Monte Carlo simulations of hydrophobic interactions: A test particle approach

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Abstract
By use of the Widom particle insertion method we have evaluated the hydrophobic force and free energy of solvation for both two Lennard‐Jones as well as two hard sphere particles in water as a function of their separation. The entropy, energy, and free energy of a single hydrophobic particle were also calculated. By simulating water confined between two hard walls, we were able to obtain the free energy of interaction between a small nonpolar particle and a nonpolar wall. The results show ‘‘contact separation’’ to be the most stable configuration in all cases studied, but the free energy barrier of separation for two nonpolar particles is rather small, of the order of kT. For a nonpolar solute in contact with a hydrophobic wall the barrier is significantly larger, of the order of 4 kT. The effect of system size and geometry on the free energy was investigated. The insertion method produces satisfactory accuracy, provided that the inserted particles are not too large, that a sufficient number of uncorrelated configurations are used, and that some effort is spent on obtaining a fully equilibrated system. The perturbation calculations can be accelerated by a simple prescreening of possible insertion sites.