Finite representation of an infinite bulk system: Solvent boundary potential for computer simulations

An approach is developed to obtain statistical properties similar to those of an infinite bulk system from computer simulations of a finite cluster. A rigorous theoretical formulation is given for the solvent boundary potential which takes the influence of the surrounding bulk into account. The solvent boundary potential is the configuration-dependent solvation free energy of an effective cluster composed of an arbitrary solute and a finite number of explicit solvent molecules embedded inside a hard sphere of variable radius; the hard sphere does not act directly on the solute or the explicit solvent molecules, and its radius varies according to the instantaneous configurations. The formulation follows from an exact separation of the multidimensional configurational Boltzmann integral in terms of the solvent molecules nearest to the solute and the remaining bulk solvent molecules. An approximation to the solvent boundary potential is constructed for simulations of bulk water at constant pressure, including the influence of van der Waals and electrostatic interactions. The approximation is illustrated with calculations of the solvation free energy of a water molecule and of sodium and potassium ions. The influence of bulk solvent on the conformational equilibrium of molecular solutes is illustrated by performing umbrella sampling calculations of n-butane and alanine dipeptide in water. The boundary potential is tested to examine the dependence of the results on the number of water molecules included explicitly in the simulations. It is observed that bulk-like results are obtained, even when only the waters in the first hydration shell are included explicitly.