Dissipative dynamics of an adsorbate near a metal surface is formulated consistently by replacing the infinite system-bath Hamiltonian by a finite surrogate Hamiltonian. This finite representation is designed to generate the true short time dynamics of a primary system coupled to a bath. A detailed wave packet description is employed for the primary system while the bath is represented by an array of two-level systems. The number of bath modes determines the period the surrogate Hamiltonian reproduces the dynamics of the primary system. The convergence of this construction is studied for the dissipating Harmonic oscillator and the double-well tunneling problem. Converged results are obtained for a finite duration by a bath consisting of 4-11 modes. The formalism is extended to dissipation caused by electron-hole-pair excitations. The stopping power for a slow moving proton is studied showing deviations from the frictional limit at low velocities. Vibrational line shapes of hydrogen and deuterium on nickel were studied. In the bulk the line shape is mostly influenced by nonadiabatic effects. The interplay between two baths is studied for low temperature tunneling between two surface sites of hydrogen on nickel. A distinction between lattice modes that enhance the tunneling and ones that suppress it was found.