Topics  主题

Valence bond model 价键模型
Crystal field theory 晶体场理论
Spectrochemical series 光谱化学系列
Crystal field stabilization
晶体场稳定
energy 能源
Molecular orbital theory 分子轨道理论
Microstates and term 微观状态和术语
$$$$quad\quad symbols  $$$$quad\quad 符号
Electronic absorption 电子吸收
$$$$quad\quad and emission spectra
$$$$quad\quad 和发射光谱
Nephelauxetic effect 肾毒性效应
Magnetic properties 磁性能
Thermodynamic aspects 热力学方面
Valence bond model 价键模型
Crystal field theory 晶体场理论
Spectrochemical series 光谱化学系列
Crystal field stabilization energy
晶体场稳定能量
Molecular orbital theory Microstates and term symbols
分子轨道理论 微观状态和术语符号
Electronic absorption and emission spectra Nephelauxetic effect Magnetic properties Thermodynamic aspects
电子吸收光谱和发射光谱 内积效应 磁性热力学方面的问题

In this chapter, we discuss complexes of the $d$$d$dd-block metals and consider bonding theories that rationalize experimental facts such as electronic spectra and magnetic properties. Most of the discussion centres on first row $d$$d$dd-block metals, for which theories of bonding are most successful. The bonding in $d$$d$dd-block metal complexes is not fundamentally different from that in other compounds, and we shall show applications of valence bond theory, the electrostatic model and molecular orbital theory.
在本章中，我们将讨论 $d$$d$dd 块状金属的络合物，并考虑可合理解释电子光谱和磁性等实验事实的成键理论。大部分讨论集中在第一行 $d$$d$dd 块状金属上，对于这些金属，成键理论是最成功的。 $d$$d$dd 块状金属配合物中的成键与其他化合物中的成键没有本质区别，我们将展示价键理论、静电模型和分子轨道理论的应用。

