Analytical Dielectric Spectrum Formula Based on Representative Frequencies

Abstract

According to experimental data available for the complex refractive index of particular dielectrics, a dielectric spectrum formula is proposed by the least square fitting technique combined with selected natural frequencies. From the dielectric spectrum formula, the spectra of optical and dielectric constants can be obtained in the whole frequency region. Three dielectrics, water, ethanol, and toluene, are taken as examples. In the region where the experimental data are available, the spectra of the optical constants calculated by the formula are in good agreement with the real refractive spectrum obtained by KramersKronig (KK) transform and the experimental imaginary refractive spectrum. In the region where no experimental data are available, the extrapolation of our formula can make predictions. The merits of the present treatment are that we are able to get the uniform spectrum formula, without splitting into different frequency sections, and the analytical form of the dielectric spectra will be useful in the theoretical description of solvation dynamics.