1,6-Anhydro-o-pyranoses and methyl 3,6-anhydro-o-pyranosides (Fig. 1) take up crystal structures'-4 in which the ring form approximates 'C,. We have applied a recently developed calculational model of saccharide optical activity to a series of anhydro sugars with the aim of interpreting observed solution rotations in terms of conformation.
The calculational method, previously described in detai15'6, has its origins in Kirkwood's polar&ability theory of optical activity'. It is less empirical than the group additivity models of Whiffen8, Brewsterg, and others, and has previously been applied to a number of monosaccharides and disaccharides5,6,'0-'2. The method is based on a coupled-oscillator model which requires the solution of the secular equations: i=l where Kj is the coulombic interaction energy of bond localized transition dipole moments. The solution yields eigenvalues, E,, specifying molecular transition energies, and eigencoefficients, Cik, which describe the molecular transition-moments as linear combinations of the unperturbed-bond transition-moments. Circular dichroic rotational strengths are obtained directly, from which the optical rotation is calculated via a Kronig-Kramers transform. We report results as the molar rotation [Ml at 589 nm. The estimated uncertainty in the calculational method6 is f24" cm2 dmol-'. A FORTRAN algorithm MOLROT is available from the author upon request.
Atomic coordinates for 1,6-anhydro-/3-D-glucopyranose were taken from the X-ray structure determination of Lindberg2; they were adapted appropriately for the corresponding galactopyranose, mannopyranose, and talopyranose. Atomic coordinates for methyl 3,6-anhydro_cY-o-galactopyranoside were taken from the X-ray structure determination of Campbell and Harding3; coordinates for the corresponding glucopyranoside and mannopyranoside, and for the p anomers,