The zone-center phonon spectra of phase-I ammonia and deuterated ammonia have been obtained from plane-wave DFT molecular dynamics and localized basis set harmonic lattice dynamics simulations. These data have proved to be excellent for benchmarking the two approaches. Significant changes to the assignments of the experimental low-frequency lattice modes are proposed on the basis of the calculated data. The magnitude of the splitting of the longitudinal and transverse optical modes has been determined and is shown to be significant in some cases. The high-frequency internal mode region of the spectrum has also been obtained and is shown to be in excellent agreement with the results of previous studies. The symmetry coordinates and Davydov splittings of the internal modes are fully analyzed.