  In this paper, we investigate the effects of full electronic correlation on
the high harmonic generation in the helium atom subjected to laser pulses of
extremely high intensity. To do this, we perform real-time propagations of the
helium atom wavefunction using quantum chemistry methods coupled to Gaussian
basis sets. The calculations are done within the real-time time-dependent
configuration interaction framework, at two levels of theory: time-dependent
configuration interation with single excitations (TD-CIS, uncorrelated method)
and time-dependent full configuration interaction (TD-FCI, fully correlated
method), and analyse obtained HHG spectra. The electronic wavefunction is
expanded in Dunning basis sets supplemented with functions adapted to
describing highly excited continuum states. We also compare the TD-CI results
with grid-based propagations of the helium atom within the
single-active-electron approximation. Our results show when including the
dynamical electron correlation, a noticeable improvement to the description of
HHG can be achieved, in terms of e.g. a more constant intensity in the lower
energy part of the harmonic plateau. However, such effects can be captured only
if the basis set used suffices to reproduce the most basic features, such as
the HHG cutoff position, at the uncorrelated level of theory.
