  A low-cost approach for stochastically sampling static exchange during
TDHF-type propagation is presented. This enables the use of an excellent hybrid
DFT starting point for stochastic GW quasiparticle energy calculations.
Generalized Kohn-Sham molecular orbitals and energies, rather than those of a
local-DFT calculation, are used for building the Green's function and effective
Coulomb interaction. The use of an optimally tuned hybrid diminishes the
starting point dependency in one-shot stochastic GW, effectively avoiding the
need for self-consistent GW iterations.