Fundamental to discussions about $d$$d$dd-block chemistry are the $3d,4d$$3d,4d$3d,4d3 d, 4 d or $5d$$5d$5d5 d orbitals for the first, second or third row $d$$d$dd-block metals, respectively. We introduced $d$$d$dd-orbitals in Section 1.6, and showed that a $d$$d$dd-orbital is characterized by having a value of the quantum number $l=2$$l=2$l=2l=2. The conventional representation of a set of five degenerate $d$$d$dd-orbitals is shown in Fig. 20.1b. ${}^{†}$${}^{†}$^(†){ }^{\dagger} The lobes of the $d_{yz},d_{xy}$$d_{yz},d_{xy}$d_(yz),d_(xy)d_{y z}, d_{x y} and $d_{xz}$$d_{xz}$d_(xz)d_{x z} orbitals point between the Cartesian axes and each orbital lies in one of the three planes defined by the axes. The $d_{x^2-y^2}$$d_{x^2-y^2}$d_(x^(2)-y^(2))d_{x^{2}-y^{2}} orbital is related to $d_{xy}$$d_{xy}$d_(xy)d_{x y}, but the lobes of the $d_{x^2-y^2}$$d_{x^2-y^2}$d_(x^(2)-y^(2))d_{x^{2}-y^{2}} orbital point along (rather than between) the $x$$x$xx and $y$$y$yy axes. We could envisage being able to draw two more atomic orbitals which are related to the $d_{x^2-y^2}$$d_{x^2-y^2}$d_(x^(2)-y^(2))d_{x^{2}-y^{2}} orbital, i.e. the $d_{z^2-y^2}$$d_{z^2-y^2}$d_(z^(2)-y^(2))d_{z^{2}-y^{2}} and $d_{z^2-x^2}$$d_{z^2-x^2}$d_(z^(2)-x^(2))d_{z^{2}-x^{2}} orbitals (Fig. 20.1c). However, this would give a total of six $d$$d$dd-orbitals. For $l=2$$l=2$l=2l=2, there are only five real solutions to the Schrödinger equation ( $m_l=+2,+1,0,-1,-2$$m_l=+2,+1,0,-1,-2$m_(l)=+2,+1,0,-1,-2m_{l}=+2,+1,0,-1,-2 ). The problem is solved by taking a linear combination of the $d_{z^2-x^2}$$d_{z^2-x^2}$d_(z^(2)-x^(2))d_{z^{2}-x^{2}} and $d_{z^2-y^2}$$d_{z^2-y^2}$d_(z^(2)-y^(2))d_{z^{2}-y^{2}} orbitals. This means that the two orbitals
讨论 $d$$d$dd 块状化学的基础是第一、第二或第三行 $d$$d$dd 块状金属的 $3d,4d$$3d,4d$3d,4d3 d, 4 d 或 $5d$$5d$5d5 d 轨道。我们在第 1.6 节中介绍了 $d$$d$dd 轨道，并说明 $d$$d$dd 轨道的特征是具有量子数 $l=2$$l=2$l=2l=2 值。图 20.1b 显示了一组五个退化 $d$$d$dd 轨道的常规表示方法。 ${}^{†}$${}^{†}$^(†){ }^{\dagger} $d_{yz},d_{xy}$$d_{yz},d_{xy}$d_(yz),d_(xy)d_{y z}, d_{x y} 和 $d_{xz}$$d_{xz}$d_(xz)d_{x z} 轨道的裂片指向笛卡尔轴之间，每个轨道位于轴所定义的三个平面之一。 $d_{x^2-y^2}$$d_{x^2-y^2}$d_(x^(2)-y^(2))d_{x^{2}-y^{2}} 轨道与 $d_{xy}$$d_{xy}$d_(xy)d_{x y} 有关，但 $d_{x^2-y^2}$$d_{x^2-y^2}$d_(x^(2)-y^(2))d_{x^{2}-y^{2}} 轨道的裂片沿 $x$$x$xx 和 $y$$y$yy 轴（而不是在这两条轴之间）指向。我们可以设想再绘制两个与 $d_{x^2-y^2}$$d_{x^2-y^2}$d_(x^(2)-y^(2))d_{x^{2}-y^{2}} 轨道相关的原子轨道，即 $d_{z^2-y^2}$$d_{z^2-y^2}$d_(z^(2)-y^(2))d_{z^{2}-y^{2}} 和 $d_{z^2-x^2}$$d_{z^2-x^2}$d_(z^(2)-x^(2))d_{z^{2}-x^{2}} 轨道（图 20.1c）。然而，这样就会产生总共六个 $d$$d$dd 轨道。对于 $l=2$$l=2$l=2l=2 ，薛定谔方程只有五个实解 ( $m_l=+2,+1,0,-1,-2$$m_l=+2,+1,0,-1,-2$m_(l)=+2,+1,0,-1,-2m_{l}=+2,+1,0,-1,-2 )。这个问题可以通过对 $d_{z^2-x^2}$$d_{z^2-x^2}$d_(z^(2)-x^(2))d_{z^{2}-x^{2}} 和 $d_{z^2-y^2}$$d_{z^2-y^2}$d_(z^(2)-y^(2))d_{z^{2}-y^{2}} 轨道进行线性组合来解决。这意味着两个轨道

are combined (Fig. 20.1c), with the result that the fifth real solution to the Schrödinger equation corresponds to what is traditionally labelled the $d_{z^2}$$d_{z^2}$d_(z^(2))d_{z^{2}} orbital (although this is actually shorthand notation for $d_{2z^2-y^2-x^2}$$d_{2z^2-y^2-x^2}$d_(2z^(2)-y^(2)-x^(2))d_{2 z^{2}-y^{2}-x^{2}} ).
结合起来（图 20.1c），结果是薛定谔方程的第五个实数解对应于传统上标记为 $d_{z^2}$$d_{z^2}$d_(z^(2))d_{z^{2}} 的轨道（尽管这实际上是 $d_{2z^2-y^2-x^2}$$d_{2z^2-y^2-x^2}$d_(2z^(2)-y^(2)-x^(2))d_{2 z^{2}-y^{2}-x^{2}} 的速记符号）。

The fact that three of the five $d$$d$dd-orbitals have their lobes directed between the Cartesian axes, while the other two are directed along these axes (Fig. 20.1b), is a key point in the understanding of bonding models for and physical properties of $d$$d$dd-block metal complexes. As a consequence of there being a distinction in their directionalities, the $d$$d$dd orbitals in the presence of ligands are split into groups of different energies, the type of splitting and the magnitude of the energy differences depending on the arrangement and nature of the ligands. Magnetic properties and electronic absorption spectra, both of which are observable properties, reflect the splitting of $d$$d$dd orbitals.
在五个 $d$$d$dd 轨道中，有三个轨道的裂片位于笛卡尔轴之间，而另外两个轨道则沿着这些轴（图 20.1b），这是理解 $d$$d$dd 块状金属配合物的成键模型和物理性质的关键点。由于它们的方向性不同，配体存在时的 $d$$d$dd 轨道会分裂成不同的能量组，分裂的类型和能量差异的大小取决于配体的排列和性质。磁性和电子吸收光谱这两种可观察到的性质都反映了 $d$$d$dd 轨道的分裂。

