Understanding Crystal Field Theory: Key Concepts and Applications

Crystal Field Theory explains how ligand interactions cause d orbital splitting in transition metals like Cobalt.

### Understanding Crystal Field Theory: A Simple Guide
* 🔍 Crystal Field Theory (CFT) explains the **splitting of d orbitals** in transition metals, such as Cobalt, when ligands like **NH3** approach them.
* ⚡ When a ligand approaches, the five d orbitals of Cobalt split into two sets due to electrostatic interactions, with the **positive charge of the metal cation attracting the negative charge of the ligand**.
* 🌀 The shapes of the five d orbitals, which include **dxy, dyz, dxz, dx²-y², and dz²**, are crucial for understanding their behavior in coordination complexes.
* 🔄 In tetrahedral complexes, ligands approach between axes, **increasing the energy of three orbitals** while **decreasing it for the other two**, whereas in octahedral complexes, ligands approach along the axes, resulting in an **opposite energy change**.
* 📊 The energy gap between these sets of orbitals, known as **Crystal Field Splitting Energy (ΔCFSE)**, varies with the strength of the ligand; **strong ligands create a larger gap** compared to weak ligands.
* 🧪 For example, in the presence of a strong ligand like NH3, iron (Fe) will fill its d orbitals in a way that may lead to a **low-spin configuration**, while a weak ligand like H2O leads to a **high-spin configuration**.
* 🔢 The electronic configurations for different ligand strengths illustrate the differences in **unpaired electrons**, determining whether the complex is **paramagnetic** or **diamagnetic**.
* ✨ By understanding these principles, one can easily **grasp the fundamentals of Crystal Field Theory** and its application to **coordination chemistry**.

super easy trick to learn Crystal Field Theory. Firstly, let me teach you that word is Crystal Field Theory. Well, consider a d-block element like Cobalt. We know that Cobalt has five d orbitals. On the other hand, consider that a strongly donating ligand like NH3 approaches near the Cobalt in order to form a coordination compound. Now listen carefully. As a result of this approaching ligand, the 5d orbitals of Cobalt will split into two sets. Let me repeat it. As a result of this approaching ligand, the 5d orbitals of Cobalt will split into two sets. Now here is one important question which you must learn. Why do the 5d orbitals of Cobalt split into two sets in the presence of a ligand? Well, it is Crystal Field Theory which explains this phenomenon. It is because of electrostatic interaction between a metal cation and a ligand that these 5d orbitals split up. For example, it is Crystal Field Theory that teaches us that every metal cation like Cobalt is acting as a

positive charge, and every ligand like NH3 is acting as a negative charge due to the electrostatic force between these two species. The 5 T orbitals of cobalt split up are backed down. So remember that it is Crystal field Theory which explains that how these 5D orbitals played when a ligand approaches near a metal kitten. Not to learn Crystal field Theory completely, firstly we have to learn the shapes of D orbitals. We know that D orbitals have five D in the red orbitals like d x y, d y z, d x z, d x squared minus Phi squared, and d z squared. Here I will teach you my personal and easy way of drawing the structures of these five orbitals. In case of D X Y, firstly I draw x-axis and then y-axis. Remember that it is up to you whatever axis you select. We know that the shape of D orbital is like double dumbbell. I draw the lobes of double dumbbell between the axis. In case of d y z, I draw y-axis and then

Z XA is I draw the lobes of double dumbbell between the x-rays in case of dzx. I draw x-axis and then Z XA is I draw the lobes of double dumbbell between the X A's in case of dx squared minus y squared. I draw x-axis and then y-axis here. This squared on X and Y reminds me to draw the lobes directly on both the axis, so I draw lobes of double dumbbell on the axis. In case of DC squared, I only draw Z-axis. This Square on Z-axis reminds me to draw one lobe on x's and put a ring at the center. So, these are the structures of 5D orbitals. Now here are some key Concepts which you must understand, otherwise you will not understand Crystal field Theory. Firstly, in case of these three orbitals, the lobes of orbitals are between xays, for example, like this slope, like this slope, and like this lobe. Secondly, in case of these two orbitals, the lobes of orbitals

