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
20.1 Introduction 20.1 导言
In this chapter, we discuss complexes of the 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 dd-block metals, for which theories of bonding are most successful. The bonding in 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 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 dd 块状金属上,对于这些金属,成键理论是最成功的。 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 dd-block chemistry are the 3d,4d3 d, 4 d or 5d5 d orbitals for the first, second or third row dd-block metals, respectively. We introduced dd-orbitals in Section 1.6, and showed that a dd-orbital is characterized by having a value of the quantum number l=2l=2. The conventional representation of a set of five degenerate dd-orbitals is shown in Fig. 20.1b. ^(†){ }^{\dagger} The lobes of the d_(yz),d_(xy)d_{y z}, d_{x y} and 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}} orbital is related to d_(xy)d_{x y}, but the lobes of the d_(x^(2)-y^(2))d_{x^{2}-y^{2}} orbital point along (rather than between) the xx and 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}} orbital, i.e. the d_(z^(2)-y^(2))d_{z^{2}-y^{2}} and d_(z^(2)-x^(2))d_{z^{2}-x^{2}} orbitals (Fig. 20.1c). However, this would give a total of six dd-orbitals. For l=2l=2, there are only five real solutions to the Schrödinger equation ( 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}} and d_(z^(2)-y^(2))d_{z^{2}-y^{2}} orbitals. This means that the two orbitals 讨论 dd 块状化学的基础是第一、第二或第三行 dd 块状金属的 3d,4d3 d, 4 d 或 5d5 d 轨道。我们在第 1.6 节中介绍了 dd 轨道,并说明 dd 轨道的特征是具有量子数 l=2l=2 值。图 20.1b 显示了一组五个退化 dd 轨道的常规表示方法。 ^(†){ }^{\dagger}d_(yz),d_(xy)d_{y z}, d_{x y} 和 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}} 轨道与 d_(xy)d_{x y} 有关,但 d_(x^(2)-y^(2))d_{x^{2}-y^{2}} 轨道的裂片沿 xx 和 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}} 轨道相关的原子轨道,即 d_(z^(2)-y^(2))d_{z^{2}-y^{2}} 和 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 dd 轨道。对于 l=2l=2 ,薛定谔方程只有五个实解 ( 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}} 和 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}} orbital (although this is actually shorthand notation for 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}} 的轨道(尽管这实际上是 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 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 dd-block metal complexes. As a consequence of there being a distinction in their directionalities, the 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 dd orbitals. 在五个 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 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 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 dd 轨道的分裂。
High- and low-spin states 高自旋和低自旋态
In Section 19.5, we stated that paramagnetism is a characteristic of some 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 dd-block metal ion, the 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 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 dd 块状金属离子中, 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。
However, magnetic data for a range of octahedral 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} 复合物的磁性数据显示,它们可分为两类:顺磁性
20.2 Bonding in d-block metal complexes: valence bond theory 20.2 d-块金属配合物中的键合:价键理论
Hybridization schemes 杂交方案
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 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 sp^(3)d,sp^(3)d^(2)s p^{3} d, s p^{3} d^{2} and 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 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-bond. The choice of particular pp or dd atomic orbitals may depend on the definition of the axes with respect to the molecular framework, e.g. in linear ML_(2)\mathrm{ML}_{2}, the M-L\mathrm{M}-\mathrm{L} vectors are usually defined to lie along the zz axis. We have included the cube in Table 20.1 only to point out the required use of an 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 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 sp^(3)d,sp^(3)d^(2)s p^{3} d, s p^{3} d^{2} 和 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 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 键。特定 pp 或 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 ML_(2)\mathrm{ML}_{2} 中, M-L\mathrm{M}-\mathrm{L} 向量通常被定义为沿 zz 轴。我们在表 20.1 中列出立方体,只是为了指出必须使用 ff 轨道。
The limitations of VB theory VB 理论的局限性
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 Cr(\operatorname{Cr}( III )(d^(3)))\left(d^{3}\right) and Fe(:}\mathrm{Fe}\left(\right. III) (d^(5))\left(d^{5}\right) and octahedral, tetrahedral and square planar complexes of Ni(II)(d^(8))\mathrm{Ni}(\mathrm{II})\left(d^{8}\right). The atomic orbitals required 我们通过考虑 Cr(\operatorname{Cr}( III )(d^(3)))\left(d^{3}\right) 和 Fe(:}\mathrm{Fe}\left(\right. III) (d^(5))\left(d^{5}\right) 的八面体络合物以及 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-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 键合框架的杂化方案。
for hybridization in an octahedral complex of a first row dd-block metal are the 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)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 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)3 d_{x y}, 3 d_{x z} and 3d_(yz)3 d_{y z} orbitals: 第一行 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)3 d_{z^{2}}, 3 d_{x^{2}-y^{2}}, 4 s, 4 p_{x}, 4 p_{y} 和 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。 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)3 d_{x y}, 3 d_{x z} 和 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 Cr(III)\mathrm{Cr}(\mathrm{III}) complexes because the three 3d3 d electrons always singly occupy different orbitals. 此图适用于所有八面体 Cr(III)\mathrm{Cr}(\mathrm{III}) 复合物,因为三个 3d3 d 电子总是单个占据不同的轨道。
For octahedral Fe(III)\mathrm{Fe}(\mathrm{III}) complexes (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 Fe^(3+)\mathrm{Fe}^{3+} ion is: 对于八面体 Fe(III)\mathrm{Fe}(\mathrm{III}) 复合物 (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 Fe^(3+)\mathrm{Fe}^{3+} 离子的电子构型为:
For a low-spin octahedral complex such as [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 [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 [FeF_(6)]^(3-)\left[\mathrm{FeF}_{6}\right]^{3-}, the five 3d3 d electrons occupy the five 3d3 d atomic orbitals (as in the free ion shown above) and the two dd orbitals required for the sp^(3)d^(2)s p^{3} d^{2} hybridization scheme must come from the 4d4 d set. With the ligand electrons included, valence bond theory describes the bonding as follows, leaving three empty 4d4 d atomic orbitals (not shown): 对于 [FeF_(6)]^(3-)\left[\mathrm{FeF}_{6}\right]^{3-} 这样的高自旋八面体配合物,五个 3d3 d 电子占据五个 3d3 d 原子轨道(如上图所示的自由离子),而 sp^(3)d^(2)s p^{3} d^{2} 杂化方案所需的两个 dd 轨道必须来自 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 4d4 d 原子轨道(未显示):
