Improved Calculation of the nπ* Rotational Strength in Polypeptides

Previous calculations of the $\mathrm{n\pi *}$ rotational strength in the $\alpha$ helix using the Kirkwood theory as extended by Moffitt and Tinoco have led to results which are of the right order of magnitude and correct sign but too small by a factor of 6–8. It is possible that contributions neglected by the Kirkwood approach, e.g., charge‐transfer transitions, are important in the $\alpha$ helix. A molecular‐orbital treatment of an amide dimer indicates that mixing of the $\mathrm{n\pi *}$ and charge‐transfer states makes a negligible contribution to the $\mathrm{n\pi *}$ rotational strength in the $\alpha$ helix. However, when two modifications are made in previous Kirkwood‐type treatments, the calculated rotational strength is found to be about − 0.2 debye bohr magnetons ${\mathrm{(D·\mu }}_B)$ , in good agreement with experiment. In addition, the calculated exciton splitting for the $\mathrm{\pi \pi *}$ transition agrees better with experiment than do previous theoretical values. The modifications are (a) a more consistent choice of permanent and transition monopole positions, and (b) solution of a secular determinant for the mixing of the $\mathrm{n\pi *}$ and $\mathrm{\pi \pi *}$ excited states, rather than using first‐order perturbation with zero‐order wavefunctions. Analyses of experimental circular‐dichroism (CD) curves as sums of Gaussians have led to $\mathrm{\pi \pi *}$ rotational strengths appreciably smaller than theoretically calculated ones. We show here that this discrepancy may be due to failure to include a non‐Gaussian term predicted by theory. Using reasonable band positions and widths, theoretical CD curves agree reasonably well with experimental curves. It is also pointed out that the exact shape of the CD curve is very sensitive to the band frequencies and widths. Therefore, observed variations in the shape may result from rather subtle changes in these parameters.