Brueckner doubles

Another technique, called Brueckner doubles, uses orbitals optimized to make single excitation contributions zero and then includes double excitations. This is essentially equivalent to CCSD in terms of both accuracy and CPU time. 

Brueckner Doubles energies, optionally including triples and quadruples (BD, BD(T), BDfTQl). 

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... 

R. Kobayashi, R. D. Amos, and N. C. Handy, Chem. Phys. Lett., 184, 195 (1991). The Analytic Gradient of the Perturbative Triple Excitations Correction to the Brueckner Doubles Method. 

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]. 

We also considered other variants of CCSD that do not use HF orbitals. In particular, we developed the coupling of CCSD and PCM when using Brueckner orbitals, for which CCSD is usually known as BD (Brueckner doubles). The Brueckner orbitals are those for which the single T amplitudes are zero. The BD method has shown remarkable robustness compared to CCSD with HF orbitals in cases where the HF wave function presents some instability (for instance, singlet-triplet instability). Therefore, our work has extended the possibility to introduce the solvent effect also in these cases. Additionally, the 0 approximation is much more effective with BD than CCSD (no S approximation can be defined for BD since there is no single T amplitudes) also in those cases where CCSD shows a large difference between this approximation and the complete method. 

BD(T) = Brueckner doubles CCSD(T) = coupled cluster HLC = higher-level correction QCISD(T) = quadratic configuration interaction. 

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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