The numerical efficiency of different schemes for solving the Liouville-von
Neumann equation within Redfield theory has been studied. Among the tested
algorithms are the general Runge-Kutta and Bulirsch-Stoer methods as well
as methods especially developed for time propagation like the Short Iterati
ve Arnoldi and Newtonian propagators. Also two different time step control
mechanisms have been applied. The calculations have been performed for a sy
stem consisting of two charge localization centers modeling electron transf
er. Two different cases have been investigated, i.e., the coherent dissipat
ionless and the dissipative case. The tested integrators perform quite diff
erently for these cases. (C) 2000 Elsevier Science B.V. All rights reserved
.