Theoretical studies on molecular magnetism and superconductivity with the generalized spin orbital(GSO)

分子簇系的电子、磁性和光学性质是非常有趣的。在理论处理中，这些通常属于强电子相关系统。因此，为了揭示功能磁性材料的机制，迫切需要对自旋相关进行研究。事实上，在由过渡金属组成的单分子磁体中，非共线磁性是通过自旋受挫和自旋退化来实现的。然而，普通的UHF和UDFT方法无法处理这类系统，必须开发基于广义自旋轨道（GSO）的GHF和GDFT方法。本课题通过数学群论的拓展、程序包的开发和计算机系统的定制等方法来探讨这一主题。我们扩展了GSO的理论框架，开发了用于非共线磁体从头计算的程序包。例如，从头算HF (GHF), GSO-LDA, GSO-GGA， GSO-LSDA+SIC和GSO-GW方法都适用于这些目的。结果表明：(1)二维和三维自旋结构在自旋受挫和自旋简并体系中最稳定。(2)当三重态氧分子解离成两个氧原子时，二维自旋结构很重要。此外，我们将它们应用于许多模型系统。磁性参数(有效交换积分（J)，各向异性参数(D)）是研究磁性的必要条件，可以通过从头计算来评估。本文研究了非线性系统中J值和D值的估计方法。

Electronic, magnetic and optical properties in cluster systems of molecules are very interesting.In theoretical treatment, these commonly belong to strong electronic correlation systems. Thus, studies for spin correlation is strongly needed in order to reveal mechanism of functional magnetic materials. Indeed, in the single molecular magnets which are composed of transition metals, noncollinear magnetism is realized with spin frustration and spin degeneration. However, ordinary UHF and UDFT methods cannot treat such systems, and the GHF and GDFT methods based on generalized spin orbital (GSO) must be developed. In this research project, we approach these theme, through extension of mathematical group theory, developing of program package and custom making of computer system.We extended theoretical framework of GSO and developed program packages for ab initio calculation for noncollinear magnets. For example, ab initio HF (GHF), GSO-LDA, GSO-GGA, GSO-LSDA+SIC and GSO-GW methods are suitable for these purpose. Using these methods, the following points were made clear : (1)2- and 3- dimensional spin structure is most stable in both spin frustration and spin degenerate systems. (2)2-dimensinal spin structure is important, when triplet oxygen molecules are dissociated into two oxygen atoms. In addition, we applied them to many model systems.Magnetic parameters (effective exchange integral (J), anisotropic parameter (D)) are essential for investigation of magnetic properties and can be evaluated by ab initio calculation. In this study, evaluation scheme for both J and D values in noncollinear systems is developed.