Electron probability distribution in AIM and ELF basins

The probabilities of finding a certain number of electrons enclosed in a given volume is calculated and discussed for a series of molecules. Two different methodologies to do the partition of the molecular space in separate volumes are investigated: the Atoms in the Molecules, AIM, topologic analysis of the density, and the topologic analysis of the Electron Localization Function (ELF). The formulas to calculate the probability distribution are reviewed and the way to implement them shortly explained. For a series of molecules, we present how the probability distribution complement the chemical information about the localization of the electrons in certain regions of the space. The calculations show that the probability of finding Z electrons in the AIM atomic basin associated to an atom of atomic number Z is, in general, low, even when the average number of electrons is close to Z. The probability distribution on the ELF basins associated to bonds yields new insight about the nature of the respective bond.