Spurred by recent experimental developments in the production of vibrationally excited molecular beams to study reactive scattering on metal surfaces, we have carried out six-dimensional quasiclassical and quantum dynamics simulations for several H 2 ͑v Ͼ 0͒-surface systems. We predict a general nonmonotonic behavior of dissociative adsorption of vibrationally excited H 2 ͑v , J =0͒ molecules as a function of incidence energy whenever this process becomes nonactivated. This prediction is based on results obtained for up to five different activated systems, including pure ͓Pt͑111͒ and Cu͑110͔͒, bimetallic alloy ͓NiAl͑110͔͒, and bimetallic pseudomorphic ͓Pd/Ru͑0001͒ and Cu/Ru͑0001͔͒ surfaces.Over the last decade, surface science theorists have made a substantial progress in the description of reactive scattering of diatomic molecules from metal surfaces ͑see Refs. 1 and 2 and references therein͒. This has been motivated by the numerous industrial processes that involve heterogeneous catalysis by a metal surface, in which molecular dissociative adsorption is the first and usually the rate-limiting step. 3 Methods of increasing complexity, based on accurate density-functional theory ͑DFT͒ descriptions of the molecule/surface interaction, 4,5 have been developed to take into account all molecular degrees of freedom ͑DOFs͒ and even phonons 6,7 and electron-hole pair excitations. 8,9 So far, six-dimensional ͑6D͒ dynamical calculations, usually within the Born-Oppenheimer and rigid surface approximations, have challenged experimental measurements to an unprecedented degree of accuracy and have provided meaningful interpretations of, sometimes striking, observations such as: the dominant out-of-plane diffraction measured for H 2 / Pt͑111͒ ͑Ref. 10͒ and H 2 / Pd͑111͒ ͑Refs. 11 and 12͒; the lack of diffraction peaks in H 2 / Pd͑110͒ due to dynamic trapping; 13 the surprisingly low reaction probability observed in N 2 / Ru͑0001͒ for incidence energies well above the minimum reaction barrier ͑MRB͒ ͑Ref. 14͒; the dramatic difference in reactivity between chemically similar systems such as N 2 / W͑100͒ and N 2 / W͑110͒ ͑Ref. 15͒; or the strong nonadiabatic effects that govern the interaction of O 2 with Al͑111͒. 16,17 Most existing experiments have exclusively considered molecules in their ground vibrational state ͑v =0͒ since they employ supersonic molecular beams in which vibrationally excited states are barely populated except at relatively high kinetic energy. 18 Vibrational excited molecules can be more efficiently obtained by using stimulated Raman pumping. [19][20][21][22] However, only very recently, the advent of experimental setups based on pulsed narrow bandwidth laser Raman excitation have made it possible to perform quantum state resolved reactivity measurements with vibrationally excited polyatomic molecules, 23 e.g., methane, 24-28 on singlecrystal surfaces. The latter experiments have provided direct evidence of the central role played by vibrational energy in activating gas-surface reactions ͑the so-called vibr...