Brueckner coupled-cluster method

L. A. Barnes and R. Lindh, Chem. Phys. Lett., 223, 207 (1994). Symmetry Breaking in O4 An Application of the Brueckner Coupled-Cluster Method. 

C. Hampel, K. A. Peterson, and H.-J. Werner, Chem. Phys. Lett., 190, 1 (1992). A Comparison of the Efficiency and Accuracy of the Quadratic Configuration Interaction (QCISD), Coupled-Cluster (CCSD), and Brueckner Coupled-Cluster (BCCD) Methods. 

Coupled cluster methods including CC2, CCSD, CCSD(T), and CC3 with RHF, ROHF, UHF, and Brueckner orbitals. 

Another approach of this kind uses the approximate Brueckner orbitals from a so-called Brueckner doubles, coupled-cluster calculation [39, 40]. Methods of this kind are distinguished by their versatility and have been applied to valence ionization energies of closed-shell molecules, electron detachment energies of highly correlated anions, core ionization... 

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. 

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]. 

Since Brueckner orbitals are defined as those for which all the single excitation amplitudes in a particular correlation method (usually coupled cluster, see below) exactly vanish, which means that T = 0, electron correlation calculations based on Brueckner orbitals generally are much less likely to be plagued by false symmetry breaking problems. And this has indeed been the observation in such systems as NO3 and O4, which are notorious for symmetry breaking effects. 

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... 

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