Generalized Extended Lagrangian Born-Oppenheimer Molecular Dynamics
  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. 
Anders M.N. Niklasson and Marc J. Cawkwell
physics.chem-ph cond-mat.mtrl-sci