However, this scheme is unrealistic because the 4d4 d orbitals are at a significantly higher energy than the 3d3 d atomic orbitals. 然而,这种方案并不现实,因为 4d4 d 轨道的能量远远高于 3d3 d 原子轨道。
Crystal field theory is an electrostatic model which predicts that the dd orbitals in a metal complex are not degenerate. The pattern of splitting of the 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 dd 轨道不是退化的。 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 3d3 d orbitals of a first row 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 ( 4d4 d ) and third ( 5d5 d ) row metal ions. 图 20.2 当第一行 M^(n+)\mathrm{M}^{n+} 离子处于八面体晶场中时,占据其 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( 4d4 d )和第三排( 5d5 d )金属离子也可以绘制类似的图表。
THEORY 理论
Box 20.1 A reminder about symmetry labels 方框 20.1 关于对称标签的提醒
The two sets of dd orbitals in an octahedral field are labelled e_(g)e_{g} and t_(2g)t_{2 g} (Fig. 20.3). In a tetrahedral field (Fig. 20.8), the labels become ee and t_(2)t_{2}. The symbols tt and ee refer to the degeneracy of the level: 八面体场中的两组 dd 轨道分别标为 e_(g)e_{g} 和 t_(2g)t_{2 g} (图 20.3)。在四面体场中(图 20.8),标记变为 ee 和 t_(2)t_{2} 。符号 tt 和 ee 指的是水平的变性:
a triply degenerate level is labelled tt; 一个三重退化水平被标记为 tt ;
a doubly degenerate level is labelled ee. 一个双重退化水平被标记为 ee 。
The uu and 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: uu 和 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_(h)O_{\mathrm{h}} character table (Appendix 3), it can be deduced (see Chapter 5) that the d_(z^(2))d_{z^{2}} and d_(x^(2)-y^(2))d_{x^{2}-y^{2}} orbitals have e_(g)e_{g} symmetry, while the d_(xy),d_(yz)d_{x y}, d_{y z} and d_(xz)d_{x z} orbitals possess t_(2g)t_{2 g} symmetry (Fig. 20.3). The energy separation between them is Delta_("oct ")\Delta_{\text {oct }} (‘delta oct’) or 10 Dq10 D q. The overall stabilization of the t_(2g)t_{2 g} orbitals equals the overall destabilization of the e_(g)e_{g} set. Thus, the two orbitals in the e_(g)e_{g} set are raised by 0.6Delta_("oct ")0.6 \Delta_{\text {oct }} with respect to the barycentre while the three in the t_(2g)t_{2 g} set are lowered by 0.4Delta_("oct ")0.4 \Delta_{\text {oct }}. Figure 20.3 also shows these energy differences in terms of 10 Dq . Both Delta_("oct ")\Delta_{\text {oct }} and 10 Dq10 D q notations are in common use, but we use Delta_("oct ")\Delta_{\text {oct }} in this book. ^(†){ }^{\dagger} The stabilization and 从 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}} 和 d_(x^(2)-y^(2))d_{x^{2}-y^{2}} 轨道具有 e_(g)e_{g} 对称性,而 d_(xy),d_(yz)d_{x y}, d_{y z} 和 d_(xz)d_{x z} 轨道具有 t_(2g)t_{2 g} 对称性(图 20.3)。它们之间的能量间隔为 Delta_("oct ")\Delta_{\text {oct }} ("delta oct")或 10 Dq10 D q 。 t_(2g)t_{2 g} 轨道的总体稳定等于 e_(g)e_{g} 轨道组的总体失稳。因此, e_(g)e_{g} 组中的两个轨道相对于原心升高了 0.6Delta_("oct ")0.6 \Delta_{\text {oct }} ,而 t_(2g)t_{2 g} 组中的三个轨道相对于原心降低了 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。 Delta_("oct ")\Delta_{\text {oct }} 和 10 Dq10 D q 都是常用符号,但我们在本书中使用 Delta_("oct ")\Delta_{\text {oct }} 。 ^(†){ }^{\dagger} 稳定和
Fig. 20.3 Splitting of the dd orbitals in an octahedral crystal field, with the energy changes measured with respect to the barycentre, the energy level shown by the hashed line. 图 20.3 八面体晶场中 dd 轨道的分裂,以及相对于极心测量到的能量变化,方格线表示能级。
destabilization of the t_(2g)t_{2 g} and e_(g)e_{g} sets, respectively, are given in terms of Delta_("oct ")\Delta_{\text {oct }}. The magnitude of Delta_("oct ")\Delta_{\text {oct }} is determined by the strength of the crystal field, the two extremes being called weak field and strong field (eq. 20.1). t_(2g)t_{2 g} 和 e_(g)e_{g} 集的失稳分别以 Delta_("oct ")\Delta_{\text {oct }} 表示。 Delta_("oct ")\Delta_{\text {oct }} 的大小取决于晶体场的强度,两个极端分别称为弱场和强场(式 20.1)。 Delta_("oct ")(\Delta_{\text {oct }}( weak field ) < Delta_("oct ")()<\Delta_{\text {oct }}( strong field )) Delta_("oct ")(\Delta_{\text {oct }}( 弱磁场 ) < Delta_("oct ")()<\Delta_{\text {oct }}( 强磁场 ))
It is a merit of crystal field theory that, in principle at least, values of Delta_("oct ")\Delta_{\text {oct }} can be evaluated from electronic absorption spectroscopic data (see Section 20.7). Consider the d^(1)d^{1} complex [Ti(OH_(2))_(6)]^(3+)\left[\mathrm{Ti}\left(\mathrm{OH}_{2}\right)_{6}\right]^{3+}, for which the ground state is represented by diagram 20.2 or the notation t_(2g)^(1)e_(g)^(0)t_{2 g}{ }^{1} e_{g}{ }^{0}. 晶体场理论的一个优点是,至少在原则上, Delta_("oct ")\Delta_{\text {oct }} 的值可以通过电子吸收光谱数据来评估(见第 20.7 节)。考虑 d^(1)d^{1} 复合物 [Ti(OH_(2))_(6)]^(3+)\left[\mathrm{Ti}\left(\mathrm{OH}_{2}\right)_{6}\right]^{3+} ,其基态用图 20.2 或符号 t_(2g)^(1)e_(g)^(0)t_{2 g}{ }^{1} e_{g}{ }^{0} 表示。
(20.2)
Factors governing the magnitude of Delta_("oct ")\Delta_{\text {oct }} (Table 20.2) are the identity and oxidation state of the metal ion and the nature of the ligands. We shall see later that Delta\Delta parameters 影响 Delta_("oct ")\Delta_{\text {oct }} 大小的因素(表 20.2)是金属离子的特性和氧化态以及配体的性质。我们将在后面看到 Delta\Delta 参数
Fig. 20.4 The electronic absorption spectrum of [Ti(OH_(2))_(6)]^(3+)\left[\mathrm{Ti}\left(\mathrm{OH}_{2}\right)_{6}\right]^{3+} in aqueous solution. 图 20.4 [Ti(OH_(2))_(6)]^(3+)\left[\mathrm{Ti}\left(\mathrm{OH}_{2}\right)_{6}\right]^{3+} 在水溶液中的电子吸收光谱。
Table 20.2 Values of Delta_("oct ")\Delta_{\text {oct }} for some dd-block metal complexes. 表 20.2 某些 dd 块状金属络合物的 Delta_("oct ")\Delta_{\text {oct }} 值。
are also defined for other ligand arrangements (e.g. Delta_("tet ")\Delta_{\text {tet }} ). For octahedral complexes, Delta_("oct ")\Delta_{\text {oct }} increases along the following spectrochemical series of ligands. The [NCS]^(-)[\mathrm{NCS}]^{-}ion may coordinate through the N - or SS-donor (distinguished in red below) and accordingly, it has two positions in the series: 也适用于其他配体排列(例如 Delta_("tet ")\Delta_{\text {tet }} )。对于八面体配合物, Delta_("oct ")\Delta_{\text {oct }} 会沿着以下配体光谱化学系列增加。 [NCS]^(-)[\mathrm{NCS}]^{-} 离子可通过 N - 或 SS 供体(下文以红色区分)进行配位,因此在该系列中有两个位置:
The spectrochemical series is reasonably general. Ligands with the same donor atoms are close together in the series. If we consider octahedral complexes of dd-block metal ions, a number of points arise which can be illustrated by the following examples: 光谱化学系列具有一定的普遍性。在该系列中,具有相同供体原子的配体相距很近。如果我们考虑 dd 块状金属离子的八面体配合物,就会出现一些问题,下面的例子可以说明这一点:
the complexes of Cr (III) listed in Table 20.2 illustrate the effects of different ligand field strengths for a given M^(n+)\mathrm{M}^{n+} ion; 表 20.2 中列出的 Cr (III) 复合物说明了不同配体场强对给定 M^(n+)\mathrm{M}^{n+} 离子的影响;
Fig. 20.5 The trend in values of Delta_("oct ")\Delta_{\text {oct }} for the complexes [M(NH_(3))_(6)]^(3+)\left[\mathrm{M}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+} where M=Co\mathrm{M}=\mathrm{Co}, Rh, Ir. 图 20.5 复合物 [M(NH_(3))_(6)]^(3+)\left[\mathrm{M}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+} 的 Delta_("oct ")\Delta_{\text {oct }} 值变化趋势,其中 M=Co\mathrm{M}=\mathrm{Co} , Rh, Ir.