are along or on the axis like this slope are this low. Now, if I ask you about tetrahedral complex and octahedral complex, can you answer it? Well, the easy trick is I select this T and tetrahedral and I write it as a four, while I select O and this octahedral and I write it like six. So, in tetrahedral complex, the central metal atom is surrounded by four ligands like CoCl4 negative 2, while in octahedral complex, the central metal atom is surrounded by six ligands like Co(NH3)6Cl3. Now, listen carefully. In case of tetrahedral complex, ligand approaches between X's. Let me repeat it. In case of tetrahedral complex, ligand approaches between x-rays. I mean, in tetrahedral complex, ligand will attack on this slope or on this slope or on this slope of orbitals. After attack, there will be interaction between electrons of ligand and electrons of orbitals. Remember that when there is interaction between electrons, the energy of orbital increases. Let me repeat this important point. When

There is interaction between electrons. Energy of orbital increases. Thus, we learned that energy of these three orbitals increases and energy of these two orbitals decreases in case of tetrahedral complex. On the other hand, in case of octahedral complex, ligand approaches along axis. I mean ligand will attack on this slope or on this lobe of metal orbital. After attack, electrons of ligand and metal orbitals will interact. Hence, energy of these two orbitals increases. Thus, we learned that energy of these two orbitals increases and energy of these three orbitals decreases. The snotty down all these important points. Now let me teach you Crystal field theory for octahedral complex. We already learned that in case of octahedral complex, energy of d x squared minus x squared and d z squared increases. Consider 5 degenerate orbitals of a metal atom. Let us strongly again like NH3 approach near this metal atom. The average energy of this 5D orbital increases. Here, a lot of students do not understand that why energy of these 5D orbital.

increases. Well, I teach them a simple example. I say, When you are in danger, your adrenaline level pumps up, and you get ready. Similarly, when a ligand comes near to a metal atom, the 5D orbitals get excited, and their average energy increases. Remember that I use the word average energy. Now, when a ligand interacts with 5D orbitals, they split into two sets. We already learned that in the case of an octahedral complex, the energy of d x squared minus y squared and d z squared increases from the average energy level because ligands like NH3 will attack along the axis, while the energy of d x y, d y z, and d x z decreases from the average energy level. We call this set of energy as EG, and we call this set of energy as t2g. Remember that the energy of each increases from the average energy level, so its value is positive 0.6 Delta. Secondly, the energy of these three orbitals decreases from the average energy level, so its value is negative 0.4 Delta. We can see that this is the energy gap.

between these two sets of orbitals. We call this energy gap as Crystal field splitting energy (ΔCFSE). Here is one important point which you must remember at any cost. Consider a strong ligand like NH3 and a weak ligand like H2O. When a strong ligand like NH3 approaches near 5D orbitals, the energy gap between these two sets of orbitals will be large. We call it a strong Field Complex. On the other hand, when a weak ligand like H2O approaches 5D orbitals, the energy gap between the two sets of orbitals will be smaller, and we call it a weak Field Complex. Now let me teach you the electronic configuration. For example, consider that iron (Fe) reacts with a strong ligand like NH3. We know that iron has six electrons. Firstly, I fill the orbital by one electron, one, two, three. Now the energy gap is very high between these two sets, so the fourth electron will stay in this orbit, the fifth electron will stay in this orbit, and the sixth electron will stay in this orbit.

now to write the electronic configuration. We know that in t2g there are six electrons, so this is the electronic configuration for this system. Secondly, we can see that in this system, the electrons are paired, so it is diamagnetic in nature. Remember that in an octahedral complex, a fourth electron enters to eg; it is a high-spin complex. A fourth electron enters to 2G; it is a low-spin complex. Here, a fourth electron enters to 2G, so it is a low-spin complex. On the other hand, consider that iron reacts with a weak ligand like H2O. We know that there are six electrons in its D orbital. Firstly, I fill the orbitals by one electron: one, two, three. Now, the energy gap between these two sets is very small, so the fourth electron will stay in this orbital. The fifth electron will stay in this orbital. Now, all the orbitals are filled. I will start refilling the orbitals. I place the sixth electron in this orbital. Lastly, I write the electronic configuration for this system. We can see

