When a gas phase atom or molecule hits a nonrigid surface, both elastic and inelastic scattering and sticking can occur. We suggest treating the dynamics of these processes using open-system density matrix theory. For the "free --> free" and "free --> bound" events at hand, both fundamental and numerical problems arise. The fundamental problem is that the adsorbate "system" is anharmonic and the coupling between the system and the substrate "bath" has to be nonlinear at least in the system coordinates. Here we propose a new Lindblad-type open-system density matrix approach which accounts for system anharmonicity and nonlinearity of the system-bath coupling. The numerical problem is that for a dissipative scattering process large basis sets or grids are required, making the storage and direct propagation of a density matrix difficult. To overcome this problem we use a mapped Fourier method which reduces the grid size and hence the storage requirements significantly. We apply the new methods and techniques to a simple model resembling the simultaneous scattering and sticking of an O-2 molecule at a metal surface.