In Section 19.5, we stated that paramagnetism is a characteristic of some $d$$d$dd-block metal compounds. In Section 20.10 we consider magnetic properties in detail, but for now, let us simply state that magnetic data allow us to determine the number of unpaired electrons. In an isolated first row $d$$d$dd-block metal ion, the $3d$$3d$3d3 d orbitals are degenerate and the electrons occupy them according to Hund’s rules: e.g. diagram 20.1 shows the arrangement of six electrons.
在第 19.5 节中，我们指出顺磁性是某些 $d$$d$dd 块状金属化合物的特征。在第 20.10 节中，我们将详细讨论磁性，但现在让我们简单地说明，磁性数据允许我们确定未配对电子的数目。在孤立的第一行 $d$$d$dd 块状金属离子中， $3d$$3d$3d3 d 轨道是退化的，电子根据亨德规则占据这些轨道：例如，图 20.1 显示了六个电子的排列。

(20.1)

However, magnetic data for a range of octahedral $d^6$$d^6$d^(6)d^{6} complexes show that they fall into two categories: paramagnetic
然而，一系列八面体 $d^6$$d^6$d^(6)d^{6} 复合物的磁性数据显示，它们可分为两类：顺磁性

Fig. 20.1 (a) The six $\mathrm{M}-\mathrm{L}$$\mathrm{M}-\mathrm{L}$M-L\mathrm{M}-\mathrm{L} vectors of an octahedral complex ${\left[{\mathrm{ML}}_6\right]}^{n+}$${\left[{\mathrm{ML}}_6\right]}^{n+}$[ML_(6)]^(n+)\left[\mathrm{ML}_{6}\right]^{n+} can be defined to lie along the $x,y$$x,y$x,yx, y and $z$$z$zz axes. (b) The five $d$$d$dd orbitals; the $d_{z^2}$$d_{z^2}$d_(z^(2))d_{z^{2}} and $d_{x^2-y^2}$$d_{x^2-y^2}$d_(x^(2)-y^(2))d_{x^{2}-y^{2}} atomic orbitals point directly along the axes, but the $d_{xy},d_{yz}$$d_{xy},d_{yz}$d_(xy),d_(yz)d_{x y}, d_{y z} and $d_{xz}$$d_{xz}$d_(xz)d_{x z} atomic orbitals point between them. © The formation of a $d_{z^2}$$d_{z^2}$d_(z^(2))d_{z^{2}} orbital from a linear combination of $d_{z^2-y^2}$$d_{z^2-y^2}$d_(z^(2)-y^(2))d_{z^{2}-y^{2}} and $d_{z^2}-x^2$$d_{z^2}-x^2$d_(z^(2))-x^(2)d_{z^{2}}-x^{2} orbitals. The orbitals have been generated using the program Orbital Viewer [David Manthey, www.orbitals.com/orb/index.html].
图 20.1 (a) 八面体复合物 ${\left[{\mathrm{ML}}_6\right]}^{n+}$${\left[{\mathrm{ML}}_6\right]}^{n+}$[ML_(6)]^(n+)\left[\mathrm{ML}_{6}\right]^{n+} 的六个 $\mathrm{M}-\mathrm{L}$$\mathrm{M}-\mathrm{L}$M-L\mathrm{M}-\mathrm{L} 向量可以定义为沿着 $x,y$$x,y$x,yx, y 和 $z$$z$zz 轴。(b) 五个 $d$$d$dd 轨道； $d_{z^2}$$d_{z^2}$d_(z^(2))d_{z^{2}} 和 $d_{x^2-y^2}$$d_{x^2-y^2}$d_(x^(2)-y^(2))d_{x^{2}-y^{2}} 原子轨道直接沿轴线指向，但 $d_{xy},d_{yz}$$d_{xy},d_{yz}$d_(xy),d_(yz)d_{x y}, d_{y z} 和 $d_{xz}$$d_{xz}$d_(xz)d_{x z} 原子轨道指向它们之间。由 $d_{z^2-y^2}$$d_{z^2-y^2}$d_(z^(2)-y^(2))d_{z^{2}-y^{2}} 和 $d_{z^2}-x^2$$d_{z^2}-x^2$d_(z^(2))-x^(2)d_{z^{2}}-x^{2} 轨道的线性组合形成 $d_{z^2}$$d_{z^2}$d_(z^(2))d_{z^{2}} 轨道。这些轨道是使用 Orbital Viewer 程序 [David Manthey, www.orbitals.com/orb/index.html] 生成的。
or diamagnetic. The former are called high-spin complexes and correspond to those in which, despite the $d$$d$dd orbitals being split, there are still four unpaired electrons. The diamagnetic $d^6$$d^6$d^(6)d^{6} complexes are termed low-spin and correspond to those in which electrons are doubly occupying three orbitals, leaving two unoccupied. High- and low-spin complexes exist for octahedral $d^4,d^5,d^6$$d^4,d^5,d^6$d^(4),d^(5),d^(6)d^{4}, d^{5}, d^{6} and $d^7$$d^7$d^(7)d^{7} metal complexes. As shown above, for a $d^6$$d^6$d^(6)d^{6} configuration, lowspin corresponds to a diamagnetic complex and high-spin to a paramagnetic one. For $d^4,d^5$$d^4,d^5$d^(4),d^(5)d^{4}, d^{5} and $d^7$$d^7$d^(7)d^{7} configurations, both high- and low-spin complexes of a given configuration are paramagnetic, but with different numbers of unpaired electrons. Magnetic properties of $d$$d$dd-block metal complexes are described in detail in Section 20.10.
或二磁性。前者被称为高自旋络合物，对应于那些尽管 $d$$d$dd 轨道被分割，但仍有四个未成对电子的络合物。二磁性的 $d^6$$d^6$d^(6)d^{6} 复合物被称为低自旋复合物，对应于电子双双占据三个轨道，剩下两个未被占据的复合物。八面体 $d^4,d^5,d^6$$d^4,d^5,d^6$d^(4),d^(5),d^(6)d^{4}, d^{5}, d^{6} 和 $d^7$$d^7$d^(7)d^{7} 金属络合物存在高自旋和低自旋络合物。如上图所示，对于 $d^6$$d^6$d^(6)d^{6} 配置，低自旋对应于二磁性复合物，而高自旋对应于顺磁性复合物。对于 $d^4,d^5$$d^4,d^5$d^(4),d^(5)d^{4}, d^{5} 和 $d^7$$d^7$d^(7)d^{7} 构型，特定构型的高自旋和低自旋络合物都具有顺磁性，但未配对电子的数目不同。第 20.10 节将详细介绍 $d$$d$dd 块状金属配合物的磁性。

