Intro to Crystal Field Theory - Online Tutor, Practice Problems & Exam Prep

Crystal field theory explains the colors and magnetic properties of transition metal coordination compounds, which form crystalline solids. Ligands create an electric field around metal cations, affecting the energy of metal d orbitals. In octahedral complexes, the ligands on the axes interact most with the d orbitals, specifically the $d^{x2}-y^2$ and $d^{z}2$ orbitals, raising their energy levels. Conversely, the orbitals between the axes interact less, resulting in lower energy. Tetrahedral complexes, on the other hand, have the greatest ligand interaction and energy increase between the axes, involving the $d_{xy}$, $d_{yz}$, and $d_{xz}$ orbitals. The geometry of the complex and the orientation of the d orbitals are crucial in determining the extent of these interactions, which in turn influence the physical properties observed in these compounds.

The study of ligand-metal interactions helped to form Ligand Field Theory which combines CFT with MO Theory.

In this video on the intro to crystal field theory, we're going to say that transition metal coordination compounds form crystalline solids. Now if we take a look here, we see this beautiful gem, this red gem. Well, crystal field theory was developed to explain the color as well as the magnetism or magnetic properties of coordination compounds.

In fact, we're going to say that coordination compounds form crystals. When we say crystals song, we're talking about crystals, hence the name for color within the name. And we're going to say it also focuses on the effects of ligands, electric field around the metal cation. Now ligands surround and create this type of magnetic well, this electric field around a metal cation. That's why the word field is also in the name.

Later on this helped to create what's known as ligand field theory. It's just a combination of crystal field theory with molecular orbital theory. So that's the origins of this whole idea of crystals and colors and magnetic properties. So as we delve into different types of complexes, we'll be touching on a little bit of each of these ideas within our videos.

The greater the interaction between the metal and its ligands then the greater the energy of its d orbitals

When it comes to ligand orbital interactions, we're going to say that the interaction between them is electrostatic and we're going to say we're going to have an increase in the energies of metal d-orbitals, which in turn causes an increase in their interactions which increases our energy. Just understand that we are going to have like charges and like charges repel one another. So we're going to have the electrons of the metal cation interacting with the electrons of our ligands. This repulsion between them causes this increase in energy.

So if we take a look here we have our up arrow which is showing an increase in energy. And what we have here initially are 5 orbitals, 5d orbitals. We're going to say these are metal d orbitals without a ligand attached. Once we bring in a ligand and attach it to the metal cation again we have to compete. We have this repulsive behavior between the electrons of the metal cation and the electrons of the ligands. This is going to cause an increase between the interactions of their electrons.

So these higher energy orbitals here are just the metal d orbitals with the ligand or ligands attached. So take from this, as we add ligands to our metal cations, we're going to see an uptick in the energy of the d orbital electrons of the metal cation.

For octahedral complexes, the greatest ligand-metal interactions occur on or along the axes.

Now, in terms of the interactions in octahedral complexes, we're going to say that the strength of ligand orbital interactions depend on complex geometry and deorbital orientation. We're going to say here that for octahedral complexes, the ligands are on the axes. So remember we say on the axes or along the axes. They're both synonymous with one another, we're going to say on the axis.

Orbitals have the greatest interaction interactions with the ligands. So if we take a look here, what we have is a representation of our octahedral species. So think of it like 2 square pyramids that are stacked on top of each other or stacked inversely to each other. Their base is touching one another. So we have these six points which represents our ligands, and in the center we have our metal cation in theory.

Now on the axis, we say that the greatest interaction again happens on the X&Y axis. Here for this One South, it's dx2-y2. And then this one we have the most interactions happening on the Z axis, so dz2. In these two on the axis examples, we'd say that an increase in interaction causes an increase in energy.

Now in between the axes we have our other three orbitals. These don't line up in the correct orientation to have the greatest interaction. So we're going to say we have less interaction in this setup, which would cause a decrease in energy, or less energy involved. So just remember, when it comes to octahedral species themselves, the greatest interaction is happening on the axes or along the axes. So in particular we're talking about dx2-y2, and dz2. So just keep that in mind.

