Calculations on small platinum-water clusters demonstrate the importance of cooperative effects on the formation of a water bilayer structure on the platinum(111) surface. If the orientation of the bridging water molecule is allowed to relax during the simulation of this bilayer, one hydrogen bond is broken in favor of the other. The desorption energy of water from the relaxed model cluster is found to be in better agreement with published thermal desorption spectra data than desorption energies arising from an ideal icelike bilayer structure.