Although VB theory (see Sections 2.1, 2.2 and 5.2) in the form developed by Pauling in the 1930s is not much used now in discussing $d$$d$dd-block metal complexes, the terminology and many of the ideas have been retained and some knowledge of the theory remains useful. In Section 5.2, we described the use of $s{p}^{3}d,s{p}^3{d}^2$$s{p}^{3}d,s{p}^3{d}^2$sp^(3)d,sp^(3)d^(2)s p^{3} d, s p^{3} d^{2} and $s{p}^{2}d$$s{p}^{2}d$sp^(2)ds p^{2} d hybridization schemes in trigonal pyramidal, square-based pyramidal, octahedral and square planar molecules. Applications of these hybridization schemes to describe the bonding in $d$$d$dd-block metal complexes are given in Table 20.1. An empty hybrid orbital on the metal centre can accept a pair of electrons from a ligand to form a $\sigma$$\sigma$sigma\sigma-bond. The choice of particular $p$$p$pp or $d$$d$dd atomic orbitals may depend on the definition of the axes with respect to the molecular framework, e.g. in linear ${\mathrm{ML}}_2$${\mathrm{ML}}_2$ML_(2)\mathrm{ML}_{2}, the $\mathrm{M}-\mathrm{L}$$\mathrm{M}-\mathrm{L}$M-L\mathrm{M}-\mathrm{L} vectors are usually defined to lie along the $z$$z$zz axis. We have included the cube in Table 20.1 only to point out the required use of an $f$$f$ff orbital.
尽管鲍林在 20 世纪 30 年代提出的 VB 理论（见第 2.1、2.2 和 5.2 节）现在在讨论 $d$$d$dd 块状金属配合物时已不太常用，但其中的术语和许多观点仍被保留下来，一些理论知识仍然有用。在第 5.2 节中，我们介绍了 $s{p}^{3}d,s{p}^3{d}^2$$s{p}^{3}d,s{p}^3{d}^2$sp^(3)d,sp^(3)d^(2)s p^{3} d, s p^{3} d^{2} 和 $s{p}^{2}d$$s{p}^{2}d$sp^(2)ds p^{2} d 杂化方案在三叉金字塔、方基金字塔、八面体和方形平面分子中的应用。表 20.1 列出了这些杂化方案在描述 $d$$d$dd 块状金属配合物成键时的应用。金属中心的空杂化轨道可以接受配体的一对电子，形成 $\sigma$$\sigma$sigma\sigma 键。特定 $p$$p$pp 或 $d$$d$dd 原子轨道的选择可能取决于相对于分子框架的轴的定义，例如，在线性 ${\mathrm{ML}}_2$${\mathrm{ML}}_2$ML_(2)\mathrm{ML}_{2} 中， $\mathrm{M}-\mathrm{L}$$\mathrm{M}-\mathrm{L}$M-L\mathrm{M}-\mathrm{L} 向量通常被定义为沿 $z$$z$zz 轴。我们在表 20.1 中列出立方体，只是为了指出必须使用 $f$$f$ff 轨道。

