Thanks azmanam for all the info! Sorry for my late reply; it was a good bit of info to take in, and I was in the middle of moving locations. At any rate, after reading through it, I naturally have a few questions if you have time to answer any at all.
1. Since you mentioned in your linked forum thread that the delocalizing effect of conjugation involves
orbitals delocalizing
with antibonding orbitals as opposed to
electrons delocalizing
into antibonding orbitals, does this mean that the only important consideration is the energy level of the antibonding orbital and that factors like molecular coefficients aren't important? For example, above in this thread was a little discussion about how viable the N-H σ* orbital was for the cis-Oxygen lone pair to conjugate with. It was mentioned that the N-H σ* orbital was not as effective for conjugation because the molecular orbital coefficient was centered on the hydrogen, which is far away from the cis-Oxygen. Is consideration of molecular orbital coefficients for the empty antibonding orbital relevant for these conjugation effects?
2. Since electrons in bonding orbitals also delocalize in part with nearby empty antibonding orbitals, does this mean that this type of conjugation is present in just about every molecule to some extent, even if the energy difference is so small that there are no conformational or structural implications? I'm just trying to wrap my head around the idea of hyperconjugation, because it was hardly mentioned in my undergraduate studies, at least not in proportion to how potentially prevalent it really is. I guess this might explain how the idea of an "electron cloud" exists as opposed to localized electrons.
3. In your blog, you open the discussion with Glucose. It was asked in the forum thread as well as by Mitch in your blog why the OH group would prefer to be equatorial while the methoxy group is axial. Technically, the O-H antibonding orbital should behave similarly to a O-C antibonding orbital with regards to conjugation facilitation.
I had a theory of my own to explain this:
The 2 O-H bond in the axial position does interact with the 1-Oxygen via the Anomeric Effect; however, in the equatorial position, it also interacts with a lone pair from the 3-Hydroxy group. Thus, the Anomeric Effect is present in both axial and equatorial conformations. The energy difference between the diastereomers is either equivalent or small enough that steric effects dominate and the equatorial position is preferred.
When the 2 O-H bond is replaced with a 2-methoxy group, the preference is axial. The axial 2 O-C σ* orbital participates as expected in the Anomeric Effect with the 1-Oxygen. In addition to this, though, a σ* orbital from C-H bond on the methoxy group is conjugated with by a lone pair from the 3-hydroxy group as well. In the equatorial position, the lone pair from the 1-Oxygen is too far from the C-H bond to conjugate appreciably with it, while the 3-hydroxy group is assisted by being one bond removed from the pyrane ring, so it can conjugate with a neighboring axially-oriented methoxy group.
Summary: In the case of 2-hydroxy, we have
one conjugative interaction no matter whether it is axial or equatorial, so steric effects are the deciding factor in prioritizing the equatorial position. In the case of 2-methoxy, we have
two conjugative interactions in the axial position, as opposed to just one in the equatorial position, and the axial position is preferred.
Anyways, that was my attempt at an explanation
It would be interesting to see whether the hydroxyl group in 2-hydroxy-3,4,5,6-tetrahydropyrane is axial or equatorial. If it's still equatorial, then I am wrong. If it is changed to axial, though, then maybe there was some interaction with the 3-hydroxy group in the Glucose case.
Thanks again for the discussion!