Introduction

Nice concise and to the point.

Cyclopentadiene

Perhaps include more explanation of kinetic vs thermodynamic control, and which one Mechanics can deal with.

Good results and comprehensive discussion.

Taxol

Nice results, well explored, and I like the way you have annotated the Jmol popups! I liked your discussion of hyper stable alkenes. Nice!

Carbene

You introduce the idea of symmetry early; good! You write "there is a bug in ChemBio 3D which causes the PM6 minimization to produce a structure for dichlorocarbene which is not symmetrical ". In fact, did you test this? Its not the structure that is unsymmetrical, but the displayed wavefunction. Always test your assertions!! In fact, it does seem the bug is restricted to PM6 and not AM1. But nice orbitals!

You might have discussed that a real geometric distortion is evident in the structure, which results in one alkene moving towards the back side of the Cl-C bond, and one not moving. This is of significant and you should discuss the origins.

There is no real need for the graphic IR spectra (which you show back to front). A Table will do in fact. "interaction between the anti alkene and C-Cl anti bonding orbital." resulting in what? Nice investigation of substituent effects. Well done.

Glycosidation

I like the way you introduce Burgi-Dunitz. I also like how you discussed the observation that for PM6, A=C, B=D but A' NE C' and B' NE D'. And also that MM2 does not show this behaviour. Excellent

Project

Why do you think "MOPAC/RM1 calculation is also included because it produced a markedly different structure for Aurone, when compared to PM6, with most twisting about the C-C bond attached to the phenyl ring." Maybe the non bonded H...H contacts, or the conjugation?

Again, no real need to show the graphical spectra; the table is again good enough. IR is not particularly informative, but you did manage to extract something interesting. UV is a bit more so (again, your spectra should be left-right reversed).

Citations

Lots, but do try to add the DOI if available, and invoke the DOI template using {{ }}.

Excellent overall.