Thermodynamically dominant hydration structures of aqueous ions

The hydration free energy of an ion is separated into a chemical term, arising due to the interaction of the ion with water molecules within the defined coordination sphere (the inner shell), a packing contribution, accounting for forming an ion-free coordination sphere (the observation volume) in the solvent, and a long range correction, accounting for the interaction of the ion with the solvent outside the coordination sphere. The chemical term is recast as a sum over coordination states, with the nth term depending on the probability of observing n water molecules in the observation volume and the free energy of assembling the n water molecules around the ion in the presence of the outer-shell solvent. Each stepwise increment in the coordination number more fully accounts for the chemical contribution, and this molecular aufbau approach is used to interrogate the thermodynamic importance of various hydration structures X [H2 O] n of X (aq) (X= Na+, K+, F-) within a classical molecular mechanics framework. States with n less than (and at best equal to) the most probable coordination state ñ account for all of the chemical term and evince the role of the ion in drawing water molecules into the coordination sphere. For states with n> ñ, the influence of the ion is tempered and changes in coordination states due to density fluctuations in water also appear important. Thus the influence of the ion on the solvent matrix is local, and only a subset of water molecules (n ñ) contributes dominantly to the hydration thermodynamics. The n=4 state of Na+ (ñ =5) and K+ (ñ =7) and the n=6 state of F- (ñ =6) are thermodynamically dominant; adding a water molecule to the dominant state additionally contributes only about 2-3 kB T toward the chemical term, but removing a water molecule is very unfavorable.