  The relativistic density functional with minimal density dependent
nucleon-meson couplings for nuclei and nuclear matter is extended to include
tensor couplings of the nucleons to the vector mesons. The dependence of the
minimal couplings on either vector or scalar densities is explored. New
parametrisations are obtained by a fit to nuclear observables with
uncertainties that are determined self-consistently. The corresponding nuclear
matter parameters at saturation are determined including their uncertainties.
An improvement in the description of nuclear observables, in particular for
binding energies and diffraction radii, is found when tensor couplings are
considered, accompanied by an increase of the Dirac effective mass. The
equations of state for symmetric nuclear matter and pure neutron matter are
studied for all models. The density dependence of the nuclear symmetry energy,
the Dirac effective masses and scalar densities is explored. Problems at high
densities for parametrisations using a scalar density dependence of the
couplings are identified due to the rearrangement contributions in the scalar
self-energies that lead to vanishing Dirac effective masses.
