Ligand Field Theory and the Jahn-Teller Effect

Summary

The script delves into the bonding and properties of transition metal complexes, focusing on concepts like VSEPR and crystal field theory. It introduces ligand field theory, which expands on crystal field theory to predict properties of transition metal complexes using molecular orbital theory. The discussion highlights the Jahn-Teller effect, a distortion that occurs in transition metal complexes to remove degeneracy in unequally occupied orbitals, leading to stability changes. The script also explains how electron arrangements in d orbitals can lead to distortions such as tetragonal elongation or compression, crucial for understanding the geometry of these complexes.

Takeaways

• 🔬 Transition metal complexes require an understanding of bonding theories and molecular geometry.
• 📚 VSEPR theory helps explain simple molecular geometries through electron cloud repulsion.
• 🧪 Crystal field theory explains how d orbitals in transition metal complexes are split in energy when coordinating ligands.
• ⚡ Ligand field theory, an extension of crystal field theory, uses molecular orbital theory to predict bonding and properties in transition metal complexes.
• 🌟 In ligand field theory, 9 valence orbitals from a metal (s, p, and d) overlap with ligand orbitals to form molecular orbitals, affecting bonding and stability.
• 📉 The Jahn-Teller effect occurs when asymmetrically filled orbitals in a complex distort the geometry to reduce energy.
• ⚖️ Octahedral complexes with d-electrons may experience tetragonal distortion depending on the electron configuration in eg or t2g orbitals.
• 📐 High spin d4, low spin d7, or d9 configurations often trigger Jahn-Teller distortions.
• 🔄 Distortions can lead to tetragonal compression or elongation depending on the orbital stabilization, particularly in eg orbitals.
• 🔍 The Jahn-Teller effect's influence on molecular geometry is important for understanding the properties and reactions of transition metal complexes.

Q & A

What is the crystal field splitting energy?

The crystal field splitting energy is the energy difference between the t2g (lower energy) and eg (higher energy) orbitals that arise when transition metal d orbitals interact with ligands, causing them to no longer be degenerate.

How does ligand field theory differ from crystal field theory?

Ligand field theory is an extension of crystal field theory and incorporates molecular orbital theory. It more accurately predicts properties of transition metal complexes, such as those gathered from spectral analysis, by considering bonding interactions between the metal's s, p, and d orbitals and ligand orbitals.

What are bonding, antibonding, and nonbonding orbitals in ligand field theory?

In ligand field theory, bonding orbitals are lower energy molecular orbitals formed from the overlap of metal and ligand atomic orbitals, while antibonding orbitals are higher energy. Nonbonding orbitals remain at the same energy as the original d orbitals of the metal.

What is the Jahn-Teller effect?

The Jahn-Teller effect describes the distortion of a transition metal complex to lower its energy by removing the degeneracy of unequally occupied orbitals. This typically occurs in nonlinear molecules, especially when d orbitals are asymmetrically filled.

In which cases will the Jahn-Teller effect not be observed?

The Jahn-Teller effect will not be observed if the d orbitals are symmetrically filled, such as in cases where either the t2g or eg orbitals are half-full or completely full.

How does Jahn-Teller distortion affect the geometry of a complex?

Jahn-Teller distortion can cause a complex to either stretch or compress along the z-axis, depending on whether the eg or t2g orbitals are affected. If the asymmetry occurs in the eg orbitals, the distortion is strong, while asymmetry in the t2g orbitals causes weaker distortions.

What happens in a d4 high spin complex during Jahn-Teller distortion?

In a d4 high spin complex, one electron in the eg orbitals will cause stabilization, either by compressing or elongating the metal-ligand bonds along the z-axis, depending on whether the dx2-y2 or dz2 orbital is lower in energy.

Why is there no Jahn-Teller distortion in a d5 high spin complex?

In a d5 high spin complex, all the orbitals are half-full, and when distributed among the new orbitals after distortion, there is no net energy change, resulting in no Jahn-Teller distortion.

What role do metal-ligand bonds play in ligand field theory?

In ligand field theory, metal-ligand bonds form through the overlap of metal's s, p, and d orbitals with the ligand orbitals, producing bonding, antibonding, and nonbonding molecular orbitals that influence the stability and geometry of the complex.

What is the significance of the dx2-y2 and dz2 orbitals in an octahedral complex?

