Understanding Maximum Probability Domains with Simple Models

The paper presents maximum probability domains (MPDs). These are regions of the three dimensional space for which the probability to find a given number of electrons is maximal. In order to clarify issues hidden by numerical uncertainties, some simple models are used. They show that MPDs reproduce features which one would expect using chemical intuition. For a given number of electrons, there can be several solutions, corresponding to different chemical situations (e. g. different bonds). Some of them can be equivalent, by symmetry. Symmetry can produce, however, alternative solutions. The models show that MPDs do not exactly partition space, and they can also be formed by disjoint subdomains. Finally, an example shows that a partition of space, as provided by loge theory, can lead to situations difficult to deal with, not present for MPDs.