Brueckner coupled-cluster theory

Aiga, F., Sasagane, K., and Itoh, R. (1994). Frequency-dependent h q)erpolariz-abilities in the Brueckner Coupled-Cluster Theory. Int. J. Quantum Chem., 51, 87-97. 

In the previous sections of this chapter, we presented the conventional treatment of the eorrelation problem in coupled-cluster theory. In the present section, we turn our attention briefly to three special correlation treatments within the general framework of coupled-cluster theory orbital-optimized and Brueckner coupled-cluster theories in Section 13.8.1 and quadratic Cl theory in Section 13.8.2. 

ORBITAL-OPTIMIZED AND BRUECKNER COUPLED-CLUSTER THEORIES... 

G. E. Scuseria, Int. ]. Quantum Chem., 55, 165 (1995). On the Connections Between Brueckner-Coupled-Cluster, Density-Dependent Hartree-Fock, and Density Functional Theory. 

The correlation treatments were done at the levels of second order perturbation theory, coupled cluster theory with single and double substitutions (CCSD) [55 59], an approximate form of CCSD, and that form with Brueckner orbitals (BO) [102], The approximate form [103,104], using herein the designation ACCSD or ACCD, has been shown to yield potential curves, potential surface slices, and properties very close to the corresponding CC results [104 106],... 

The PCM coupled-cluster theory has been presented at the coupled-cluster single and double (CCSD) excitation level approximation [9, 11], at the Brueckner doubles (BD) coupled-cluster level [12], and within the symmetry adapted cluster (SAC) method [10]. 

At this point, we mention that the orbital-rotation parameters may also be determined by extending the projeetion manifold to the single excitations, replacing the orbital conditions (13.8.22) by the amplitude equations (13.8.20) for the singles. This approach is called Brueckner coupled-cluster (BCC) theory [5,31,32]. In BCC theory, neither the energy nor the amplitude equations depend on the multipliers and no multipliers must be set up to obtain the BCC wave function. 

Chapter 13 discusses coupled-cluster theory. Important concepts such as connected and disconnected clusters, the exponential ansatz, and size-extensivity are discussed the Unked and unlinked equations of coupled-clustCT theory are compared and the optimization of the wave function is described. Brueckner theory and orbital-optimized coupled-cluster theory are also discussed, as are the coupled-cluster variational Lagrangian and the equation-of-motion coupled-cluster model. A large section is devoted to the coupled-cluster singles-and-doubles (CCSD) model, whose working equations are derived in detail. A discussion of a spin-restricted open-shell formalism concludes the chapter. 

Many-body methods, based on the linked-cluster expansion (LCE), were first developed by Brueckner [1] and Goldstone [2] in the 1950s for nuclear physics problems. Perturbation-theory applications to atomic and molecular systems (in a numerical, one-center frame) were pioneered by Kelly [3] in the early 1960s. Basis sets were later introduced, first in second-order [4] and then in third-order [5]. The 1970s saw a proliferation of molecular applications with basis sets, under the names of many-body perturbation theory (MBPT) [6] or the Moller-Plesset method [7]. Nowadays, many-body methods offer some of the most powerful tools in the quantum chemistry arsenal, in particular the coupled-cluster (CC) method, and are available in many widely used quantum chemistry program packages. 

For correlated methods such as truncated configuration interaction (CID or CISD), coupled cluster (CCD or CCSD), quadratic configuration interaction (QCISD) and Brueckner doubles (BD) (see Configuration Interaction and Coupled-cbister Theory), the energy and wavefunction can be written as... 

The 1960s saw the applications of the many-body perturbation theory developed during the 1950s by Brueckner [16], Goldstone [11] and others, to the atomic structure problem by Kelly [22-31], These applications used the numerical solutions to the Hartree-Fock equations which are available for atoms, because of the special coordinate system. Kelly also reported applications to some simple hydrides in which the hydrogen atom nucleus is treated as an additional perturbation. At about the same time, Cfzek [32] developed the formalism of the coupled cluster approach for use in the context of molecular electronic structure theory. 

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