.g., the complete active space coupled‐cluster (CASCC) theory] and canonical transformation (CT) theory are covered as well. The comparison is done on the basis of formal arguments, implementation issues, and numerical results. Although a final and generally accepted multireference CC theory is still lacking, it is emphasized that recent developments render the new MRCC schemes useful tools for solving chemical problems. © 2012 John Wiley & Sons, Ltd. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods

(a) Chemical structure of p‐benzyne. (b) Schematic representation of the near‐degenerate pair of molecular orbitals for p‐benzyne. (c) Illustration of the strongly correlated electron pair in the biradicalic p‐benzyne (see text).

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Energetic ordering of the monocyclic and bicyclic forms of 2,6‐pyridyne as obtained from different levels of theory using the cc‐pVTZ basis set and the Mk‐MRCCSD/cc‐pCVTZ geometries from Ref 82. The energies are given relative to the bicyclic form. (Reproduced with permission from Ref 90. Copyright 2010, American Chemical Society.)

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Orbital energy levels (two‐configuration self‐consistent field) and contour plots of the active orbitals of o‐benzyne, m‐benzyne, and p‐benyzne.

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Error with respect to the full configuration‐interaction limit (in mEh) in the potential energy curve of the 1A1 ground state of BeH2 as calculated at various levels of theory using a CAS(2,2) and the (Be: 3s1p, H: 2s) basis set from Ref 6.

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Error with respect to full configuration‐interaction (in mEh) for the potential energy curves of the 1Σ+ ground state of hydrogen fluoride (left) and the ground state of molecular nitrogen. The calculations for hydrogen fluoride employ the DZV basis set and all multireference treatments are based on a CAS(2,2) reference function. For N2, a cc‐pVDZ basis set and a CAS(6,6) reference is used. The 1s orbitals are excluded from the correlation treatment in all cases. The two curves for Mk‐MRCCSD are obtained for (delocalized) pseudo‐canonical (ps‐c.) and localized (loc.) CASSCF orbitals, respectively.

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(a) Origin of the redundancy problem: relation of model space determinants and the determinants of the projection space. (b) Relation of model space and projection space determinants after invoking the sufficiency conditions.

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Electronic Structure Theory > Ab Initio Electronic Structure Methods

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