Near-degeneracy effects

Correlation effects in molecules are normally partitioned into near-degeneracy effects (static correlation) and dynamic correlation. Qualitatively they differ in the way they separate the electrons. Static correlation leads to a large separation in space of the two electrons in a pair, for example on two different atoms in a dissociation process. Dynamic correlation on the other hand deals... 

Different electronic states have in many cases veiy differently shaped orbitals and the error introduced by using a common set cannot always be fully recovered by the MR-CI treatment. A well optimized wave function is especially important for the calculation of transition properties like the transition moments and the oscillator strength. A state specific calculation of the orbitals is more important for obtaining accurate values of the transition moments than extensive inclusion of correlation. Since excited states commonly exhibit large near-degeneracy effects in the wave function an MCSCF treatment then becomes necessary. 

Having decided about the basis set, we now turn to the problem of choosing an appropriate form of the wave function. Since we are going to calculate an energy difference between two electronic states, it is clear that we have to include as much correlation effects as possible. We shall do that in two steps In the first step we try to account for the near degeneracy effects by using the CASSCF method with an appropriate choice of the active space. On top of that we shall have to perform multi-reference Cl calculations to account for the dynamical correlation energy. 

One of the most powerful tools presently available for accurate electronic structure calculations is the multiconfiguration reference CI(SD) method. In MR-CI(SD) wavefunctions, all configurations that are singly or doubly excited relative to any of the reference eonfigurations are taken into account, and their coefficients are determined variationally. The reference wavefunctions are usually optimized by the MCSCF method. They should properly describe the dissociation of bonds and near-degeneracy effects. If the reference wavefunction includes the most important double excitations from the... 

The C2 molecule offers an example where near-degeneracy effects have large amplitudes even near the equilibrium internuclear separation. The ground... 

The present review has presented some illustrations of the CASSCF method. The method has been applied to a number of problems not considered here. Core ionization and shake-up spectra have been successfully analysed in terms of near-degeneracy effects in the ionized states. The shake-up spectra of p-nitroaniline ° and p-aminobenzonitrile ° highlight this type of application. Studies of valence ionization spectra have been done for ozoneand acetylene s . 

In this last section we will take a short sidestep from the main subject of this chapter to look at another aspect of computational chemistry where multiconfig-urational methods, in particular CASSCF, come in very handy, i.e., the description of excited states. Indeed, one of the nice features of the CASSCF method is that it can generally be used for excited states as well as for the ground state. All it takes is to optimize a set of orbitals for the excited state in question (which is not always straightforward in cases where different roots are close in energy and may flip [10]) or, alternatively, for an average of a set of excited states. It is important to realize, however, that the calculation of excited states imposes additional demands on the active space, other than to include all near-degeneracy effects. The rule is simple and self-evident all orbitals that are either populated... 

Another reason for going beyond the single configuration scheme is related to near degeneracy effects which mean that several configurations will in-... 

A series of carbide diatomics, CaC, ZnC, BeC, and MgC, were another challenge for the MR BWCCSD to treat systems of multireference nature caused by near-degeneracy effects. The task was to examine theoretically [79,80] the competing and states. In Table 18.3 we present results for CaC. 

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