Intruders coupled-cluster theory

U. Kaldor, Intruder states and incomplete model spaces in multireference coupled-cluster theory The 2p states of Be, Phys. Rev. A 38 (1988) 6013. 

Hubac and his co-workers222"231 have explored the use of Brillouin-Wigner perturbation theory in solving the coupled cluster equations. For the case of a single reference function, this approach is entirely equivalent to other formulations of the coupled cluster equations. However, for the multireference case, the Brillouin-Wigner coupled cluster theory shows some promise in that it appears to alleviate the intruder state problem. No doubt perturbative analysis will help to gain a deeper understanding of this approach. 

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. 

The first term in Equation 6.2 is a direct term similar to the matrix elements of similarity-transformed Hamiltonians in single reference coupled cluster theory, while the second term is a coupling term that describes the coupling between model functions. It has been shown that the structme of the coupling term is crucial for ensuring that the theory is both size-extensive and intruder-free. 

The application of the Brillouin-Wigner coupled cluster theory to the multireference function electron correlation problem yields two distinct approaches (i) the multi-root formalism which was discussed in Section 4.2.2 and (ii) the single-root formalism described in the previous subsections of this section. Section 4.2.3. The multiroot multi-reference Brillouin-Wigner coupled cluster formalism reveals insights into other formulations of the multi-reference coupled cluster problem which often suffer from the intruder state problem which, and in practice, may lead to spurious... 

In Brillouin-Wigner coupled cluster theory, the simple a posteriori correction described above is exact in the case of the single-reference formalism. In the state-specific multi-reference Brillouin-Wigner coupled cluster theory, the simple a posteriori correction is approximate. An iterative correction for lack of extensivity has been studied by Kttner [38], but this reintroduces the intruder state problem. 

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