the complexes of Fe (II) and Fe(III)\mathrm{Fe}(\mathrm{III}) in Table 20.2 illustrate that for a given ligand and a given metal, Delta_("oct ")\Delta_{\text {oct }} increases with increasing oxidation state; 表 20.2 中的 Fe (II) 复合物和 Fe(III)\mathrm{Fe}(\mathrm{III}) 表明,对于给定配体和给定金属, Delta_("oct ")\Delta_{\text {oct }} 随着氧化态的增加而增加;
where analogous complexes exist for a series of M^(n+)\mathrm{M}^{n+} metals ions (constant nn ) in a triad, Delta_("oct ")\Delta_{\text {oct }} increases significantly down the triad (e.g. Fig. 20.5); 在三元组中存在一系列 M^(n+)\mathrm{M}^{n+} 金属离子(常数 nn )的类似配合物时, Delta_("oct ")\Delta_{\text {oct }} 会沿着三元组向下显著增加(如图 20.5);
for a given ligand and a given oxidation state, Delta_("oct ")\Delta_{\text {oct }} varies irregularly across the first row of the dd-block, e.g. over the range 8000 to 14000cm^(-1)14000 \mathrm{~cm}^{-1} for the [M(OH_(2))_(6)]^(2+)\left[\mathrm{M}\left(\mathrm{OH}_{2}\right)_{6}\right]^{2+} ions. 对于给定的配体和给定的氧化态, Delta_("oct ")\Delta_{\text {oct }} 在 dd 块的第一行不规则变化,例如,对于 [M(OH_(2))_(6)]^(2+)\left[\mathrm{M}\left(\mathrm{OH}_{2}\right)_{6}\right]^{2+} 离子,在 8000 到 14000cm^(-1)14000 \mathrm{~cm}^{-1} 的范围内变化。
Trends in values of Delta_("oct ")\Delta_{\text {oct }} lead to the conclusion that metal ions can be placed in a spectrochemical series which is independent of the ligands: 从 Delta_("oct ")\Delta_{\text {oct }} 值的变化趋势可以得出这样的结论:金属离子可以被归入一个与配体无关的光谱化学系列:
rarr_("" increasing field strength "")^("{:[Mn(II) < Ni(II) < Co(II) < Fe(III) < Cr(III) < Co(III)],[ < Ru(" III ") < Mo(III) < Rh(" III ") < Pd(II) < Ir(" III ") < Pt(" IV ")]:}")\xrightarrow[\text { increasing field strength }]{\begin{array}{l}
\operatorname{Mn}(\mathrm{II})<\mathrm{Ni}(\mathrm{II})<\mathrm{Co}(\mathrm{II})<\mathrm{Fe}(\mathrm{III})<\mathrm{Cr}(\mathrm{III})<\mathrm{Co}(\mathrm{III}) \\
<\mathrm{Ru}(\text { III })<\mathrm{Mo}(\mathrm{III})<\operatorname{Rh}(\text { III })<\operatorname{Pd}(\mathrm{II})<\operatorname{Ir}(\text { III })<\operatorname{Pt}(\text { IV })
\end{array}}
We now consider the effects of different numbers of electrons occupying the dd orbitals in an octahedral crystal field. For a d^(1)d^{1} system, the ground state corresponds to the configuration t_(2g)^(1)t_{2 g}{ }^{1} (20.2). With respect to the barycentre, there is a stabilization energy of -0.4Delta_("oct ")-0.4 \Delta_{\text {oct }} (Fig. 20.3). This is the so-called crystal field stabilization energy, CFSE.^(†)C F S E .^{\dagger} For a d^(2)d^{2} ion, the ground state configuration is t_(2g)^(2)t_{2 g}{ }^{2} and the CFSE =-0.8Delta_("oct ")=-0.8 \Delta_{\text {oct }} (eq. 20.2). A d^(3)d^{3} ion (t_(2g)^(3))\left(t_{2 g}{ }^{3}\right) has a CFSE =-1.2Delta_("oct ")=-1.2 \Delta_{\text {oct }}. 现在我们来考虑八面体晶场中占据 dd 轨道的不同电子数的影响。对于 d^(1)d^{1} 系统,基态对应于构型 t_(2g)^(1)t_{2 g}{ }^{1} (20.2)。相对于重心,存在 -0.4Delta_("oct ")-0.4 \Delta_{\text {oct }} 的稳定能(图 20.3)。这就是所谓的晶体场稳定能, CFSE.^(†)C F S E .^{\dagger} 对于 d^(2)d^{2} 离子,基态构型为 t_(2g)^(2)t_{2 g}{ }^{2} ,CFSE 为 =-0.8Delta_("oct ")=-0.8 \Delta_{\text {oct }} (式 20.2)。 d^(3)d^{3} 离子 (t_(2g)^(3))\left(t_{2 g}{ }^{3}\right) 的 CFSE 为 =-1.2Delta_("oct ")=-1.2 \Delta_{\text {oct }} 。
CFSE =-(2xx0.4)Delta_("oct ")=-0.8Delta_("oct ")=-(2 \times 0.4) \Delta_{\text {oct }}=-0.8 \Delta_{\text {oct }}
(20.3)
(20.4)
For a ground state d^(4)d^{4} ion, two arrangements are possible: the four electrons may occupy the t_(2g)t_{2 g} set with the configuration t_(2g)^(4)t_{2 g}{ }^{4} (20.3), or may singly occupy four dd orbitals, t_(2g)^(3)e_(g)^(1)t_{2 g}{ }^{3} e_{g}{ }^{1} (20.4). Configuration 20.3 corresponds to a low-spin arrangement, and 20.4 to a high-spin case. The preferred configuration is that with the lower energy and depends on whether it is energetically preferable to pair the fourth electron or promote it to the e_(g)e_{g} level. Two terms contribute to the electron-pairing energy, PP, which is the energy required to transform two electrons with parallel spin in different degenerate orbitals into spin-paired electrons in the same orbital: 对于基态 d^(4)d^{4} 离子,有两种可能的排列方式:四个电子可以占据配置为 t_(2g)^(4)t_{2 g}{ }^{4} 的 t_(2g)t_{2 g} 集 (20.3),也可以单独占据四个 dd 轨道,即 t_(2g)^(3)e_(g)^(1)t_{2 g}{ }^{3} e_{g}{ }^{1} (20.4)。配置 20.3 相当于低自旋排列,配置 20.4 相当于高自旋排列。优选的构型是能量较低的构型,取决于在能量上是将第四个电子配对还是将其提升到 e_(g)e_{g} 电平。电子配对能量 PP 有两个项,即把不同退化轨道中两个自旋平行的电子转变为同一轨道中自旋配对的电子所需的能量:
the loss in the exchange energy (see Box 1.7) which occurs upon pairing the electrons; 电子配对时产生的交换能损失(见方框 1.7);
the coulombic repulsion between the spin-paired electrons. 自旋配对电子之间的库仑斥力。
For a given d^(n)d^{n} configuration, the CFSE is the difference in energy between the dd electrons in an octahedral crystal field and the dd electrons in a spherical crystal field (see Fig. 20.2). To exemplify this, consider a d^(4)d^{4} configuration. In a spherical crystal field, the dd orbitals are degenerate and each of four orbitals is singly occupied. In an octahedral crystal field, eq. 20.3 shows how the CFSE is determined for a high-spin d^(4)d^{4} configuration (20.4). 对于给定的 d^(n)d^{n} 配置,CFSE 是八面体晶场中 dd 电子与球面晶场中 dd 电子之间的能量差(见图 20.2)。为了说明这一点,请考虑 d^(4)d^{4} 配置。在球形晶场中, dd 轨道是退化的,四个轨道中的每个轨道都被单个占据。在八面体晶场中,公式 20.3 显示了如何确定高自旋 d^(4)d^{4} 配置 (20.4) 的 CFSE。
CFSE =-(3xx0.4)Delta_("oct ")+0.6Delta_("oct ")=-0.6Delta_("oct ")=-(3 \times 0.4) \Delta_{\text {oct }}+0.6 \Delta_{\text {oct }}=-0.6 \Delta_{\text {oct }}
