Interpretation of molecular intracule and extracule density distributions in terms of valence bond structures: Two-electron systems and processes

The topological features of molecular intracule and extracule densities and their Laplacian distributions computed at the HF and CISD levels of theory are interpreted in terms of valence bond (VB) structures, By mapping each VB structure of a system onto its intracule and extracule density distributions, the values of the intracule and extracule densities can be associated with the contribution of each VB structure or group of structures to the total wave function. Difference maps between the Laplacian of intracule and extracule densities calculated at the HF and CISD levels are used to identify which VB structures are given more or less weight upon inclusion of electron correlation. As application examples, the topological features of the intracule and extracule density distributions for the H-2 and linear H-3(+) two-electron systems are rationalized in terms of the contributions of different VB structures. Moreover, their respective dissociation reactions, H-2 --> H-. + H-. and H-3(+) --> H-2 + H+, have been studied using the same interpretative analysis. The evolution of the values of the intracule and extracule densities, in those points associated with VB structures, is found to be in qualitative agreement with the change of the weight of each VB structure to the total wave function along the reaction coordinate.