New particle formation in the atmosphere is initiated by nucleation of gas-phase species. The small molecular clusters that act as seeds for new particles are stabilized by the incorporation of an ion. Ion-induced nucleation of molecular cluster ions containing sulfuric acid generates new particles in the 0 background troposphere. The addition of a proton-accepting species to sulfuric acid cluster ions can further stabilize them and may promote nucleation under a wider range of conditions. To understand and accurately predict atmospheric nucleation, the stabilities of each molecular cluster within a chemical family must be known. We present the first comprehensive measurements of the ammonia-sulfuric acid positive ion cluster system NH4+(NH3)(n)(H2SO4)(s). Enthalpies and entropies of individual growth steps within this system were measured using either an ion flow reactor-mass spectrometer system under equilibrium conditions or by thermal decomposition of clusters in an ion trap mass spectrometer. Low level ab initio structural calculations provided inputs to a master equation model to determine bond energies from thermal decomposition measurements. Optimized ab initio structures for clusters up through n = 3, s = 3 are reported. Upon addition of ammonia and sulfuric acid pairs, internal proton transfer generates multiple NH4+ and HSO4- ions within the clusters. These multiple-ion structures are up to 50 kcal mol(-1) more stable than corresponding isomers that retain neutral NH3 and H2SO4 species. The lowest energy n = s clusters are composed entirely of ions. The addition of acid-base pairs to the core NH4+ ion generates nanocrystals that begin to resemble the ammonium bisulfate bulk crystal starting with the smallest n = s cluster, NH4+(NH3)(1)(H2SO4)(1). In the absence of water, this cluster ion system nucleates spontaneously for conditions that encompass most of the free troposphere.