We derive a low-scaling G
0
W
0 algorithm for molecules
using pair atomic density fitting
(PADF) and an imaginary
time representation of the Green’s function and describe its
implementation in the Slater type orbital (STO)-based Amsterdam density
functional (ADF) electronic structure code. We demonstrate the scalability
of our algorithm on a series of water clusters with up to 432 atoms
and 7776 basis functions and observe asymptotic quadratic scaling
with realistic threshold qualities controlling distance effects and
basis sets of triple-ζ (TZ) plus double polarization quality.
Also owing to a very small prefactor, a G
0
W
0 calculation for the largest of these
clusters takes only 240 CPU hours with these settings. We assess the
accuracy of our algorithm for HOMO and LUMO energies in the GW100
database. With errors of 0.24 eV for HOMO energies on the quadruple-ζ
level, our implementation is less accurate than canonical all-electron
implementations using the larger def2-QZVP GTO-type basis set. Apart
from basis set errors, this is related to the well-known shortcomings
of the GW space-time method using analytical continuation techniques
as well as to numerical issues of the PADF approach of accurately
representing diffuse atomic orbital (AO) products. We speculate that
these difficulties might be overcome by using optimized auxiliary
fit sets with more diffuse functions of higher angular momenta. Despite
these shortcomings, for subsets of medium and large molecules from
the GW5000 database, the error of our approach using basis sets of
TZ and augmented double-ζ (DZ) quality is decreasing with system
size. On the augmented DZ level, we reproduce canonical, complete
basis set limit extrapolated reference values with an accuracy of
80 meV on average for a set of 20 large organic molecules. We anticipate
our algorithm, in its current form, to be very useful in the study
of single-particle properties of large organic systems such as chromophores
and acceptor molecules.