For a low-spin d^(4)d^{4} configuration (20.3), the CFSE consists of two terms: the four electrons in the t_(2g)t_{2 g} orbitals give rise to a -1.6Delta_("oct ")-1.6 \Delta_{\text {oct }} term, and a pairing energy, PP, must be included to account for the spin-pairing of two electrons. Now consider a d^(6)d^{6} ion. In a spherical crystal field (Fig. 20.2), one dd orbital contains spin-paired electrons, and each of four orbitals is singly occupied. On going to the high-spin d^(6)d^{6} configuration in the octahedral field (t_(2g)^(4)e_(g)^(2))\left(t_{2 g}{ }^{4} e_{g}{ }^{2}\right), no change occurs to the number of spin-paired electrons and the CFSE is given by eq. 20.4. 对于低自旋 d^(4)d^{4} 构型 (20.3),CFSE 包含两个项: t_(2g)t_{2 g} 轨道中的四个电子产生一个 -1.6Delta_("oct ")-1.6 \Delta_{\text {oct }} 项,还必须包含一个配对能 PP 来解释两个电子的自旋配对。现在考虑一个 d^(6)d^{6} 离子。在球形晶场中(图 20.2),一个 dd 轨道包含自旋配对电子,四个轨道中的每个轨道都被单个占据。当进入八面体场 (t_(2g)^(4)e_(g)^(2))\left(t_{2 g}{ }^{4} e_{g}{ }^{2}\right) 中的高自旋 d^(6)d^{6} 构型时,自旋配对电子的数量不会发生变化,CFSE 由式 20.4 给出。
CFSE =-(4xx0.4)Delta_("oct ")+(2xx0.6)Delta_("oct ")=-0.4Delta_("oct ")=-(4 \times 0.4) \Delta_{\text {oct }}+(2 \times 0.6) \Delta_{\text {oct }}=-0.4 \Delta_{\text {oct }}
For a low-spin d^(6)d^{6} configuration (t_(2g)^(6)e_(g)^(0))\left(t_{2 g}{ }^{6} e_{g}{ }^{0}\right) the six electrons in the t_(2g)t_{2 g} orbitals give rise to a -2.4Delta_("oct ")-2.4 \Delta_{\text {oct }} term. Added to this is a pairing energy term of 2P2 P which accounts for the spinpairing associated with the two pairs of electrons in excess of the one in the high-spin configuration. Table 20.3 lists values of the CFSE for all d^(n)d^{n} configurations in an octahedral crystal field. Inequalities 20.5 and 20.6 show the requirements for high- or low-spin configurations. Inequality 20.5 holds when the crystal field is weak, whereas expression 20.6 is true for a strong crystal field. Figure 20.6 summarizes the preferences for low- and high-spin d^(5)d^{5} octahedral complexes. 对于低自旋 d^(6)d^{6} 配置 (t_(2g)^(6)e_(g)^(0))\left(t_{2 g}{ }^{6} e_{g}{ }^{0}\right) , t_(2g)t_{2 g} 轨道中的六个电子会产生一个 -2.4Delta_("oct ")-2.4 \Delta_{\text {oct }} 项。此外,还有一个 2P2 P 的配对能量项,用于解释与高自旋构型中一个电子对之外的两个电子对相关的自旋配对。表 20.3 列出了八面体晶场中所有 d^(n)d^{n} 构型的 CFSE 值。不等式 20.5 和 20.6 显示了对高或低自旋构型的要求。当晶体场较弱时,不等式 20.5 成立,而表达式 20.6 则适用于强晶体场。图 20.6 总结了低自旋和高自旋 d^(5)d^{5} 八面体配合物的优先选择。 {:[" For high-spin: ",Delta_("oct ") < P],[" For low-spin: ",Delta_("oct ") > P]:}\begin{array}{ll}\text { For high-spin: } & \Delta_{\text {oct }}<P \\ \text { For low-spin: } & \Delta_{\text {oct }}>P\end{array}
We can now relate types of ligand with a preference for high- or low-spin complexes. Strong field ligands such as [CN]^(-)[\mathrm{CN}]^{-}favour the formation of low-spin complexes, while weak field ligands such as halides tend to favour high-spin complexes. However, we cannot predict whether high- or low-spin complexes will be formed unless we have accurate values of Delta_("oct ")\Delta_{\text {oct }} and PP. On the other hand, with some experimental knowledge in hand, we can make some comparative 现在,我们可以将配体类型与对高或低自旋配合物的偏好联系起来。强场配体(如 [CN]^(-)[\mathrm{CN}]^{-} )倾向于形成低自旋络合物,而弱场配体(如卤化物)则倾向于形成高自旋络合物。然而,除非我们掌握了 Delta_("oct ")\Delta_{\text {oct }} 和 PP 的准确值,否则无法预测会形成高或低自旋配合物。另一方面,如果我们掌握了一些实验知识,就可以对高自旋或低自旋络合物的形成进行一些比较。
Table 20.3 Octahedral crystal field stabilization energies (CFSE) for d^(n)d^{n} configurations; pairing energy, PP, terms are included where appropriate (see text). High- and low-spin octahedral complexes are shown only where the distinction is appropriate. 表 20.3 d^(n)d^{n} 配置的八面体晶场稳定能 (CFSE);配对能 PP 项在适当的地方包括在内(见正文)。高自旋和低自旋八面体配合物仅在需要区分时才显示。
d^(n)d^{n}
High-spin == weak field 高自旋 == 弱场
Electronic configuration 电子配置
CFSE
Electronic configuration 电子配置
CFSE
d^(1)d^{1}
t_(2g)^(1)e_(g)^(0)t_{2 g}{ }^{1} e_{g}{ }^{0}
-0.4Delta_("oct ")-0.4 \Delta_{\text {oct }}
d^(2)d^{2}
t_(2g)^(2)e_(g)^(0)t_{2 g}{ }^{2} e_{g}{ }^{0}
-0.8Delta_("oct ")-0.8 \Delta_{\text {oct }}
d^(3)d^{3}
t_(2g)^(3)e_(g)^(0)t_{2 g}{ }^{3} e_{g}{ }^{0}
-1.2Delta_("oct ")-1.2 \Delta_{\text {oct }}
d^(4)d^{4}
t_(2g)^(3)e_(g)^(1)t_{2 g}{ }^{3} e_{g}{ }^{1}
-0.6Delta_("oct ")-0.6 \Delta_{\text {oct }}
t_(2g)^(4)e_(g)^(0)t_{2 g}{ }^{4} e_{g}{ }^{0}
-1.6Delta_("oct ")+P-1.6 \Delta_{\text {oct }}+P
d^(5)d^{5}
t_(2g)^(3)e_(g)^(2)t_{2 g}{ }^{3} e_{g}{ }^{2}
0
t_(2g)^(5)e_(g)^(0)t_{2 g}{ }^{5} e_{g}{ }^{0}
-2.0Delta_("oct ")+2P-2.0 \Delta_{\text {oct }}+2 P
d^(6)d^{6}
t_(2g)^(4)e_(g)^(2)t_{2 g}{ }^{4} e_{g}{ }^{2}
-0.4Delta_("oct ")-0.4 \Delta_{\text {oct }}
t_(2g)^(6)e_(g)^(0)t_{2 g}{ }^{6} e_{g}{ }^{0}
-2.4Delta_("oct ")+2P-2.4 \Delta_{\text {oct }}+2 P
Fig. 20.6 The occupation of the 3d3 d orbitals in weak and strong field Fe^(3+)(d^(5))\mathrm{Fe}^{3+}\left(d^{5}\right) complexes. 图 20.6 弱场和强场 Fe^(3+)(d^(5))\mathrm{Fe}^{3+}\left(d^{5}\right) 复合物中 3d3 d 轨道的占据情况。
predictions. For example, if we know from magnetic data that [Co(OH_(2))_(6)]^(3+)\left[\mathrm{Co}\left(\mathrm{OH}_{2}\right)_{6}\right]^{3+} is low-spin, then from the spectrochemical series we can say that [Co(ox)_(3)]^(3-)\left[\mathrm{Co}(\mathrm{ox})_{3}\right]^{3-} and [Co(CN)_(6)]^(3-)\left[\mathrm{Co}(\mathrm{CN})_{6}\right]^{3-} will be low-spin. The only common high-spin cobalt(III) complex is [CoF_(6)]^(3-)\left[\mathrm{CoF}_{6}\right]^{3-}. 预测。例如,如果我们从磁性数据中得知 [Co(OH_(2))_(6)]^(3+)\left[\mathrm{Co}\left(\mathrm{OH}_{2}\right)_{6}\right]^{3+} 是低自旋的,那么我们就可以从光谱化学系列中得知 [Co(ox)_(3)]^(3-)\left[\mathrm{Co}(\mathrm{ox})_{3}\right]^{3-} 和 [Co(CN)_(6)]^(3-)\left[\mathrm{Co}(\mathrm{CN})_{6}\right]^{3-} 将是低自旋的。唯一常见的高自旋钴(III)配合物是 [CoF_(6)]^(3-)\left[\mathrm{CoF}_{6}\right]^{3-} 。
Self-study exercises 自学练习
All questions refer to ground state electronic configurations. 所有问题均涉及基态电子构型。
Draw energy level diagrams to represent a high-spin d^(6)d^{6} electronic configuration for an octahedral (O_(h))\left(O_{\mathrm{h}}\right) complex. Confirm that the diagram is consistent with a value of CFSE=-0.4Delta_("oct ")\mathrm{CFSE}=-0.4 \Delta_{\text {oct }}. 绘制能级图,表示八面体 (O_(h))\left(O_{\mathrm{h}}\right) 复合物的高自旋 d^(6)d^{6} 电子构型。确认该图与 CFSE=-0.4Delta_("oct ")\mathrm{CFSE}=-0.4 \Delta_{\text {oct }} 值一致。
Why does Table 20.3 not list high- and low-spin cases for all d^(n)d^{n} configurations? 为什么表 20.3 没有列出所有 d^(n)d^{n} 配置的高自旋和低自旋情况?
