We have studied the interaction of H(2) on Cu(111) using quasi-classical and quantum dynamics, and a chemically accurate six-dimensional potential energy surface (PES). The PES was computed using the specific reaction parameter (SRP) approach to density functional theory (DFT), in an implementation adapted to molecules interacting with metal surfaces. To perform this study we have applied the Born-Oppenheimer static surface (BOSS) approximation, i.e., we used both the Born-Oppenheimer (BO) and the static surface (SS) approximations. We show that our theoretical approach accurately describes experiments on dissociative adsorption, the effect of molecular vibrational and rotational motion on dissociative (associative) adsorption (desorption), and rotational excitation upon scattering. More specifically, dynamics calculations on reactive scattering of H(2) reproduce reaction probabilities measured in molecular beam experiments, effective barrier heights describing the dependence of reaction on the initial rovibrational state, and data on rotationally inelastic scattering with chemical accuracy (i.e., within 1 kcal mol(-1) approximately 4.2 kJ mol(-1)). These processes are not affected much by surface motion, either because they were measured using a low surface temperature, T(s), or because the computed observable is independent of T(s). However, we show that to account for the dependence of molecular orientation on a reaction the inclusion of surface motion is required. We have also found that vibrational excitation is poorly described within the BOSS approximation, suggesting a breakdown of this approximation.