A theory for the nematic-isotropic (N-I) phase transition of prolate u
niaxial molecules with longitudinal dipole moments is presented. The t
heory is based on the variational cluster expansion, truncated after t
he two-molecule term, and is implemented for polar hard spherocylinder
s with and without attractions, and for polar linear arrays of Lennard
-Jones interaction centres. We find that the dipole interactions subst
antially shift the N-I transition temperature and strongly promote ant
iparallel molecular association, but have a weak effect on the order p
arameters, the pressure, and the N-I coexistence densities. The effect
of dipoles on phase stability is very sensitive to their position wit
hin the molecular frame. Off-centre dipoles are shown to give rise to
phase re-entrance according to the sequence N-I-N on heating at consta
nt density. The theory does not predict a stable ferroelectric nematic
phase.