A study of transition metal oxides by using the methods beyond LDA

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Concrete research theme of our project is as follows :(1) Extension of the Local Density Approximation (Beyond LDA) : LSDA+U method and the Dynamical Mean Field Theory and their application to the transition metal compounds,(2) Direct approach to the first principle electronic structure calculations of strongly correlated electron systems : GW approximation,(3) Large scale calculations of electron structures in realistic Systems : {Order-N} method in the first principle molecular dynamics,(1) In the LSDA+U formalism, the Hubbard type on-site atomic Coulomb parameter $U$ and exchange interaction $J$ are included in the representation of the local basis set, and the formulation is invariant under the rotation operation. This method is applied to the systems of the spin, charge andorbital ordering in transition metal compounds, such as(1a) Nd$_{0.5}$Sr$_{0.5}$MnO$_3$, (1b) La$_{7/8}$Sr$_{1/8}$MnO$_3$,(lc) LaSr$_2$MnO$_4$, (1d) YNiO$_3$ and NdNiO$_3$, (1e) La$_{2-x}$Sr$_{x}$NiO$_{4}$.(2) T … More he LDA even gives a wrong prediction for the ground-state in somestrongly correlated systems such as the transition metal oxides. This failures are caused due to the lack of nonlocality and dynamical effects in the treatment of electron-electron correlation. The $GW$ approximaton (GWA) is a simple but excellent approximation to give an expression of the self-energy including the dynamical correlation. In the present work the GWA is applied to several non-magnetic oxides, insulating MgO, CaO and metallic TiO, VO. the $GW$ band gap in the MgO and CaO, is in good agreement with the experiment. TiO and VO are the metallic and non-magnetic oxides.(3) We have developed a variational and/or perturbative order-N algorithm for large-scale electronic-structure calculations, based on the localized-state theory. Construction of such localized states is equivalent to a unitary transformation of eigenstates (Wannier states). As an application of our scheme, we perform dynamical fracture simulations of silicon with external load. Less