Configuration interaction features

While the theoretician might be interested in the subtle features of a problem which can only be revealed by explicit computation, the organic chemist is more interested in a general qualitative theory which can be directly applicable to problems of interest without the need of computer assistance. Hence, we should reduce the quantitative scheme to a qualitative scheme which can still retain the important features of the theory. The various steps which one has to follow in attempting a qualitative configuration interaction analysis are given below ... 

The ideal calculation would use an infinite basis set and encompass complete incorporation of electron correlation (full configuration interaction). Since this is not feasible in practice, a number of compound methods have been introduced which attempt to approach this limit through additivity and/or extrapolation procedures. Such methods (e.g. G3 [14], CBS-Q [15] and Wl [16]) make it possible to approximate results with a more complete incorporation of electron correlation and a larger basis set than might be accessible from direct calculations. Table 6.1 presents the principal features of a selection of these methods. 

In this paper, the main features of the two-step method are presented and PNC calculations are discussed, both those without accounting for correlation effects (PbF and HgF) and those in which electron correlations are taken into account by a combined method of the second-order perturbation theory (PT2) and configuration interaction (Cl), or PT2/CI [100] (for BaF and YbF), by the relativistic coupled cluster (RCC) method [101, 102] (for TIF, PbO, and HI+), and by the spin-orbit direct-CI method [103, 104, 105] (for PbO). In the ab initio calculations discussed here, the best accuracy of any current method has been attained for the hyperfine constants and P,T-odd parameters regarding the molecules containing heavy atoms. 

It is now possible to draw a correlation diagram between the states, as shown in Figure 7.13. The crucial feature to note here is that the Ax to Ax correlations which would seem to follow from direct orbital,correlations cannot and do not actually occur, because of what is called the noncrossing rule. Two states of the same symmetry cannot cross, in the manner indicated by the dotted lines, because of electron repulsion. Instead, as they approach they turn away from each other so that the lowest 4, states on each side are correlated with each other as shown by the full lines. The repulsive interaction is similar in essence to that involved in configuration interaction in naphthalene, as discussed in Section 7.6. Indeed, the noncrossing rule is no more than a special but straightforward instance of configuration interaction. 

Additional feature A limited configuration interaction calculation is... 

Apart from the interest in the properties of the excited configurations themselves, their influence on the f-electrons has been studied extensively. As mentioned in the beginning of this section, mixing with excited configurations is responsible for the observed intensities of f-f transitions. This feature will be discussed in sect. 5.3.1. The influence on the center of gravity of the multiplets is also taken into account in most studies via the two-body and three-body configuration interaction parameters. 

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