Free energy of cavity formation in liquid water and hexane

The difference between the work of forming a cavity in water versus organic solvents is believed to play an important role in making apolar solutes less soluble in water than in these solvents, a property commonly referred to as the hydrophobic effect. In this study, two methods are applied, using molecular dynamics simulations, to compute the free energy of forming spherical cavities in the water and hexane liquids. One, based on the free energy perturbation approach, involves gradually growing into the liquid a soft cavity, by turning on a repulsive potential. The other computes the likelihood of finding a natural cavity in configurational data of neat liquids. In addition, the free energy of cavity formation in the two liquids is evaluated by the scale particle theory. Using all three approaches, we investigate how this free energy is influenced by the different descriptions of the cavity-solvent system: the perturbation method considers soft cavities whereas the statistical approach and scale-particle theory deal with hard sphere cavities. Also the scale-particle theory uses a simplified representation of the solvent while the computational procedures use an atomic description. The results of the perturbation approach show that it is more costly to accommodate a cavity of molecular size in water than in hexane, in agreement with previous evaluations, based on the statistical approach. In hexane, we obtain a rather similar cavity size dependence of the free energy computed with the two simulation methods. In principle, this should also be the case for water. We find, however, significantly higher free energy values in water with the statistical method than with the perturbation approach. This result is confirmed by an analysis of the structure of water around the cavities. Ways of bringing the two calculations to converge to the same result are discussed.