Fully optimized geometries are computed at the Hartree-Fock level for formamide and methylamine with basis sets ranging up to ones that are triple-zeta plus two sets of polarization functions in the valence shell. The effect of very diffuse s and p functions is also examined. The relation of basis set size and composition to the computed amino group out-of-plane angle and to the related localized molecular orbitals is systematically investigated and compared with scattered results previously reported for other systems. It is concluded that the amino group angle is the result of a delicate balance between lone pair character of the nitrogen electrons and delocalization of these electrons into other portions of the molecule. Polarization functions in the nitrogen basis set are necessary to provide for proper description of the lone pair character, but even in methylamine the delocalization is not properly described without an extensive basis set, either polarization functions or very diffuse s and p functions, on the other heavy atoms. The effect is extreme for molecules such as formamide, aniline, and PF2NH2, where very large basis sets are required to obtain the correct out-of-plane angle.