Intruder states, appearance

The procedure above can work only if the effect of the level shift is negligible in the stable case when no intruder state appears. Otherwise, we have introduced a new parameter into the model over which we have no control. The behavior of the level-shifted CASPT2 approach has recently been tested in a series of calculations on the N2 and Ct2 molecules [26]. The first test was performed on the potential curve for the... 

The two methodologies should not be considered as contradictory they may be used in conjunction, as has been mentioned. It may be useful for instance to use the projection approach, defining a valence effective Hamiltonian, which will be later mimicked (as H O by simulation techniques. The diabatization potential energy surfaces might be an important step to define valence states, in regions where non-valence intruder states appear, before simulating them by pseudo-Hamiltonian techniques. 

Hamiltonian has been diagonalized, a correction is applied for the appearance of the level shift in the denominators of the expressions for E,2). This level shift method has been applied successfully to a wide variety of problems in the field of spectroscopy and can be considered as a pragmatic solution to the intruder state problem inherent to perturbation theory. All CASSCF / CASPT2 calculations presented here have been done with MOLCAS-4 [27]. 

Basing on the nuclear shell-model and concentrating on the monopole,pairing and quadrupole corrections originating from the nucleon-nucleon force,both the appearance of low-lying 0+ intruder states near major closed shell (Z=50, 82)and sub-shell regions (Z=40,64) can be described.Moreover,a number of new facets related to the study of intruder states are presented. 

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. 

To summarize this section one should say that an effective Hamiltonian treatment of the core electron effect faces a contradiction between the necessity to use extended valence basis sets for the extraction and the risk of appearance of core excited intruder states. One should also recognize that this approach leads to p-electron operators for atoms involving p valence electrons and seems much more difficult to handle than the monoelectronic core pseudopotentials extracted by simulation techniques and discussed in Section IV of the present contribution. As a counterpart one should mention that this core effective Hamiltonian would be much superior, since it would include for instance the core-valence correlation effects which play such an important role in alkali- or alkaline-earth-containing molecules. 

There is thus little hope, in our opinion, for a rigorous definition of valence minimal basis set effective Hamiltonians. To build them, the use of the diatomic effective Hamiltonian may be useful, but some supplementary assumptions should be made, along a physically grounded model, to define for instance three-body polarization energies and the energies of highly hybridized or multi-ionic VB structures. One should realize the physical origin of these numerous troubles they essentially come from the inclusion of the ionic determinants in the model space. This inclusion first resulted in intruder state problems for the diatom it also leads to the appearance of multiply ionic structures in the valence minimal basis set space of the cluster. It seems that, even for H, the definition of a full valence space is too ambitious. 

It is interesting to note that the intruder state problem, which appeared explicitly in the effective Hamiltonian approach, is also present in pseudo-Hamiltonian formalisms when the simulation is too ambitious and claims to concern some states strongly mixed with other states out of the model. 

There is another trouble known as intruder states, i.e. states which are of unexpectedly low energy. How can these states appear Firstly, the Cl states known as front door intruders appear, if some im-... 

The FSCC equation (2.7) is solved iteratively, usually by the Jacobi algorithm. As in other CC approaches, denominators of the form Eq —E ) appear, originating in the left-hand side of the equation. The well-known intruder state problem, appearing when some Q states are close to and strongly interacting with P states, may lead to divergence of the CC iterations. The intermediate Hamiltonian method avoids this problem in many cases and allows much larger and more flexible P spaces. 

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