Pair-correlation entropy of hydrophobic hydration: decomposition into translational and orientational contributions and analysis of solute-size effects.

We develop an efficient method to evaluate the translational and orientational contributions to the solute-water pair-correlation entropy that is a major component of the hydration entropy. A water molecule is modeled as a hard sphere of diameter dS=0.28 nm in which a point dipole and a point quadrupole of tetrahedral symmetry are embedded. A hard sphere of diameter dM, a hydrophobic solute, is immersed at infinite dilution in the model water. The pair-correlation entropy is decomposed into the translational and orientational contributions in an analytical manner using the angle-dependent Ornstein-Zernike integral equation theory. The two contributions are calculated for solutes with a variety of sizes (0.6<or=dM/dS<or=30). The effects of the solute-water attractive interaction are also studied. As dM becomes larger, the percentage of the orientational contribution first increases, takes a maximum value at dM=DM (DM/dS depends on the strength of the solute-water attractive interaction and is in the range of 1.4-2), and then decreases toward a limiting value. The percentage of the orientational contribution reduces progressively as the solute-water attractive interaction becomes stronger. The physical origin of the maximum orientational restriction at dM=DM is discussed in detail.