We describe and apply a new procedure that allows a direct determination of dissociation energies of polyatomic systems (clusters, fullerenes, polymers, and other molecules) without any modeling of the systems under investigation. As an example, we have determined the dissociation energies of a series of gold clusters Au(+)n. A comparison with values obtained from statistical models of unimolecular dissociation shows that these models significantly fail to describe the data. In contrast, the new method yields values which are an order of magnitude more accurate, thus allowing one to experimentally set benchmarks for any theory which attempts to describe activated processes.