Method perturbation, Brillouin-Wigner

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

Elimination of the size-extensivity error in the MRBWCC theory was suggested by Hubac and Wilson [68]. The Brillouin-Wigner perturbation theory has been known notoriously as a method not furnishing size extensivity. There was therefore every reason to believe that the size-extensivity error in MR BWCCSD originated from the use of the Brillouin-Wigner type resolvent (15) instead of the Rayleigh-Schrodinger... 

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

The Brillouin-Wigner perturbation theory can be employed to solve the equations associated with an explicit many-body method. 

Size consistency of the Brillouin-Wigner perturbation theory is studied using the Lippmann-Schwinger equation and an exponential ansatz for the wave function. Relation of this theory to the coupled cluster method is studied and a comparison through the effective Hamiltonian method is also provided. 

A posteriori corrections can be developed for calculations performed by using the Brillouin-Wigner perturbation expansion. These a posteriori corrections can be obtained for the Brillouin-Wigner perturbation theory itself and, more importantly, for methods, such as limited configuration interaction or multi-reference coupled cluster theory, which can be formulated within the framework of a Brillouin-Wigner perturbation expansion. 

These a posteriori corrections are based on a very simple idea which is suggested by the work of Brandow [10]. Brandow used the Brillouin-Wigner perturbation theory as a starting point for a derivation of the Goldstone linked diagram expansion by elementary time-independent methods . At a NATO Advanced Study Institute held in 1991, Wilson wrote [112] ... 

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. 

Multireference Brillouin-Wigner coupled clusters method with noniterative perturbative conrtected triples... 

In spite of this progress, problems remain and the description of electron correlation in molecules will remain an active field of research in the years ahead. The most outstanding problem is the development of robust theoretical apparatus for handling multi-reference treatments. Methods based on Rayleigh-Schrodinger perturbation theory suffer from the so-called intruder state problem. In recent years, it has been recognized that Brillouin-Wigner perturbation theory shows promise as a robust technique for the multi-reference problem which avoids the intruder state problem. 

As an alternative to Brillouin-Wigner perturbation theory, we may consider Rayleigh-Schrddinger perturbation theory, which is size consistent. In this method the total energy is computed in a stepwise manner... 

T/ie Goldstone expansion is rederived by elementary time-independent methods, starting from Brillouin-Wigner (BW) perturbation theory. Interaction energy terms AE are expanded out of the BW energy denominators, and the series is then rearranged to obtained the linked-cluster result. ... 

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