Topological Analysis of the Electron Density Distribution in Perturbed Systems. I. The Effect of Charge on the Bond Properties of Hydrogen Fluoride
Within the framework of the molecular orbital (MO) theory, the addition of one electron to the 4σ antibonding orbital of the neutral (F···H) system or the removal of one electron from its π nonbonding orbitals, leading to (F···H)- and to (F···H)+, has permitted the investigation of these charge perturbations on the bond properties of the hydrogen fluoride molecule by using the topological analysis of ρ(r). For (F···H), (F···H)-, and (F···H)+, the topological and energetic properties calculated at the F···H bond critical point (BCP) have been related to the 3σ bonding molecular orbital (BMO) distribution, as this orbital is the main contributor to ρ(r) at the interatomic surface. The analysis has been carried out at several F···H internuclear distances, ranging from 0.8 to 3.0 Å. As far as the BMO distribution results from its interaction with the average Coulomb and exchange potential generated by the charge filling the other MOs, and in particular by the π and 4σ electrons, the comparison between the BCP properties calculated for the charged systems and those corresponding to the neutral one permits the interpretation of the differences in terms of the charge perturbation on BMO. Along with the BCP properties of (F···H), (F···H)-, and (F···H)+, the interaction energy magnitudes of these systems have been also calculated within the same range of internuclear distances, indicating that the applied perturbations do not break the F−H bond but soften it, giving rise to the stable species (F−H)- and (F−H)+. Comparing the three systems at their equilibrium geometries, the most stable configuration, which corresponds to the unperturbed (F···H) system, shows the highest quantity and the most locally concentrated charge density distribution, along with the largest total electron energy density magnitude, at the interatomic surface as a consequence of the BMO contraction toward the fluorine nucleus in (F···H)+ and of the BMO expansion toward both nuclei in (F···H)-. On the other hand, if the comparison is carried out at the equilibrium distance of (F···H) (deq0), this one exhibits both the smallest total energy density magnitude and the largest quantity of bonding charge at the interatomic surface. Hence, being the signature of the most stable configuration, the characteristic magnitudes of the neutral system ρ(deq0), 2ρ(deq0), and H(deq0) appear as boundary conditions at the interatomic surface of its unperturbed and relaxed electron distribution.