On the full topology of the Laplacian of the electron density

In this work we briefly review the use of the function L(r), which is defined as minus the Laplacian of the electron density, V(2)p, in the context of the theory of 'atoms in molecules'. The topology of L(r) can be almost faithfully mapped onto the electron pairs of the VSEPR model, The computation of the gradient vector field L(r) opens new avenues for the further quantification of this mapping. Although major questions are still outstanding this contribution explores for the first time the full topology of L(r) for a molecule. In water there are four regions: the Core Shell Charge Concentration (CSCC), the Core Shell Charge Depletion (CSCD), the Valence Shell Charge Concentration (VSCC) and the Valence Shell Charge Depletion (VSCD). Each region has a set of L(r) critical points coagulating in a graph, except the CSCC. In analogy with the topology of the electron density we propose the term basin interaction line for the pair of gradient paths linking two basins in L(r), and the term interbasin surface for the surface separating two basins. We present a systematic study of the water molecule, which possesses 43 critical points in L(r). The question is raised how a basin in L(r) can be linked with the domain of the VSEPR model. (C) 2000 Elsevier Science S.A. All rights reserved.