Aiming to treat multidimensional quantum dissipative dynamics of adsorbates at surfaces, we consider application of several variants of the Monte Carlo wave packet method to an exemplary problem, the desorption induced by electronic transitions (DIET) of NO from a Pt(111) surface with a two-state two-dimensional model. We investigate the convergence of stochastic unravelling schemes of different order for 'rare' observables characteristic for this test system. (C) 2002 Elsevier Science B.V. All rights reserved.