  We introduce the concept of maximum probability domains (MPDs), developed in
the context of the analysis of electronic densities, in the study of the
microscopic spatial structures of liquids. The idea of locating a particle in a
three dimensional region, by determining the domain where the probability of
finding that, and only that, particle is maximum, gives an interesting
characterization of the local structure of the liquid. The optimization
procedure, required for the search of the domain of maximum probability, is
carried out by the implementation of the level set method. Results for a couple
of case studies are presented, to illustrate the structure of liquid water at
ambient conditions and upon increasing pressure from the point of view of MPDs
and to compare the information encoded in the solvation shells of sodium in
water with, once again, that extracted from the MPDs.
