Nonnuclear attractor

The AIM scheme is popular due to its reliability with large basis sets for which some other schemes fail. Unfortunately, the numerical surface finding and integration involved in this scheme are not completely robust. For example, nonnuclear attractor compounds like Li2 and Na clusters have maxima in the middle... 

Some caution should be used when using the topological method. (Actually, caution should be used with all methods.) The coincidence of (3,-3) critical points with atomic nuclei is not guaranteed. Very early in the development of the topological theory, Li2, Be2, and C2 were found to have a (3,-3) critical point that did not correspond with a nucleus (called a nonnuclear attractor). Such cases were at first thought to be artifacts of incomplete basis sets and/or incomplete inclusion of electron correlation. However, later examinations have found that some of these nonnuclear attractors persist even with extremely large basis sets and with extensive inclusion of electron correlation. Therefore, it is possible for an atomic basin to be well defined... 

On the Presence of Nonnuclear Attractors in the Charge Distribution of Li and Na Clusters. 

These are maxima, minima, and saddle points. If we start from an arbitrary point and follow the direction of Vp, we end up at a maximum of p. Its position may correspond to any of the nuclei or to a non-nuclear concentration distribution (Fig. 11.2). Formally, positions of the nuclei are not the stationary points because Vp has a discontinuity here connected to the cusp condition (see Chapter 10, p. 585), but the largest maxima correspond to the positions of the nuclei. Maxima may appear not only at the positions of the nuclei, but also elsewhere (nonnuclear attractors, (Fig. 11.2a). The compact set of starting points which converge in this way... 

Impurity/Doping. - Baruah et focused entirely on p s topology of impurity doped small Li clusters (Li Mg and Li Be clusters for n = 1-6). The authors reported that Li-Li bonds were observed for clusters with n 4 in the Li Mg series, while for 5 the Li atoms form bonds only with the impurity atom. These statements are incorrect since they ignore the presence of nonnuclear attractors, which were nevertheless extensively mentioned. 

In order to tell whether a particular critical point represents a maximum (nonnuclear attractor), a minimum or a saddle point we have to calculate at this point... 

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