Circular dichroism of unordered polymers: Extended time dependent Hartree theory for polypeptides

Abstract

Equations describing circular dichroism (CD) and optical rotatory dispersion (ORD) of a system of unordered polymers in solution are derived via a linear response method in terms of exact states of the system. Origin dependent extrinsic magnetic moment operators are not used. After a multipole expansion of the induced transverse current and a long wavelength expansion of the susceptibilities, the equation of motion of the radiation field’s average vector potential is solved and a definition of the refractive index provides an account of CD−ORD. It is shown that the contribution to the current by the susceptibility characterizing induced electric dipole polarization through intrinsic magnetic dipolar coupling with the curl of the radiation field is identical to the contribution by the susceptibility characterizing induced magnetic dipole polarization through electric dipolar coupling with the radiation field only for isotropic media. Approximate polypeptide susceptibilities are obtained by an extension of the time dependent Hartree scheme. The extension is shown to be necessary when electric and nπ* magnetic dipole transitions are degenerate or near degenerate, for which anomalous dispersion arises and rotational strength is not conserved. The resulting susceptibilities are obtained from the solution to a normal mode problem. The normal modes are determined not only by electric dipolar coupling but also by the coupling of electric quadrupoles with others and with electric dipoles. The time dependent Hartree scheme is then on a comparable level with the matrix scheme, and the two methods are discussed.