Context. It is well known that cool star atmospheres depart from local thermodynamic equilibrium (LTE). Making an accurate abundance determination requires taking those effects into account, but the necessary non-LTE (hereafter NLTE) calculations are often lacking.
Aims: Our goal is to provide detailed estimates of NLTE effects for FGK type stars for all spectral lines from the ultraviolet (UV) to the near infrared (NIR) that are potentially useful as abundance diagnostics. The first paper in this series focusses on the light elements Na, Mg, and Al.
Methods: The code PySME was used to compute curves of growth for 2158 MARCS model atmospheres in the parameter range 3800 < Teff < 8000 K, 0.0 < log(g) < 5.5, and −5 < [Fe/H] < +0.5. Two microturbulence values, 1 and 2 kms−1, and nine abundance points spanning −1 < [X/Fe] < 1 for element X, are used to construct individual line curves of growth by calculating the equivalent widths of 35 Na lines, 134 Mg lines, and 34 Al lines. The lines were selected in the wavelength range between 2000 Å and 3 µm.
Results: We demonstrate the power of the new grids with LTE and NLTE abundance analysis by means of equivalent width measurements of five benchmark stars; the Sun, Arcturus, HD 84937, HD 140283 and HD 122563. For Na, the NLTE abundances are lower than in LTE and show markedly reduced line-to-line scatter in the metal-poor stars. For Mg, we confirm previous reports of a significant ~0.25 dex LTE ionisation imbalance in metal-poor stars that is only slightly improved in NLTE (~0.18 dex). LTE abundances based on Mg II lines agree better with models of Galactic chemical evolution. For Al, NLTE calculations strongly reduce an ~0.6 dex ionisation imbalance seen in LTE for the metal-poor stars. The abundance corrections presented in this work are in good agreement with previous studies for the subset of lines that overlap, with the exception of strongly saturated lines.
Conclusions: A consensus between different abundance diagnostics is the most powerful tool available to stellar spectroscopists to assess the accuracy of the models. Here we report that NLTE abundance analysis in general leads to improved agreement, in particular for metal-poor stars. The residual scatter is believed to be caused mainly by unresolved blends and/or poor atomic data, with the notable exception of Mg, which calls for further investigation.

Full Tables B.1, B.2, B.3 are only available at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/cat/J/A+A/665/A33