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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 H + 2 in intense laser fields where reference calculations are available. It is then applied to study the ionization of non-aligned H + 2 and H 2 . Striking differences in the orientation dependence between both molecules are found. Surprisingly, enhanced ionization is predicted for perpendicularly aligned molecules.

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We propose a method to quantitatively estimate the error made with a finite basis expansion in time-dependent calculations. This method is applied to the hydrogen atom in intense laser fields and used to compare different basis sets with each other. We also show how to construct a Gaussian basis set suitable for the description of ionization dynamics in intense laser fields.

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