We perform benchmark calculations
of the Bethe–Salpeter
vertical excitation energies for the set of 28 molecules constituting
the well-known Thiel’s set, complemented by a series of small
molecules representative of the dye chemistry field. We show that
Bethe–Salpeter calculations based on a molecular orbital energy
spectrum obtained with non-self-consistent G0W0 calculations starting from
semilocal DFT functionals dramatically underestimate the transition
energies. Starting from the popular PBE0 hybrid functional significantly
improves the results even though this leads to an average −0.59
eV redshift compared to reference calculations for Thiel’s
set. It is shown, however, that a simple self-consistent scheme at
the GW level, with an update of the quasiparticle
energies, not only leads to a much better agreement with reference
values, but also significantly reduces the impact of the starting
DFT functional. On average, the Bethe–Salpeter scheme based
on self-consistent GW calculations comes close to
the best time-dependent DFT calculations with the PBE0 functional
with a 0.98 correlation coefficient and a 0.18 (0.25) eV mean absolute
deviation compared to TD-PBE0 (theoretical best estimates) with a
tendency to be red-shifted. We also observe that TD-DFT and the standard
adiabatic Bethe–Salpeter implementation may differ significantly
for states implying a large multiple excitation character.
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