Example

Here it says which set of D orbitals below will interact the most with the ammonia ligands within this coordination complex. All right. So remember this is our complex ion portion and this is what we care about. The chlorine over here is just a counter ion.

Now here we have 6 ammonia molecule ligands attached to our iron. So this is an octahedral complex and when it comes to octahedral complexes, the greatest interactions are happening along the axis or on the axes. And that only happens for two types of orbitals and there would be D_x²-y² and D_z².

If we look at our options, the only one that has only those two orbitals and nothing else would be option E. Here option E would be our final answer.

For tetrahedral complexes, the greatest ligand-metal interactions occur in between the axes.

Now, with interactions in tetrahedral complexes, we're going to say that the ligands are aligned in between the axes, and we're going to say in between the axes. The orbitals there have the greatest interactions with the ligands. So if we take a look here, think of a cube, the cube here, we have our four points in terms of this cube. And we're going to say that this point and this point are the ones that are nearest us. And you can see that these two dots here are smaller because they're in the back.

If you were to take those four points and have them represent our four ligands, you couldn't shift this over and put it amongst all of these axes, your XY and Z axes. Now remember, in between the axes deals with dxy, dyz and dxz. Along or on the axis, Well, that's reserved for dx2-y2 and dz2. Now remember, for tetrahedral complexes, the greatest interaction is in between the axes.

So here we have the greatest interaction amongst these three orbitals, which will result in a great amount of energy for the ones on the axis. They don't quite line up in the way that has the greatest interaction between the ligand and the metal cation. Because of this, we're going to see a decrease in interaction, which is going to result in a decrease in energy. So remember, with tetrahedral complexes, the greatest interaction between the metal cation and the ligand lies in between the axes, and keep in reference these particular deorbitals dxy, dyz and dxz.

Example

Identify the D orbital or orbitals with the highest energy in the complex shown below. Here we have zinc as our metal cation connected to 4 hydroxide ions. Doing this gives us an overall charge of 2 minus. Now the way that it's depicted shows that this is a tetrahedral complex, and with tetrahedral complexes the greatest interaction happens in between the axes.

Remember, the orbitals that lie in between the axes would be dxy, dyz and dxz. These remaining 2 are the ones that are along the axes or on the axes, so they would not have the greatest interaction. So AB and C are the correct orbitals, and because of that the answer would have to be option G.

So we're talking about AB and C as being the D orbitals with the highest energy in this tetrahedral complex.

For an octahedral complex, which set of d orbitals is expected to be at the lowest energy?

• A. d_xy, d_yz, d_z²
• B. d_yz, d_xz, d_z²
• C. d_xy, d_yz, d_xz
• D. d_xy, d_yz, d_x²–y²
• E. d_yz, d_x²–y², d_z²

Here’s what students ask on this topic:

What is crystal field theory?

Crystal Field Theory (CFT) is a model in chemistry that describes the breaking of degeneracies of electron orbital states, usually d or f orbitals, due to a static electric field produced by a surrounding charge distribution. This is typically relevant for transition metal complexes where the central metal ion is surrounded by ligands--molecules or ions that donate pairs of electrons to the metal.

In CFT, the approach is to consider how the energy levels of the d orbitals are affected by the presence of the ligands. The ligands are treated as point charges (or sometimes as dipoles), and the effect they have on the energy of the d orbitals of the metal ion is calculated. Depending on the geometry of the complex (octahedral, tetrahedral, square planar, etc.), the d orbitals will split into groups with different energies. This splitting can influence the color, magnetism, and reactivity of the complex.

CFT helps in understanding the electronic transitions that give rise to the colors of transition metal complexes, and it provides a basis for predicting the magnetic properties of these complexes. However, it does not take into account the covalent aspects of the metal-ligand bond, which are described by Molecular Orbital Theory.

What does crystal field theory explain?

Crystal Field Theory (CFT) explains how the distribution of electrons in the d-orbitals of transition metal ions is affected by the presence of surrounding ligands. Ligands are ions or molecules that can donate electron pairs to the metal ion, forming a coordination complex. CFT provides insight into the color, magnetism, and stability of these complexes.

The theory posits that when ligands approach the central metal ion, they interact with the d-orbitals differently depending on their spatial orientation. This interaction causes a splitting of the d-orbital energy levels into two sets: the higher energy e_g and the lower energy t_2g orbitals. The specific pattern and extent of splitting depend on the geometry of the complex (e.g. octahedral, tetrahedral, square planar).

Electrons will fill these split d-orbitals according to the Aufbau principle and Hund's rule, leading to various electronic configurations. The differences in energy between these split orbitals can absorb certain wavelengths of light, which is often observed as the color of the complex. Additionally, the electron configuration can affect the magnetic properties of the complex, making CFT valuable for predicting magnetic behavior.

How to do crystal field theory?

Crystal Field Theory (CFT) is a model that describes the breaking of degeneracies of electron orbital states, usually d or f orbitals, due to a static electric field produced by a surrounding charge distribution. This theory is particularly useful in the study of transition metal complexes.

Here's a simplified approach to apply Crystal Field Theory:

1. Identify the Central Metal Ion: Determine the metal ion at the center of the complex.
2. Determine the Coordination Number: Count the number of ligands attached to the metal ion. Common coordination numbers are 4 (tetrahedral, square planar) and 6 (octahedral).
3. Consider the Geometry of the Complex: The geometry will affect the arrangement of the d-orbitals. In an octahedral field, the d-orbitals split into two sets with different energy levels (eg, d_x²-y² and d_z² have higher energy than d_xy, d_xz, and d_yz).
4. Apply the Crystal Field Splitting: Place the electrons of the metal ion into the d-orbitals according to the splitting pattern and the Pauli Exclusion Principle and Hund's Rule (electrons fill each orbital singly before pairing).

Which of the following is not explained by crystal field theory?

Crystal Field Theory (CFT) is a model that describes the electronic structure of metal complexes, focusing on the interaction between the central metal ion and the surrounding ligands. However, there are several phenomena that CFT does not explain:

1. The magnetic properties of coordination compounds are only partially explained by CFT. It can predict whether a complex is paramagnetic or diamagnetic by considering the presence of unpaired electrons, but it cannot accurately describe the magnetic moment of transition metal complexes.
2. CFT does not account for the covalent character of the bonding in metal complexes. It treats the metal-ligand bond as purely ionic, where ligands are considered as point charges that create an electrostatic field affecting the d-orbitals of the metal ion.
3. The theory does not explain the color of the complexes accurately in all cases. While it can predict that color is due to d-d transitions, it cannot always predict the correct wavelengths or intensities of the absorption responsible for the observed colors.
4. CFT does not consider the influence of ligand orbitals and their overlap with metal orbitals, which is a key aspect of the more advanced Molecular Orbital Theory (MOT).

In summary, while CFT is useful for understanding some aspects of the electronic structure and properties of metal complexes, it does not provide a comprehensive explanation for all observed phenomena.

What is the pairing energy in crystal field theory?

In crystal field theory, pairing energy is the energy required to pair up electrons within the same orbital. When a metal ion is surrounded by ligands, the degenerate d-orbitals (which are of equal energy in an isolated atom) split into different energy levels due to the electrostatic interactions between the d-orbitals and the electric fields created by the surrounding ligands. This splitting creates a crystal field stabilization energy (CFSE) for the system.

If an electron is to be paired with another in the same orbital, it must overcome the repulsion between the two negatively charged electrons. The pairing energy is the energy cost of this process. It's significant because it can influence the distribution of electrons among the d-orbitals in a transition metal complex, which in turn affects the complex's color, magnetic properties, and chemical behavior. If the pairing energy is higher than the energy gap between different d-orbitals, it can be energetically favorable for electrons to remain unpaired in higher energy orbitals. Conversely, if the pairing energy is lower, electrons will pair up in the lower energy orbitals.