The dissociative adsorption of a diatomic molecule on a moving metal surface is described using the density matrix. By writing the full system-bath wavefunction in a multiconfiguration form and performing the thermal averages analytically, the reduced density matrix can be computed exactly by evolving several coupled wave vectors. The usual weak-coupling and Markov-bath assumptions are avoided. Exact and approximate calculations are implemented for the case of D2 dissociation on a model Cu surface, at high energies and over a wide range of surface temperatures, with promising results.