This short section on VB theory is included for historical reasons, and we illustrate the limitations of the VB model by considering octahedral complexes of $\mathrm{Cr}($$\mathrm{Cr}($Cr(\operatorname{Cr}( III $)\left(d^3\right)$$)\left(d^3\right)$)(d^(3)))\left(d^{3}\right) and $\mathrm{Fe}($$\mathrm{Fe}\left(\right.$Fe(:}\mathrm{Fe}\left(\right. III) $\left(d^5\right)$$\left(d^5\right)$(d^(5))\left(d^{5}\right) and octahedral, tetrahedral and square planar complexes of $\mathrm{Ni}(\mathrm{II})\left(d^8\right)$$\mathrm{Ni}(\mathrm{II})\left(d^8\right)$Ni(II)(d^(8))\mathrm{Ni}(\mathrm{II})\left(d^{8}\right). The atomic orbitals required
我们通过考虑 $\mathrm{Cr}($$\mathrm{Cr}($Cr(\operatorname{Cr}( III $)\left(d^3\right)$$)\left(d^3\right)$)(d^(3)))\left(d^{3}\right) 和 $\mathrm{Fe}($$\mathrm{Fe}\left(\right.$Fe(:}\mathrm{Fe}\left(\right. III) $\left(d^5\right)$$\left(d^5\right)$(d^(5))\left(d^{5}\right) 的八面体络合物以及 $\mathrm{Ni}(\mathrm{II})\left(d^8\right)$$\mathrm{Ni}(\mathrm{II})\left(d^8\right)$Ni(II)(d^(8))\mathrm{Ni}(\mathrm{II})\left(d^{8}\right) 的八面体、四面体和方形平面络合物，来说明 VB 模型的局限性。所需的原子轨道

Table 20.1 Hybridization schemes for the $\sigma$$\sigma$sigma\sigma-bonding frameworks of different geometrical configurations of ligand donor atoms.
表 20.1 配体供体原子不同几何构型的 $\sigma$$\sigma$sigma\sigma 键合框架的杂化方案。

for hybridization in an octahedral complex of a first row $d$$d$dd-block metal are the $3d_{z^2},3d_{x^2-y^2},4s,4p_x,4p_y$$3d_{z^2},3d_{x^2-y^2},4s,4p_x,4p_y$3d_(z^(2)),3d_(x^(2)-y^(2)),4s,4p_(x),4p_(y)3 d_{z^{2}}, 3 d_{x^{2}-y^{2}}, 4 s, 4 p_{x}, 4 p_{y} and $4p_z$$4p_z$4p_(z)4 p_{z} (Table 20.1). These orbitals must be unoccupied so as to be available to accept six pairs of electrons from the ligands. The ${\mathrm{Cr}}^{3+}\left(d^3\right)$${\mathrm{Cr}}^{3+}\left(d^3\right)$Cr^(3+)(d^(3))\mathrm{Cr}^{3+}\left(d^{3}\right) ion has three unpaired electrons and these are accommodated in the $3d_{xy},3d_{xz}$$3d_{xy},3d_{xz}$3d_(xy),3d_(xz)3 d_{x y}, 3 d_{x z} and $3d_{yz}$$3d_{yz}$3d_(yz)3 d_{y z} orbitals:
第一行 $d$$d$dd 块状金属的八面体配合物中的杂化轨道是 $3d_{z^2},3d_{x^2-y^2},4s,4p_x,4p_y$$3d_{z^2},3d_{x^2-y^2},4s,4p_x,4p_y$3d_(z^(2)),3d_(x^(2)-y^(2)),4s,4p_(x),4p_(y)3 d_{z^{2}}, 3 d_{x^{2}-y^{2}}, 4 s, 4 p_{x}, 4 p_{y} 和 $4p_z$$4p_z$4p_(z)4 p_{z} （表 20.1）。这些轨道必须是空闲的，以便从配体中接受六对电子。 ${\mathrm{Cr}}^{3+}\left(d^3\right)$${\mathrm{Cr}}^{3+}\left(d^3\right)$Cr^(3+)(d^(3))\mathrm{Cr}^{3+}\left(d^{3}\right) 离子有三个未成对电子，这些电子被容纳在 $3d_{xy},3d_{xz}$$3d_{xy},3d_{xz}$3d_(xy),3d_(xz)3 d_{x y}, 3 d_{x z} 和 $3d_{yz}$$3d_{yz}$3d_(yz)3 d_{y z} 轨道中：

