We investigated the reliability of our silicon atomic model and the influence of non-local thermodynamical equilibrium (NLTE) on the formation of neutral silicon (Si I) lines in the near-infrared (near-IR) H-band. We derived the differential Si abundances for 13 sample stars with high-resolution H-band spectra from the Apache Point Observatory Galactic Evolution Experiment (APOGEE), as well as from optical spectra, both under local thermodynamical equilibrium (LTE) and NLTE conditions. We found that the differences between the Si abundances derived from the H-band and from optical lines for the same stars are less than 0.1 dex when the NLTE effects included, and that NLTE reduces the line-to-line scatter in the H-band spectra for most sample stars. These results suggest that our Si atomic model is appropriate for studying the formation of H-band Si lines. Our calculations show that the NLTE corrections of the Si I H-band lines are negative, i.e. the final Si abundances will be overestimated in LTE. The corrections for strong lines depend on surface gravity, and tend to be larger for giants, reaching ∼ −0.2 dex in our sample, and up to ∼ −0.4 dex in extreme cases of APOGEE targets. Thus, the NLTE effects should be included in deriving silicon abundances from H-band Si I lines, especially for the cases where only strong lines are available.

Aiming at testing the validity of our magnesium atomic model and investigating the effects of non-local thermodynamical equilibrium (NLTE) on the formation of the H-band neutral magnesium lines, we derive the differential Mg abundances from selected transitions for 13 stars either adopting or relaxing the assumption of local thermodynamical equilibrium (LTE). Our analysis is based on high-resolution and high signal-tonoise ratio H-band spectra from the Apache Point Observatory Galactic Evolution Experiment (APOGEE) and optical spectra from several instruments. The absolute differences between the Mg abundances derived from the two wavelength bands are always less than 0.1 dex in the NLTE analysis, while they are slightly larger for the LTE case. This suggests that our Mg atomic model is appropriate for investigating the NLTE formation of the H-band Mg lines. The NLTE corrections for the Mg I H-band lines are sensitive to the surface gravity, becoming larger for smaller log g values, and strong lines are more susceptible to departures from LTE. For cool giants, NLTE corrections tend to be negative, and for the strong line at 15765Å they reach −0.14 dex in our sample, and up to −0.22 dex for other APOGEE stars. Our results suggest that it is important to include NLTE corrections in determining Mg abundances from the H-band Mg I transitions, especially when strong lines are used.

A calcium atomic model is updated using collisional rates from new quantum-mechanical computations. We investigated the reliability of the model atom and the non-local thermodynamic equilibrium (NLTE or non-LTE) effects on the formation of Ca i lines in both optical and H bands. NLTE and local thermodynamical equilibrium calcium abundances of 13 sample stars are derived from high-resolution and high signal-to-noise ratio optical spectra and the Apache Point Observatory Galactic Evolution Experiment (APOGEE) data. The results suggest that the updated calcium atomic model is appropriate for studying the formation of H-band calcium lines because our NLTE analyses not only reduce the line-to-line spread of derived abundances, but also lead to consistent optical-line-based and H-band-line-based abundances with a difference of −0.009 ± 0.035 dex and a calcium ionization balance between Ca i and Ca ii. In the stellar fundamental parameter space that our sample stars cover, NLTE corrections for H-band Ca i lines are small, within 0.03 dex. Even in the extreme cases of the APOGEE data, the NLTE corrections on selected H-band Ca i lines are within 0.1 dex.