Alpha-D-Glucopyranose
By Nathan E. Schultz and Matthew J. Stockinger
A Spartan calculation (HF/STO3G) showed the ground state energy of the alpha form to be -447431.52 kcal/mol.
The Alpha From is 4.88 kcal/mol more stable!!
note - HF/STO3G is not quantitatively accurate, but it is qualitatively accurate.
It turns out that the alpha form is more stable because it has achieved maximal separation of the ring-oxygen's dipole with the dipole on the anomeric substituent. The distance between the oxygens of interest is 2.35 Angstroms (0.05 Angstroms greater than beta)
The Alpha Form has a dipole of 3.363 Debye and is oriented in the opposite direction of beta's dipole.
A map of the electrostatic potential helps to visualize why the alpha form is actually more stable.

The low population of alpha is a solvent effect and not a result of sterics.
Spartan is also able to perform qualitative calculations on molecules. The PM3-SM3 model (developed by Chris Cramer and Donald Truhlar at the University of Minnesota) was used.
Unfortuntely, the alpha is still lower in energy (-253.03 kcal/mol), but the solvation energy {alpha --> alpha(aq)} is actually lower than for the beta form.
alpha --> alpha(aq) = 15.185 kcal/mol
That difference is not huge, however, and the alpha form is still lower in energy than the beta form. weird.
Another difference is that the alpha form now has a lower dipole (1.86 Debye) and it is oriented in a different direction.
Also, pictorial representations of the dipole show that they are roughly aligned in the same direction.

It turns out that this problem was a lot more complicated than we had thought. A great reference (that we found after doing the project) is:
Quantum Chemical Conformational Analysis of Glucose in
Aqueous Solution, C. J. Cramer and D. G. Truhlar, Journal of the American Chemical
Society 115, 5745-5753 (1993).
Conclusions are that the alpha form is more stable. However, the solvent plays a big part in the beta stabilization. The beta form is actually "easier" to put into solution, but the alpha form is still lower in energy. The answer could be in one of the effects that PM3-SM3 does not calculate. The effects that it does calculate are:
-accurate account of the hydrophobic effect for hydrocarbons
-electric polarization of the solvent
-free energy of cavitation
-dispersion interactions
The stabilizing effect is not one of the above.