With the electrons from the six ligands included and a hybridization scheme applied for an octahedral complex, the diagram becomes:
将六个配体的电子包含在内，并采用八面体络合物的杂化方案，图表就变成了这样：

This diagram is appropriate for all octahedral $\mathrm{Cr}(\mathrm{III})$$\mathrm{Cr}(\mathrm{III})$Cr(III)\mathrm{Cr}(\mathrm{III}) complexes because the three $3d$$3d$3d3 d electrons always singly occupy different orbitals.
此图适用于所有八面体 $\mathrm{Cr}(\mathrm{III})$$\mathrm{Cr}(\mathrm{III})$Cr(III)\mathrm{Cr}(\mathrm{III}) 复合物，因为三个 $3d$$3d$3d3 d 电子总是单个占据不同的轨道。

For octahedral $\mathrm{Fe}(\mathrm{III})$$\mathrm{Fe}(\mathrm{III})$Fe(III)\mathrm{Fe}(\mathrm{III}) complexes $\left(d^5\right)$$\left(d^5\right)$(d^(5))\left(d^{5}\right), we must account for the existence of both high- and low-spin complexes. The electronic configuration of the free ${\mathrm{Fe}}^{3+}$${\mathrm{Fe}}^{3+}$Fe^(3+)\mathrm{Fe}^{3+} ion is:
对于八面体 $\mathrm{Fe}(\mathrm{III})$$\mathrm{Fe}(\mathrm{III})$Fe(III)\mathrm{Fe}(\mathrm{III}) 复合物 $\left(d^5\right)$$\left(d^5\right)$(d^(5))\left(d^{5}\right) ，我们必须考虑到高自旋和低自旋复合物的存在。自由 ${\mathrm{Fe}}^{3+}$${\mathrm{Fe}}^{3+}$Fe^(3+)\mathrm{Fe}^{3+} 离子的电子构型为：

For a low-spin octahedral complex such as ${[\mathrm{Fe}(\mathrm{CN}{)}_6]}^{3-}$${\left[\mathrm{Fe}(\mathrm{CN}{)}_6\right]}^{3-}$[Fe(CN)_(6)]^(3-)\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}, we can represent the electronic configuration by means of the following diagram where the electrons shown in red are donated by the ligands:
对于 ${[\mathrm{Fe}(\mathrm{CN}{)}_6]}^{3-}$${\left[\mathrm{Fe}(\mathrm{CN}{)}_6\right]}^{3-}$[Fe(CN)_(6)]^(3-)\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-} 这样的低自旋八面体复合物，我们可以用下图来表示其电子构型，其中红色显示的电子由配体提供：

For a high-spin octahedral complex such as ${\left[{\mathrm{FeF}}_6\right]}^{3-}$${\left[{\mathrm{FeF}}_6\right]}^{3-}$[FeF_(6)]^(3-)\left[\mathrm{FeF}_{6}\right]^{3-}, the five $3d$$3d$3d3 d electrons occupy the five $3d$$3d$3d3 d atomic orbitals (as in the free ion shown above) and the two $d$$d$dd orbitals required for the $s{p}^3{d}^2$$s{p}^3{d}^2$sp^(3)d^(2)s p^{3} d^{2} hybridization scheme must come from the $4d$$4d$4d4 d set. With the ligand electrons included, valence bond theory describes the bonding as follows, leaving three empty $4d$$4d$4d4 d atomic orbitals (not shown):
对于 ${\left[{\mathrm{FeF}}_6\right]}^{3-}$${\left[{\mathrm{FeF}}_6\right]}^{3-}$[FeF_(6)]^(3-)\left[\mathrm{FeF}_{6}\right]^{3-} 这样的高自旋八面体配合物，五个 $3d$$3d$3d3 d 电子占据五个 $3d$$3d$3d3 d 原子轨道（如上图所示的自由离子），而 $s{p}^3{d}^2$$s{p}^3{d}^2$sp^(3)d^(2)s p^{3} d^{2} 杂化方案所需的两个 $d$$d$dd 轨道必须来自 $4d$$4d$4d4 d 集合。在包含配体电子的情况下，价键理论对成键进行了如下描述，留下了三个空的 $4d$$4d$4d4 d 原子轨道（未显示）：

