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

本课题的具体研究内容如下：（1）局域密度近似的推广（Beyond LDA）：LSDA+U方法和动力学平均场理论及其在过渡金属化合物中的应用，（2）强关联电子系统第一原理电子结构计算的直接方法：GW近似，（3）现实系统中电子结构的大规模计算：第一性原理分子动力学中的{Order-N}方法，（1）在LSDA+U形式中，Hubbard型在位原子库仑参数U$和交换相互作用J$被包含在局域基组的表示中，并且该形式在旋转操作下是不变的。本文将此方法应用于过渡金属化合物的自旋、电荷和轨道有序系统，如（1a）Nd$_{0.5}$Sr$_{0.5}$MnO $_3 $，（1b）La$_{7/8}$Sr$_{1/8}$MnO $_3 $，（1c）LaSr $_{2}$MnO $_4 $，（1d）YNiO $_3 $和NdNiO $_3 $，（1e）La$_{2-x}$Sr$_{x}$NiO$_{4}$。(2)不 ...更多信息 LDA甚至对某些强关联体系如过渡金属氧化物的基态给出了错误的预言。这种失败是由于在处理电子-电子关联时缺乏非定域性和动力学效应造成的。GW近似（GWA）是一种简单但很好的近似，它给出了包含动力学关联的自能表达式。在目前的工作中，GWA适用于几个非磁性氧化物，绝缘MgO，CaO和金属TiO，VO。在MgO和CaO中的$GW$带隙，与实验符合得很好。TiO和VO是金属和非磁性氧化物。(3)基于定域态理论，我们发展了一种用于大尺度电子结构计算的变分和/或微扰N阶算法。这种局域态的构造等价于本征态（Wannier态）的幺正变换。作为我们的计划的应用，我们进行动态断裂模拟硅与外部负载。少

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