Helical polymer circular dichroism: Transition matrix theory for polypeptides

A Green operator technique used within a linear response framework is employed to present a transition matrix theory of long helical polymer circular dichroism. Specializing to a polypeptide, simple closed form expressions are obtained for the circular dichroism. The formulation clearly shows (1) how the ΠΠ* exciton system gives rise to the ’’helix band’’ and ’’radial bands’’; (2) how the coupling of the ΠΠ* and nΠ* transition densities gives rise to a band centered at the unperturbed nΠ* transition frequency which is balanced in rotational strength by bands at the ΠΠ* perpendicular and parallel polarized transition frequencies; and (3) how interaction of these low energy transitions with high energy transitions can alter all of the above mentioned bands.