Given that [Co(OH_(2))_(6)]^(3+)\left[\mathrm{Co}\left(\mathrm{OH}_{2}\right)_{6}\right]^{3+} is low-spin, explain why it is possible to predict that [Co(" bpy ")_(3)]^(3+)\left[\mathrm{Co}(\text { bpy })_{3}\right]^{3+} is also low-spin. 鉴于 [Co(OH_(2))_(6)]^(3+)\left[\mathrm{Co}\left(\mathrm{OH}_{2}\right)_{6}\right]^{3+} 是低自旋的,请解释为什么可以预测 [Co(" bpy ")_(3)]^(3+)\left[\mathrm{Co}(\text { bpy })_{3}\right]^{3+} 也是低自旋的。
Jahn-Teller distortions 扬-泰勒失真
Octahedral complexes of d^(9)d^{9} and high-spin d^(4)d^{4} ions are often distorted, e.g. CuF_(2)\mathrm{CuF}_{2} (the solid state structure of which contains octahedrally sited Cu^(2+)\mathrm{Cu}^{2+} centres, see Section 21.12) and [Cr(OH_(2))_(6)]^(2+)\left[\mathrm{Cr}\left(\mathrm{OH}_{2}\right)_{6}\right]^{2+}, so that two metal-ligand bonds (axial) are different lengths from the remaining four (equatorial). This is shown in structures 20.5 (elongated octahedron) and 20.6 (compressed octahedron). ^(†){ }^{\dagger} For a high-spin d^(4)d^{4} d^(9)d^{9} 和高自旋 d^(4)d^{4} 离子的八面体配合物通常会发生变形,例如 CuF_(2)\mathrm{CuF}_{2} (其固态结构包含八面体位置的 Cu^(2+)\mathrm{Cu}^{2+} 中心,见第 21.12 节)和 [Cr(OH_(2))_(6)]^(2+)\left[\mathrm{Cr}\left(\mathrm{OH}_{2}\right)_{6}\right]^{2+} ,因此两个金属配位键(轴向)与其余四个金属配位键(赤道)的长度不同。如结构 20.5(拉长的八面体)和 20.6(压缩的八面体)所示。 ^(†){ }^{\dagger} 对于高自旋 d^(4)d^{4}
ion, one of the e_(g)e_{g} orbitals contains one electron while the other is vacant. If the singly occupied orbital is the d_(z^(2))d_{z^{2}}, most of the electron density in this orbital will be concentrated between the cation and the two ligands on the zz axis. Thus, there will be greater electrostatic repulsion associated with these ligands than with the other four, and therefore the complex suffers elongation (20.5). Conversely, occupation of the d_(x^(2)-y^(2))d_{x^{2}-y^{2}} orbital would lead to elongation along the xx and yy axes as in structure 20.6. A similar argument can be put forward for the d^(9)d^{9} configuration in which the two orbitals in the e_(g)e_{g} set are occupied by one and two electrons respectively. Electron-density measurements confirm that the electronic configuration of the Cr^(2+)\mathrm{Cr}^{2+} ion in [Cr(OH_(2))_(6)]^(2+)\left[\mathrm{Cr}\left(\mathrm{OH}_{2}\right)_{6}\right]^{2+} is approximately d_(xy)^(1)d_(yz)^(1)d_(xz)^(1)d_(z^(2))^(1)d_{x y}{ }^{1} d_{y z}{ }^{1} d_{x z}{ }^{1} d_{z^{2}}{ }^{1}. The corresponding effect when the t_(2g)t_{2 g} set is unequally occupied is expected to be very much smaller since the orbitals are not pointing directly at the ligands. This expectation is usually, but not invariably, confirmed experimentally. Distortions of this kind are called Jahn-Teller or tetragonal distortions. 离子,其中一个 e_(g)e_{g} 轨道包含一个电子,而另一个则空置。如果单个占据的轨道是 d_(z^(2))d_{z^{2}} ,则该轨道中的大部分电子密度将集中在阳离子和 zz 轴上的两个配位体之间。因此,与其他四个配位体相比,这些配位体的静电斥力会更大,从而使复合物受到拉伸 (20.5)。相反,占据 d_(x^(2)-y^(2))d_{x^{2}-y^{2}} 轨道将导致沿 xx 和 yy 轴伸长,如结构 20.6 所示。对于 d^(9)d^{9} 构型也可以提出类似的论点,其中 e_(g)e_{g} 组中的两个轨道分别被一个和两个电子占据。电子密度测量结果证实, [Cr(OH_(2))_(6)]^(2+)\left[\mathrm{Cr}\left(\mathrm{OH}_{2}\right)_{6}\right]^{2+} 中 Cr^(2+)\mathrm{Cr}^{2+} 离子的电子构型近似于 d_(xy)^(1)d_(yz)^(1)d_(xz)^(1)d_(z^(2))^(1)d_{x y}{ }^{1} d_{y z}{ }^{1} d_{x z}{ }^{1} d_{z^{2}}{ }^{1} 。当 t_(2g)t_{2 g} 离子组被不等占位时,由于轨道并不直接指向配体,因此相应的影响预计会小得多。这一预期通常会在实验中得到证实,但并非一成不变。这种畸变被称为扬-泰勒畸变或四方畸变。
The Jahn-Teller theorem states that any non-linear molecular system in a degenerate electronic state will be unstable and will undergo distortion to form a system of lower symmetry and lower energy, thereby removing the degeneracy. 扬-泰勒(Jahn-Teller)定理指出,任何处于退化电子态的非线性分子体系都将是不稳定的,并将发生畸变,形成对称性更低和能量更低的体系,从而消除退化现象。
Fig. 20.7 The relationship between a tetrahedral ML_(4)\mathrm{ML}_{4} complex and a cube; the cube is readily related to a Cartesian axis set. The ligands lie between the x,yx, y and zz axes. Compare this with an octahedral complex, where the ligands lie on the axes. 图 20.7 四面体 ML_(4)\mathrm{ML}_{4} 复合物与立方体之间的关系;立方体很容易与笛卡尔轴集联系起来。配体位于 x,yx, y 和 zz 轴之间。与八面体配合物相比,配位体位于轴上。
The observed tetragonal distortion of an octahedral [ML_(6)]^(n+)\left[\mathrm{ML}_{6}\right]^{n+} complex is accompanied by a change in symmetry ( O_(h)O_{\mathrm{h}} to D_(4h)D_{4 \mathrm{~h}} ) and a splitting of the e_(g)e_{\mathrm{g}} and t_(2g)t_{2 \mathrm{~g}} sets of orbitals (see Fig. 20.10). Elongation of the complex (20.5) is accompanied by the stabilization of each dd orbital that has a zz component, while the d_(xy)d_{x y} and d_(x^(2)-y^(2))d_{x^{2}-y^{2}} orbitals are destabilized. 在观察到八面体 [ML_(6)]^(n+)\left[\mathrm{ML}_{6}\right]^{n+} 复合物发生四方畸变的同时,对称性也发生了变化(从 O_(h)O_{\mathrm{h}} 变为 D_(4h)D_{4 \mathrm{~h}} ),而且 e_(g)e_{\mathrm{g}} 和 t_(2g)t_{2 \mathrm{~g}} 两组轨道也发生了分裂(见图 20.10)。伴随着复合物 (20.5) 的拉长,每个具有 zz 成分的 dd 轨道都变得稳定,而 d_(xy)d_{x y} 和 d_(x^(2)-y^(2))d_{x^{2}-y^{2}} 轨道则变得不稳定。
The tetrahedral crystal field 四面体晶体场
