This question is about ions in water, both in reality and as handled by MD (explicit solvent) and QM methods (eg AIMD). Basically the question is this: why are ions not always paired?
For a back of the envelope calculation take K+ with radius 0.14nm and Cl- with radius 0.18nm or so. The electrostatic energy to separate the ion pair to infinity is 138/(0.14+0.18) = 430kJ/mol. Water (eg TIP3P model) has diameter around 0.3nm and partial charges around -0.8 on oxygen and +0.4 on hydrogen; the energy to separate a water-water pair is 20-30kJ/mol (lower in vacuum, higher if surrounded by water). If we think of inserting a water between an ion pair as breaking two water-water pairs (+50kJ/mol), separating the ions by the diameter of a water (+200kJ/mol or so) and adding two favorable ion-water interactions - I’m really having a hard time seeing how the ion-water interactions would add up to more than the energy needed to separate the ions. And that’s just for adding one water directly in between; separating the ions all the way (until they’re fully hydrated and almost fully screened so they can float around independently) would be even less favorable.
Can anyone explain intuitively what drives the separation of ion pairs? (hydration by multiple waters, overpolarization of the waters, small diameter of the hydrogen atoms allowing them to get closer to negative ion, etc). Is there a simple MD model that would show how that works?
Have there been any studies (either MD or QM) that specifically compare the potential energy (or free energy) of an ion pair in water vs two separate ions in water?