The lowest energy triplet state, T-1, of organometallic complexes based on iridium(III) is of fundamental interest, as the behavior of molecules in this state determines the suitability of the complex for use in many applications, e.g., organic light-emitting diodes. Previous characterization of T-1 in fac-Ir(ppy)(3) suggests that the trigonal symmetry of the complex is weakly broken in the excited state. Here we report relativistic time dependent density functional calculations of the zero-field splitting (ZFS) of fac-Ir(ppy)(3) in the ground state (S-0) and lowest energy triplet (T-1) geometries and at intermediate geometries. We show that the energy scale of the geometry relaxation in the T-1 state is large compared to the ZFS. Thus, the natural analysis of the ZFS and the radiative decay rates, based on the assumption that the structural distortion is a small perturbation, fails dramatically. In contrast, our calculations of these quantities are in good agreement with experiment.