Inertial effects in anomalous dielectric relaxation of symmetrical top molecules.

The linear dielectric response of an assembly of noninteracting symmetrical top molecules (each of which is free to rotate in space) is evaluated in the context of fractional dynamics. The infinite hierarchy of differential-recurrence relations for the relaxation functions appropriate to the dielectric response is derived by using the underlying inertial fractional Klein-Kramers equation. On solving this hierarchy in terms of matrix continued fractions (as in the normal rotational diffusion), the complex dynamic susceptibility is obtained and is calculated for typical values of the model parameters. For the limiting case of spherical top molecules, the solution is obtained in terms of an ordinary continued fraction. It is shown that the model can reproduce nonexponential anomalous dielectric relaxation behavior at low frequencies (omegatau<or=1, where tau is the Debye relaxation time) and the inclusion of inertial effects ensures that optical transparency is regained at very high frequencies (in the far infrared region) so that Gordon's sum rule for integral dipolar absorption is satisfied.