Ab initio prediction of optical rotation: comparison of density functional theory and Hartree-Fock methods for three 2,7,8-trioxabicyclo[3.2.1]octanes.

We report ab initio calculations of the frequency-dependent electric dipole-magnetic dipole polarizabilities, beta(nu), at the sodium D line frequency and, thence, of the specific rotations, alpha, of 2,7,8-trioxabicyclo[3.2.1]octane, 1, and its 1-methyl derivative, 2, using the Density Functional Theory (DFT) and Hartree-Fock/Self-Consistent Field (HF/SCF) methodologies. Gauge-invariant (including) atomic orbitals (GIAOs) are used to ensure origin-independent alpha values. Using large basis sets which include diffuse functions DFT alpha values are in good agreement with experimental values (175.8 degrees and 139.2 degrees for (1S,5R)-1 and -2, respectively); errors are in the range 25-35 degrees. HF/SCF alpha values, in contrast, are much less accurate; errors are in the range 75-95 degrees. The use of small basis sets which do not include diffuse functions substantially lowers the accuracy of predicted alpha values, as does the use of the static limit approximation: beta(nu) approximately beta(o). The use of magnetic-field-independent atomic orbitals, FIAOs, instead of GIAOs, leads to origin-dependent, and therefore nonphysical, alpha values. We also report DFT calculations of alpha for the 1-phenyl derivative of 1, 3. DFT calculations find two stable conformations, differing in the orientation of the phenyl group, of very similar energy, and separated by low barriers. Values of alpha predicted using two different algorithms for averaging over phenyl group orientations are in good agreement with experiment. In principle, the absolute configuration (AC) of a chiral molecule can be assigned by comparison of the optical rotation predicted ab initio to the experimental value. Our results demonstrate the critical importance of the choice of ab initio methodology in obtaining reliable optical rotations and, hence, ACs, and show that, at the present time, DFT constitutes the method of choice.