Brillouin-Wigner coupled cluster singles

Demel, O. Rittner, J. Carsky, R. Hubac, I. Multireference Brillouin-Wigner coupled cluster singles and doubles study of the singlet-triplet separation in alkylcarbenes, 7. Phys. Chem. A 2004, 70S, 3125-3128. 

Multireference Brillouin- Wigner coupled cluster singles and doubles study of the singlet-triplet... 

Single-root multi-reference Brillouin-Wigner coupled cluster single- and double-excitations approximation... 

So far, we have specified the wave operator H in the BW form (15). If we adopt an exponential ansatz for the wave operator Cl, we can speak about the single-root multireference Brillouin-Wigner coupled-cluster (MR BWCC) theory. The simplest way how to accomplish the idea of an exponential expansion is to exploit the so-called state universal or Hilbert space exponential ansatz of Jeziorski and Monkhorst [23]... 

Demel, O. Pittner, J. Multireference Brillouin-Wigner coupled cluster method with singles, doubles, and triples efficient implementation and comparison with approximate approaches, 7. Chem. Phys. 2008,128,104108-104111. 

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. 

Single-root multireference Brillouin-Wigner coupled-cluster theory. Rotational barrier of the N2H2... 

In section 6.1 we briefly describe the single reference Brillouin-Wigner coupled cluster expansions. The multireference case is considered in more detail in section 6.2. 

SINGLE REFERENCE BRILLOUIN-WIGNER COUPLED CLUSTER EXPANSIONS... 

Like CC, BWCC is fully extensive. Furthermore, the truncated forms of the Brillouin-Wigner coupled cluster expansion involving single and double substitutions usually designated BWCCD corresponding to the approximation (67) and BWCCSD corresponding to the approximation... 

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... 

In Section 4.2.3.1, we have defined the wave operator, 12, in the Brillouin-Wigner form (4.92). If we adopt an exponential ansatz for the wave operator, 12, we can develop the single-root (state-specific) multi-reference Brillouin-Wigner coupled-cluster (MR Bwcc) theory. This is the purpose of the present section. 

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... 

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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