Chemical Physics ELSEVIER Chemical Physics 211 (1996) 265-276 Stochastic wave packet vs. direct density matrix solution of Liouville-von Neumann equations for photodesorption problems Peter Saalfrank lnstitut fiir Physikalische und Theoretische Chemic, Freie Universitdt Berlin, TakustraJ3e 3, D-14195 Berlin, Germany Received 1 February 1996 Abstract The performance of stochastic wave packet approaches is contrasted with a direct method to numerically solve quantum open system Liouville-von Neumann equations for photodesorption problems. As a test case a simple one-dimensional two- state model representative for NO/Pt( 111 ) is adopted. Both desorption induced by electronic transitions (DIET) treated by a single-dissipative channel model, and desorption induced by multiple electronic transitions (DIMET) treated by a double- dissipative channel model, are considered. It is found that stochastic wave packets are a memory-saving alternative to direct matrix propagation schemes. However, if statistically rare events as for example the bond breaking in NO/Pt( 111 ) are of interest, the former converges only slowly to the exact results. We also find that - in the case of coordinate-independent rates - Gadzuk's "jumping wave packet and weighted average" procedure frequently employed to describe DIET dynamics, is a rapidly converging variant of the stochastic wave packet approach, and therefore rigorously equivalent to the exact solution of a Liouville-von Neumann equation. The usual stochastic (Monte Carlo) wave packet approach, however, is more generally applicable, and allows for example to quantify the notion of "multiple" in DIMET processes. 1. Introduction Photochemistry at adsorbate-covered metal sur- faces, and in particular the hot-electron mediated desorption of neutrals by visible lasers is presently the focus of intensive fundamental and applied research. Depending on whether the exciting laser has temporal widths in the ns or in the fs-ps domain, one discrim- inates between DIET (Desorption Induced by Elec- tronic Transitions) and DIMET (Desorption Induced by Multiple Electronic Transitions), respectively [ 1 ]. Both these indirect photodesorption processes are be- lieved to be initialized by the creation of non-thermal (DIET) or thermal (DIMET) high-energy distribu- tions among the metal electrons. The absorbed energy is then - in the form of adparticle electronic excita- tions - partially transferred to and temporarily stored in the adsorbate-surface complex. Upon relaxation of the excited complex on an ultrashort (fs) timescale back to the ground state, a part of the energy may be used to break the metal-adsorbate bond and/or to excite internal degrees of freedom. From the theoretical modelling point of view, the desorption process can in simple cases be de- scribed with one-dimensional (molecule-surface co- ordinate Z) electronic two-state scenarios (ground state Vg(Z), excited state Ve(Z)). Two important and well-known representatives of this class are the Menzel-Gomer-Redhead [2,3] (MGR) and the Antoniewicz [4] models, respectively. Variants of these are multiple-state models including non-Born- Oppenheimer couplings [5,6], or multi-dimensional 0301-0104/96/$15.00 Copyright (~) 1996 Elsevier Science B.V. All rights reserved. P11S0301-0104(96)00178-4