Molecular Theory of the Dielectric Constant of Nonpolar Gases

Abstract

A theory of molecular polarization is developed which applies to nonpolar gases consisting of axially symmetric molecules. The interaction Hamiltonian of the system includes induced dipole and induced and permanent quadrupole contributions. The average induced dipole moment of a molecule is evaluated through third order of perturbation theory, following earlier calculations for hydrogen and helium atoms by Jansen and Mazur. General equations are given for the induced dipole moment in terms of tensors ${\mathrm{T}}^{\mathrm{}\left(2\right)\mathrm{}}$, ${\mathrm{T}}^{\mathrm{}\left(3\right)\mathrm{}}$, ${\mathrm{T}}^{\mathrm{}\left(4\right)\mathrm{}}$, characteristic for dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole interactions, respectively; and characteristic functions $C_1, C_2, \cdots C_7$, depending upon the molecular charge distributions. It is shown that $\alpha$ in the Clausius-Mossotti equation is in general not equal to the polarizability of a free molecule, but depends on the density of the system.