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Knowledge about water desorption is important to give a full picture of water diffusion in montmorillonites (MMT), which is a driving factor in MMT swelling. The desorption paths and energetics of water molecules from the surface of MMT with trapped Li(+), Na(+) or K(+) counterions were studied using periodic density functional theory calculations. Two paths--surface and vacuum desorption--were designed for water desorption starting from a stationary structure in which water bonds with both the counterion and the MMT surface. Surface desorption is energetically more favorable than vacuum desorption due to water-surface hydrogen bonds that help stabilize the intermediate structure of water released from the counterion. The energy barriers of water desorption are in the order of Li(+) > Na(+) > K(+), which can be attributed to the short ionic radius of Li(+), which favors strong binding with the water molecule. The temperature dependence of water adsorption and desorption rates were compared based on the computed activation energies. Our calculations reveal that the water desorption on the MMT surface has a different mechanism from water adsorption, which results from surface effects favoring stabilization of water conformers during the desorption process.