  We describe an all-electron $G_0W_0$ implementation for periodic systems with
$k$-point sampling implemented in a crystalline Gaussian basis. Our
full-frequency $G_0W_0$ method relies on efficient Gaussian density fitting
integrals and includes both analytic continuation and contour deformation
schemes. Due to the compactness of Gaussian bases, no virtual state truncation
is required as is seen in many plane-wave formulations. Finite size corrections
are included by taking the $q \to 0$ limit of the Coulomb divergence. Using our
implementation, we study quasiparticle energies and band structures across a
range of systems including molecules, semiconductors, rare gas solids, and
metals. We find that the $G_0W_0$ band gaps of traditional semiconductors
converge rapidly with respect to the basis size, even for the conventionally
challenging case of ZnO. Using correlation-consistent bases of polarized
triple-zeta quality, we find the mean absolute relative error of the
extrapolated $G_0W_0$@PBE band gaps to be only 5.2% when compared to
experimental values. For core excitation binding energies (CEBEs), we find that
$G_0W_0$ predictions improve significantly over those from DFT if the $G_0W_0$
calculations are started from hybrid functionals with a high percentage of
exact exchange.
