Real-Time Time-Dependent Density Functional Theory plus the Hubbard U and Simulations of Fast Responses of Condensed Matters

We have developed the real-time evolution package of the time-dependent density functional theory, in which Kohn-Sham orbitals evolve along with the self-consistent evolution of density and Hamiltonian and the Hubbard U potential is incorporated as an explicit descriptor of the electrons correlation. We applied this method to a few exemplary phenomena of ultrafast dynamics of the non-equilibrium states of condensed matters in femtosecond range. As example studies, we present the high speed motion of alkali atoms on metal surface and the exchange of electron between localized defects and metallic bath. The real-time dynamics along the transition of few-layer graphene into nanometer-thick diamond will be discussed. We also present the role phonon on the metal-insulator phase transition of transition-metal oxide bulk structures. The implementation details for the Hubbard U potential not only using atom-centered atomic orbitals but, for some particular defect states, using molecular orbitals are also to be presented