Single-reference Brillouin-Wigner coupled cluster theory

Hubac and his co-workers222"231 have explored the use of Brillouin-Wigner perturbation theory in solving the coupled cluster equations. For the case of a single reference function, this approach is entirely equivalent to other formulations of the coupled cluster equations. However, for the multireference case, the Brillouin-Wigner coupled cluster theory shows some promise in that it appears to alleviate the intruder state problem. No doubt perturbative analysis will help to gain a deeper understanding of this approach. 

In this way, we have obtained a set of closed equations for the m2 operator. Equations (3.132) and (3.274) form the basis of the coupled cluster approximation at the double excitation level. The formalism discussed above can be used in the derivation of the single-reference Brillouin-Wigner coupled cluster theory. 

Single-reference Brillouin-Wigner coupled cluster theory... 

We turn now to the calculation of the effective Hamiltonian (4.98) for single-root multi-reference Brillouin-Wigner coupled cluster theory. Using the Hilbert space exponential ansatz of Jeziorski and Monkhorst, expression (4.103), the off-diagonal... 

In Section 4.2.3.2, we presented the basic equations of single-root (state-specific) multi-reference Brillouin-Wigner coupled cluster theory. We derived these equations from the single-root (state-specific) multi-reference Brillouin-Wigner perturbation theory presented in Section 4.2.3.1. In this section, we turn our attention to the coupled cluster single- and double-excitations approximation, ccsd. We present... 

The application of the Brillouin-Wigner coupled cluster theory to the multireference function electron correlation problem yields two distinct approaches (i) the multi-root formalism which was discussed in Section 4.2.2 and (ii) the single-root formalism described in the previous subsections of this section. Section 4.2.3. The multiroot multi-reference Brillouin-Wigner coupled cluster formalism reveals insights into other formulations of the multi-reference coupled cluster problem which often suffer from the intruder state problem which, and in practice, may lead to spurious... 

In Brillouin-Wigner coupled cluster theory, the simple a posteriori correction described above is exact in the case of the single-reference formalism. In the state-specific multi-reference Brillouin-Wigner coupled cluster theory, the simple a posteriori correction is approximate. An iterative correction for lack of extensivity has been studied by Kttner [38], but this reintroduces the intruder state problem. 

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