Approximation of rotational strengths from molar rotation data and generation of rotatory dispersion curves for d-camphor-10-sulfonate.

Starting with the expression for optical rotatory dispersion in the absorption region that was arrived at by Condon, two series were considered for the purpose of achieving the experimentally observed, steeper wavelength dependence in the absorption region while retaining the established 1/lambda(2) law in regions removed from absorption. The first two terms of one series in which the second term exhibits a 1/lambda(6) wavelength dependence were found to calculate satisfactorily the optical rotatory dispersion curve of d-camphor-10-sulfonate from 400 mmu to 190 mmu when only three bands were considered. Evaluated at the extrema, the two-term expression can be approximated by a simple equation which allows calculation of the rotational strength of a nonoverlapping band by using only the wavelength and molar rotation of the extrema and the index of refraction of the solution. The rotational strengths calculated from optical rotatory dispersion data in this manner closely agree with those calculated from corresponding circular dichroism data. Thus when position and magnitude of rotatory dispersion extrema alone are reported for carbonyls, it is suggested that such published data may be converted to approximate rotational strengths.