  We derive an analytic expression for the average difference between the
forces on the ions in a Car-Parrinello simulation and the forces obtained at
the same ionic positions when the electrons are at their ground state. We show
that for common values of the fictitious electron mass, a systematic bias may
affect the Car-Parrinello forces in systems where the electron-ion coupling is
large. We show that in the limit where the electronic orbitals are rigidly
dragged by the ions the difference between the two dynamics amounts to a
rescaling of the ionic masses, thereby leaving the thermodynamics intact. We
study the examples of crystalline magnesium oxide and crystalline and molten
silicon. We find that for crystalline silicon the errors are very small. For
crystalline MgO the errors are very large but the dynamics can be quite well
corrected within the rigid-ion model. We conclude that it is important to
control the effect of the electron mass parameter on the quantities extracted
from Car-Parrinello simulations.
