Quantum mechanical calculations were used to obtain energies for reactants, transition states, and products so that reaction energetics and barriers could be obtained. The Gaussian 03 (29) suite of programs were used in our calculations, which were designed to obtain minima in potential energy surfaces corresponding to stable molecular species and saddle points that correspond to transition states. For this study, the hybrid density functional, B3LYP (25, 26), was used to obtain molecular geometries and energies. More accurate energies were obtained for the monosaccharides using the complete basis set (CBS) approach termed CBS-QB3 (30), in which the geometry is optimized using B3LYP/6-311G(d, p) and the energy is extrapolated to the complete basis set limit with MP2. Comparison of results from these techniques to the experimental values for the G2 set of molecules (31) shows that the standard deviation for the B3LYP technique with a split-level basis set (6-31G[d, p]) is about (32) 3 kcal mol-1 while the standard deviation for CBS-QB3 is (30) 1.2 kcal mol-1. The B3LYP technique can underestimate transition states (33-37) by up to 5 kcal mol-1, but the CBS-QB3 approach provides much better estimates of transition state energies (38).

The starting geometries for stable species were selected from the low energy conformers from CPMD calculations and literature results. The optimized geometries of reactants and products had no imaginary vibrational frequencies, whereas transition states had exactly one. Transition states were also confirmed by visual inspection of the motion of the imaginary frequency and by intrinsic reaction coordinate (IRC) calculations (39, 40). Reaction energy barriers, Ea, were determined as the difference in total energies of the transition state and the reactant, including the zero-point energy.