that there are four electrons in t2g and two electrons in EG. I write T2 G4 and eg2, so this is the electronic configuration of this system. Secondly, we can see that there are unpaired electrons present in this system, so it is paramagnetic in nature. Here, the fourth electron enters to EG, so it is a high-spin complex. Therefore, using this trig, we can easily draw cfd for the octahedral complex. Finally, let me teach you CFT for the tetrahedral complex. We already know that the energy of d x y, d y z, and d x z increases in the case of the octahedral complex. Now, consider 5D generate orbitals. Let us strong ligand like NH3 approach near these orbitals. Their average energy increases after interaction. These orbitals split into two cells. The energy of d x y, d y z, and d x z increases, while that of d x squared minus y squared and d z squared decreases. This set is t2g, and this set is eg. The energy of t2g increased, so its

value is positive 0.4 Delta, and the energy of EG decreases, so its value is negative 0.6 Delta. We can see that this is the energy gap between these two cells. We call it as Crystal field splitting energy, also it is a strong field ligand. Now consider a weak ligand like H2O. We know that in case of a weak ligand, the energy gap between the two sets of orbitals will be smaller. We call it weak field ligand. Now let me teach you the electronic configuration. Consider Cobalt react with NH3. We know that it has 7 electrons and its orbital. Firstly, I fill the orbitals by one electron, one and two. Now the energy gap is very high between these two sets, so the third electron will stay in this orbital. The fourth electrons will stay in this orbital. Now these orbitals are filled. The fifth electron will jump to this set. The sixth electron will stay in this orbital, and the seventh electron will stay in this orbital. I write the electronic configuration which is equal to EG for electrons E2 G3.

electrons. Secondly, the electrons are unpaired, so it is paramagnetic in nature. Remember that in the case of a tetrahedral complex, if the third electron enters to t2g, it is a high spin. If the third electron enters to eg, it is a low spin. Here, the third electron enters to EG, so it is a low spin complex. On the other hand, consider that Cobalt reacts with a weak ligand like H2O. We know that there are seven electrons in its orbital. The first electron will stay here, and the second electron will stay here. Now, the energy gap between these two sets is very small, so the third electron will stay here, the fourth electron will stay here, the fifth electron will stay here. Now, I double fill the orbital. The sixth electron will stay here, and the second electron will stay here. Now, I write the electronic configuration. EG for electrons, T2G3 electrons. Secondly, the electrons are unpaired, so it is paramagnetic in nature. Here, the third electron enters to t2g, so it is a high spin complex. Therefore, using this super easy trick, we

can easily understand and learn Crystal Field Theory.

Crystal Field Theory | Easy Trick

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Crystal Field Theory explains the splitting of Cobalt's 5d orbitals into two sets due to the electrostatic interaction with a strongly donating ligand like NH3.

The theory emphasizes the positive charge of the metal cation and the negative charge of the ligand, driving the orbital splitting.

Additionally, the shapes of the five d orbitals are crucial for understanding the theory, with each orbital having a distinct double dumbbell shape and specific lobe arrangements.

Tetrahedral complexes have a central metal atom surrounded by four ligands, while octahedral complexes have six ligands.

In tetrahedral complexes, ligands approach the metal atom's orbitals, causing an increase in the energy of three orbitals and a decrease in two.

In octahedral complexes, ligands attack along the axis, leading to an increase in the energy of two orbitals and a decrease in three, resulting in a split into two sets of energy levels: EG and t2g.

Crystal Field Splitting and Electronic Configuration

Crystal field splitting energy (ΔCFSE) is the energy gap between two sets of orbitals, influenced by the strength of ligands.

Strong ligands like NH3 create a large energy gap, resulting in a strong field complex, while weak ligands like H2O create a smaller gap, leading to a weak field complex.

The electronic configuration of iron (Fe) varies with the ligand strength, resulting in different spin states and magnetic properties.

Electronic Configuration and Crystal Field Theory

The system has four electrons in t2g and two in EG, making it paramagnetic and a high-spin complex.

In the tetrahedral complex, strong ligands like NH3 cause the orbitals to split, creating a positive energy gap for t2g and a negative gap for EG.

Weak ligands like H2O result in a smaller energy gap between the two sets of orbitals.

Electrons in a tetrahedral complex can be high spin or low spin, depending on which orbital they enter.

Cobalt's reaction with a weak ligand like H2O leads to a small energy gap, causing the third electron to enter the t2g orbital and resulting in a high spin complex.

The unpaired electrons in the complex make it paramagnetic in nature.