  With the continuous growth of processing power for scientific computing,
first principles Born-Oppenheimer molecular dynamics (MD) simulations are
becoming increasingly popular for the study of a wide range of problems in
materials science, chemistry and biology. Nevertheless, the computational cost
still remains prohibitively large in many cases, particularly in comparison to
classical MD simulations using empirical force fields. Here we show how to
circumvent the major computational bottleneck in Born-Oppenheimer MD
simulations arising from the self-consistent-charge optimization. The
optimization-free quantum mechanical MD method is demonstrated for density
functional tight-binding theory. The molecular trajectories are almost
indistinguishable from an "exact" microcanonical Born-Oppenheimer MD simulation
even when linear scaling sparse matrix algebra is used. Our findings
drastically reduce the computational gap between classical and quantum
mechanical MD simulations.
