Dielectric Response and Linear Absorption Spectroscopy of Ionic Systems

Time-dependent electric fields applied to ionic systems can induce both a dielectric and a conductive response, leading to the generation of macroscopic polarization and current, respectively. It has long been recognized that it is not possible to determine the two types of responses separately. However, this aspect is often not adequately accounted for in dielectric and absorption spectroscopies of ionic systems. To clarify this, we theoretically investigate the dielectric and conductive responses of ionic systems containing polyatomic ions based on linear response theory. We derive general expressions for the frequency-dependent dielectric functions, conductivity, and absorption coefficient, including those measured experimentally. Furthermore, we show that the dielectric and conductive responses cannot be uniquely distinguished even at the theoretical level and, therefore, cannot represent experimentally measured quantities. Instead, dielectric and absorption spectra of ionic systems should be expressed in terms of the generalized dielectric function that encompasses both dielectric and conductive responses. We propose a computational method to calculate this generalized dielectric function reliably. Model calculations on concentrated aqueous solutions of NaCl, a monatomic salt, and LiTFSI, a polyatomic salt, show that the dielectric and linear absorption spectra of the two systems based on the generalized dielectric function are significantly different from purely dielectric counterparts in the far-IR, terahertz, and lower-frequency regions. Moreover, the spectra are mainly determined by the autocorrelations of total dipole and total current, but dipole-current cross-correlation can also significantly contribute to the spectra of the LiTFSI solution. The present theoretical approach could be extended to nonlinear spectroscopy of ionic liquids and electrolyte solutions.