However, this scheme is unrealistic because the $4d$$4d$4d4 d orbitals are at a significantly higher energy than the $3d$$3d$3d3 d atomic orbitals.
然而，这种方案并不现实，因为 $4d$$4d$4d4 d 轨道的能量远远高于 $3d$$3d$3d3 d 原子轨道。

Crystal field theory is an electrostatic model which predicts that the $d$$d$dd orbitals in a metal complex are not degenerate. The pattern of splitting of the $d$$d$dd orbitals depends on the crystal field, this being determined by the arrangement and type of ligands.
晶体场理论是一种静电模型，它预测金属复合物中的 $d$$d$dd 轨道不是退化的。 $d$$d$dd 轨道的分裂模式取决于晶体场，这是由配体的排列和类型决定的。

Fig. 20.2 The changes in the energies of the electrons occupying the $3d$$3d$3d3 d orbitals of a first row ${\mathrm{M}}^{n+}$${\mathrm{M}}^{n+}$M^(n+)\mathrm{M}^{n+} ion when the latter is in an octahedral crystal field. The energy changes are shown in terms of the orbital energies. Similar diagrams can be drawn for second ( $4d$$4d$4d4 d ) and third ( $5d$$5d$5d5 d ) row metal ions.
图 20.2 当第一行 ${\mathrm{M}}^{n+}$${\mathrm{M}}^{n+}$M^(n+)\mathrm{M}^{n+} 离子处于八面体晶场中时，占据其 $3d$$3d$3d3 d 轨道的电子的能量变化。能量变化以轨道能量表示。第二排（ $4d$$4d$4d4 d ）和第三排（ $5d$$5d$5d5 d ）金属离子也可以绘制类似的图表。

The two sets of $d$$d$dd orbitals in an octahedral field are labelled $e_g$$e_g$e_(g)e_{g} and $t_{2g}$$t_{2g}$t_(2g)t_{2 g} (Fig. 20.3). In a tetrahedral field (Fig. 20.8), the labels become $e$$e$ee and $t_2$$t_2$t_(2)t_{2}. The symbols $t$$t$tt and $e$$e$ee refer to the degeneracy of the level:
八面体场中的两组 $d$$d$dd 轨道分别标为 $e_g$$e_g$e_(g)e_{g} 和 $t_{2g}$$t_{2g}$t_(2g)t_{2 g} （图 20.3）。在四面体场中（图 20.8），标记变为 $e$$e$ee 和 $t_2$$t_2$t_(2)t_{2} 。符号 $t$$t$tt 和 $e$$e$ee 指的是水平的变性：

The $u$$u$uu and $g$$g$gg labels are applicable only if the system possesses a centre of symmetry (centre of inversion) and thus are used for the octahedral field, but not for the tetrahedral one:
$u$$u$uu 和 $g$$g$gg 标签仅适用于具有对称中心（反转中心）的系统，因此用于八面体场，而不适用于四面体场：

