  Extended Lagrangian Born-Oppenheimer molecular dynamics based on Kohn-Sham
density functional theory is generalized in the limit of vanishing
self-consistent field optimization prior to the force evaluations. The
equations of motion are derived directly from the extended Lagrangian under the
condition of an adiabatic separation between the nuclear and the electronic
degrees of freedom. We show how this separation is automatically fulfilled and
system independent. The generalized equations of motion require only one
diagonalization per time step and are applicable to a broader range of
materials with improved accuracy and stability compared to previous
formulations.
