Linear response Fano–DeVoe polarizability theory for biopolymers composed of chiral chromophores: Infinite order dipole–dipole approximation calculations of circular dichroism and ultraviolet band shapes of α-helical and β-pleated polypeptides

The first order dimer model made by Stiles and Buckingham for predicting optical activity has been extended up to an infinite order N-mer model within the framework of the Fano–DeVoe type dipole approximation. The present formalism involves four mechanisms (1) the Kirkwood–Moffitt coupled oscillator mechanism through the Coulombic interactions; (2) the local asymmetric mechanism due to the intrinsic monomer optical activity; (3) the indirect electric–magnetic coupling mechanism through the Coulombic interactions; (4) the Condon, Alter, Eyring (CAE) direct electric–magnetic coupling mechanism through the electrostatic interactions between the upper to upper state transition moments on a certain site and the permanent dipole moments on the other sites. However, mechanism (4) must be excluded if we follow the Fano–DeVoe approximation, whereas it is indispensable for circular dichroism (CD) calculations of polypeptides to incorporate the CAE electric–magnetic coupling mechanism. This requirement is attained by assuming the intra-amide monomer intensity borrowing of the very weak 210 nm region nπ* state from the strong 190 nm region ππ* state through the CAE electrostatic interactions on the basis of the Schellman–Oriel perturbation equation and the Bayley–Nielsen–Schellman secular matrix theory. The present theory has particularly well predicted the CD band shapes of α-polypeptides even with the dipole approximation. The contributions due to the asymmetric fields have been found to become specifically large, while the coupled oscillator mechanism has been calculated to be a leading term.