The importance of pre-nucleation cluster stability as the key parameter controlling nucleation of atmospheric airborne ions is well-established. In this Article, large ternary ionic (HSO(4)(-))(H(2)SO(4))(m)(NH(3))(H(2)O)(n) clusters have been studied using Density Functional Theory (DFT) and composite ab initio methods. Twenty classes of clusters have been investigated, and thermochemical properties of common atmospheric (HSO(4)(-))(H(2)SO(4))(m)(NH(3))(0)(H(2)O)(k) and (HSO(4)(-))(H(2)SO(4))(m)(NH(3))(1)(H(2)O)(n) clusters (with m, k, and n up to 3) have been obtained. A large amount of new themochemical and structural data ready-to-use for constraining kinetic nucleation models has been reported. We have performed a comprehensive thermochemical analysis of the obtained data and have investigated the impacts of ammonia and negatively charged bisulfate ion on stability of binary clusters in some detail. The comparison of theoretical predictions and experiments shows that the PW91PW91/6-311++G(3df,3pd) results are in very good agreement with both experimental data and high level ab initio CCSD(T)/CBS values and suggest that the PW91PW91/6-311++G(3df,3pd) method is a viable alternative to higher level ab initio methods in studying large pre-nucleation clusters, for which the higher level computations are prohibitively expensive. The uncertainties in both theory and experiments have been investigated, and possible ways of their reduction have been proposed.