Octahedron has a centre of symmetry
八面体有一个对称中心

Tetrahedron has no centre of symmetry
四面体没有对称中心
For more on the origins of symmetry labels: see Chapter 5.
关于对称标签的起源：请参阅第 5 章。
From the $O_{\mathrm{h}}$$O_{\mathrm{h}}$O_(h)O_{\mathrm{h}} character table (Appendix 3), it can be deduced (see Chapter 5) that the $d_{z^2}$$d_{z^2}$d_(z^(2))d_{z^{2}} and $d_{x^2-y^2}$$d_{x^2-y^2}$d_(x^(2)-y^(2))d_{x^{2}-y^{2}} orbitals have $e_g$$e_g$e_(g)e_{g} symmetry, while the $d_{xy},d_{yz}$$d_{xy},d_{yz}$d_(xy),d_(yz)d_{x y}, d_{y z} and $d_{xz}$$d_{xz}$d_(xz)d_{x z} orbitals possess $t_{2g}$$t_{2g}$t_(2g)t_{2 g} symmetry (Fig. 20.3). The energy separation between them is ${\mathrm{\Delta }}_{\text{oct}}$${\mathrm{\Delta }}_{\text{oct }}$Delta_("oct ")\Delta_{\text {oct }} (‘delta oct’) or $10Dq$$10Dq$10 Dq10 D q. The overall stabilization of the $t_{2g}$$t_{2g}$t_(2g)t_{2 g} orbitals equals the overall destabilization of the $e_g$$e_g$e_(g)e_{g} set. Thus, the two orbitals in the $e_g$$e_g$e_(g)e_{g} set are raised by $0.6{\mathrm{\Delta }}_{\text{oct}}$$0.6{\mathrm{\Delta }}_{\text{oct }}$0.6Delta_("oct ")0.6 \Delta_{\text {oct }} with respect to the barycentre while the three in the $t_{2g}$$t_{2g}$t_(2g)t_{2 g} set are lowered by $0.4{\mathrm{\Delta }}_{\text{oct}}$$0.4{\mathrm{\Delta }}_{\text{oct }}$0.4Delta_("oct ")0.4 \Delta_{\text {oct }}. Figure 20.3 also shows these energy differences in terms of 10 Dq . Both ${\mathrm{\Delta }}_{\text{oct}}$${\mathrm{\Delta }}_{\text{oct }}$Delta_("oct ")\Delta_{\text {oct }} and $10Dq$$10Dq$10 Dq10 D q notations are in common use, but we use ${\mathrm{\Delta }}_{\text{oct}}$${\mathrm{\Delta }}_{\text{oct }}$Delta_("oct ")\Delta_{\text {oct }} in this book. ${}^{†}$${}^{†}$^(†){ }^{\dagger} The stabilization and
从 $O_{\mathrm{h}}$$O_{\mathrm{h}}$O_(h)O_{\mathrm{h}} 字符表（附录 3）可以推断出（见第 5 章）， $d_{z^2}$$d_{z^2}$d_(z^(2))d_{z^{2}} 和 $d_{x^2-y^2}$$d_{x^2-y^2}$d_(x^(2)-y^(2))d_{x^{2}-y^{2}} 轨道具有 $e_g$$e_g$e_(g)e_{g} 对称性，而 $d_{xy},d_{yz}$$d_{xy},d_{yz}$d_(xy),d_(yz)d_{x y}, d_{y z} 和 $d_{xz}$$d_{xz}$d_(xz)d_{x z} 轨道具有 $t_{2g}$$t_{2g}$t_(2g)t_{2 g} 对称性（图 20.3）。它们之间的能量间隔为 ${\mathrm{\Delta }}_{\text{oct}}$${\mathrm{\Delta }}_{\text{oct }}$Delta_("oct ")\Delta_{\text {oct }} （"delta oct"）或 $10Dq$$10Dq$10 Dq10 D q 。 $t_{2g}$$t_{2g}$t_(2g)t_{2 g} 轨道的总体稳定等于 $e_g$$e_g$e_(g)e_{g} 轨道组的总体失稳。因此， $e_g$$e_g$e_(g)e_{g} 组中的两个轨道相对于原心升高了 $0.6{\mathrm{\Delta }}_{\text{oct}}$$0.6{\mathrm{\Delta }}_{\text{oct }}$0.6Delta_("oct ")0.6 \Delta_{\text {oct }} ，而 $t_{2g}$$t_{2g}$t_(2g)t_{2 g} 组中的三个轨道相对于原心降低了 $0.4{\mathrm{\Delta }}_{\text{oct}}$$0.4{\mathrm{\Delta }}_{\text{oct }}$0.4Delta_("oct ")0.4 \Delta_{\text {oct }} 。图 20.3 还以 10 Dq 的形式显示了这些能量差异。 ${\mathrm{\Delta }}_{\text{oct}}$${\mathrm{\Delta }}_{\text{oct }}$Delta_("oct ")\Delta_{\text {oct }} 和 $10Dq$$10Dq$10 Dq10 D q 都是常用符号，但我们在本书中使用 ${\mathrm{\Delta }}_{\text{oct}}$${\mathrm{\Delta }}_{\text{oct }}$Delta_("oct ")\Delta_{\text {oct }} 。 ${}^{†}$${}^{†}$^(†){ }^{\dagger} 稳定和