Electronic localization function nodal planes

The question remains whether the nodal planes, essential for the qualitative analysis, remain in the more advanced calculations of wavefunctions. To test this point, the electronic localization function (ELF) as implemented by B. Silvi and A. Savin [24] is used. In Figure 3 we summarize the results. 

This phenomenon is best illustrated by considering a tt radical system (Fig. 26.6a), in which the C-H bond lies on the nodal plane of the carbon p,j orbital that carries some unpaired spin density. As depicted in Fig. 26.6b, the local electronic structure around the carbon center can be described in terms of the ctch and CTch orbitals i and , respectively) of the C-H bond and the p orbital (< ) of the carbon atom. To a first approximation, the up- and down-spin electrons in ctch are regarded to have an identical spatial function, which leads to no unpaired spin density on the H atom. From the viewpoint of perturbation theory, this corresponds to the unperturbed electronic structure. However, this picture is not complete, because EPR experiments show the presence of a small amount of unpaired spin density on the H atom. 

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