Now we consider the tetrahedral crystal field. Figure 20.7 shows a convenient way of relating a tetrahedron to a Cartesian axis set. With the complex in this orientation, none of the metal dd orbitals points exactly at the ligands, but the d_(xy),d_(yz)d_{x y}, d_{y z} and d_(xz)d_{x z} orbitals come nearer to doing so than the d_(z^(2))d_{z^{2}} and d_(x^(2)-y^(2))d_{x^{2}-y^{2}} orbitals. For a regular tetrahedron, the splitting of the dd orbitals is therefore inverted compared with that for a regular octahedral structure, and the energy difference (Delta_("tet "))\left(\Delta_{\text {tet }}\right) is smaller. If all other things are equal (and of course, they never are), the relative splittings Delta_("oct ")\Delta_{\text {oct }} and Delta_("tet ")\Delta_{\text {tet }} are related by eq. 20.7 现在我们来看看四面体晶场。图 20.7 展示了将四面体与笛卡尔轴集联系起来的便捷方法。当复合物处于这个方向时,没有一个金属 dd 轨道完全指向配位体,但是 d_(xy),d_(yz)d_{x y}, d_{y z} 和 d_(xz)d_{x z} 轨道比 d_(z^(2))d_{z^{2}} 和 d_(x^(2)-y^(2))d_{x^{2}-y^{2}} 轨道更接近于指向配位体。因此,对于正四面体来说, dd 轨道的分裂与正八面体结构的分裂相比是相反的,能量差 (Delta_("tet "))\left(\Delta_{\text {tet }}\right) 较小。如果所有其他条件都相同(当然,从来没有相同过),那么相对分裂 Delta_("oct ")\Delta_{\text {oct }} 和 Delta_("tet ")\Delta_{\text {tet }} 的关系式为公式 20.7 Delta_("tet ")=(4)/(9)Delta_("oct ")~~(1)/(2)Delta_("oct ")\Delta_{\text {tet }}=\frac{4}{9} \Delta_{\text {oct }} \approx \frac{1}{2} \Delta_{\text {oct }}
Figure 20.8 compares crystal field splitting for octahedral and tetrahedral fields. Remember, the subscript gg in the symmetry labels (see Box 20.1) is not needed in the tetrahedral case. 图 20.8 比较了八面体场和四面体场的晶体场分裂。请记住,对称性标签中的下标 gg (见方框 20.1)在四面体情况下是不需要的。
While one can anticipate that tetrahedral complexes will be high-spin, the effects of a strong field ligand which also lowers the symmetry of the complex can lead to a low-spin ‘distorted tetrahedral’ system. This is a rare situation, and is observed in the cobalt(II) complex shown in Fig. 20.9. The lowering in symmetry from a model T_(d)T_{\mathrm{d}}CoL_(4)\mathrm{CoL}_{4} complex to C_(3v)CoL_(3)XC_{3 \mathrm{v}} \mathrm{CoL}_{3} \mathrm{X} results in the change in orbital energy levels (Fig. 20.9). If the a_(1)a_{1} orbital is sufficiently stabilized and the ee set is significantly destabilized, a low-spin system is energetically favoured. 虽然我们可以预料到四面体配合物会是高自旋的,但强场效应配体也会降低配合物的对称性,从而导致低自旋的 "扭曲四面体 "体系。图 20.9 所示的钴(II)配合物中就出现了这种罕见的情况。从模型 T_(d)T_{\mathrm{d}}CoL_(4)\mathrm{CoL}_{4} 复合物到 C_(3v)CoL_(3)XC_{3 \mathrm{v}} \mathrm{CoL}_{3} \mathrm{X} 的对称性降低导致了轨道能级的变化(图 20.9)。如果 a_(1)a_{1} 轨道足够稳定,而 ee 组明显不稳定,那么低自旋系统在能量上就会受到青睐。
Second and third row metal d^(8)d^{8} complexes (e.g. Pt(II),Pd(II)\mathrm{Pt}(\mathrm{II}), \mathrm{Pd}(\mathrm{II}), Rh(I),Ir(I)\mathrm{Rh}(\mathrm{I}), \mathrm{Ir}(\mathrm{I}) ) are invariably square planar. 第二排和第三排金属 d^(8)d^{8} 复合物(如 Pt(II),Pd(II)\mathrm{Pt}(\mathrm{II}), \mathrm{Pd}(\mathrm{II}) , Rh(I),Ir(I)\mathrm{Rh}(\mathrm{I}), \mathrm{Ir}(\mathrm{I}) )无一例外都是方形平面。
Other crystal fields 其他晶体领域
Crystal field theory: uses and limitations 晶体场理论:用途和局限性
20.4 Molecular orbital theory: octahedral complexes 20.4 分子轨道理论:八面体配合物
In this section, we consider another approach to the bonding in metal complexes: the use of molecular orbital theory. In contrast to crystal field theory, the molecular orbital model considers covalent interactions between the metal centre and ligands. 在本节中,我们将探讨金属配合物成键的另一种方法:分子轨道理论。与晶体场理论不同,分子轨道模型考虑的是金属中心与配体之间的共价相互作用。
Complexes with no metal-ligand pi\pi-bonding 无金属配体 pi\pi 键的配合物
We illustrate the application of MO theory to dd-block metal complexes first by considering an octahedral complex such as [Co(NH_(3))_(6)]^(3+)\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+} in which metal-ligand sigma\sigma-bonding is dominant. In the construction of an MO energy level diagram for such a complex, many approximations are made and the result is only qualitatively accurate. Even so, the results are useful for an understanding of metal-ligand bonding. 我们首先考虑一个八面体配合物,如 [Co(NH_(3))_(6)]^(3+)\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+} ,其中金属配体 sigma\sigma 键占主导地位,以此说明 MO 理论在 dd 块状金属配合物中的应用。在绘制这种络合物的 MO 能级图时,需要进行很多近似处理,因此结果只能说是定性准确。即便如此,这些结果对于理解金属-配体键合还是很有用的。
symmetry (see Appendix 3), the ss orbital has a_(1g)a_{1 g} symmetry, the pp orbitals are degenerate with t_(1u)t_{1 u} symmetry, and the dd orbitals split into two sets with e_(g)(d_(z^(2)):}e_{g}\left(d_{z^{2}}\right. and d_(x^(2)-y^(2))d_{x^{2}-y^{2}} orbitals) and t_(2g)(d_(xy),d_(yz):}t_{2 g}\left(d_{x y}, d_{y z}\right. and d_(xz)d_{x z} orbitals) symmetries, respectively (Fig. 20.12). Each ligand, L, provides one orbital and derivation of the ligand group orbitals for the O_(h)L_(6)O_{\mathrm{h}} \mathrm{L}_{6} fragment is analogous to those for the F_(6)\mathrm{F}_{6} fragment in SF_(6)\mathrm{SF}_{6} (see Fig. 5.27, eqs. 5.26-5.31 and accompanying text). These LGOs have a_(1g),t_(1u)a_{1 g}, t_{1 u} and e_(g)e_{g} symmetries (Fig. 20.12). Symmetry matching between metal orbitals and LGOs allows the construction of the MO diagram shown in Fig. 20.13. Combinations of the metal and ligand orbitals generate six bonding and six antibonding molecular orbitals. The metal d_(xy),d_(yz)d_{x y}, d_{y z} and d_(xz)d_{x z} atomic orbitals have t_(2g)t_{2 g} symmetry and are non-bonding (Fig. 20.13). The overlap between the ligand and metal ss and pp orbitals is greater than that involving the metal dd orbitals, and so the a_(1g)a_{1 g} and t_(1u)t_{1 u} MOs are stabilized to a greater extent than the e_(g)e_{g} MOs. In an octahedral complex with no pi\pi-bonding, the energy difference between the t_(2g)t_{2 g} and e_(g)^(**)e_{g}{ }^{*} levels corresponds to Delta_("oct ")\Delta_{\text {oct }} in crystal field theory (Fig. 20.13). 