We have used ab initio quantum mechanical (QM) methods to determine the potential energy of pseudorotation for 3,3-dihydroxy-5-methyl-2-(1-pyrollyl)tetrahydrofuran and 4-hydroxy-5-methyl-2-(1-pyrollyl)-tetrahydrofuran, close analogues of 2＇-deoxyribose and ribose sugars. The pyrrole is a substitute for the naturally occurring nucleic acid bases: adenine, thymine, guanine, cytosine, and uracil. At the highest calculation level (LMP2/cc-pVTZ(-f)//HF/6-31G**) for 2＇-deoxyribose, we find the C2＇-endo conformation is the global minimum. The C3＇-endo conformation is a local minimum 0.6 kcal/mol higher in energy, and an eastern barrier of 1.6 kcal/mol separates the two minima. Pseudorotation energies of ribose are quite complex and are strongly affected by local orientations of the 2＇ and 3＇ hydroxyl groups. When the hydroxyl groups are allowed to assume any conformation, the global minimum remains the C2＇-endo conformation. The eastern barrier increases slightly to 1.8 kcal/mol, and the C3＇-endo local minimum lies 0.6 kcal/mol above the global minimum. Constraining the torsion angle of the C3＇ hydroxyl group to -146 degrees, as is found in RNA polymers, results in the C3＇-endo conformation becoming the only energy minimum with a C2＇-endo conformation 1.9 kcal/mol higher in energy. Bond angles within the pentofuranose ring are correlated to the pseudorotational phase, as is observed by X-ray crystallography and is predicted by pseudorotation theory. Finally, a force field for use in molecular mechanics and dynamics simulations is presented which reproduces the QM potential energies for the 2＇-deoxyribose and ribose sugars.