我們用基於密度泛函理論的編碼程式研究層狀氫氧化物的電子能帶與其雌性結構，和六硼化物的拓樸相變. 部分氫氧化物有反鐵慈半導體的。鑭系六硼化物有很多特別的物理性質，例如近藤絕緣體或強關聯電子系統。我們試著找出+U與其拓樸相變關係。

We use VASP code which is based on density functional and plane wave method to study the electronic structure of layered metal hydroxides, and topological phase transition of Lanthanide hexaborides. Some of layered metal hydroxides have antiferromagnetic insulator band structures. Lanthanide hexaborides have wide physics properties, such as Kondo effect or strong correlated f electrons. We try to find the most stable spin structure of Cobalt hydroxides and Iron hydroxides and topological phase transition of Lanthanide hexaborides with Hubbard +U parameters.

1. Introduction ................1
1.1 Density functional theory ......................1
1.2 Hohenberg and Kohn theory ...................2
1.3 Local density approximation and generalized gradient approximation .........................6
1.4 LDA+U and GGA+U.........................................7
1.5 topological insulators and Kondo effect..............8
2. Investigation of Brucite-like Divalent metal
hydroxides ...................... 11
2.1 Introduction ................................... 11
2.2 Computational details ....................... 13
2.3 Single lattice calculation ........... 14
2.4 Spin structure determined...................... 17
2.5 Appendix ....... 28
2.6 Conclusion ........ 31
3. Investigation of Topological Phase Transition in Metal
Hexaborides ...................... 32
3.1 Introduction .............................. 32
3.2 Crystal structure ......................... 33
3.3 Computational details .......... 36
3.4 Electronic structure ..................... 37
3.5 Appendix ... 59
3.6 Conclusion .... 60
4. References .................. 62

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