The Chemistry of d- and f- Block: The Origin of Colour in Complexes, Magnetism, and Isomerism
In this section, we will have a discussion about the consequences of crystal field theory which is the colour in complexes and magnetism. In this discussion, the crystal field theory will rationalise the origin of both properties. Furthermore, the geometry of complexes could also form the isomerism which can give different characters of complexes.
To begin with, we will see the absorption spectrum of [Ti(OH2)6]3+ which has the configuration of d1 as shown below.
From the figure above, it is shown that the complex absorbs maximum around 20 000 cm-1 which give the complex has deep purple colour. This phenomenon can be simply explain when the complex absorbs photons (or light sources) the electron is excited into higher level and back again by releasing energy. In [Ti(OH2)6]3+ case, the electron at t2g level is excited into eg level and the colour of the complex is corresponded to the energy gap of Δo. Therefore, different metal ions and ligands would give different colour as the Δo is different.
However, two energy levels do not imply a transition may take place as the transitions are governed by selection rules. The first rule is symmetry selection rule which is also known as the Laporte rule. This rule applies to the molecules with a centre of symmetry, such as an octahedral compound. In an octahedron, electrons may only move from gerade to ungerade orbitals or ungerade to gerade orbitals (e.g. d to p or p to d). Hence, gerade-gerade or ungerade-ungerade transition are not allowed by this rule. If we look back to our [Ti(OH2)6]3+ case, the electronic transition is not allowed because it is d-d transition; [Ti(OH2)6]3+ should be colourless. However, in a solution, the complex is not a static compound which is always vibrate and this vibration causes loss of centre of symmetry. Therefore, d-d transition might happen and this vibration causes mixing of p and d orbital which also allows the electronic transition. Furthermore, this rule is not applied to tetrahedron.
The second rule that governs the electronic transition which is spin selection rule. This rule states the electronic transition is allowed if the spin does not change during the transition, therefore if we look back to [Ti(OH2)6]3+ case, the transition is allowed as long as the electron spin does not change as shown in figure below. The implication of these rules is in nature, ruby and sapphire is a coloured mineral. This is caused by ruby contains Cr3+ impurity and sapphire contains Ti/Fe impurities in octahedron environment and d-d transitions occur. Another example is in permanganate, [MnO4]-, which has no d electron but has very strong purple colour. This colour comes from the charge (electrons) transfer from ligands to metal centre ion because it has empty d-orbital and this also cause an absorption at UV range.
From the crystal field theory, we can also predict the magnetism in complex compound, even we can predict how big the magnetism in a complex. In a simple way, any unpaired electrons cause paramagnetic characteristic and all paired electrons cause diamagnetic property. This magnetic properties cause by electrons in atoms are "in motion" and moving electrons causes an electric current. This currents set up magnetic fields and electrons in atoms affect magnetic properties. This magnetic fields affect the distribution of electrons in atoms and the resulting induced field opposes the applied field, hence this is diamagnetism. The diamagnetic effects are smaller than paramagnetic effects, so paramagnetism effect swamps the diamagnetic effects from all the other electrons.
There are 2 types of paramagnetism effect which are spin angular momentum and orbital angular momentum. Spin angular momentum is only counted from the number unpaired electron with the equation below.
Where is μeff measured in Bohr-Magneton, μb. (1 μb = 9.274×10−24 J T−1).
Another paramagnetism effect is orbital angular momentum which is a function of s, p, d, and f orbital population and it is important for 2nd and 3rd row. However, this parameter is difficult to calculate. From this magnetism there is a practical consequences which is used in magnetism measurement by using instrument such as Gouy balance. In Gouy balance, diamagnetic compounds show a decrease in weight when turning magnet on and when paramagnetic compounds shown an increase in weight when turning magnet on. A balance allows determination of the magnetic moment.
The consequence of geometry in complex can cause isomerism. When two or more complexes of the same empirical formula exist but which have different structures, they are referred to isomers. There are 2 classes of isomerism which are constitutional isomerism and stereoisomerism. Constitutional isomers have the same empirical formulae, but the atom connectivities differ and stereoisomers have the same atom-atom connectivities but the individual atoms are arranged differently in space.
There are some sub-classes of constitutional isomers and the first one is linkage isomerism. The linkage isomerism is the complex still has the same ligands, but the atoms that joins to the metal ion is different, and the common case is in NO2-. In this ligand the O and N atom can bind into the central metal ion as a ligand, so when M-NO2 is called nitro and when M-ONO is called nitrito.
Another isomer is coordination isomers where there is an interchange of ligands from two complexes salt as demonstrated below.
The third sub-class is ionisation isomerism where there is an interchange between ligands and the counter ion as shown below.
Another sub-class is solvate isomerism and this type is almost similar with ionisation isomerism but the ligand that involves in here is OH2.
Besides that, isomerism can also happen in the ligands as demonstrated below which is called ligands isomerism.
In this case, changing n-propyl to i-propyl causes a change in geometry at the metal (even the magnetism is also different with each other).
