Coloured Complexes (HL) | 有色配合物（HL）

📚 Coloured Complexes (HL) | 有色配合物（HL）

Transition metal complexes are famous for their vivid colours, from the deep blue of copper(II) sulfate crystals to the intense purple of potassium permanganate solutions. At the heart of this phenomenon lie d-d electronic transitions within partially filled d orbitals. Understanding why and how colour arises is a central part of the IB Chemistry HL curriculum, linking atomic structure, bonding and spectroscopy.

过渡金属配合物以其鲜艳的颜色而闻名，从硫酸铜晶体的深蓝色到高锰酸钾溶液的浓紫色。这种现象的核心在于部分填充的 d 轨道内的 d-d 电子跃迁。理解颜色产生的原因和机制是 IB 化学 HL 课程的核心内容，将原子结构、化学键和光谱学紧密联系在一起。

1. Transition Metal Ions and Their d Orbitals | 过渡金属离子及其 d 轨道

Transition metals are defined as elements that form at least one stable ion with a partially filled d subshell. In free gaseous ions the five d orbitals (d_xy, d_xz, d_yz, d_x²−y², d_z²) are degenerate, meaning they have the same energy.

过渡金属被定义为能够形成至少一种具有部分填充 d 亚层稳定离子的元素。在自由的气态离子中，五个 d 轨道（d_xy、d_xz、d_yz、d_x²−y²、d_z²）是简并的，即它们具有相同的能量。

When a transition metal ion is surrounded by ligands in a complex, the degeneracy is lifted. The ligands are Lewis bases that donate lone pairs of electrons into empty hybrid orbitals of the metal ion, creating an electric field that interacts differently with the various d orbitals.

当过渡金属离子在配合物中被配体包围时，简并性被解除。配体是路易斯碱，将孤对电子提供给金属离子的空的杂化轨道，产生一个电场，该电场与各个 d 轨道的相互作用不同。

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2. Crystal Field Theory: d-Orbital Splitting | 晶体场理论：d 轨道分裂

Crystal field theory (CFT) treats the interaction between the metal ion and the ligands as purely electrostatic. The ligands are modelled as negative point charges that repel the electrons in the d orbitals of the central metal ion.

晶体场理论（CFT）将金属离子与配体之间的相互作用视为纯静电作用。配体被模拟为负点电荷，排斥中心金属离子 d 轨道中的电子。

In an octahedral complex, six ligands approach along the x, y and z axes. The d orbitals that point directly along the axes, d_x²−y² and d_z², experience a stronger repulsion and are raised to a higher energy level. The orbitals that lie between the axes, d_xy, d_xz and d_yz, experience less repulsion and are lowered in energy.

在八面体配合物中，六个配体沿 x、y 和 z 轴靠近。直接指向轴的 d 轨道——d_x²−y² 和 d_z²——受到更强的排斥，能量升高。位于轴之间的轨道——d_xy、d_xz 和 d_yz——受到较小的排斥，能量降低。

This splitting of the d orbitals into two sets is called crystal field splitting, and the energy difference between the two sets is denoted Δ_oct (octahedral splitting energy).

d 轨道分裂为两组的情况称为晶体场分裂，两组之间的能量差记为 Δ_oct（八面体分裂能）。

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3. Octahedral Splitting Diagram | 八面体场分裂图

In an octahedral field the lower-energy set is labelled t_2g and the higher-energy set is labelled e_g. The t_2g set contains three orbitals, while the e_g set contains two orbitals.

在八面体场中，低能组标记为 t_2g，高能组标记为 e_g。t_2g 组包含三个轨道，e_g 组包含两个轨道。

The energy gap Δ_oct corresponds to the energy of photons in the visible region of the electromagnetic spectrum for many transition metal complexes. When an electron absorbs a photon of exactly this energy, it can be promoted from the t_2g level to the e_g level in a d-d transition.

对于许多过渡金属配合物，Δ_oct 的能量与电磁波谱可见光区域的光子能量相对应。当一个电子恰好吸收一个具有此能量的光子时，它就可以通过 d-d 跃迁从 t_2g 能级激发到 e_g 能级。

The relationship between splitting energy and wavelength is given by Δ_oct = hc / λ, where h is Planck's constant, c is the speed of light, and λ is the wavelength of absorbed light.

分裂能与波长的关系为 Δ_oct = hc / λ，其中 h 为普朗克常数，c 为光速，λ 为被吸收光的波长。

Δ_oct = hc / λ

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4. Tetrahedral and Square Planar Splitting | 四面体和平面正方形分裂

In a tetrahedral complex the four ligands approach between the axes. The splitting pattern is inverted relative to the octahedral case: the d_xy, d_xz and d_yz orbitals (now labelled t₂) are raised in energy, while d_x²−y² and d_z² (labelled e) are lowered.

