  We report calculations of the high harmonic generation spectra of the
C\textsubscript{60} fullerene molecule, employing a diverse set of real-time
time-dependent quantum chemical methods. All methodologies involve expanding
the propagated electronic wavefunction in bases consisting of the ground and
singly excited time-independent eigenstates obtained through the solution of
the corresponding linear-response equations. We identify the correlation and
exchange effect in the spectra by comparing the results from methods relying on
the Hartree-Fock reference determinant with those obtained using approaches
based on the density functional theory with different exchange-correlation
functionals. The effect of the full random phase approximation treatment of the
excited electronic states is also analyzed and compared with the configuration
interaction singles and the Tamm-Dancoff approximation. We also showcase that
the real-time extension of the semiempirical method INDO/S can be effectively
applied for an approximate description of laser-driven dynamics in large
systems.
