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

‡We describe the use of singular value decomposition in transforming genome-wide expression data from genes 3 arrays space to reduced diagonalized ‘‘eigengenes’’ 3 ‘‘eigenarrays’’ space, where the eigengenes (or eigenarrays) are unique orthonormal superpositions of the genes (or arrays). Normalizing the data by filtering out the eigengenes (and eigenarrays) that are inferred to represent noise or experimental artifacts enables meaningful comparison of the expression of different genes across different arrays in different experiments. Sorting the data according to the eigengenes and eigenarrays gives a global picture of the dynamics of gene expression, in which individual genes and arrays appear to be classified into groups of similar regulation and function, or similar cellular state and biological phenotype, respectively. After normalization and sorting, the significant eigengenes and eigenarrays can be associated with observed genome-wide effects of regulators, or with measured samples, in which these regulators are overactive or underactive, respectively.

Singular Value Decomposition for Genome-Wide Expression Data Processing and Modeling

Multireference nature of chemistry: the coupled-cluster view.

Explicitly correlated R12/F12 methods for electronic structure.

The past few years have seen a particularly rich period in the development of the explicitly correlated R12 theories of electron correlation. These theories bypass the slow convergence of conventional methods, by augmenting the traditional orbital expansions with a small number of terms that depend explicitly on the interelectronic distance r 12. Amongst the very numerous discoveries and developments that we will review here, two stand out as being of particular interest. First, the fundamental numerical approximations of the R12 methods withstand the closest scrutiny: Kutzelnigg's use of the resolution of the identity and the generalized Brillouin condition to avoid many-electronic integrals remains sound. Second, it transpires that great gains in accuracy can be made by changing the dependence on the interelectronic coordinate from linear (r 12) to some suitably chosen short-range form (e.g., exp(−αr 12)). Modern R12 (or F12) methods can deliver MP2 energies (and beyond) that are converged to chemical a...

R12 methods in explicitly correlated molecular electronic structure theory

A method is presented which combines coupled cluster (CC) and configuration interaction (CI) to describe accurately potential-energy surfaces (PESs). We use the cluster amplitudes extracted from the complete active space CI calculation to manipulate nondynamic correlation to tailor a single reference CC theory (TCC). The dynamic correlation is then incorporated through the framework of the CC method. We illustrate the method by describing the PESs for HF, H2O, and N2 molecules which involve single, double, and triple bond-breaking processes. To the dissociation limit, this approach yields far more accurate PESs than those obtained from the conventional CC method and the additional computational cost is negligible compared with the CC calculation steps. We anticipate that TCC offers an effective and generally applicable approach for many problems.

Coupled-cluster method tailored by configuration interaction.

To assess the separation of dynamic and nondynamic correlations and orbital choice, we calculate the molecular structure and harmonic vibrational frequencies of ozone with the recently developed tailored coupled cluster singles and doubles method (TCCSD). We employ the Hartree-Fock and complete active space (CAS) self-consistent field (SCF) orbitals to perform TCCSD calculations. When using the Hartree-Fock orbitals, it is difficult to reproduce the experimental vibrational frequency of the asymmetric stretching mode. On the other hand, the TCCSD based on the CASSCF orbitals in a correlation consistent polarized valence triple zeta basis yields excellent results with the two symmetric vibrations differing from the experimental harmonic values by 2 cm^(−1) and the asymmetric vibration differing by 9 cm^(−1).

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Tailored coupled cluster singles and doubles method applied to calculations on molecular structure and harmonic vibrational frequencies of ozone.

We present a method for the approximate solution of the coupled-cluster (CC) equation, based upon the singular value decomposition (SVD). The key idea of this method is that we use SVD for the cluster amplitudes to exploit the physically important states in the CC equation. This method enables us to significantly reduce the computational requirements for CC calculations without losing the essence of the method. Relationships to the density matrix renormalization group theory and the local correlation methods are mentioned. We perform pilot calculations on some atoms and molecules to investigate the applicability of the method.

Singular value decomposition approach for the approximate coupled-cluster method

http://theochem.kuchem.kyoto-u.ac.jp/public/HTT02CPL.pdf

Application of the transcorrelated Hamiltonian to the linearized coupled cluster singles and doubles model

A biorthogonal formulation is applied to the non-Hermite transcorrelated Hamiltonian, which treats a large amount of the dynamic correlation effects implicitly. We introduce biorthogonal canonical orbitals diagonalizing the non-Hermitian Fock operator. We also formulate many-body perturbation theory for the transcorrelated Hamiltonian. The biorthogonal self-consistent field followed by the second order perturbation theory are applied to some pilot calculations including small atoms and molecules.

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Osamu Hino

Papers

Coupled-cluster method tailored by configuration interaction.

Tailored coupled cluster singles and doubles method applied to calculations on molecular structure and harmonic vibrational frequencies of ozone.

Singular value decomposition approach for the approximate coupled-cluster method

Application of the transcorrelated Hamiltonian to the linearized coupled cluster singles and doubles model

Biorthogonal approach for explicitly correlated calculations using the transcorrelated Hamiltonian