Perturbation theory Brillouin-Wigner, multireference

Multireference coupled cluster method based on the Brillouin-Wigner perturbation theory... 

Chapter 18 - Multireference coupled cluster method based on the Brillouin-Wigner perturbation theory. Pages 465-481, Petr Carsky, Jin Pittner and Ivan Hubac... 

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. 

Multireference second-order Brillouin-Wigner perturbation theory Molecular Physics 102,701 (2004)... 

Multireference Second-order Many-body Perturbation Theory, Intruder States and Brillouin-Wigner Perturbation Theory through Second Order. -... 

Let us consider a />-state system and obtain an explicit formulation of the multireference Brillouin-Wigner perturbation theory for this case. In the -state case, we have a reference space spaimed by p functions, o, 4>i,. .., The projector onto this space is... 

A posteriori corrections to second order multireference Brillouin-Wigner perturbation theory based on the identity ... 

In this section, we present Brillouin-Wigner perturbation theory in both its single reference and its multireference form. This will serve both to emphasize the similarity of single reference and multireference formulations of Brillouin-Wigner perturbation theory and to establish notation for later sections. In section 3.1, we define the basic concepts of any perturbation theory. The definition of single and multireference spaces is considered in section 3.2 and the model wave function is described in section 3.3. The Brillouin-Wigner expansion is developed in section 3.4. 

Brillouin-Wigner perturbation theory can be developed for both the single reference function case and the multireference function case using a common formalism. This contrasts with the situation for Rayleigh-Schrodinger perturbation theory. We shall, therefore, consider the single reference and multireference formalisms together. 

Single state coupled cluster expansions and multireference coupled cluster expansions based on the generalized Brillouin-Wigner pertm bation theory have been described elsewhere [19]. The generalized Brillouin-Wigner perturbation theory can also be applied to the configuration interaction problem. 

Unlike the BWCCSD method, the MR-BWCCSD theory, the BWCISD theory and the MR-BWCISD theory do not support energies which scale linearly with the number of electrons in the system. In the multireference cases, that is MR-BWCCSD and MR-BWCISD theories, this lack of ex-tensivity arise both from nonlinear terms in the matrix elements of the effective hamiltonian and from diagonalization of the effective hamiltonian when an incomplete model space is employed. By exploiting the known relation between the Brillouin-Wigner and the Rayleigh-Schrddinger denominators it is possible to devise a posteriori corrections to methods formulated within the framework of Brillouin-Wigner perturbation theory. 

BWPT = Brillouin-Wigner perturbation theory EN = Epstein-Nesbet FCI = full Cl MBPT = many-body perturbation theory MRS PT = multireference state perturbation theory PT = perturbation theory RSPT = Rayleigh-SchrSdinger perturbation theory SRS PT = single-reference state perturbation theory. 

Keywords Many-body theory Brillouin-Wigner theory State-specific multireference correlation problem Many-body perturbation theory Coupled cluster theory Configuration interaction Collaborative virtual enviroments... 

Many-body Brillouin-Wigner second-order perturbation theory using a multireference formulation an application to bond breaking in the diatomic hydrides BH and FH Molecular Physics 104, 2367 (2006)... 

Excitation energies in Brillouin-Wigner-based multireference perturbation theory International Journal of Quanlum Chemistry 70,613 (1998)... 

In 1967, Brandow [69] used the Brillouin-Wigner expansion in his derivation of a multireference many-body (Rayleigh-Schrodinger) perturbation theory. In the abstract to his paper entitled Tinked-Cluster expansions for the nuclear many-body problem Brandow writes ... 

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