Brillouin-Wigner perturbation theory application

Today, there remain a number of problems in molecular electronic structure theory. The most outstanding of these is undoubtedly the development of a robust theoretical apparatus for the accurate description of dissociative processes which usually demand the use of multi-reference functions. This requirement has recently kindled a renewal of interest in the Brillouin-Wigner perturbation theory and its application to such problems. This contribution describes the application of... 

On the application of Brillouin- Wigner perturbation theory to a relativistic and non-relativistic hydrogenio model problem... 

The above extracts serve to demonstrate what had until recently been the standard view of Brillouin-Wigner perturbation theory and its applicability to many-body systems. 

In this chapter, we come to the central purpose of this volume - the application of Brillouin-Wigner methods to many-body atomic and molecular systems. We have seen in Chapter 2 that Brillouin-Wigner perturbation theory [2-4] leads to energy expressions with denominators which contain the exact energy, . As a consequence of this, the Brillouin-Wigner expansion yields energy components which scale non-linearly with the number of electrons in the system. The method does not have. 

If j) is a determinant related to one of the reference determinants by a double replacement, then k) involves, at most, quadruple replacements with respect to 1 ) in eq. (4.193). Repeated application of the Lippmann-Schwinger-file equation [160] leads to higher order replacements. If we restrict the degree of replacement admitted in (4.193) then we realize a limited multi-reference configuration interaction method. It is this realization of the multi-reference limited configuration interaction method that we use to obtain an a posteriori correction based on Brillouin-Wigner perturbation theory. 

In the context of the Wigner-Seitz theory, in 1937 Brillouin [7] gave a formal analysis of the atomic energy variations under boundary deformations using contact coordinate transformations that transform the boundary modifications into Hamiltonian transformations for a fixed region and generate the associated commutation relations. This allows application of the usual form of perturbation theory for the problem. 

We shall provide an overview of the applications that have been made over the period being review which demonstrate the many-body Brillouin-Wigner approach for each of these methods. By using Brillouin-Wigner methods, any problems associated with intruder states can be avoided. A posteriori corrections can be introduced to remove terms which scale in a non linear fashion with particle number. We shall not, for example, consider in any detail hybrid methods such as the widely used ccsd(t) which employs ccsd theory together with a perturbative estimate of the triple excitation component of the correlation energy. 

Many-body Brillouin- Wigner second-order perturbation theory an application to the autoaromatisation of hex-3-ene-1,5-dlyne (the Bergman reaction)... 

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)... 

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