lemonoman's compound is more precisely defined - its t. movies was not as precise
I said t
-butoxide too! Check the post above!
As for why we came to the same set of reagents, I think it's just that those are standard thermodynamic alkylation conditions. t
-Butoxides are the classic way to generate thermodynamic enolates for reasons I'm sure your professor discussed (high basicity, low nucleophilicity, etc.). As for MeI, that's pretty much one of the very best alkylating agents there is. It's cheap, easy to work with, and gives almost exclusively C-alkylated products (as opposed to O-alkylated products, again for MO reasons). So, there is no magic to two organic chemists coming up with nearly identical conditions, it's just knowing some fundamental organic chemistry!
Here is a brief MO rationale for the alpha-alkylation:
Alkylating agents like MeI are strongly influenced by overlap with the molecular orbital of the nucleophile. With "harder" alkylating agents such as MeOTf, the electrostatic attraction becomes more important, so the electrophile is attracted to the most electron rich part of the nucleophile; in this case that would be oxygen. However, as I said, MeI reacts preferentially with the highest energy orbital
, i.e. the HOMO of the nucleophile. If you draw out the HOMO of an enolate, you would find that you have a small lobe on oxygen and a large lobe on carbon, so when orbital overlap is important, you expect reaction at carbon because the carbon centered lobe contributes more to the HOMO. To explain the O-alkylation products you need to look at the next lowest MO, or the sHOMO, which contains a large lobe on oxygen and a small lobe on carbon. The sHOMO is lower in energy because it has a lot of electron density on the more electronegative atom, oxygen.
When you get to extended enolates, you can draw similar HOMO diagrams, but you will find that if you do the calculations, the size of the orbitals decreases the further out that you go on the extended enolate, so the largest lobe of the HOMO of an extended enolate is still on the alpha carbon. This can be explained by the principle of least motion, that is, you don't have to move the electrons as far from the oxygen to the alpha carbon as you would need to move them from the oxygen to the gamma carbon (think resonance structures!)
I hope this helps. I can draw some pictures later, if need be.