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.
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