  We present a highly efficient method for the extraction of optical properties
of very large molecules via the Bethe-Salpeter equation. The crutch of this
approach is the calculation of the action of the effective Coulombic
interaction, $W$, through a stochastic TD Hartree propagation, which uses only
10 stochastic orbitals rather than propagating the full sea of occupied states.
This leads to a scaling that is at most cubic in system size, with trivial MPI
parallelization. We apply this new method to calculate the spectra and
electronic density of the dominant excitons of a carbon-nanohoop bound
fullerene system with 520 electrons, using less than 4000 core hours.
