Brueckner doubles methods

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 Brueckner-reference method discussed in Section 5.2 and the cc-pvqz basis set without g functions were applied to the vertical ionization energies of ozone [27]. Errors in the results of Table IV lie between 0.07 and 0.17 eV pole strengths (P) displayed beside the ionization energies are approximately equal to 0.9. Examination of cluster amplitudes amd elements of U vectors for each ionization energy reveals the reasons for the success of the present calculations. The cluster operator amplitude for the double excitation to 2bj from la is approximately 0.19. For each final state, the most important operator pertains to an occupied spin-orbital in the reference determinant, but there are significant coefficients for 2h-p operators. For the A2 case, a balanced description of ground state correlation requires inclusion of a 2p-h operator as well. The 2bi orbital s creation or annihilation operator is present in each of the 2h-p and 2p-h operators listed in Table IV. Pole strengths are approximately equal to the square of the principal h operator coefiScient and contributions by other h operators are relatively small. 

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... 

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. 

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... 

There are a few minor variations on the CC methods. The quadratic configuration interaction including singles and doubles (QCISD)" ° method is nearly equivalent to CCSD. Another variation on CCSD is to use the Brueckner orbitals. Brueckner orbitals are a set of MOs produced as a linear combination of the HF MOs such that all of the amplitudes of the singles configurations ( f) are zero. This method is called BD and differs from CCSD method only in fifth order." Inclusion of triples configurations in a perturbative way, BD(T), is frequently more stable (convergence of the wavefunction is often smoother) than in the CCSD(T) treatment. 

In the last decade, a few approaches have been developed and applied in which the orbitals used in the CC calculation are optimized self-consistently with the energy. These include (a) the Brueckner CC (B-CC) methods in which the orbitals are chosen so that the T (single excitation) amplitudes vanish [107,108,110] and (b) the optimized-orbital CC (OO-CC) doubles approach in which the CCD energy is minimized [201,244]. Since the parameters used in these methods (orbital rotation coefficients and cluster amplitudes) are... 

An extensive study of the BH molecule has been presented by Ingamells et a/.107 The static a, / and tensors are computed by finite field and perturbation methods using Hartree-Fock, MP2, MP4 (including single, double, triple and quadruple substitutions), the Brueckner variant of the CCSD(T) method and DFT with the B3LYP functional. Contributions from vibration at MP2 level and rotation at Hartree-Fock level are calculated. The frequency dependence of the vibrational contribution is analysed. 

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