  We combine first principles density functional calculations with empirical
relationships for the Coulomb interactions in the `monomer' model of
$\kappa$-(BEDT-TTF)$_2X$. This enables us to calculate the parameters for the
model of coupled dipolar and spin degrees of freedom proposed by Hotta [Phys.
Rev. B $\textbf{82}$, 241104 (2010)], and Naka and Ishihara [J. Phys. Soc.
Japan $\textbf{79}$, 063707 (2010)]. In all materials studied, retaining only
the largest interactions leads to a transverse field Ising model of the
dipoles. This quantifies, justifies and confirms recent claims that the dipoles
are of crucial importance for understanding these materials. We show that two
effects are responsible for a range of behaviors found in the dipoles in
different $\kappa$-(BEDT-TTF)$_2X$ salts. (i) The inter-dimer hopping,
$t_{b1}$, which gives rise to the "transverse field" in the Ising model for the
dipoles ($H^T=2t_{b1}$), is between a third and a tenth smaller in the mercuric
materials than for the mercury-free salts. (ii) The Ising model of dipoles is
in the quasi-one-dimensional limit for the mercuric salts, but
quasi-two-dimensional (between the square and isotropic triangular limits) for
the mercury-free materials. Thus, the dimensionless critical field is much
smaller in the mercuric compounds. Effect (ii) is much larger than effect (i).
Simple explanations of both effects based on the band structures of the
different salts are given. We show that dipolar order and even short-range
dipolar correlations have a profound impact on the nature of the interdimer
magnetic (superexchange) interactions. For example, dipole crystallization
drives the materials towards quasi-one-dimensional magnetic interactions, which
could be important for understanding the spin liquids found in some of these
materials.
