Another in my GAMESS series on quantum chemistry. GAMESS is unquestionably a magnificent piece of work. All the people who have produced it should be very proud.
With the steady improvement of my skill using GAMESS, I was able to find the chemical reaction I was looking for in that earlier post. The basis set strongly influenced the reaction pathway in this one. Here is the transfer of a proton in water from one hydroxide to another.
I won’t talk a huge amount about this. The intent was simply to put up the pictures. This is the reaction by which protons are transferred around in water. This is the alkaline version of the reaction. I haven’t looked for it yet, but I suspect there is a homologous reaction under acidic conditions, involving hydronium only. It may be possible for this reaction to occur directly between hydronium and hydroxide, but I’m not sure there’s a stationary state possible in that system: the electrostatics will probably create a very steep potential energy gradient between the two molecules which may not have a stationary point in the middle (may depend on the solvent model to introduce screening).
The lesson: protons are probably never actually free in water.
I came back to the hydronium-only puzzle. This condition would be encountered in water where the pH is lower than 7. Turns out that my read of the situation as described above is slightly off.
This model is an attempt to find the reaction that I thought about above, where two waters hand a proton back and forth, taking turns being the hydronium ion. This geometry is achieved not purely by Hartree-Fock, but by Density Functional Theory (DFT) using a coulomb attenuated functional called CAMB3LYP with the 6-31G** basis set as a reference. I have also included a good quality polarizable continuum model in order to kind of pretend other waters are present here, even though they aren’t. This improves the energy estimates over a pure Hartree-Fock calculation by including correlation energy in DFT. It’s imperfect because DFT has some troubles with very soft interactions, but it’s easier to do than configuration interaction, which I’m still learning to master. When I started looking for the transition state for this reaction, I discovered something rather extraordinary.
Neither water molecule wants to be hydronium. What’s depicted in this animated gif is the energy minimum of the system, which happens to have a imaginary hessian mode. The transition state is the lowest free energy geometry of this system! When you try to find the reaction path by kicking the proton away from the transition state, it rolls back down the force gradient into the transition state (I thought for sure GAMESS was broken!). As such, the proton sits there and oscillates around this equilibrium point without going and really dedicating itself to one water molecule or another. It isn’t exactly dissociated: as you can see from the electron density above, the proton sits in an electron density flux tube in the channel between the two water molecules, binding the waters together.
This is the perhaps the true nature of how protons exist in water under acidic conditions! I would need to simulate the direct presence of a third water to see how the flux tube breaks.