Optical Rotation of Oriented Helices. III. Calculation of the Rotatory Dispersion and Circular Dichroism of the Alpha- and 310-Helix

Abstract

We have carried out a calculation of the optical rotatory dispersion (ORD) of α‐and 310‐helices which is essentially complete within the limitations of the Kirkwood approximation and its extensions. This treatment predicts that right‐handed helices will exhibit three rotatory bands at wavelengths greater than 190 mμ. The sign and position of these predicted bands are in good agreement with experiment. The predicted rotational strengths do not agree so well, but are in sufficiently good accord to provide strong support to the assignment of the longest‐wavelength band to the amide nπ* transition, and the shortest‐wavelength band thus far observed to a composite band due both to the perpendicular‐polarized exciton component and to the intrinsic rotational strength of the NV 1 transition. Calculation of the ORD and CD (circular dichroism) of the α‐helix from the calculated rotational strengths gives results in fair agreement with experiment, especially when the nπ* rotational strength is adjusted to agree with that observed in CD experiments. An analysis of the calculated ORD curves according to the Moffitt—Yang and Shechter—Blout procedures leads to values for the parameters in these equations which agree well with experiment in the case of the α‐helix. A similar treatment of the 310‐helix indicates that this helix can be distinguished from the α‐helix by: (a) appreciably more positive rotations in the visible region, (b) appreciably larger absolute values of b 0, A(α, ρ)225 and A(α, ρ)193. The dependence of various rotatory parameters on the length of the helix has been studied. The dispersion parameters b 0, A(α, ρ)225 and A(α, ρ)193, as well as the depth of the 233 mμ trough appear to be the least sensitive to chain length. The magnitude of the maximum at 198 mμ, however, seems quite chain‐length dependent, and therefore is probably not suitable as a measure of helix content.