Brillouin-Wigner coupled cluster theory

The use of the exponential ansatz in formulating a quantum mechanical many-body theory was briefly described in Chapter 3, Section 3.3.2. This approach was first realized in nuclear physics by Coester and Ktimmel [81,82] and its introduction into quantum chemistry is usually attributed to Click. [76]. A recent overview of this method has been given by Paldus [73]. The single-reference coupled cluster approach has been described [83] as 

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Multireference Brillouin-Wigner Coupled-Cluster Theory. 

I. Hubac, Size Extensive Brillouin-Wigner Coupled-Cluster Theory. In A. Tsipis, V. S. Popov, D. R. Herschbach, and J. S. Avery (Eds.) New Methods in Quantum... 

Multireference Brillouin-Wigner Coupled-Cluster Theory (I. Hubac, J. Masik, P. Mach, J. Urban P. Babinec)... 

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. 

Brillouin-Wigner coupled cluster theory Fock-space approach Journal of Chemical Physics 117, 9580 (2002)... 

Size-extensivity correction for the state-spedfic multireference Brillouin-Wigner coupled-cluster theory... 

Multireference Brillouin- Wigner coupled-cluster theory. Single-root approach Advances in Quanlum Chemistry 31, 75 (1999)... 

Comparison of the Biillouin-Wigner coupled cluster theory wth the standard coupled cluster theory. Cancellation of disconnected terms in the Brillouin Wigner coupled cluster theory Czechoslovak Chemical Communications 62, 829 (1997)... 

Size-consistent Brillouin-Wigner Perturbation-Theory with an Exponentially Parametrized Wave-Function- Brillouin Wigner Coupled Cluster Theory The Physical Review A 50, 4558 (1994)... 

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. 

These two possible formulations of multi-reference Brillouin-Wigner coupled cluster theory are discussed further below. In Section 4.2.2.1, we present a multiroot formulation of Brillouin-Wigner theory. This formalism is employed in Section 4.2.2.2 to develop a multi-root, multi-reference Brillouin-Wigner coupled cluster theory, using a Hilbert space approach. In Section 4.2.2.3, we discuss the basic approximations employed in the multi-reference Brillouin-Wigner coupled cluster method. 

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

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... 

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... 

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