对称性(见附录 3), ss 轨道具有 a_(1g)a_{1 g} 对称性, pp 轨道具有 t_(1u)t_{1 u} 退化对称性, dd 轨道分为两组,分别具有 e_(g)(d_(z^(2)):}e_{g}\left(d_{z^{2}}\right. 和 d_(x^(2)-y^(2))d_{x^{2}-y^{2}} 轨道)和 t_(2g)(d_(xy),d_(yz):}t_{2 g}\left(d_{x y}, d_{y z}\right. 和 d_(xz)d_{x z} 轨道)对称性(图 20.12)。每个配体 L 提供一个轨道, O_(h)L_(6)O_{\mathrm{h}} \mathrm{L}_{6} 片段配体组轨道的推导类似于 SF_(6)\mathrm{SF}_{6} 中 F_(6)\mathrm{F}_{6} 片段的推导(见图 5.27、公式 5.26-5.31 和附文)。这些 LGO 具有 a_(1g),t_(1u)a_{1 g}, t_{1 u} 和 e_(g)e_{g} 对称性(图 20.12)。通过金属轨道和 LGO 之间的对称匹配,可以构建图 20.13 所示的 MO 图。金属轨道和配体轨道的组合产生了六个成键分子轨道和六个反键分子轨道。金属 d_(xy),d_(yz)d_{x y}, d_{y z} 和 d_(xz)d_{x z} 原子轨道具有 t_(2g)t_{2 g} 对称性,并且不成键(图 20.13)。配体与金属 ss 和 pp 轨道之间的重叠程度大于金属 dd 轨道之间的重叠程度,因此 a_(1g)a_{1 g} 和 t_(1u)t_{1 u} 原子轨道的稳定程度大于 e_(g)e_{g} 原子轨道。在没有 pi\pi 键的八面体配合物中, t_(2g)t_{2 g} 和 e_(g)^(**)e_{g}{ }^{*} 电平之间的能量差相当于晶体场理论中的 Delta_("oct ")\Delta_{\text {oct }} (图 20.13)。
in low-spin [Co(NH_(3))_(6)]^(3+),18\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}, 18 electrons (six from Co^(3+)\mathrm{Co}^{3+} and two from each ligand) occupy the a_(1g),t_(1u),e_(g)a_{1 g}, t_{1 u}, e_{g} and t_(2g)MOst_{2 g} \mathrm{MOs} 在低自旋 [Co(NH_(3))_(6)]^(3+),18\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}, 18 电子(六个来自 Co^(3+)\mathrm{Co}^{3+} ,两个来自配体)占据 a_(1g),t_(1u),e_(g)a_{1 g}, t_{1 u}, e_{g} 和 t_(2g)MOst_{2 g} \mathrm{MOs}
in high-spin [CoF_(6)]^(3-),18\left[\mathrm{CoF}_{6}\right]^{3-}, 18 electrons are available, 12 occupying the a_(1g),t_(1u)a_{1 g}, t_{1 u} and e_(g)MOse_{g} \mathrm{MOs}, four the t_(2g)t_{2 g} level, and two the e_(g)^(**)e_{g}{ }^{*} level. 在高自旋 [CoF_(6)]^(3-),18\left[\mathrm{CoF}_{6}\right]^{3-}, 18 电子中,12 个占据 a_(1g),t_(1u)a_{1 g}, t_{1 u} 和 e_(g)MOse_{g} \mathrm{MOs} 层,4 个占据 t_(2g)t_{2 g} 层,2 个占据 e_(g)^(**)e_{g}{ }^{*} 层。
Complexes with metal-ligand pi\pi-bonding 具有金属配体 pi\pi 键的配合物
A pi\pi-acceptor ligand accepts electrons from the metal centre in an interaction that involves a filled metal orbital and an empty ligand orbital. pi\pi-Donor ligands include Cl^(-),Br^(-)\mathrm{Cl}^{-}, \mathrm{Br}^{-}and I^(-)\mathrm{I}^{-}and the metalligand pi\pi-interaction involves transfer of electrons from filled ligand pp orbitals to the metal centre (Fig. 20.14a). Examples of pi\pi-acceptor ligands are CO,N_(2),NO\mathrm{CO}, \mathrm{N}_{2}, \mathrm{NO} and alkenes, and the metal-ligand pi\pi-bonds arise from the pi\pi 受体配体从金属中心接受电子,这种相互作用涉及一个充满的金属轨道和一个空的配体轨道。 pi\pi -供体配体包括 Cl^(-),Br^(-)\mathrm{Cl}^{-}, \mathrm{Br}^{-} 和 I^(-)\mathrm{I}^{-} ,金属配体 pi\pi -相互作用涉及电子从填充配体 pp 轨道转移到金属中心(图 20.14a)。 pi\pi 受体配体的例子有 CO,N_(2),NO\mathrm{CO}, \mathrm{N}_{2}, \mathrm{NO} 和烯,金属配体 pi\pi 键产生于
Fig. 20.13 An approximate MO diagram for the formation of [ML_(6)]^(n+)\left[\mathrm{ML}_{6}\right]^{n+} (where M is a first row metal) using the ligand group orbital approach; the orbitals are shown pictorially in Fig. 20.12. The bonding only involves M-Lsigma\mathrm{M}-\mathrm{L} \sigma-interactions. 图 20.13 使用配体基团轨道法形成 [ML_(6)]^(n+)\left[\mathrm{ML}_{6}\right]^{n+} (其中 M 为第一排金属)的近似 MO 图;轨道如图 20.12 所示。成键只涉及 M-Lsigma\mathrm{M}-\mathrm{L} \sigma 相互作用。
Fig. 20.14 pi20.14 \pi-Bond formation in a linear L-M-L\mathrm{L}-\mathrm{M}-\mathrm{L} unit in which the metal and ligand donor atoms lie on the xx axis: (a) between metal d_(xz)d_{x z} and ligand p_(z)p_{z} orbitals as for L=I^(-)\mathrm{L}=\mathrm{I}^{-}, an example of a pi\pi-donor ligand, and (b) between metal d_(xz)d_{x z} and ligand pi^(**)\pi^{*}-orbitals as for L=CO\mathrm{L}=\mathrm{CO}, an example of a pi\pi-acceptor ligand. 图 20.14 pi20.14 \pi -线性 L-M-L\mathrm{L}-\mathrm{M}-\mathrm{L} 单元中的成键,其中金属和配体供体原子位于 xx 轴上:(a) 金属 d_(xz)d_{x z} 和配体 p_(z)p_{z} 轨道之间,如 L=I^(-)\mathrm{L}=\mathrm{I}^{-} ( pi\pi 供体配体的一个例子);以及 (b) 金属 d_(xz)d_{x z} 和配体 pi^(**)\pi^{*} 轨道之间,如 L=CO\mathrm{L}=\mathrm{CO} ( pi\pi 受体配体的一个例子)。
Although Figs. 20.13 and 20.15 are qualitative, they reveal important differences between octahedral [ML_(6)]^(n+)\left[\mathrm{ML}_{6}\right]^{n+} complexes containing sigma\sigma-donor, pi\pi-donor and pi\pi-acceptor ligands: 虽然图 20.13 和 20.15 是定性的,但它们揭示了含有 sigma\sigma 供体、 pi\pi 供体和 pi\pi 受体配体的八面体 [ML_(6)]^(n+)\left[\mathrm{ML}_{6}\right]^{n+} 复合物之间的重要差异:
Delta_("oct ")\Delta_{\text {oct }} decreases on going from a sigma\sigma-complex to one containing pi\pi-donor ligands; 从 sigma\sigma 复合物到含有 pi\pi 供体配体的复合物, Delta_("oct ")\Delta_{\text {oct }} 会减少;
for a complex with pi\pi-donor ligands, increased pi\pi-donation stabilizes the t_(2g)t_{2 g} level and destabilizes the t_(2g)^(**)t_{2 g}{ }^{*}, thus decreasing Delta_("oct ")\Delta_{\text {oct }}; 对于具有 pi\pi 供体配体的配合物, pi\pi 供体的增加会稳定 t_(2g)t_{2 g} 水平,破坏 t_(2g)^(**)t_{2 g}{ }^{*} 的稳定性,从而降低 Delta_("oct ")\Delta_{\text {oct }} ;
