Single-root multi-reference Brillouin-Wigner coupled cluster theory Hilbert space approach

Single-root multi-reference Brillouin-Wigner coupled cluster theory Hilbert space approach 

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. 

The simplest way to realize an exponential expansion is to employ the exponential ansdtz of Jeziorski and Monkhorst [87] which exploits a complete model space. This is the approach that we followed in Section 4.2.2.2 in developing a multi-root multireference Brillouin-Wigner coupled cluster theory. The Jeziorski and Monkhorst exponential ansatz may be written 

If we now substitute the Hilbert space exponential ansatz of Jeziorski and Monkhorst, expression (4.103), for the wave operator, 17, then we obtain the following system of equations 

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