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Cyclopentadiene

Nice and concise with good results. Perhaps some explanation of what kinetic control actually is with a diagram?

Taxol

Your structures seem to be the enantiomers of the real taxol? This does not matter here, but it might if you are calculating eg optical properties?

You report only a single chair? Could there be others, possibly lower in energy? What about the twist boats?

I am struggling with "Both values are lower than 17 kcal/mol" Where did this come from? A hyper stable alkene is presumably more stable than it should be with respect to hydrogenation. So the higher energy the hydrogenated product, the more hyper-stable the alkene? So your statement does not seem to make sense? What can you compare your result to to check?

NMR

Your 17 and 18 are twist boats? The instructions say do only one of them. This might explain "an inaccurate conformation of the molecule in these regions,".

Could you find an explanation for "the maximum deviation observed is for carbon 4, that is for the spiroatom. "? (hint, read the recommended literature!!).

Expoxides

Xray

For the Shi you mention briefly the anomeric effect but you do not then explain how the bond lengths you measured are influenced by it. Requires some background reading. You missed a bit of a trick here.

Nice measurements for the Jacobsen.

NMR

There are many lit values for the NMR of styrene epoxide, you quote only one? Did you know there are more, or did you quote the first you found? Bit worried about the poor fit of the 13C!

Rotation

Table 16. You quote the configuration of the lit epoxides, but what configuration did your calculation relate to? Thus you get the opposite sign for the methyl styrene epoxide? This is the CRUCIAL bit of the entire expt, and you have to triple check this sort of thing. For example, did you calculate the (R,R) methyl styrene epoxide? Your text is not clear on this point. What is the point of the VCD diagram? No discussion! Do not include diagrams just to "bulk out" your report.

TS

No need for Table 17 really! Just quote the energy differences, in kcal or kJ, and not a whole table of numbers. You are also comparing the TS in pairs. This suggests you have not quite grasped the essentials, which is to find the LOWEST for each diastereomer, and NOT to compare them in pairs.

You conclude that SS is in greatest excess (Table 21). (The captions just say TS1 etc. But make it clear which catalyst and substrate. It is difficult to immediately tell if you do not put it into the caption). But how can this be if R,R is lower in energy?

I think a free energy difference of 13.08 J does NOT lead to an ee of 99% (Table 26). Since each enantiomer is ~50% (K=~1), how can the ee be 99% What was the equation you used?

NCI

Not sure what relevance arrows 3 and 4 have to the enantioselection, which is after all what you are trying to explain! Only 2 is really relevant, but your discussion does not tease much more out.

QTAIM

Arrow 1 is good!

New alkene

Hm. Bit spoilt by "However the corresponding alkene could not be found in the Sigma-Aldrich catalogue.".

Overall, I think you need to check your arguments a bit more carefully, more thinking about the results needed!