  We present an abundance analysis of the low-metallicity benchmark red giant
star HD 122563 based on realistic, state-of-the-art, high-resolution,
three-dimensional (3D) model stellar atmospheres including non-grey radiative
transfer through opacity binning with four, twelve, and 48 bins. The 48-bin 3D
simulation reaches temperatures lower by ~ 300 - 500 K than the corresponding
1D model in the upper atmosphere. Small variations in the opacity binning,
adopted line opacities, or chemical mixture can cool the photospheric layers by
a further ~ 100 - 300 K and alter the effective temperature by ~ 100 K. A 3D
local thermodynamic equilibrium (LTE) spectroscopic analysis of Fe I and Fe II
lines gives discrepant results in terms of derived Fe abundance, which we
ascribe to non-LTE effects and systematic errors on the stellar parameters. We
also determine C, N, and O abundances by simultaneously fitting CH, OH, NH, and
CN molecular bands and lines in the ultraviolet, visible, and infrared. We find
a small positive 3D-1D abundance correction for carbon (+0.03 dex) and negative
ones for nitrogen (-0.07 dex) and oxygen (-0.34 dex). From the analysis of the
[O I] line at 6300.3 {\AA}, we derive a significantly higher oxygen abundance
than from molecular lines (+0.46 dex in 3D and +0.15 dex in 1D). We rule out
important OH photodissociation effects as possible explanation for the
discrepancy and note that lowering the surface gravity would reduce the oxygen
abundance difference between molecular and atomic indicators.