在四面体配合物中，四个配体沿轴之间靠近。分裂模式与八面体情况相反：d_xy、d_xz 和 d_yz 轨道（现标记为 t₂）能量升高，而 d_x²−y² 和 d_z²（标记为 e）能量降低。

The tetrahedral splitting energy Δ_tet is only about 4/9 of Δ_oct for the same metal ion and ligands. Consequently, tetrahedral complexes usually absorb in the lower-energy (longer-wavelength) part of the visible spectrum.

对于相同的金属离子和配体，四面体分裂能 Δ_tet 仅约为 Δ_oct 的 4/9。因此，四面体配合物通常吸收可见光谱中较低能量（较长波长）的部分。

Square planar complexes can be viewed as an extreme distortion of the octahedron where the two ligands along the z-axis are removed. This leads to a more complex splitting pattern with four distinct energy levels. The d_x²−y² orbital is particularly high in energy, which is important for complexes of d⁸ ions like Ni(II) and Pt(II).

平面正方形配合物可视为八面体的一种极端畸变，其中沿 z 轴的两个配体被移除。这导致了具有四个不同能级的更复杂的分裂模式。d_x²−y² 轨道能量特别高，这对于 d⁸ 离子（如 Ni(II) 和 Pt(II)）的配合物很重要。

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5. The Origin of Colour: d-d Transitions | 颜色的起源：d-d 跃迁

Colour in transition metal complexes arises because the d-d energy gap lies within the visible region (roughly 400–700 nm). White light passing through the complex loses some wavelengths by absorption; the transmitted light is a mixture of the remaining wavelengths and appears coloured to our eyes.

过渡金属配合物的颜色来源于 d-d 能隙恰好位于可见光区（大约 400–700 nm）。白光通过配合物时某些波长的光被吸收；透射光是剩余波长的混合光，在我们的眼中呈现颜色。

A d-d transition involves an electron moving from a lower-energy d orbital to a higher-energy d orbital. Only ions with partially filled d subshells (d¹ to d⁹) can exhibit such transitions. Ions with d⁰ (e.g. Sc³⁺, Ti⁴⁺) or d¹⁰ (e.g. Zn²⁺, Cu⁺) have either no d electrons or a completely filled d subshell, so d-d transitions are impossible.

d-d 跃迁涉及电子从较低能量的 d 轨道移动到较高能量的 d 轨道。只有具有部分填充 d 亚层（d¹ 至 d⁹）的离子才能表现出此类跃迁。具有 d⁰（如 Sc³⁺、Ti⁴⁺）或 d¹⁰（如 Zn²⁺、Cu⁺）的离子要么没有 d 电子，要么 d 亚层完全填满，因此 d-d 跃迁不可能发生。

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6. Complementary Colours and the Colour Wheel | 互补色与色轮

The colour we observe is the complementary colour of the light that has been absorbed. A simple colour wheel helps predict the observed colour: if a complex absorbs violet light (short wavelength, high energy) it appears yellow-green; if it absorbs red light (long wavelength, low energy) it appears blue-green.

我们观察到的颜色是被吸收光线的互补色。一个简单的色轮可以帮助预测观察到的颜色：如果配合物吸收紫光（短波长，高能量），则呈现黄绿色；如果吸收红光（长波长，低能量），则呈现蓝绿色。

Colour absorbed / 吸收颜色	Approx. λ (nm)	Colour observed / 观察颜色
Violet / 紫	400–435	Yellow-green / 黄绿色
Blue / 蓝	435–480	Yellow / 黄色
Green-blue / 绿蓝色	480–490	Orange / 橙色
Blue-green / 蓝绿色	490–500	Red / 红色
Green / 绿	500–560	Purple / 紫色
Yellow-green / 黄绿色	560–580	Violet / 紫色
Yellow / 黄	580–595	Blue / 蓝色
Orange / 橙	595–650	Green-blue / 绿蓝色
Red / 红	650–700	Blue-green / 蓝绿色

For example, [Cu(H₂O)₆]²⁺ absorbs mainly in the orange-red region, so the transmitted light is blue, giving the characteristic blue colour of aqueous copper(II) ions.

例如，[Cu(H₂O)₆]²⁺ 主要吸收橙红色区域的光，因此透射光呈蓝色，呈现出水合铜(II)离子特有的蓝色。

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7. The Spectrochemical Series | 光谱化学序列

Different ligands produce different magnitudes of crystal field splitting Δ. The spectrochemical series is an experimentally determined ordering of ligands according to their ability to split the d orbitals. Strong-field ligands cause large splitting, while weak-field ligands cause small splitting.

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