Delta_("oct ")\Delta_{\text {oct }} values are relatively large for complexes containing pi\pi-acceptor ligands, and such complexes are likely to be low-spin; 对于含有 pi\pi 受体配体的配合物, Delta_("oct ")\Delta_{\text {oct }} 值相对较大,这类配合物很可能是低自旋的;
The above points are consistent with the positions of the ligands in the spectrochemical series; pi\pi-donors such as I^(-)\mathrm{I}^{-} 上述观点与配体在光谱化学系列中的位置相一致; pi\pi 供体,如 I^(-)\mathrm{I}^{-}
Show that, under O_(h)O_{\mathrm{h}} symmetry, the LGO in diagram (a) belongs to a t_(2g)t_{2 g} set. 证明在 O_(h)O_{\mathrm{h}} 对称性下,图 (a) 中的 LGO 属于 t_(2g)t_{2 g} 集。
Worked example 20.2 18-Electron rule 工作示例 20.2 18 电子规则
We could extend our arguments to complexes such as [CrO_(4)]^(2-)\left[\mathrm{CrO}_{4}\right]^{2-} and [MnO_(4)]^(-)\left[\mathrm{MnO}_{4}\right]^{-}showing how pi\pi-donor ligands help to stabilize high oxidation state complexes. However, for a valid discussion of these examples, we need to construct new MO diagrams appropriate to tetrahedral species. To do so would not provide much more insight than we have gained from considering the octahedral case, and interested readers are directed to more specialized texts. ^(†){ }^{\dagger} 我们可以将论点扩展到 [CrO_(4)]^(2-)\left[\mathrm{CrO}_{4}\right]^{2-} 和 [MnO_(4)]^(-)\left[\mathrm{MnO}_{4}\right]^{-} 等配合物,展示 pi\pi 供体配体如何帮助稳定高氧化态配合物。不过,为了对这些例子进行有效的讨论,我们需要构建适合四面体物种的新 MO 图。这样做不会比我们在考虑八面体情况时获得更多的启示,感兴趣的读者可参阅更专业的文章。 ^(†){ }^{\dagger}
20.5 Ligand field theory 20.5 配体场理论
Although we shall not be concerned with the mathematics of ligand field theory, it is important to comment upon it briefly since we shall be using ligand field stabilization energies (LFSEs) later in this chapter. 虽然我们不会关注配体场理论的数学问题,但由于本章后面我们将使用配体场稳定能量(LFSE),因此有必要对其进行简要评述。
Ligand field theory is an extension of crystal field theory which is freely parameterized rather than taking a localized field arising from point charge ligands. 配体场理论是晶体场理论的延伸,它是自由参数化的,而不是采用点电荷配体产生的局部场。
Ligand field, like crystal field, theory is confined to the role of dd orbitals, but unlike the crystal field model, the ligand field approach is not a purely electrostatic model. It is a freely parameterized model, and uses Delta_("oct ")\Delta_{\text {oct }} and Racah parameters (to which we return later) which are obtained from electronic spectroscopic (i.e. experimental) data. Most importantly, although (as we showed in the last section) it is possible to approach the bonding in dd-block metal complexes by using molecular orbital theory, it is incorrect to state that ligand field theory is simply the application of MO theory. ^(***){ }^{\star} 配体场理论与晶体场理论一样,仅限于 dd 轨道的作用,但与晶体场模型不同的是,配体场方法并不是一个纯粹的静电模型。它是一个自由参数化模型,使用的 Delta_("oct ")\Delta_{\text {oct }} 和 Racah 参数(我们稍后再谈)是从电子光谱(即实验)数据中获得的。最重要的是,虽然(正如我们在上一节所展示的)可以通过使用分子轨道理论来研究 dd 块状金属配合物中的成键情况,但认为配体场理论仅仅是 MO 理论的应用是不正确的。 ^(***){ }^{\star}
20.6 Describing electrons in multi-electron systems 20.6 描述多电子系统中的电子
In crystal field theory, we consider repulsions between dd-electrons and ligand electrons, but ignore interactions between dd-electrons on the metal centre. This is actually an aspect of a more general question about how we describe the interactions between electrons in multi-electron systems. We will now show why simple electron configurations such as 2s^(2)2p^(1)2 s^{2} 2 p^{1} or 4s^(2)3d^(2)4 s^{2} 3 d^{2} do not uniquely define the arrangement of the electrons. This leads us to an introduction of term 在晶体场理论中,我们考虑了 dd 电子和配体电子之间的斥力,但忽略了金属中心上 dd 电子之间的相互作用。这实际上是一个更普遍问题的一个方面,即我们如何描述多电子系统中电子之间的相互作用。现在,我们将说明为什么 2s^(2)2p^(1)2 s^{2} 2 p^{1} 或 4s^(2)3d^(2)4 s^{2} 3 d^{2} 等简单的电子构型不能唯一定义电子的排列。这就引出了一个术语
symbols for free atoms and ions. For the most part, use of these symbols is confined to our discussions of the electronic spectra of dd - and ff-block complexes. In Section 1.7, we showed how to assign a set of quantum numbers to a given electron. For many purposes, this level of discussion is adequate. However, for an understanding of electronic spectra, a more detailed discussion is required. Before studying this section, you should review Box 1.4. 自由原子和离子的符号。在大多数情况下,这些符号的使用仅限于我们对 dd - 和 ff 块状复合物电子光谱的讨论。在第 1.7 节中,我们展示了如何为给定电子分配一组量子数。就许多目的而言,这种程度的讨论已经足够。但是,为了理解电子光谱,需要进行更详细的讨论。在学习本节之前,请先复习方框 1.4。
The quantum number JJ takes values (L+S),(L+S-1)dots(L+S),(L+S-1) \ldots|L-S||L-S|, and these values fall into the series 0,1,2dots0,1,2 \ldots or (1)/(2),(3)/(2),(5)/(2)\frac{1}{2}, \frac{3}{2}, \frac{5}{2} … (like jj for a single electron, JJ for the multi-electron system must be positive or zero). It follows that there are: 量子数 JJ 取值为 (L+S),(L+S-1)dots(L+S),(L+S-1) \ldots|L-S||L-S| ,这些值落入系列 0,1,2dots0,1,2 \ldots 或 (1)/(2),(3)/(2),(5)/(2)\frac{1}{2}, \frac{3}{2}, \frac{5}{2} 中......(就像单电子的 jj 和多电子系统的 JJ 必须为正或零)。由此可见,有
(2L+1)(2 L+1) possible values of JJ for L < SL<S. (2L+1)(2 L+1)JJ 的可能值为 L < SL<S 。
The value of M_(J)M_{J} denotes the component of the total angular momentum along the zz axis. Just as there are relationships between SS and M_(S)M_{S}, and between LL and M_(L)M_{L}, there is one between JJ and M_(J)M_{J} : M_(J)M_{J} 的值表示总角动量沿 zz 轴的分量。正如 SS 和 M_(S)M_{S} 之间、 LL 和 M_(L)M_{L} 之间存在关系一样, JJ 和 M_(J)M_{J} 之间也存在关系: