Basic Concept
When a transition metal atom or molecule is by itself, all five of the d orbitals have an equal energy but are at different spacial orientations around the nucleus. The orbital dz² has lobes along the z axis and circling around the metal ion parallel to the x and y axes. The orbital dx²-y² has lobes lying on the x and y axes and for the dxy, dxz, and dyz axes lobes occupy the regions in the planes of the respective axes rather than lie on the axes. When electrons from a ligand approach a metal ion some follow a more direct line of oposition from the d orbital electrons than others, depending on the structure of the molecule. We will first look at a molecule with an octahedral structure. Ligands approach the metal ion along the z,x and y axes. Therefore, the electrons in the dz² and dx²-y² orbitals, which lie along the z axis and the x and y axes respectively, feel the most repulsion. It takes more energy to have an electron in these orbitals than it would to put an electron in one of the other orbitals. This causes a splitting in the energy level of the d orbitals known as crystal field splitting. Crystal field splitting is denoted by ∆₀, with the subscript o in this case to show it refers to an ocrahedral complex. The dz² and dx²-y² orbitals energies increase from the normal energy of the d orbitals and the dxy, dxz, and dyz orbitals decrease with respect to this normal energy. Because the dxy, dxz, and dyz orbitals decrease in energy, they become more stable.
dz², dx²-y²
____ ____ ____ ____ ____ dz², dx²-y²,dxy, dxz, dyz go to:
dxy, dxz, dyz
For a transition metal complex, the d orbitals have this energy distribution however which electrons get placed into which orbitals can be different. According to Hund's rule, the electrons are initially placed into the lowest energy orbitals, thus being the dxy, dxz, and dyz orbitals. The next electron however can be different. If the dxy, dxz, and dyz orbitals are looked at as their own energy level, according to the Aufbau Principle it would seem like the next electrons should fill the dxy, dxz, and dyz orbitals and pair up with the electrons already in these orbitals. This too however requires energy, known as pairing energy. If the pairing energy is less than the crystal field splitting energy, ∆₀, then the next electrons go into the dxy, dxz, and dyz orbitals because greater stability is found in going into the orbital with lower energy. This situation causes there to be the least amount of unpaired electrons and is known as low spin. If the pairing energy is greater than ∆₀ then the next electrons go into the dz² and dx²-y² orbitals as unpaired electrons.This situation allows for the most number of unpaired electrons, which is known as a high spin molecule. Ligands that cause a transition metal to have a small crystal field splitting will also have a high spin. These ligands are known as weak-field ligands. Ligands that produce a large crystal field splitting have a low spin and are called strong field ligands. Ligands can be ordered by their abilities to cause crystal field splitting and this ordering is known as the spectrochemical series. An example is below.
In addition to octahedral complexes, there are also tetrahedral complexes and square planar complexes. These complexes differ from the octrahedral complex in regards to which orbital levels are raised in energy due to interference with electrons from ligands. For the tetrahedral complex, the dxy, dxz, and dyz orbitals are raised in energy while the dz², dx²-y² orbitals are lowered. For the square planar complexes, there is the greatest interferance with the dx²-y² orbital so it has the greatest energy. The next orbital with the greatest interference is dxy, followed below by dz². The orbitals with the lowest energy are the dxz and dyz orbitals. There is a large energy seperation between the dz² orbital and the dxz and dyz orbitals, meaning that the crystal field splitting energy is large. We find that the square planar complexes have the greatest crystal field splitting out of all the complexes. This means that most square planar complexes are low spin, strong field ligands.
