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Time-dependent quantum chemical methods coupled to Gaussian basis sets aregaining popularity in modeling the electron dynamics of atoms and moleculesinteracting with intense laser fields. Two approaches most widely used for thispurpose, the real-time time-dependent configuration interaction singles and thereal-time time-dependent density functional theory, both have theirlimitations, so the development of more accurate yet computationally efficienttime-dependent methods is still in demand. In this work we explore theapplicability of the real-time time-dependent configuration interaction singlesand doubles (RT-TDCISD) in modeling strong field phenomena. Since the maindrawback of RT-TDCISD is its unfavourable scaling, we develop severalalgorithms for reducing the effective propagation space by selecting these CISDeigenstates that should have dominant contribution to the time-evolution of thewavefunction. We test them by performing calculations of the high harmonicspectra of the H\textsubscript{2} molecule. We find out that the laser-drivenelectron dynamics is mostly realized in a very small subspace of eigenstatesdominated by single excitations, that constitutes about one percent of thewhole CISD eigenspectrum. Therefore, by properly selecting this subspace onecan reduce the dimension of the propagation equation by two orders of magnitudewithout affecting the time-resolved observables.

Exploring the attosecond laser-driven electron dynamics in the hydrogen  molecule with different real-time time-dependent configuration interaction  approaches