  We propose a novel method to describe realistically ionization processes with
absorbing boundary conditions in basis expansion within the formalism of the
so-called Non-Adiabatic Quantum Molecular Dynamics. This theory couples
self-consistently a classical description of the nuclei with a quantum
mechanical treatment of the electrons in atomic many-body systems. In this
paper we extend the formalism by introducing absorbing boundary conditions via
an imaginary potential. It is shown how this potential can be constructed in
time-dependent density functional theory in basis expansion. The approach is
first tested on the hydrogen atom and the pre-aligned hydrogen molecular ion
H2+ in intense laser fields where reference calculations are available. It is
then applied to study the ionization of non-aligned H2+ and H2. Striking
differences in the orientation dependence between both molecules are found.
Surprisingly, enhanced ionization is predicted for perpendicularly aligned
molecules.
