Nuclear attractors

The other problem in the AIM approach is the presence of non-nuclear attractors in certain metallic systems, such as lithium and sodium clusters. While these are of interest by themselves, they spoil the picture of electrons associated with nuclei forming atoms within molecules. 

There are indications that the appearance of non-nuclear attractors in silicon is basis-set dependent. 

The value of the electron density at the bond critical point correlates with the strength-of the bond, the bond order. As mentioned above there are certain systems like metal clusters which have non-nuclear centred attractors. The corresponding bond critical points have electron densities at least an order of magnitude smaller than normal single bonds, and the value of the density at the local maximum is only slightly larger than at the bond critical point. The non-nuclear attractors are thus only weakly defined. 

The other problem in the AIM approach is the presence of non-nuclear attractors in... 

Fig. 11.2. How does the electronic density change in space Panel (a) illustrates the non-nuclear attractor maxiuium of p). Note that we can tell the signs of some second derivatives (curvatures) computed at the intersection of black lines (slope), the radial curvature is positive, while the two lateral ones (only one of them is shown) are negative. If for the function shown,...

In order to tell whether a particular critical point represents a maximum (non-nuclear attractor), a minimum or a saddle point we have to calculate at this point the Hessian i.e., the matrix of the second derivatives , where = x, 2 = y, h = Now, the stationary point is... 

All three eigenvalues are negative-we have a maximum of p (non-nuclear attractor Fig. 11.2a). 

Levy minimization (p. 679) local density approximation. LDA (p. 687) non-nuclear attractor (p. 670) one-particle density matrix (p. 698) Perdew-Wang functional (p. 688) self-interaction energy (p. 708) spin polarization (p. 687)... 

The conflict mechanism, which corresponds to an abrupt switching of nuclear attractors, is one of only two possible mechanisms for bringing about a change in structure. 

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. The compact set of starting points which converge in this way to the same maximum is called the basin of attraction of this maximum, and the position of the maximum is known as attractor. The position may correspond to any of the nuclei or to a non-nuclear electronic distribution non-nuclear attractors, Fig. 11.2.a). The largest maxima correspond to the positions of the nuclei. 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. 504). A basin has its neighbour-basins and the border between the basins (a surface) satisfies Vp - n = 0, where n is a unit vector perpendicular to the surface (Fig. 11.2.b,c). 

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