We
present a new computational technique to quantify the solubility
of planar molecules in a solvent. Solubility is calculated as the
critical concentration at which solute molecules cease to stack as
columns, but rather aggregate in all directions. An explicit expression
for the solubility is obtained, which involves the potential of mean
force between two solute molecules as a function of their center-of-mass
distance in the limit of infinite dilution. This function can be easily
obtained from molecular dynamics simulations involving a pair of solute
molecules in a solvent using the umbrella-sampling method. As a validation
of our approach, we use a generic coarse-grained molecular model to
represent the molecular interactions of polycyclic-aromatic-hydrocarbon.
Within that coarse-grained model, the solubility of pyrene and acenaphthene
in heptane is estimated through large molecular dynamics simulations
and compared to the experimental results. The umbrella-sampling method,
applied to single pairs of these molecules in the solvent, provides
the values of the critical cluster size in the theoretical model of
molecular stacking. Umbrella-sampling simulations for the first members
of the polycyclic-aromatic-hydrocarbon series then are used to predict
their solubilities through our theoretical method. Within the typical
uncertainty associated with theoretical solubility estimates, the
agreement of our results with the experimental values is quite remarkable
for most of the members of the series in a wide range of molecular
masses, which confirms the general validity of the method in the case
of planar molecules. Among the molecules explored, agreement with
experiment fails for anthracene, for which the experimental solubility
is clearly out of the general trend along the polycyclic-aromatic-hydrocarbon
series, indicating that the coarse-grained representation used here
is not able to capture its peculiarity. The new methodology can be
applied to planar molecules to obtain relatively accurate values of
solubility at a very low computational cost.