  This paper deals with the critical issue of approximating the pre-exponential
factor in semiclassical molecular dynamics. The pre-exponential factor is
important because it accounts for the quantum contribution to the semiclassical
propagator of the classical Feynman path fluctuations. Pre-exponential factor
approximations are necessary when chaotic or complex systems are simulated. We
introduced pre-exponential factor approximations based either on analytical
considerations or numerical regularization. The approximations are tested for
power spectrum calculations of more and more chaotic model systems and on
several molecules, for which exact quantum mechanical values are available. The
results show that the pre-exponential factor approximations introduced are
accurate enough to be safely employed for semiclassical simulations of complex
systems.
