Many-body Brillouin-Wigner methods

Brillouin-Wigner methods offer a promising solution to these difficulties. (See the volume entitled Brillouin-Wigner methods for many-body systems [95] for details.)... 

In this article, we describe a quantum chemical project focussed on the development of state-specific many-body Brillouin-Wigner methods which was undertaken during the period 1994-2010. We outline the motivation for this project, survey the progress made and consider the prospects for future progress. The Brillouin-Wigner methodology has been shown [49,51,124] to provide an approach to the many-body... 

Parts of this article are taken from the authors book entitled Brillouin-Wigner Methods for Many-Body Systems. 

Brillouin-Wigner methods to many-body systems and, in particular, to molecular systems requiring a multi-reference formalism. 

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. 

We leave it as an exercise for the interested reader to consider the application of Brillouin-Wigner methods, together with an a posteriori extensivity correction where appropriate, to other approximation techniques in molecular structure theory. The Brillouin-Wigner approach is a very general technique which has been largely overlooked in many-body studies of molecules and which shows considerable promise for situations in which a single reference formalism is inadequate. 

We do not proposed to describe here the theoretical details of many-body Brillouin-Wigner methodology. They can be found in our book Brillouin-Wigner Methods for Many-Body Systems. Here we concentrate on applications of Brillouin-Wigner methods to many-body systems in chemistry and physics. Previous reviews can be found in our article in the Encyclopedia of Computational Chemistry [49] and in our review entitled Brillouin-Wigner expansions in quantum chemistry Bloch-... 

In this review, we have described the development and application of many-body Brillouin-Wigner methods for the molecular electronic structure problem. In our recent monograph [51], we suggest that such methods will have a broad range of applications in studies of the solid state, in condensed matter theory, in material science and in nuclear physics. In this final section, we shall concentrate on two areas of molecular electronic structure research for which many-body Brillouin-Wigner methodology shows promise. 

PUBLICATIONS ON MANY-BODY BRILLOUIN-WIGNER METHODS... 

Fig. 2.7 The webpages entitled PUBLICATIONS ON MANY-BODY BRILLOUIN-WIGNER METHODS (Taken from the webpage quantumsystems.googlepages.com/BriIIoum-Wigner)...

Brillouin-Wigner Methods for Many-Body Systems 3... 

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 volume describes the application of Brillouin-Wigner methods to many-body systems and, in particular, to molecular systems requiring a multi-reference formalism. 

The use of BriUouin-Wigner perturbation theory in describing many-body systems has been critically re-examined in recent years [69-96]. It has been shown that under certain well-defined circumstances, it can be regarded as a valid many-body theory. The primary purpose of this volume is to provide a detailed and coherent account of the Brillouin-Wigner methods in the study of the many-body problem in atomic and molecular quantum mechanics. 

This monograph is concerned with the application of Brillouin-Wigner methods to the many-body problem in atoms and molecules. 

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