  Absorbing boundary conditions in the form of a complex absorbing potential
are routinely introduced in the Schr\"odinger equation to limit the
computational domain or to study reactive scattering events using the
multi-configurational time-dependent Hartree method (MCTDH). However, it is
known that a pure wave-function description does not allow the modeling and
propagation of the remnants of a system of which some parts are removed by the
absorbing boundary. It was recently shown [S. Selst{\o} and S. Kvaal, J. Phys.
B: At. Mol. Opt. Phys. {\bfseries 43} (2010), 065004] that a master equation of
Lindblad form was necessary for such a description. We formulate a
multiconfigurational time-dependent Hartree method for this master equation,
usable for any quantum system composed of any mixture of species. The
formulation is a strict generalization of pure-state propagation using standard
MCTDH. We demonstrate the formulation with a numerical experiment.
