The valence shell charge concentration VSCC

Extrema in the Laplacian of p are classified by rank and signature in the same way as are critical points in the charge density. The critical points in the Laplacian occur where V(V p) = 0 and the eigenvalues of the Hessian of V p are the principal curvatures of V p at the critical point. The topological discussions will always refer to the negative of the Laplacian, the quantity 

The outer quantum shell of an atom is divided into an inner region over which 0 and an outer one over which 0. The portion of the shell over which V p 0, is called the valence-shell charge concentration or VSCC. Within this shell is the sphere over whose surface the valence electronic charge is maximally and uniformly concentrated. 

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The Laplacian thus displays where the electronic charge is locally concentrated or depleted [25, 26]. The topology of the valence shell charge concentration (VSCC), the region of the outer shell of an atom over which V p < 0, is in accordance with the Lewis and valence shell electron pair repulsion model. To each local maximum in the VSCC, a pair of bonded or non-bonded electrons can be assigned (Fig. 2). 

Fig. 9 Representations of minus the Laplacian of the electron dcmsity or the L-fimction in methanal (a) constant value contour plots (solid lines for positive values) in the molecular plane the K shell of the C and O atoms is very close to the respective nuclear positions (b) slice through a 3D envelope of the L-function being zero (c) the critical points (maximum =p rp/e = (3,-3) and saddle point = green = (3,-1)) in the valence shell charge concentration (VSCC) region and (d) L-graph, schematically showing the connectivity (edges) between the maxima (at the vertices)...

Isovalue surfaces of L(r) = 0 for CO (left) and BH3 (right) showing regions of valence-shell charge concentration (VSCC, inside surfaces) and depletion (VSCD, holes) that define the reactive surface and direction of interaction between a Lewis base and a Lewis acid. Adapted from ref [42]. Copyright 1994 Oxford University Press USA. 

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