Wigner method

We recently presented a correlation method based on the Wigner intracule, in which correlation energies are calculated directly from a Hartree-Fock waveftmction. We now describe a self-consistent form of this approach which we term the Hartree-Fock-Wigner method. The efficacy of the new scheme is demonstrated using a simple weight function to reproduce the correlation energies of the first- and second-row atoms with a mean absolute deviation of 2.5 m h. 

K. Imre, E. Ozizmir, M. Rosenbaum, and P. F. Zweifel. Wigner method in quantum statistical mechanics. Journal of Mathematical Physics, 8(5) 1097-1108, 1967. 

Imre, K., Ozimir, E., Rosenbaum, M., Zweifel, P.F. Wigner method in quantum statistical mechanics. J. Math. Phys. 8 1097 (1967). 

Brown, R.C. and Heller, E.J. (1981). Classical trajectory approach to photodissociation The Wigner method, J. Chem. Phys. 75, 186-188. 

Sheppard, M.G. and Walker, R.B. (1983). Wigner method studies of ozone photodissociation, J. Chem. Phys. 78, 7191-7199. 

Final-state rovibrational distributions following 266 nm photo- 462 dissociation of O3 calculated using Wigner method with classical trajectories... 

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

E. P. Wigner Method and Apparatus L. Ohlinger for Conducting a G. Young Nuclear Chain... 

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. 

In this section, we digress to review the use of collaborative virtual environments in prosecuting research on Brillouin-Wigner methods. ... 

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)...

Hubac I, Wilson S (2010) BriHouin-Wigner methods for many-body systems. Progress in theoretical chemistry physics, vol 21. Springer, Dordrecht/New York... 

Note that the wave operator arising in the Rayleigh-Schrodinger formalism, Q can be related to the wave operators in the Brillouin-Wigner method through the relation... 

In this work, we adopt the simple and computationally inexpensive Wigner method in the calculation of tunnelling corrections to the rate... 

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

---