Besides that, polymerisation isomerism can also happen such as in ([ReCl4]-)n.
The second class of isomers is stereoisomers where there is related with spacial arrangement of a compound. The first type os stereosimers is geometric isomers. Geometric isomers can happen in square planar complex to give cis- and trans- compounds as demonstrated in [Pt(NH3)2Cl2], and also can happen in octahedral complex to give fac- and mer- compounds as shown in example below of [Co(NH3)3(OH2)3]3+.
Another type of geometrical isomerism is polytopal isomerism where a complex with the same ligands and coordination number exists as different geometry in a crystal such as [Ni(CN)5]3- in [Cr(en)3][Ni(CN)5].3/2H2O.
The last type of stereoisomers is optical isomers. A compound that is not superimposable on its own mirror image is called chiral compound. A pair of isomeric chiral complexes which are mirror images of each other are called optical isomers and the two mirror-image isomers are called enantiomers. Furthermore, tetrahedral complexes have the potential for optical isomerism. The optical isomerism can also happen in octahedral complex with at least 2 chelating ligands in it.
To begin with, we will see the absorption spectrum of [Ti(OH2)6]3+ which has the configuration of d1 as shown below.
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| The absorption spectrum of [Ti(OH2)6]3+ |
However, two energy levels do not imply a transition may take place as the transitions are governed by selection rules. The first rule is symmetry selection rule which is also known as the Laporte rule. This rule applies to the molecules with a centre of symmetry, such as an octahedral compound. In an octahedron, electrons may only move from gerade to ungerade orbitals or ungerade to gerade orbitals (e.g. d to p or p to d). Hence, gerade-gerade or ungerade-ungerade transition are not allowed by this rule. If we look back to our [Ti(OH2)6]3+ case, the electronic transition is not allowed because it is d-d transition; [Ti(OH2)6]3+ should be colourless. However, in a solution, the complex is not a static compound which is always vibrate and this vibration causes loss of centre of symmetry. Therefore, d-d transition might happen and this vibration causes mixing of p and d orbital which also allows the electronic transition. Furthermore, this rule is not applied to tetrahedron.
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| The allowed electronic transition of d1 |
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| Ruby (left) and sapphire (right) |
From the crystal field theory, we can also predict the magnetism in complex compound, even we can predict how big the magnetism in a complex. In a simple way, any unpaired electrons cause paramagnetic characteristic and all paired electrons cause diamagnetic property. This magnetic properties cause by electrons in atoms are "in motion" and moving electrons causes an electric current. This currents set up magnetic fields and electrons in atoms affect magnetic properties. This magnetic fields affect the distribution of electrons in atoms and the resulting induced field opposes the applied field, hence this is diamagnetism. The diamagnetic effects are smaller than paramagnetic effects, so paramagnetism effect swamps the diamagnetic effects from all the other electrons.
There are 2 types of paramagnetism effect which are spin angular momentum and orbital angular momentum. Spin angular momentum is only counted from the number unpaired electron with the equation below.
Another paramagnetism effect is orbital angular momentum which is a function of s, p, d, and f orbital population and it is important for 2nd and 3rd row. However, this parameter is difficult to calculate. From this magnetism there is a practical consequences which is used in magnetism measurement by using instrument such as Gouy balance. In Gouy balance, diamagnetic compounds show a decrease in weight when turning magnet on and when paramagnetic compounds shown an increase in weight when turning magnet on. A balance allows determination of the magnetic moment.
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| The schematic diagram of Gouy balance (left) and magnetic suscepbility balance (right) |
The consequence of geometry in complex can cause isomerism. When two or more complexes of the same empirical formula exist but which have different structures, they are referred to isomers. There are 2 classes of isomerism which are constitutional isomerism and stereoisomerism. Constitutional isomers have the same empirical formulae, but the atom connectivities differ and stereoisomers have the same atom-atom connectivities but the individual atoms are arranged differently in space.
There are some sub-classes of constitutional isomers and the first one is linkage isomerism. The linkage isomerism is the complex still has the same ligands, but the atoms that joins to the metal ion is different, and the common case is in NO2-. In this ligand the O and N atom can bind into the central metal ion as a ligand, so when M-NO2 is called nitro and when M-ONO is called nitrito.
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| Linkage isomerism |
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| Coordination isomers |
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| Ionisation isomerism |
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| Solvate isomerism |
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| Ligands isomerism |
Besides that, polymerisation isomerism can also happen such as in ([ReCl4]-)n.
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| Polymerisation isomerism |
The second class of isomers is stereoisomers where there is related with spacial arrangement of a compound. The first type os stereosimers is geometric isomers. Geometric isomers can happen in square planar complex to give cis- and trans- compounds as demonstrated in [Pt(NH3)2Cl2], and also can happen in octahedral complex to give fac- and mer- compounds as shown in example below of [Co(NH3)3(OH2)3]3+.
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| Geometrical isomerism |
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| Polytopal isomerism |
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| Optical isomerism |
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