Extended Lagrangian Born-Oppenheimer Molecular Dynamics with DFT+U

Extended Lagrangian Born-Oppenheimer molecular dynamics (XL-BOMD) [Phys. Rev. Lett. vol. 100, 123004 (2008)] is combined with Kohn-Sham density functional theory (DFT) using a DFT+U correction based on the Hubbard model. This combined XL-BOMD and DFT+U approach allows efficient Born-Oppenheimer molecular dynamics simulations with orbital-dependent corrections beyond regular Kohn-Sham density functional theory. The extended Lagrangian formulation eliminates the need for the iterative self-consistent-field optimization of the electronic ground state prior to the force evaluations, which is required in regular direct Born-Oppenheimer molecular dynamics simulations. This method provides accurate and stable molecular trajectories, while reducing the computational cost per time step. The combined XL-BOMD and DFT+U approach is demonstrated with molecular dynamics simulations of a nitromethane molecular liquid and a system of solid nuclear fuel, UO$_2$, using self-consistent-charge density functional based tight-binding theory.