Parametrization of linear dielectric response

The quantum linear response of a dielectric to an external electric field yields expressions for the dielectric susceptibility and the associated impulse response function. These are measured properties that, during analysis, are often "curve-fitted" to diverse forms of parametric functional forms that shall herein be referred to as fit-functions. The main purpose of this paper is to show, from a very general linear response formalism that encompasses virtually all microscopic models of dielectric response, that there are constraints on the forms that the susceptibilities must obey and to examine common parametrizations of the dielectric function in light of these constraints. Naturally these constraints should, whenever possible, be in-built into the fit-functions employed. The linear response approach due to Madden and Kivelson [Adv. Chem. Phys. 56, 467 (1984)], where the cause is considered to be a uniform external field, E(ext)(t), is utilized as it affords a much more straightforward interaction term, viz., -M·E(ext)(t), (M being the system's total electric dipole moment operator) than would be the case if the mean internal field (or "Maxwell field") were taken as the cause. It is shown that this implies definite relations between the quasipermittivity, ζ(ω), of the Madden-Kivelson approach and the normal permittivity, χ(ω)≡ε(ω)-ε(0). These relations indicate a condition for the divergence of the normal susceptibility, which, arguably, marks the onset of a ferroelectric transition in "sufficiently polar" dielectrics. Finally, some common parametric "fit-function" forms are investigated as to whether they comply with the constraints that the formalism imposes, and examples are given of their associated Cole-Cole plots in typical cases involving one or more relaxation times.