Coupled Cluster Approaches

These results are compared with those obtained by Oddershede and Svendsen (18) using SOPPA or Sunil and Jordan (19) using MP4 or a coupled cluster approach, but without vibronic correction. 

Munzarova, M., Kaupp, M., 1999, A Critical Validation of Density Functional and Coupled Cluster Approaches for the Calculation for EPR Hyperfine Couphng Constants in Transition Metal Complexes , J. Phys. Chem. A, 103, 9966. 

CCSD(T) Coupled cluster approach with single and double substitutions and inclusion... 

Another standard for quality/price is defined within the coupled cluster approach. In particular, the CCSD(T) method [42] is nowadays generally accepted as the most accurate method which can be applied systematically for systems of a reasonable size. One must nevertheless be aware of the high computational cost of the method, which is often used only for energy calculations on geometries optimized with other computational methods. 

A standard method of improving on the Hartree-Fock description is the coupled-cluster approach [12, 13]. In this approach, the wavefunction CC) is written as an exponential of a cluster operator T working on the Hartree-Fock state HF), generating a linear combination of all possible determinants that may be constructed in a given one-electron basis,... 

A different way to approximate SS-MRCC is the so-called externally corrected CCSD (ec-CCSD) [13-17], The ec-CCSD method is based on the Coupled Cluster Approach (CCA). In CCA the exact wavefunction is written in an exponential form,... 

The relativistic coupled cluster method starts from the four-component solutions of the Drrac-Fock or Dirac-Fock-Breit equations, and correlates them by the coupled-cluster approach. The Fock-space coupled-cluster method yields atomic transition energies in good agreement (usually better than 0.1 eV) with known experimental values. This is demonstrated here by the electron affinities of group-13 atoms. Properties of superheavy atoms which are not known experimentally can be predicted. Here we show that the rare gas eka-radon (element 118) will have a positive electron affinity. One-, two-, and four-components methods are described and applied to several states of CdH and its ions. Methods for calculating properties other than energy are discussed, and the electric field gradients of Cl, Br, and I, required to extract nuclear quadrupoles from experimental data, are calculated. 

By adopting the no-pair approximation, a natural and straightforward extension of the nonrelativistic open-shell CC theory emerges. The multireference valence-universal Fock-space coupled-cluster approach is employed [25], which defines and calculates an effective Hamiltonian in a low-dimensional model (or P) space, with eigenvalues approximating some desirable eigenvalues of the physical Hamiltonian. The effective Hamiltonian has the form [26]... 

One method of determining nuclear quadrupole moment Q is by measuring the quadrupole coupling constant, given by eqQ/h, where e is the charge of the electron and q the electric field gradient due to the electrons at the atomic nucleus. The extraction of Q depends on an accurately calculated q. As a test of our finite-field relativistic coupled cluster approach, preliminary results for Cl, Br, and I are presented. 

J. D. Watts, G. W. Trucks, and R. J. Bartlett, The unitary coupled-cluster approach and molecular properties. Applications of the UCC(4) method. Chem. Phys. Lett. 157, 359-366 (1989). 

S. A. Kucharski and R. J. Bartlett, Fifth-Order Many-Body Perturbation Theory and Its Relationship to Various Coupled-Cluster Approaches, Volume 18 of Advances in Quantum Chemistry Wiley, Hoboken, NJ, 1986, p. 281. 

Lee, Y.S., Kucharski, S.A., Bartlett, R.J. A coupled-cluster approach with triple excitations. J. Chem. Phys. 1984, 81, 5906-12. 

Paldus, J., Takahashi, M., Cho, R.W.H. Coupled-cluster approach to electron correlation in one dimension cyclic polyene model in delocalized basis. Phys. Rev. B 1984, 30, 4267. 

Calculation of properties using the flnite-fleld method [115, 116] and Eq. (6.5) within the coupled-cluster approach is described in section 9. 

Results. Calculations were carried out at two internuclear separations, the equilibrium Re = 2.0844 A as in Ref. [89], and 2.1 A, for comparison with Ref. [127]. The relativistic coupled cluster (RCC) method [130, 131] with only single (RCC-S) or with single and double (RCC-SD) cluster amplitudes is used (for review of different coupled cluster approaches see also [132, 133] and references). The RCC-S calculations with the spin-dependent GRECP operator take into account effects of the spin-orbit interaction at the level of the one-configurational SCF-type method. The RCC-SD calculations include, in addition, the most important electron correlation effects. 

It is appropriate at this point to compare some formal properties of the three general approaches to dynamical correlation that we have introduced configuration interaction, perturbation theory, and the coupled-cluster approach. First, we note that taken fax enough (all degrees of excitation in Cl and CC, infinite order of perturbation theory) all three approaches will give the same answer. Indeed, in a complete one-paxticle basis all three will then give the exact answer. We axe concerned in this section with the properties of truncated Cl and CC methods and finite-order perturbation theory. 

Gauss has derived shielding theory with electron correlated calculations in the Moller-Plesset expansion (43,44) and also in the coupled cluster approach (45). He has provided benchmark calculations on a set of small molecules shown in Tables II and III at the CCSD(T) level (46). 

A. Landau, E. Eliav, Y. Ishikawa, U. Kaldor, Mixed-sector intermediate Hamiltonian Fock-space coupled cluster approach, J. Chem. Phys. 121(14) (2004) 6634. 

Jiri Cizek s research program centers on the quantum theory of molecular electronic structure and related developments in quantum chemical methodology, coupled-cluster approaches to many-electron correlation problems,105 large-order perturbation theory,106 dynamical groups and exactly solvable models, lower bounds, and the use of symbolic computation language in physics and in chemistry. 

For the treatment of electron correlation, Cizek uses classical techniques as well as techniques based on mathematical methods of quantum field theory, namely, a coupled-cluster approach. A rapid development and deployment of these methods during the past decade was stimulated by the realization of the importance of size consistency or size extensivity in the studies of reactive chemical processes. Although truly remarkable accuracy and development have been achieved for ground states of closed-shell systems, an extension to quasidegenerate and general open-shell systems is most challenging. Cizek also works on the exploitation of these approaches to study the electronic structure of extended systems (molecular crystals, polymers107). His many interests in-... 

The relation between the supermolecule coupled cluster approach and the perturbation theory of intermolecular forces in even less obvious than the case of the Mpller-Plesset theory, and no formal analysis has been reported in the literature thus far. Rode et al.68 analyzed the long-range behavior of the CCSD(T) method65, and showed that this method, although very popular and in principle accurate, may lead to wrong results for systems with the electrostatic term strongly depending on the electronic correlation, e.g. the CO dimer. 

Bartlett RJ (1989) Coupled-cluster approach to molecular structure and spectra a step toward predictive quantum chemistry. J Phys Chem 93 1697-1708... 

Kucharski SA, Bartlett RJ (1986) First-order many-body perturbation theory and its relationship to various coupled-cluster approaches. Adv Quantum Chem 18 281-344... 

Dalgaard E, Monkhorst HJ (1983) Some aspects of the time-dependent coupled-cluster approach to dynamic response functions. Phys Rev A 28 1217—1222. 

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