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Static-lattice calculations have been employed to model the phases of VO₂ and V_1−δW_δO₂. Interatomic potentials were empirically fitted to reproduce the low- and high-temperature phases (monoclinic and tetragonal, respectively) of vanadium dioxide as well as the monoclinic phase of tungsten dioxide. For pure VO₂, we located the soft modes of the high-temperature phase, which characterize the initial atomic displacements that lead to the displacive phase transition to the low-temperature phase. The T = 0 structure of the saddle point, where only half of the one-dimensional chains have undergone Peierls distortions, and the ionic motion along the lowest-energy path for the phase transition are described. For V_1−δW_δO₂, we found that doping significantly stabilizes the high-temperature phase relative to the low-temperature phase, which explains the observed depression in the transition temperature as δ …