Indices of Refraction, Susceptibilities, and Correlation Functions

Abstract

The previously derived phenomenological Maxwell equation [R. L. Fulton, J. Chem. Phys. 50, 3355 (1969)] is used to give a general description of the propagation of electromagnetic radiation in media which are invariant under translations and rotations. The connections between the complex indices of refraction and correlation functions are derived with a minimum of hypotheses about the nature of the medium. It is shown that the commonly assumed connection between the complex angle of rotation of plane polarized light in optically active media and correlation functions is more general than the usual derivation indicates. The correct inclusion of the frequency dependence of the index of refraction in the connection between the optical parameters and the Fourier transform of the dipole–dipole correlation function is shown to give rise to qualitative and quantitative changes of infrared band shapes, including the narrowing of lines, in the cases of C₆F₆ (1527 cm⁻¹), C₆H₆ (678 cm⁻¹), and CHCl₃ (760 cm⁻¹). The contribution of the 1527‐cm⁻¹ band of C₆F₆ to the time dependent dipole–dipole correlation function is found, obtaining a relaxation time of ${\tau }_r\text{\hspace{0.17em}=\hspace{0.17em}1.07}$ psec when the frequency dependence of the index of refraction is correctly included as compared to a value of ${\tau }_r\text{\hspace{0.17em}=\hspace{0.17em}0.58}$ psec when the variation is disregarded. The correlation functions arising from the cosine and the sine Fourier transforms of the 522‐cm⁻¹ band of CH₃I are determined, the comparison of which with the dipole–dipole correlation function illustrates the necessity of retaining both transforms in the calculation of the correlation function.