  We present an efficient general approach to first principles molecular
dynamics simulations based on extended Lagrangian Born-Oppenheimer molecular
dynamics in the limit of vanishing self-consistent field optimization. The
reduction of the optimization requirement reduces the computational cost to a
minimum, but without causing any significant loss of accuracy or longterm
energy drift. The optimization-free first principles molecular dynamics
requires only one single diagonalization per time step and yields trajectories
at the same level of accuracy as "exact", fully converged, Born-Oppenheimer
molecular dynamics simulations. The optimization-free limit of extended
Lagrangian Born-Oppenheimer molecular dynamics therefore represents an ideal
starting point for a robust and efficient formulation of a new generation first
principles quantum mechanical molecular dynamics simulation schemes.
