This is the first paper in a series dealing with optical Nitrogen spectroscopy of O-type stars, aiming at the analysis of Nitrogen abundances. We implemented a new Nitrogen model atom into the NLTE atmosphere/spectrum synthesis code FASTWIND, and compare the resulting optical NIII lines at 4634/40/42 A with other predictions, mostly from Mihalas & Hummer (1973, ApJ 179, 827,`MH), and from the alternative code CMFGEN. Using similar model atmospheres as MH (not blanketed and wind-free), we are able to reproduce their results, in particular the triplet emission lines. According to MH, these should be strongly related to dielectronic recombination (DR) and the drain by certain two-electron transitions. However, using realistic, fully line-blanketed atmospheres at solar abundances, the key role of DR controlling these emission features is superseded -- for O-star conditions -- by the strength of the stellar wind and metallicity. In the case of wind-free models, the resulting lower ionizing EUV-fluxes severely suppress the emission. As the mass-loss rate is increased, pumping through the NIII resonance line(s) in the presence of a near-photospheric velocity field results in a net optical triplet line emission. A comparison with results from CMFGEN is mostly satisfactory, except for the range 30 kK < Teff < 35 kK, where CMFGEN triggers the triplet emission at lower Teff than FASTWIND. This effect could be traced down to line overlap effects between the NIII and OIII resonance lines that so far cannot be simulated by FASTWIND. Since the efficiency of DR and `two electron drain strongly depends on the degree of line-blanketing/-blocking, we predict the emission to become stronger in a metal-poor environment, though lower wind-strengths and Nitrogen abundances might counteract this effect. Weak winded stars should display less triplet emission than stars with `normal winds.
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