Brillouin-Wigner theory

In the proceedings of the Quantum Systems in Chemistry Physics XII workshop [1], Wilson and Hubac [2] described A Collaborative Virtual Environment for Molecular Electronic Structure Theory involving eight scientists from six countries which was created in order to develop many-body methods based on Brillouin-Wigner theory under the auspices of the eu cost programme. 

Many-Body Brillouin-Wigner Theories Development and Prospects... 

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

Multi-reference Brillouin-Wigner theory overcomes the intruder state problem because the exact energy is contained in the denominator factors. Calculations are therefore state specific , that is they are performed for one state at a time. This is in contrast to multi-reference Rayleigh-Schrddinger perturbation theory which is applied to a manifold of states simultaneously. Multi-reference Brillouin-Wigner perturbation theory is applied to a single state. Wenzel and Steiner [105] write (see also [106]) ... 

Equation 2.50 is the Bloch equation for multi-reference Brillouin-Wigner theory. It should be emphasized that the wave operator (A) has the subscript /z indicating that it is state-specific. 

We have developed a prototype collaborative virtual environment, which actively supports human-human communication in addition to human-machine conununi-cation, for molecular electronic structure theory. We submit that key elements of e-science, such as collaborative virtual environments, will evolve most rapidly and deliver a functionality required by practicing scientists if they are developed as part of a research project in the target discipline. This is the approach that we have followed in this work. We have developed a collaborative virtual environment for molecular electronic structure theory whilst undertaking research into aspects of the Brillouin-Wigner theory for many-body systems. Others working in molecular physics and quantum chemistry may find this a usefiil starting point for the development of improved environments. Such environments wiU undoubtedly evolve with time as higher bandwidths and new tools become available. 

Multireference coupled-cluster calculations on the energy of activation in the automerization of cyclobutadiene Assessment of the state-specific multireference Brillouin-Wigner theory Journal of Chemical Physics 112, 8785 (2000)... 

See Chap. 1 of reference [51] for a brief discussion of the contribution of Lennard-Jones to Brillouin-Wigner theory. 

The current volume presents the compilation of splendid contributions distributed over 21 chapters. The very first chapter contributed by Istvan Hargittai presents the historical account of development of structural chemistry. It also depicts some historical memories of scientists presented in the form of their pictures. This historical description covers a vast period of time. Intruder states pose serious problem in the multireference formulation based on Rayleigh-Schrodinger expansion. Ivan Hubac and Stephen Wilson discuss the ciurent development and future prospects of Many-Body Brillouin-Wigner theories to avoid the problem of intruder states in the next chapter. The third chapter written by Vladimir Ivanov and collaborators reveals the development of multireference state-specific coupled cluster theory. The next chapter from Maria Barysz discusses the development and application of relativistic effects in chemical problems while the fifth chapter contributed by Manthos Papadopoulos and coworkers describes electronic, vibrational and relativistic contributions to the linear and nonlinear optical properties of molecules. 

They also noted that Brillouin-Wigner theory... 

These two possible formulations of multi-reference Brillouin-Wigner coupled cluster theory are discussed further below. In Section 4.2.2.1, we present a multiroot formulation of Brillouin-Wigner theory. This formalism is employed in Section 4.2.2.2 to develop a multi-root, multi-reference Brillouin-Wigner coupled cluster theory, using a Hilbert space approach. In Section 4.2.2.3, we discuss the basic approximations employed in the multi-reference Brillouin-Wigner coupled cluster method. 

Brillouin-Wigner theory has been largely neglected in the quantum chemistry and molecular physics literature, because it is found to lack extensivity. Brillouin-Wigner perturbation theory contains terms in each order which do not scale linearly with particle number and furthermore, these terms are not cancelled in a given order. This lack of extensivity is associated with the presence of the exact energy in the denominator factors. 

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