In an octahedral complex, the dx2-y2 and dz2 orbitals (eg orbitals) are higher in energy compared to the t2g orbitals, and their degeneracy can be broken by Jahn-Teller distortion, leading to different energy distributions and affecting the geometry of the complex.

Outlines

00:00

🔬 Introduction to Transition Metal Complexes

This paragraph revisits the basics of transition metal complexes, emphasizing the importance of reviewing key concepts like VSEPR theory and crystal field theory. It explains how d orbitals are split when coordinating with ligands, creating lower-energy t2g orbitals (dxy, dxz, dyz) and higher-energy eg orbitals (dx2-y2, dz2). The energy difference between these orbitals is referred to as the crystal field splitting energy. The paragraph introduces ligand field theory as a refinement of crystal field theory, built on molecular orbital theory, and highlights its predictive power in explaining spectral data of metal complexes.

05:04

⚛️ Ligand Field Theory and Molecular Orbital Interactions

This section delves into ligand field theory, explaining how the theory expands on crystal field theory by applying molecular orbital concepts. It describes the interaction between metal orbitals (4s, 4p, 3d) and ligand orbitals, which leads to the formation of bonding, antibonding, and nonbonding molecular orbitals. In the example of a cobalt complex with six ammonia ligands, the resulting molecular orbitals follow predictable filling patterns, with bonding and nonbonding orbitals being populated and antibonding orbitals remaining empty. This results in a stable octahedral structure, while ligand field theory offers insight into how ligand interactions influence orbital energies.

⚠️ The Jahn-Teller Effect in Transition Metal Complexes

The paragraph introduces the Jahn-Teller effect, explaining that it occurs in transition metal complexes when d orbitals are asymmetrically filled. This leads to a distortion in molecular geometry to reduce degeneracy and stabilize the complex. In octahedral complexes, if the d orbitals are filled symmetrically, no distortion occurs, but in cases like high-spin d4, low-spin d7, or d9 complexes, distortion is common. The example of a copper 2+ octahedral complex is provided, where t2g orbitals are fully occupied and eg orbitals experience uneven filling, leading to a geometrical distortion known as tetragonal distortion.

🔄 Tetragonal Distortion and Orbital Energy Splitting

This section further explores tetragonal distortion, focusing on the energy changes that occur between the dx2-y2 and dz2 orbitals. The distortion causes one orbital to rise in energy and the other to lower, leading to a reshuffling of energy levels in dxy, dxz, and dyz orbitals as well. This results in either elongation or compression along the z-axis, depending on which orbital becomes lower in energy. Examples of different complexes are provided, showing how d4 high-spin complexes exhibit tetragonal compression or elongation, whereas d5 high-spin complexes remain distortion-free due to half-filled orbitals.

Keywords

💡Transition Metal Complexes

Transition metal complexes are compounds consisting of a central metal ion, usually a transition metal, bonded to surrounding molecules or ions known as ligands. In the video, the focus is on how these complexes participate in various reactions and the theories that describe their bonding and structure, such as crystal field theory and ligand field theory.

💡VSEPR Theory

Valence Shell Electron Pair Repulsion (VSEPR) theory is used to predict the shape of molecules based on the repulsion between electron clouds. The video references VSEPR theory as a foundational concept from general chemistry, which helps explain molecular geometries before introducing more complex models for transition metal complexes.

💡Crystal Field Theory

Crystal field theory describes how the five d orbitals in transition metal complexes split into different energy levels when ligands approach the metal ion. The video explains that this splitting leads to two sets of orbitals: t2g (lower energy) and eg (higher energy). The energy difference between these sets, known as crystal field splitting energy, is crucial in understanding the bonding and properties of these complexes.

💡Ligand Field Theory

Ligand field theory is an extension of crystal field theory, incorporating molecular orbital theory to better predict the properties of transition metal complexes. It focuses on the interaction between the metal’s s, p, and d orbitals with ligand orbitals, leading to the formation of bonding, antibonding, and nonbonding molecular orbitals. The video highlights how this theory can predict data from spectral analysis.

💡Molecular Orbitals

Molecular orbitals are formed by the overlap of atomic orbitals from the metal and ligands in a complex. According to ligand field theory, the overlap between the metal’s 9 valence orbitals (s, p, d) and the ligands' orbitals results in bonding, antibonding, and nonbonding molecular orbitals. These orbitals explain the stability and bonding of transition metal complexes.

