This is a follow up to

this post. Briefly, we have computed $\Delta E_{rxn}$ and $\Delta E^\ddagger$ for about 32,500 molecules using xTB and PM3 respectively. We can afford to do a reasonably careful (DFT/TZV) study on at most 50 molecules, so the next question is how to identify the top 50 candidates. In other words to what extent can we trust the conformational search and the xTB and PM3 energies?

To try to answer the latter question we (i.e.

Mads) randomly chose 20, 60, and 20 molecules with high, medium, and low xTB-$\Delta E_{rxn}$ values and recomputed $\Delta E_{rxn}$ at the M06-2X/6-31G(d) level of theory using the lowest xTB-energy DHA and VHF structures as starting geometries. The results are shown below

The vertical and and horizontal lines denote $\Delta E_{rxn}$ and $\Delta E^\ddagger$, respectively, for an experimentally characterised "reference" compound that we want to improve upon, i.e. we are looking for compounds that have larger $\Delta E_{rxn}$ and $\Delta E^\ddagger$ values. $\Delta E_{rxn}$ should ideally be at least 5 kcal/mol higher than the reference (but in general as large as possible) and $\Delta E^\ddagger$ should be at least 2 kcal/mol higher than the reference, but anything higher than that is not necessarily better. The half life depends very sensitively on the barrier, and is hard to compute accurately, so we have to be careful about excluding molecules with high storage capacity in cases where the barrier is close to the reference.

Using these criteria I would select 5 points for further study indicated by the red points (let's call them Square, Star, Triangle, Dot, and Diamond). Square is clearly the most promising one with significantly higher $\Delta E_{rxn}$ and $\Delta E^\ddagger$ compared to the reference. The remaining 4 points are chosen because they either have reasonably high $\Delta E_{rxn}$ and $\Delta E^\ddagger$-values that are only a few kcal/mol below the reference (Triangle and Star) or reasonably high $\Delta E^\ddagger$ and $\Delta E_{rxn}$ that are somewhat (ca 3 kcal/mol) higher than the reference. I'd call the last 4 points pseudo-positives.

The corresponding plot for SQM storage energies and barrier heights is shown above. The good news is that Square is still the clear winner and I would also have picked Star and Triangle for further investigation. However, there are many more points that I also would picked (false pseudo-positives) and Diamond and Dot would not have been picked (false pseudo-negatives).

The false positives are due to PM3 overestimating the barrier, so let's use B3LYP/6-31+G(d)//xTB barriers instead. Square is still the winner, Star would still be picked (but not Triangle), and the false positives are gone. However, the barriers for Dot and Diamond are now so low that they will not be picked (false pseudo-negatives).

**Summary and outlook**
SQM finds the only true positive (Square). PM3 tends to over estimate the barrier relative to the reference, which leads to false pseudo-positives. xTB tends to underestimate the storage capacity which leads to a few false pseudo-negatives. DFT/PM3 barriers removes the false pseudo-positives but also leads to some false pseudo-negatives.

The above plot shows the molecules with an xTB storage energy that is at least 4 kcal/mol higher than the reference (4 rather than 5 kcal/mol since xTB tends to underestimate the storage energy). The solid line shows the reference barrier and the dotted line lies 2 kcal/mol above that (since PM3 tends to underestimate the barrier). There are 41 points above that line, including good old Square, that we should investigate further and it's probably also good to look at a few more points with very high storage energy and reasonably high barrier.

But all this assumes that we can trust the conformational search so this has to be tested next.

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