Calculating KIEs from the Gaussian free energies has a few disadvantages. The alternative is to calculate the KIEs from the Bigeleisen equation using programs that do so directly, such as quiver. It has been shown (I can find the ref if you want) that the former is more susceptible to errors in the low frequencies than the latter. Both benefit from cancellation of errors, so errors from the free-energy procedure are usually negligible, but the Bigeleisen equation is set up in a way that cancels errors in small numbers instead of errors in large numbers. A minor issue is that Gaussian does not quite give enough digits for 13C KIEs – a millionth of a hartree starts to make a difference. A third issue is that it is more work. From ordinary Gaussian outputs including a frequency calculation, I can have a complete set up isotope effects including tunneling corrections in about a minute.

To not include a tunneling correction for 13C KIEs is to ignore the literature that shows that tunneling corrections improve predictions. The effects are not negligible.

When a calculational prediction is wrong, it seems to be absolutely routine for the difference to be ascribed to some intractable or incalculable extra factor, rather than a direct error in calculated energies, geometries, or mechanism. This is done every day with entropy. Your worry about anharmonic corrections seems to fall into this category. Before you go down that road, it would seem that you should first explain a literature full of correct isotope effect predictions.

Finally, there is a rather important pattern that emerges when you do a lot of differing calculations on a reaction and check to see which correctly predict the KIEs. The calculations that give correct predictions also have about the same TS geometry. The calculations that give wrong predictions give differing geometries. The geometries might be “right for the wrong reason” but one can usually live with that. Errors are not due to the bogeyman, they are due to errors in transition states. All of this (with some caveats) is buried in that obscure JACS journal somewhere.

]]>Yes, the computed KIE are what might be called “true” KIE, since they do not depend on the assumption of an internal site unaffected by them, and since this assumption turned out not to be quite 1.00, a small correction could be applied.

Regarding choice of functional, one could endlessly try any of the other 200+ available to seek small improvement. My choice of ωB97XD was based on experiences calibrating it for activation free energies against CCSD(T) calculations of the same system (doi: 10.1021/10.1021/ma300803b). I would think that any errors could just as well arise from other assumptions, such as harmonic frequencies, as from the choice of functional. Clearly, the B3LYP gas phase result may be one of those “right answer for the wrong reasons” cases that are quite common.

It would indeed also be good to see if anharmonic corrections affected calculated KIE significantly. I suspect not for 13C, but it might change the 2H ones. Unfortunately cubic force constants are far more arduous to compute for the models here than quadratic ones (indeed effectively impossible). It could be (perhaps has been) done for smaller reactions? Perhaps a suitable one for anharmonic study might be the HCl elimination reaction from chloroalkanes that I reported calculated KIE for back in 1981, doi: 10.1039/C39810000939. That has the advantage that the experiments are done in the gas phase.

]]>Your way of comparing predicted and experimental KIEs is a little off, due to the detail that the experimental KIEs made the assumption that the methyl group KIE was negligible. One you allow for this, ωB97XD/Def2-TZVPP/SCRF=xylenes doesn’t really perform as well as many other DFTs, including amusingly B3LYP/6-31G* gas phase.

Anyone who heard one of my talks between 1996 and 2005 would have seen slides comparing predicted and experimental isotope effects for this reaction. Over the years we have used that as a test case for how DFT methods performed with cycloadditions and the effect of doing the calculations in differing ways. Solvent models and bigger basis sets and dispersion corrections don’t make much difference. Many DFTs do fine, but notably M06-2X makes the TS too synchronous (I have seen enough in other cases to believe this is a systematic error). CVT/SCT does not make much difference here, except that it improves the two harder “inside” H/D KIEs a little, but it is painful to get numerical convergence.

There are of course lots and lots of papers making comparisons of calculated and experimental KIEs, thinking off the top of my head of papers from Saunders, Schramm, Paneth, Hess, Schaad, Houk, and Wolfsberg. We have 28 JACS papers doing this in one way or another.

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