On the work function and the charging of small (r <= 5 nm) nanoparticles in plasmas, Physics of Plasmas, 2017. 24 electron field emission (EFE), thermionic electron emission (TIE), and electron impact detachment. Here we report theoretical vales of the work function in this size range. Density functional theory (DFT) is used to calculate the work functions for a set of NP charge numbers, sizes and shapes, using copper for a case study. An analytical approximation is shown to give quite accurate work functions provided that >0.4 nm, i.e., consisting of about > 20 atoms, and provided also that the NPs have relaxed to close to spherical shape.For smaller sizes W deviates from the approximation, and also depends on the charge number. Some consequences of these results for nanoparticle charging are outlined. In particular, a decrease in W for NP radius below about 1 nm has fundamental consequences for their charge in a plasma environment, and thereby on the important processes of NP nucleation, early growth, and agglomeration.