Structural properties of water molecules near the 1.0, 2.0, and 4.0 nm gold nanoparticles. (a) Reduced density of water molecules in the radial direction and distributions of (b) cos θ and (c) cos α in the [−1, 1] range. The two angles, θ and α, characterize the orientation of the water dipole moment and the water O—H bond relative to the radial direction from the nanoparticle.