Stochastic wave packet vs. direct density matrix solution of Liouville-von Neumann equations for photodesorption problems

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 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.