1. I would be interested in how you know the Na is not associated? I dare say at infinite dilution, but even if surrounded by solvent it seems likely that a Na(+) would be in proximity (let us not use the loaded word “associated”). Might that not affect vibrations/rotations?

2. I do not think I was claiming to have myself modelled a complete system. Indeed, my posts show, I hope, my model evolving. In a sense, it was a devil’s advocate position. I was asking “show me that the Na and explicit solvent are not important”; I wanted rather more than just “the right answer is obtained with them missing”. I am not yet convinced they are not important, although you probably have lots of evidence you have not presented here.

3. My point again was that a complete absence of both Na(+) and hydrogen bonding solvent could itself be regarded as “nonphysical”, the elephants in the room if you like. I do indeed sometimes ask students “can you put 100g of just chloride anions into a reaction flask?”

4. In a blog there is an opportunity to show science “behind the scenes”. In this case, you can see me asking a question “what might be missing?”, adding it into to a first attempt at a model (using H(+), trying a second model with two Na(+), and suggesting at the end that a further model appropriate for exploring the formation of the second product is needed using the classical transition state approach.

Indeed the reader can also see you, I (and others) participating in a friendly discussion to explore some fascinating themes.

]]>I started to write a much longer discussion but at the end of a couple of pages I realized that I was less than half done with a post that perhaps no one would read. So let me outline my points and I can elaborate as desired.

1. The sodium ion is probably not associated, but to the degree that it is it makes no experimental difference.

2. Even if it were involved, simply throwing in a sodium ion and finding a saddle point would hardly constitute the theme of modeling a complete system. Polar reactions in solution occur by ensembles of transition states.

3. The blog models that include zero sodium ions, or two sodium ions, or next, three plus a hydroxide ion, are, well, our polite word is “nonphysical.” Aside from the particular models being inconsistent with experimental observations, dancing motions of protons or sodium ions are always sexy to the eye but real reactions almost never happen this way.

4. Computational studies by any approach provide _models_ of mechanisms, and these models only become science only when they make predictions of experimental observations. Until they do so, and their predictions are found to reasonably fit with experiment, they haven’t left the starting gate. I would disagree with considering models that fit with experimental observations and those that have not been shown to fit, or are in fact inconsistent, on an equal footing, in the manner of a news story.

Regarding the (over)simplification of the models, I tend to approach the other way around, making the model more complex little by little until I either learn nothing new (sometimes) or until the model becomes so large that I cannot calculate it with my computer resources (most of the time).

Really, any geometry proposed is a hypothesis, and the computation is our way of testing for its “validity”. So, I guess one can always analyze the diverse hypotheses and decide which ones do not represent anything new. Of course, computation can always reorganize the system in an unforseen hypothesis, in a similar way to an experiment that yields an unforseen product.

Finally, I think one should not abuse Occam by discarding a hypothesis that “does not add anything new”. I prefer to say that several hypotheses are undistinguishable by the current experimental knowledge, and I may even try to suggest an experiment that could distinguish among them.

Thank you again for keeping this blog.

]]>Of course, now that one has learnt something, one could try trimming this model down to just one Na and seeing what happens (one could probably also trim off one water as well).

This now raises a more subtle problem. At what point does one decide that the model is trimmed down to its essential features, and no more? My hypothesis I am testing here is that trimming it down to remove the 2Na(+) and the water molecules entirely would reduce down to Bogle and Singleton’s original model, which (so I am suggesting) might (only might) be a step too far in simplification. To put it another way, if the model with two Na(+) and water/hydroxide results in the same dynamic behaviour as the original model, then the larger more complex model explains nothing new, and so is not needed (Occam). However, if the larger model does not give the same dynamic behaviour as the one without the extra ingredient, them perhaps this larger model is a better description after all.

This problem always raises it head when dealing with explicit solvent molecules. But in a sense, it is similar to another question; how large a basis set should one use to describe the wavefunction? The CBS (complete basis set) limit suggests one will approach better solutions as one does. Perhaps the same applies to solvent molecules (and the law of diminishing return).

**A postscript**. I am reminded, in the above discussion of Kaluza-Klein theory. This dates back to 1921, when Kaluza extended Einstein’s space-time to five dimensions, and found that the general theory of relativity also could be made to incorporate Maxwell’s equations for an electromagnetic field. A single set of equations which described two fundamental fields. As I understand it, this apparent elegance was not met with great enthusiasm. It predicted nothing new over the individual field theories, no new experiment to test new predictions, just mathematical elegance. Of course, Paul Dirac then based his life on (and won the Nobel prize for) mathematical elegance in quantum mechanics. But his equations did manage to predict the positron!

**Another postscript**. Now I am really going well beyond what I truly understand. But Dirac formulated a description of the energy of an electron in its own field. I am intrigued by the SM Higgs Boson, and the difficulty of understanding how it gives mass to itself! Enough!!