Electron correlation coupled cluster approach

For a more accurate treatment of electron correlation, coupled-cluster (CC) approaches [23] enter into play. While the full CC singles, doubles, triples (CCSDT) model [24] and augmented CCSDT approaches that feature corrections for quadruple and even higher excitations [25, 26] are currently too expensive, CC singles and doubles (CCSD) approximation [27] and CCSD augmented by a perturbative treatment of triple excitations, CCSD(T) [28], are more feasible and rather widely adopted. 

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. 

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. 

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. 

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). 

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. 

T. J. Lee, A. P. Rendell, and P. R. Taylor, /. Phys. Chem., 94,5463 (1990). Comparison of the Quadratic Configuration Interaction and Coupled-Cluster Approaches to Electron Correlation Including the Effect of Triple Excitations. 

Congress of Quantum Chemistry, P.-O. Lowdin and B. Pullman, Eds., D. Reidel, Dordrecht, 1983, pp. 31-60. Coupled Cluster Approaches to the Many-Electron Correlation Problem. 

Comparison of the Brueckner and Coupled-Cluster Approaches to Electron Correlation. 

Keywords many-electron correlation problem, post-Hartree-Fock methods, coupled cluster approaches, configuration interaction, externally corrected coupled cluster methods, reduced multireference coupled cluster method... 

In our previous work [96], we have developed an alternative multireference method, block correlated coupled cluster (BCCC) approach, for the electronic structure calculation of systems with noticeable multireference character. In this approach, the reference function is expressed as the tensor product of the most important many-electron states in each block, assuming that all orbitals in a system... 

The thesis begins with Section 2, where a brief history about the explicitly correlated approaches is presented. This is followed by Section 3 with general remarks about standard and explicitly correlated coupled-cluster theories. In Section 4, the details about the CCSD(F12) model relevant to the implementation in TuRBOMOLE are presented. The usefulness of the developed tool is illustrated with the application to the problems that are of interest to general chemistry. A very accurate determination of the reactions barrier heights of two CH3+CH4 reactions has been carried out (Section 5) and the atomization energies of 106 medium-size and small molecules were computed and compared with available experimental thermochemical data (Section 6). The ionization potentials and electron affinities of the atoms H, C, N, O and F were obtained and an agreement with the experimental values of the order of a fraction of a meV was reached (Section 7). Within all applications, the CCSD(F12) calculation was only a part of the whole computational procedure. The contributions from various levels of theory were taken into account to provide the final result, that could be successfully compared to the experiment. 

Approaches which consider one state at a time are often referred to as one-state or state-selective or single-root . They were first proposed in the late 1970s. A paper published by Harris [113] in 1977, entitled Coupled cluster methods for excited states, first introduced the state-selective approach. Four papers which were published in 1978 and 1979 advancing the state-selective approach parts 6 and 7 of a series of papers entitled Correlation problems in atomic and molecular systems part 6 entitled Coupled cluster approach to open-shell systems by Paldus et al. [114] and part 7 with the title Application of the open-shell coupled cluster approach to simple TT-electron model systems by Saute, Paldus and Cfzek [115], and two papers by Nakatsuji and Hirao on the Cluster expansion of wavefunction, the first paper [116] having the subtitle Symmetry-adapted-cluster expansion, its variational determination, and extension of open-shell theory and the second paper [117] having the subtitle Pseudo-orbital theory based on sac expansion and its application to spin-density of open-shell systems. 

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