We have performed a first principle study of structural and phase stabilization of beta-La2-xLxMo2O9 (L = Gd, Sm, Nd and Bi) and La2Mo2-yMyO9 (M = Cr, W). The substitutional-site properties were discussed in terms of the empirical parameter, bond valence sums (BVS), which characterizes the interactions between atoms and its nearest-neighbor atoms and correlates well with the stability of the structure. We found that Gd. Sm and Nd atoms prefer the crystallographic sites with largest BVS values. The nonlinear dependence of cell parameter on W content in W-doped systems results from the nonlinear change in Mo/W-O bond length with W content. The decrease of cohesive energy and the deviation of BVS values from the expected values upon the Gd, Sm, Nd and W-doped concentration help us understand the experimentally observed stabilization of the beta phase to lower temperatures in these doped system. The O ion diffusion properties in W-doped systems have been studied using the nudged elastic band method and the dinner method. We found that, W-doping leads to the obvious increase in the energy barriers of O ion concerted diffusion. In addition, there is a remarkable decrease in the difference of energy barriers between two diffusion channels involving O(1) ion, which sheds light on only one relaxation peak in the mechanical relaxation measurement in W-doped system, compared to undoped system. (C) 2009 Elsevier B.V. All rights reserved.