Bethe-Salpeter equation spectra for very large systems

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 time-dependent Hartree propagation, which uses only ten 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 parallelization of the calculation. 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.