  An exact integral formula for the Kirkwood correlation factor of isotropic
polar fluids $g_K$ is derived from the equilibrium averaged rotational Dean
equation, which as compared to previous approaches easily lends itself to
further approximations. The static linear permittivity of polar fluids
$\epsilon$ is calculated as a function of temperature, density and molecular
dipole moment in vacuo for arbitrary pair interaction potentials. Then, using
the Kirkwood superposition approximation for the three-body orientational
distribution function, we suggest a simple way to construct model potentials of
mean torques considering permanent and induced dipole moments. We successfully
compare the theory with the experimental temperature dependence of the static
linear permittivity of various polar fluids such as a series of linear
monohydroxy 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. We
demonstrate that comparing the value of $g_K$ with unity in order to deduce the
alignment state of permanent dipole pairs, as is currently done is in many
situations, is a misleading oversimplification, while the correct alignment
state is revealed when considering the proper interaction potential. Moreover
we show, that picturing H-bonding polar fluids as polar molecules with
permanent and induced dipole moments without invoking any specific H-bonding
mechanism is in many cases sufficient to explain experimental data of the
static dielectric constant. In this light, the failure of the theory to
describe the experimental temperature dependence of the static dielectric
constant of glycerol, a non-rigid polyalcohol, is not due to the lack of
specific H-bonding mechanisms, but rather to an oversimplified model potential
for that particular molecule.
