多核磁耦合体系的理论研究
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摘要
多核金属磁耦合体系在分子磁性材料、生命体系等领域得到了广泛的应用，是配位化学最活跃的研究领域之一。多核金属耦合体系的研究作为现代化学研究的一个边缘学科，已成为物理学、化学、生命科学和材料科学的交汇点。近年来，多核金属体系的研究迅速发展，各种新奇的配合物不断涌现。该类体系因为顺磁离子相互作用而具有特殊功能：金属离子通过电子传递的相互作用，以及它们与桥基和端基配体的协调作用，呈现出不同于单核配合物的化学活性、物理性质和生物活性。因此，用理论化学手段研究多金属耦合体系中顺磁离子之间的相互作用及磁-构效关系，具有重要意义。
本文在密度泛函(DFT)的框架下，结合对称性破损方法，对几类体系的磁耦合行为做了较系统的研究，得到了以下结果：
1、给出了配位场条件下的磁耦合常数表达式
我们以局域d-电子模型为基础，从配位场条件下的磁轨道表达式出发，计算出各个微观状态(单行列式)的能量，用微扰理论描写单三重态的能量差，得到双同核体系的磁耦合常数表达式。磁耦合常数的表达式中包含库仑积分、交换积分和K-S轨道能量差，用单行列式来计算这些参数的数值。即利用DFT方法可以用交换积分和库仑积分得出参数的性质，来求算同核过渡双金属分子的磁耦合常数。
2、给出了直线型三核和三角形型三核体系磁耦合常数的表达式
对直线型三核体系，假设每个磁中心只有一个成单电子(以三核铜(Ⅱ)体系为例)，两个端基铜离子的配位环境是等价的。采用较简便的方法，即比较高自旋态与低自旋态的自旋排布波函数，由自旋态能量差与磁耦合常数的关系式，得出了直线型三核体系磁耦合常数的表达式。
Study on polymetal coupling interaction system is always the most active and wide field in cooperation chemistry. Many special characters induced by interaction among paramagnetic ions, attracted much attention in the field of physics, chemistry, biology and material science. Nowadays, the research on polynuclear complexes develops rapidly, and many novel complexes have been synthesized. The metal ions in polymetal coupling interaction system depend on electron transfer interaction and harmonized interaction among them and bridged groups and terminal groups, presents chemical reactivity, physical property and biological activity different from mononuclear complexes. As a result, it is important to investigate interaction among paramagnetic ions and magneto-structural correlation in such systems by theoretical chemistry method. In this paper, magnetic coupling behavior of some systems has been performed using the broken symmetry approach with the framework of density functional theory (DFT). Many conclusive are derived as follows:
1. The formula of exchange coupling constant under ligand field is given. A DFT based ligand field model for magnetic exchange coupling in homonuclear transition metal dimmer complexes is presented. It is based on a model of localized d-electrons. Firstly, the energy of all microstates (single determinants) were calculated. Secondly, perturbation theory yielded for the magnetic coupling constants. In this formula, magnetic coupling constant is
expressed by Coulomb integrals (J_(aa), J_(bb) and J_(ab)), exchange integrals (K_(ab))
and the K-S orbital energy difference (ε(b)-ε(a)). We used single
determinants to express these parameters. So on a procedure allowing to express its parameters in terms of exchange and Coulomb integrals from DFT calculations of a homonuclear dimmer complex., we gained the expression of the magnetic coupling costants.
本文在密度泛函(DFT)的框架下，结合对称性破损方法，对几类体系的磁耦合行为做了较系统的研究，得到了以下结果：
1、给出了配位场条件下的磁耦合常数表达式
我们以局域d-电子模型为基础，从配位场条件下的磁轨道表达式出发，计算出各个微观状态(单行列式)的能量，用微扰理论描写单三重态的能量差，得到双同核体系的磁耦合常数表达式。磁耦合常数的表达式中包含库仑积分、交换积分和K-S轨道能量差，用单行列式来计算这些参数的数值。即利用DFT方法可以用交换积分和库仑积分得出参数的性质，来求算同核过渡双金属分子的磁耦合常数。
2、给出了直线型三核和三角形型三核体系磁耦合常数的表达式
对直线型三核体系，假设每个磁中心只有一个成单电子(以三核铜(Ⅱ)体系为例)，两个端基铜离子的配位环境是等价的。采用较简便的方法，即比较高自旋态与低自旋态的自旋排布波函数，由自旋态能量差与磁耦合常数的关系式，得出了直线型三核体系磁耦合常数的表达式。
Study on polymetal coupling interaction system is always the most active and wide field in cooperation chemistry. Many special characters induced by interaction among paramagnetic ions, attracted much attention in the field of physics, chemistry, biology and material science. Nowadays, the research on polynuclear complexes develops rapidly, and many novel complexes have been synthesized. The metal ions in polymetal coupling interaction system depend on electron transfer interaction and harmonized interaction among them and bridged groups and terminal groups, presents chemical reactivity, physical property and biological activity different from mononuclear complexes. As a result, it is important to investigate interaction among paramagnetic ions and magneto-structural correlation in such systems by theoretical chemistry method. In this paper, magnetic coupling behavior of some systems has been performed using the broken symmetry approach with the framework of density functional theory (DFT). Many conclusive are derived as follows:
1. The formula of exchange coupling constant under ligand field is given. A DFT based ligand field model for magnetic exchange coupling in homonuclear transition metal dimmer complexes is presented. It is based on a model of localized d-electrons. Firstly, the energy of all microstates (single determinants) were calculated. Secondly, perturbation theory yielded for the magnetic coupling constants. In this formula, magnetic coupling constant is
expressed by Coulomb integrals (J_(aa), J_(bb) and J_(ab)), exchange integrals (K_(ab))
and the K-S orbital energy difference (ε(b)-ε(a)). We used single
determinants to express these parameters. So on a procedure allowing to express its parameters in terms of exchange and Coulomb integrals from DFT calculations of a homonuclear dimmer complex., we gained the expression of the magnetic coupling costants.
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