  A model for positron binding to polar molecules is considered by combining
the dipole potential outside the molecule with a strongly repulsive core of a
given radius. Using existing experimental data on binding energies leads to
unphysically small core radii for all of the molecules studied. This suggests
that electron-positron correlations neglected in the simple model play a large
role in determining the binding energy. We account for these by including
polarization potential via perturbation theory and non-perturbatively. The
perturbative model makes reliable predictions of binding energies for a range
of polar organic molecules and hydrogen cyanide. The model also agrees with the
linear dependence of the binding energies on the polarizability inferred from
the experimental data [Danielson et al 2009 J. Phys. B: At. Mol. Opt. Phys. 42
235203]. The effective core radii, however, remain unphysically small for most
molecules. Treating molecular polarization non-perturbatively leads to
physically meaningful core radii for all of the molecules studied and enables
even more accurate predictions of binding energies to be made for nearly all of
the molecules considered.
