  Time-dependent quantum chemical methods coupled to Gaussian basis sets are
gaining popularity in modeling the electron dynamics of atoms and molecules
interacting with intense laser fields. Two approaches most widely used for this
purpose, the real-time time-dependent configuration interaction singles and the
real-time time-dependent density functional theory, both have their
limitations, so the development of more accurate yet computationally efficient
time-dependent methods is still in demand. In this work we explore the
applicability of the real-time time-dependent configuration interaction singles
and doubles (RT-TDCISD) in modeling strong field phenomena. Since the main
drawback of RT-TDCISD is its unfavourable scaling, we develop several
algorithms for reducing the effective propagation space by selecting these CISD
eigenstates that should have dominant contribution to the time-evolution of the
wavefunction. We test them by performing calculations of the high harmonic
spectra of the H\textsubscript{2} molecule. We find out that the laser-driven
electron dynamics is mostly realized in a very small subspace of eigenstates
dominated by single excitations, that constitutes about one percent of the
whole CISD eigenspectrum. Therefore, by properly selecting this subspace one
can reduce the dimension of the propagation equation by two orders of magnitude
without affecting the time-resolved observables.
