Direct configuration interaction

Key words Electron correlation - Configuration interaction - Direct configuration interaction - Self-consistent electron pair theories - Local correlation... 

The minimal basis description of H2 allows for the construction of three excited configurations two singly excited determinants logOul and doubly excited determinant of the form 4 d) = doubly excited configuration interacts directly with the reference and, in the limit Tab —> 00,... 

Werner H-J 1987 Matrix-formulated direct multiconfigurational self-consistent field and multi reference configuration interaction methods Adv. Chem. Phys. 69 1... 

A is a parameter that can be varied to give the correct amount of ionic character. Another way to view the valence bond picture is that the incorporation of ionic character corrects the overemphasis that the valence bond treatment places on electron correlation. The molecular orbital wavefimction underestimates electron correlation and requires methods such as configuration interaction to correct for it. Although the presence of ionic structures in species such as H2 appears coimterintuitive to many chemists, such species are widely used to explain certain other phenomena such as the ortho/para or meta directing properties of substituted benzene compounds imder electrophilic attack. Moverover, it has been shown that the ionic structures correspond to the deformation of the atomic orbitals when daey are involved in chemical bonds. 

It is possible to use full or limited configuration interaction wavefunctions to construct poles and residues of the electron propagator. However, in practical propagator calculations, generation of this intermediate information is avoided in favor of direct evaluation of electron binding energies and DOs. 

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. 

B. O. Roos and P.E.M. Siegbahn The Direct Configuration Interaction Method from Molecular Integrals.,... 

B. O. Roos and P.E.M. Siegbahn The Direct Configuration Interaction Method from Molecular Integrals., inH. F. S. III(ed.) Methods of Electronic Stmcture Theory., Plenum, New York, p. 277 (1977). 

The import of diabatic electronic states for dynamical treatments of conical intersecting BO potential energy surfaces is well acknowledged. This intersection is characterized by the non-existence of symmetry element determining its location in nuclear space [25]. This problem is absent in the GED approach. Because the symmetries of the cis and trans conformer are irreducible to each other, a regularization method without a correct reaction coordinate does not make sense. The slope at the (conic) intersection is well defined in the GED scheme. Observe, however, that for closed shell structures, the direct coupling of both states is zero. A configuration interaction is necessary to obtain an appropriate description in other words, correlation states such as diradical ones and the full excited BB state in the AA local minimum cannot be left out the scheme. 

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. 

HJ.Wemer, Matrix-Formulated Direct Multiconfigurational Self Consistent Field and Multiconfiguration Reference Configuration-Interaction Methods. 

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