💡T2g and Eg Orbitals

In crystal field theory, the d orbitals of the metal ion split into two groups: the lower-energy t2g orbitals (dxy, dxz, dyz) and the higher-energy eg orbitals (dx2-y2, dz2). The splitting of these orbitals due to the ligands' interactions is key to understanding the behavior of transition metal complexes. The video explains how the electron distribution in these orbitals influences phenomena like the Jahn-Teller effect.

💡Jahn-Teller Effect

The Jahn-Teller effect describes how certain transition metal complexes distort their geometry to remove the degeneracy of unequally occupied orbitals, lowering the overall energy of the complex. The video discusses how this effect occurs in cases where d orbitals are asymmetrically filled, particularly in high-spin d4, low-spin d7, or d9 complexes, leading to distortions like tetragonal elongation or compression.

💡Antibonding Orbitals

Antibonding orbitals are molecular orbitals that are higher in energy than the original atomic orbitals and, when populated, weaken the bond between the metal and ligands. In the video, it is mentioned that in a stable octahedral transition metal complex, the antibonding orbitals remain empty, contributing to the stability of the complex.

💡Nonbonding Orbitals

Nonbonding orbitals are molecular orbitals that have the same energy as the original atomic orbitals and do not contribute to bonding. In the context of ligand field theory, the video explains that the nonbonding orbitals in a transition metal complex remain at the energy level of the d orbitals and are fully populated, contributing to the stability of the complex.

💡Tetragonal Distortion

Tetragonal distortion refers to a type of distortion in transition metal complexes, particularly octahedral ones, caused by the Jahn-Teller effect. This distortion occurs when the degeneracy between the eg or t2g orbitals is broken, causing either elongation or compression along the z-axis. The video explains how this distortion affects the energy levels of the d orbitals and influences the geometry of the complex.

Highlights

Introduction to transition metal complexes and the need to discuss their reactions.

Recap of VSEPR theory and its relevance to understanding molecular geometries.

Crystal field theory and its application to transition metal complexes, particularly d-orbital splitting.

Introduction of t2g and eg orbitals, which explains the energy difference in d-orbital splitting.

Definition of crystal field splitting energy and its role in transition metal complexes.

Introduction to ligand field theory, extending crystal field theory, and its reliance on molecular orbital theory.

Ligand field theory's ability to predict properties of transition metal complexes through spectral data.

Explanation of how 9 valence orbitals in metals interact with 6 degenerate ligand orbitals to form 15 molecular orbitals.

Discussion of bonding, nonbonding, and antibonding orbitals in metal-ligand interactions.

The stability of octahedral complexes and how covalent bonding arises from orbital overlap.

Description of the Jahn-Teller effect and its role in removing degeneracy in unequally occupied orbitals.

Common situations like high spin d4, low spin d7, or d9 that trigger the Jahn-Teller effect.

Detailed breakdown of tetragonal distortion and its impact on d-orbital energy, leading to either compression or elongation along the z-axis.

Examples of high spin d4 complexes showing how Jahn-Teller distortion leads to energy stabilization through orbital rearrangement.

Contrast between the absence of distortion in high spin d5 complexes and the presence of distortion in other configurations.

Transcripts

By now we have become somewhat familiar with  transition metal complexes, but before examining  

the reactions they can participate in, we need  to discuss a few more of their properties. First  

let us recall some of the theories we know  regarding chemical bonding and molecular geometry.  

Way back at the beginning of general  chemistry we learned about VSEPR theory,  

and the repulsion between electron clouds that  determines the geometries of simple molecules.  

We also discussed crystal field theory,  and the complications that arise when  

looking at transition metal complexes which  utilize d orbitals. We saw that the five  

d orbitals in a given energy level are no  longer degenerate when coordinating to ligands,  

because some of these orbitals sit on axes  which accommodate the metal-ligand bonds,  

whereas some orbitals sit between these axes. So  we introduced the concept of t2g orbitals, which  

are the lower-energy dxy, dxz, and dyz orbitals,  and the higher-energy eg orbitals, which are the  

dx2-y2 and dz2 orbitals, and we called the energy  between them the crystal field splitting energy.  

Now we have to build on this understanding  of bonding in transition metal complexes  

by supplementing with another theory called ligand  field theory, which can be thought of as somewhat  

of an extension of crystal field theory. Ligand field theory is based on molecular  

orbital theory, and it is a bit more successful  in predicting certain properties of transition  

metal complexes, such as certain  data gathered from spectral analysis.  

