  Artificial molecular states of double quantum dots defined in bilayer
graphene are studied with the atomistic tight-binding and its low-energy
continuum approximation. We indicate that the extended electron wave functions
have opposite parities on each of the sublattices at both graphene layers and
that the ground-state wave function components change from bonding to
antibonding with the interdot distance. In the weak coupling limit -- the most
relevant for the quantum dots defined electrostatically -- the signatures of
the interdot coupling include -- for the two-electron ground state -- formation
of states with symmetric or antisymmetric spatial wave functions split by the
exchange energy. In the high energy part of the spectrum the states with both
electrons in the same dot are found with the splitting of energy levels
corresponding to simultaneous tunneling of the electron pair from one dot to
the other.
