  We examine the low-energy spectrum and polarisation of the dipole moments of
two static polar molecules under the influence of an external dc electric field
and their anisotropic dipole-dipole interaction. We model the molecules as
quantum rigid rotors to take their rotational degrees of freedom into account,
and consider a selection of linear, symmetric and asymmetric top molecules. We
provide a comprehensive examination of the energy spectra and polarisation of
the dipoles for varying inter-molecular separation and direction of the
electric field, and find that the properties of the molecules depend strongly
on the field's direction at short separations, showing the importance of
accounting for molecular rotation. Our results provide important insight into
applications of cold molecules for quantum computation and molecular dipolar
gases.