As mentioned above, Crystal Field Theory is based primarily on symmetry of ligands around a central metal/ion and how this anisotropic (properties depending on direction [4]) ligand field affects the metal's atomic orbitals; the energies of which may increase, decrease or not be affected. Once the ligands' electrons interact the electrons of the d-orbital, the electrostatic interactions cause the energy level of the d-orbitals to fluctuate depending on the orientation and the nature of the ligands. For example, the oxidation state and the strength of the ligands determine how big the splitting is going to be; the bigger the oxidation state or the stronger the ligand, the bigger the splitting.Here are some ligands in order from weakest to strongest:
I- < Br- < Cl- < SCN- < F- < OH- < ox2-< ONO- < H2O < SCN- < EDTA4- < NH3 < en < NO2- < CN-
Follow Hund's rule for filling the electrons in the correct energy level. When the splitting is bigger than the spin pairing energy (the energy required to pair two electrons in the same orbital), the electrons pair up and complete the lower orbitals first.The electrons subsequently fill the upper energy levels and this process is called low spin because it allows less electrons to stay unpaired. When the splitting is smaller than the pairing energy, the electrons will partially fill the lower energy levels, then partially fill the higher energy levels before pairing begins. This is called high spin because there is a higher chance of having more unpaired electrons.
Description of the d Orbitals
In order to understand Crystal Field Theory, one has to know the description of the lobes.
- dxy: the four lobes lie in-between the x and the y axes.
- dxz: the four lobes lie in-between the x and the z axes.
- dyz: the four lobes lie in-between the y and the z axes.
- d(x2-y2): the four lobes lie on the x and y axes.
- dz2: there are two lobes on the z axes and there is a donut shape ring that lies on the xy plane around the other two lobes.
Different Complexes
Octahedral Complex
[5]
In an octahedral complex, there are six ligands attached to the central transition metal. The d orbital splits into two different levels. The bottom three energy levels are named dxy, dxz, and dyz (also referred to as to as t2g). The two upper d energy levels are named dx²-y², and dz² (also referred to as eg). The reason for the splitting is because of the electrostatic interactions between the electrons of the ligand (white in the above diagram) and the lobes of the d-orbital (pink in the diagram above). For an octahedral the electrons are attracted to the axes. Any orbital that has a lobe on the axes moves to a higher energy level. This means the dx2-y2 and the dz2 have a higher energy level (for an octahedral).
The difference in height of the splitting is called delta octahedral (Δoct). Based off of the size of Δoct and the strength of the ligand, this can be both high spin or low spin.
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Color of Complex: The distance that the electrons have to move from t2g from eg, dictates the energy that the complex will absorb from white light, which will determine the color that is reflects.
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Magnetism and Magnetic Properties: Whether it is paramagnetic or diamagnetic will be mostly determined by if it is a high spin or low spin.
Tetrahedral
[5]
For a tetrahedral, there are four ligands attached to the central metal. The d orbital also split into two different levels in a different way. The top three energy levels are named dxy, dxz, and dyz. The two bottom d energy levels are named dx²-y², and dz². The reason for this is because the electrons are attracted away from the axes. Any orbital that has a lobe in-between the the axes moves to a higher energy level. This means the dxy, the dxz, and the dyz have a higher energy level.
The difference in height of the splitting is called delta tetrahedral (Δt). The size of Δt tends to be smaller than the pairing energy, so it is usually high spin.
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Color of Complex: The distance that the electrons have to move from one energy level to another, dictates the energy that the complex will absorb from white light, which will determine the color that is reflects.
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Magnetism:Because it tends to be high spin, it is usually paramagnetic.
Square Planar
[5]
For a square planar, there are also four ligands. However, this differs in that the electrons of the ligands are attracted to only the xy plane. Any orbital in the xy plane has a higher energy level. There are four different energy levels for the square planar (from the highest energy level to lowest energy level): dx2-y2, dxy, dz2, and both dxz and dyz.
The difference in height of the splitting (from highest orbital to lowest orbital) is called delta square planar (Δsp). The size of Δsp tends to be larger then the pairing energy, so it is usually low spin.
Color of Complex: The distance that the electrons have to move from one energy level to another, dictates the energy that the complex will absorb from white light, which will determine the color that is reflects.
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Magnetism: Because it tends to be low spin, it is usually diamagnetic.
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