This model deals with the s, p, and d orbitals  that are possessed by a metal for a given shell,  

which gives a total of 9 valence orbitals for  the metal. These are the orbitals that will  

participate in bonding interactions with ligands.  Let’s say we are looking at 4s, 4p, and 3d  

orbitals, such as with the cobalt center in this  complex with six ammonia ligands and a 3+ charge.  

According to this model, we have six degenerate  ligand orbitals that house the electrons involved  

in the metal-ligand bonds, and when the 9 orbitals  from the metal overlap with these 6 orbitals from  

the ligands, 15 molecular orbitals will be  produced. Six of these are bonding orbitals,  

which are all of a lower energy than the  original atomic orbitals, six are antibonding,  

which are of a higher energy than the original  atomic orbitals, and the remaining three are  

nonbonding orbitals, which have the same  energy as the 3d orbitals on the metal.  

The molecular orbitals are populated precisely  as we would expect, from lowest energy and moving  

upwards, which in this case leaves us with all  of the bonding orbitals full, as well as the  

nonbonding, and the antibonding are all empty.  This results in a very stable octahedral complex,  

where metal-ligand bonding occurs due  to the overlap of these atomic orbitals,  

which accounts for covalent bonding. Ligand field  theory also describes the manner in which these d  

orbitals are affected differently by different  sets of ligands, and can have their energies  

raised or lowered depending on the strength  of their interaction with the ligands. 

There is much more that we could discuss regarding  ligand field theory, but let’s return to crystal  

field theory and discuss a particular ramification  that will be of interest to us in learning about  

transition metal complexes. The Jahn-Teller  effect, also known as Jahn-Teller distortion,  

is a phenomenon which describes the way  that nonlinear molecules, and in particular  

transition metal complexes, may distort their  geometry in order to remove the degeneracy  

of unequally occupied orbitals in order to lower  the overall energy of the complex. In other words,  

this is something that will happen when the d  orbitals are not filled in a symmetrical manner.  

Taking a typical octahedral complex, we recall  that the d orbitals are split up into the  

lower-energy t2g orbitals and the higher energy  eg orbitals. If electrons are arranged in these  

orbitals in a symmetrical manner, with one or  both of these sets of orbitals either half full or  

completely full, the Jahn-Teller effect will not  be observed. In any other case, it will. So high  

spin d4, low spin d7 or d9, these will be common  situations that elicit the Jahn-Teller effect. 

Let us now understand precisely what kind of  distortion will occur. Take for example an  

octahedral copper complex with a 2+ charge. This  will have 9 electrons distributed around these d  

orbitals, with the t2g orbitals completely  full, while the eg orbitals will be one full  

and the other half full. These eg orbitals  are degenerate as shown, but the Jahn-Teller  

effect predicts that the complex will distort  in such a way that the degeneracy is eliminated,  

which we call tetragonal distortion. When this  happens, between the dx2-y2 and dz2 orbitals,  

one will become higher energy than the other, and  they will end up the same distance away from the  

original orbital in energy, in either direction.  The same goes for the other three orbitals,  

where the dxy will no longer be the same energy as  the dxz and dyz. One set will be higher-energy and  

the other set will be lower-energy, compared with  the original energies, and the distance to the dxy  

will be twice the distance to the others,  because of the 1 to 2 ratio. As a result of  

this activity the complex will either stretch  or compress along the z axis. If the asymmetry  

is in the t2g orbitals, the effect is weak.  If in the eg orbitals, the effect is strong. 

Here are some examples so we can get a better  understanding. First, a d4 high spin complex.  

For these orbitals down here, there is no  net energy change. But for the ones up here,  

this lone electron will become lower in  energy as it moves to the dx2-y2 orbital.  

This stabilization produces a tetragonal  compression, so the metal-ligand bonds along the  

z axis will compress. If instead the dz2 orbital  is the lower-energy orbital for a d4 high spin  

complex, we will get the same stabilization but  we will observe tetragonal elongation, where these  

bonds will stretch instead of compress, due to the  shape and orientation of the dz2 orbital. Compare  

these to a d5 high spin complex, where now all  the orbitals are half full, so when distributed  

amongst the new orbitals there is actually no  net energy change and therefore no distortion. 

The Jahn-Teller effect will be something to  keep in mind when considering the geometry and  

properties of transition metal complexes. Now  let’s move on to our next topic in the series.