Layer-by-layer construction of diamond devices for spin-sensing calls for the atomistic understanding of the nitrogen species on diamond surfaces. Motivated by recent experiments, we used density functional theory simulations to examine the adsorption of nitrogen species (N, NH, and NH2) on bare and hydrogenated diamond(001) surfaces. On the bare substrate, we find that nitrogen species favor to attack the CC dimers at low coverages, forming N(ad) and NH(ad) in a bridge configuration and NH2(ad) in a terminal configuration. At increasing coverages up to one full monolayer, the computed adsorption geometries and energetics suggest that the adsorbate-adsorbate interactions are attractive for N(ad), but repulsive for NH(ad) and NH2(ad). On the hydrogenated substrate, the adsorbed nitrogen species are subject to structural modification, as resulted from the weakened adsorbate-substrate interactions. Further, we calculated the vibration of nitrogen species and the 1s core-level shift of surface carbons, providing atomistic insights into the nature of surface bonding. Lastly, we simulated images of representative nitrogen species adsorbed on diamond(001), guiding future work using scanning tunneling microscopy.