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Cyclopentadiene

Good results. Good discussion, but a little bit more on the origins of kinetic vs thermodynamic control (and how you might model these using computational techniques) would have improved even further.

Taxol

Good energies, nice geometries. But each of 9 and 10 can have TWO chair conformations. Did you try to see if the other in each case was lower?

NMR

Again, your dithiane 18 is a nice geometry, but could it have been the other chair isomer?

incorrectly predicts extra peaks in the wrong regions It will not predict the wrong number of peaks, merely have errors in the shift.

You have listed the differences between calc and expt, but a nice graphical presentation of this is always easier to interpret. Oddly, the boat seems a better match than the chair!

Epoxides

Xray

One fo the three pairs of anomeric bond length is much different from the other two. Did you spot anything unique to this combination. Another explanation could be invoked by looking at the relative positions of the atoms- the lone pair on O6 cannot align itself anti-periplanar to the could have been followed up for example.

But good analysis here!

NMR

No real need for so many graphical spectra. We just want a statistical analysis of the fit between theory and expt, rather than lots of spectra.

Rotations

Styrene oxide= 30.47 deg. DOI:10042/27326 , lit. value = 32.1 deg[14] What absolute configuration was your calculation (not mentioned)? What absolute configuration is the lit (not mentioned)? This is the absolute core of the expt, and your (absence) of proper labels has let you down here! Your task is to see if the signs match, but without this information the expt cannot be completed!

TS

the Gibbs free energy difference = -5.34 kcalmol-1. You need to convert this into an enantiomeric excess.

NCI and QTAIM

Good analysis of the NCI. None unfortunately for the QTAIM.

Suggestion

I think you misunderstood. We want an alkene suggesting, and it has to be commercially available. Is that true here? Interesting molecule if the alkene is available though.

Overall, a pretty good effort! Well done.