  We analyze the electric dipole moments (PDMs) and static electric dipole
polarizabilities of the alkali--alkaline-earth (Alk-AlkE) dimers by employing
finite-field coupled-cluster methods, both in the frameworks of
non-relativistic and four-component spinfree relativistic theory. In order to
carry out comparative analyses rigorously, we consider those Alk-AlkE molecules
made out of the lightest to the medium-heavy constituent atoms (Alk: Li to Rb
and AlkE: Be through Sr). We present behaviour of electron correlation effects
as well as relativistic effects with the size of the molecules. Uncertainties
to the above quantities of the investigated Alk-AlkE molecules are inferred by
analyzing our results from different form of Hamiltonian, basis set, and
perturbative parameter in a few representative molecules. We have also provided
empirical relations by connecting average polarizabilities of the Alk-AlkE
molecules with their PDMs, and atomic numbers and polarizabilities of the
corresponding Alk and AlKE atoms, which can be used to roughly estimate the
average polarizabilities of other heavier Alk-AlkE molecules. We finally give
our recommended results, and compare them with the literature values.
