Sputtering of condensed-phase ammonium nitrate yields many positive and negative cluster ion series derived from different ionic cores. The cluster cores are surrounded by varying numbers of ammonium nitrate monomer units. Most interesting is the extensive series of negative cluster ions of the form [(NH4NO3)(n)NO3](-), n greater than or equal to 3. The corresponding positive clusters, [(NH4NO3)(n)NH4](+), are also very extensive but also include the smallest ions, n = 1 and 2. Collision-induced dissociation of mass-selected cluster ions suggests that the first two members of the negative series, n = 1 and n = 2, are not detected because they rearrange and lose one or more ammonia molecules. Gradient-density-functional calculations using two different functionals predict that NH4NO3 is strongly hydrogen bonded and that [(NH4NO3)NO3](-) has no hydrogen bonds. This is consistent with this ion rearranging by loss of NH3 to form the strongly hydrogen-bonded ion [H(NO3)(2)](-). Rearrangements involving loss of ammonia molecules in the negative-ion spectrum and nitric acid molecules in the positive-ion spectrum lead to a rich variety of other, less extensive, series of sputtered ions from this complex solid. Both relative gradient-density-functional energies correlate well with whether or not various ions are observable experimentally.