  We perform semi-classical molecular dynamics simulations of screening by
bound electrons in low energy nuclear reactions. In our simulations quantum
effects corresponding to the Pauli and Heisenberg principle are enforced by
constraints. In addition to the well known adiabatic and sudden limits, we
propose a new "dissipative limit" which is expected to be important not only at
high energies but in the extremely low energy region. The dissipative limit is
associated with the chaotic behavior of the electronic motion. It affects also
the magnitude of the enhancement factor. We discuss also numerical experiments
using polarized targets. The derived enhancement factors in our simulation are
in agreement with those extracted within the $R$-matrix approach.
