  We report on an implementation of the multiconfigurational time-dependent
Hartree method (MCTDH) for spin-polarized fermions (MCTDHF). Our approach is
based on a mapping for opera- tors in Fock space that allows a compact and
efficient application of the Hamiltonian and solution of the MCTDHF equations
of motion. Our implementation extends, builds on and exploits the recursive
implementation of MCTDH for bosons (R-MCTDHB) package. Together with R-MCTDHB,
the present implementation of MCTDHF forms the MCTDH-X package. We benchmark
the accuracy of the algorithm with the harmonic interaction model and a
time-dependent generalization thereof. These models consider parabolically
trapped particles that interact through a harmonic interaction potential. We
demonstrate, that MCTDHF is capable of solving the time-dependent many-fermion
Schr\"odinger equation to an in principle arbitrary degree of precision and can
hence yield numerically exact results even in the case of Hamiltonians with
time-dependent one-body and two-body potentials. As an application we study the
problem of two initially parabolically confined and charged fermions tunneling
through a barrier to open space. We demonstrate the validity of a model
proposed previously for the many-body tunneling to open space of bosonic
particles with contact interactions [Proc. Natl. Acad. Sci. USA 109,
13521-13525 (2012)]. The many-fermion tunneling can be built up from
sequentially happening single-fermion tunneling processes. The characteristic
momenta of these processes are determined by the chemical potentials of trapped
subsystems of smaller particle numbers: the escaped fermions convert the
different chemical potentials into kinetic energy. Using the two-body
correlation function, we present a detailed picture of the sequentiality of the
process and are able to tell tunneling from over-the-barrier escape.
