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An exact integral formula for the Kirkwood correlation factor of isotropicpolar fluids $g_K$ is derived from the equilibrium averaged rotational Deanequation, which as compared to previous approaches easily lends itself tofurther approximations. The static linear permittivity of polar fluids$\epsilon$ is calculated as a function of temperature, density and moleculardipole moment in vacuo for arbitrary pair interaction potentials. Then, usingthe Kirkwood superposition approximation for the three-body orientationaldistribution function, we suggest a simple way to construct model potentials ofmean torques considering permanent and induced dipole moments. We successfullycompare the theory with the experimental temperature dependence of the staticlinear permittivity of various polar fluids such as a series of linearmonohydroxy alcohols, water, tributyl phosphate, acetonitrile, acetone,nitrobenzene and dimethyl sulfoxide, by fitting only one single parameter,which describes the induction to dipole-dipole energy strength ratio. Wedemonstrate that comparing the value of $g_K$ with unity in order to deduce thealignment state of permanent dipole pairs, as is currently done is in manysituations, is a misleading oversimplification, while the correct alignmentstate is revealed when considering the proper interaction potential. Moreoverwe show, that picturing H-bonding polar fluids as polar molecules withpermanent and induced dipole moments without invoking any specific H-bondingmechanism is in many cases sufficient to explain experimental data of thestatic dielectric constant. In this light, the failure of the theory todescribe the experimental temperature dependence of the static dielectricconstant of glycerol, a non-rigid polyalcohol, is not due to the lack ofspecific H-bonding mechanisms, but rather to an oversimplified model potentialfor that particular molecule.

Temperature dependence of the static permittivity andintegral formula for the Kirkwood correlation factor ofsimple polar fluids