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, ∇ 2 ρ , 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.