결정장 이론의 이해: 주요 개념 및 응용

### 크리스탈 필드 이론 이해: 간단한 가이드
* 🔍 결정장 이론(CFT)은 **NH3와 같은 리간드가 코발트 같은 전이 금속에 접근할 때 d 궤도가 분리되는 현상**을 설명합니다.
* ⚡ 리간드가 접근하면 정전기적 상호작용으로 인해 **코발트의 5개의 d 오비탈이 두 세트로 분리**되고, 금속 양이온의 양전하가 리간드의 음전하를 끌어당깁니다.
* 🌀 **dxy, dyz, dxz, dx²-y², dz² 등 다섯 개의 d 궤도의 모양**은 조정 복합체에서 이들의 행동을 이해하는 데 매우 중요합니다.
* 🔄 사면체 착물에서는 리간드가 축 사이로 접근하여 **세 개의 궤도는 에너지를 증가**시키고 나머지 두 개의 궤도는 감소시키는 반면, 팔면체 착물에서는 리간드가 축을 따라 접근하여 **반대 에너지 변화를 일으킵니다.**
* 📊 이러한 궤도 세트 사이의 에너지 갭, 즉 결정장 분할 에너지(ΔCFSE)는 리간드의 강도에 따라 달라지며, **강한 리간드는 약한 리간드에 비해 더 큰 갭**을 생성합니다.
* 예를 들어, **NH3와 같은 강한 리간드**가 있는 경우 철(Fe)은 저스핀 구성으로 이어질 수 있는 방식으로 d 오비탈을 채우고, **H2O와 같은 약한 리간드**가 있는 경우 고스핀 구성으로 이어집니다.
* 🔢 서로 다른 리간드 강도에 대한 전자 구성은 **짝을 이루지 않은 전자의 차이**를 보여주며, 복합체가 **상자성인지 반자성인지**를 결정합니다.
* ✨ 이러한 원리를 이해하면 **결정장 이론의 기초와 배위 화학에 대한 응용**을 쉽게 파악할 수 있습니다.

결정장 이론은 리간드 상호작용이 코발트와 같은 전이 금속에서 어떻게 궤도 분할을 일으키는지 설명합니다.

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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결정장 이론은 NH3와 같이 강하게 공여하는 리간드와의 정전기적 상호작용으로 인해 코발트의 5차원 궤도가 두 세트로 분리되는 현상을 설명합니다.

이 이론은 금속 양이온의 양전하와 리간드의 음전하가 궤도 분할을 주도한다는 점을 강조합니다.

또한 다섯 개의 오비탈의 모양은 이론을 이해하는 데 매우 중요한데, 각 오비탈은 뚜렷한 이중 덤벨 모양과 특정 엽 배열을 가지고 있습니다.

사면체 착물은 중심 금속 원자를 4개의 리간드로 둘러싸고 있는 반면, 팔면체 착물은 6개의 리간드를 가지고 있습니다.

사면체 착물에서 리간드는 금속 원자의 궤도에 접근하여 세 개의 궤도는 에너지를 증가시키고 두 개의 궤도는 감소시킵니다.

팔면체 착물에서는 리간드가 축을 따라 공격하여 두 개의 궤도는 에너지가 증가하고 세 개의 궤도는 감소하여 두 세트의 에너지 레벨로 분할됩니다: EG와 t2g.

크리스탈 필드 분할 및 전자 구성

결정장 분할 에너지(ΔCFSE)는 리간드의 강도에 영향을 받는 두 궤도 세트 사이의 에너지 간격을 말합니다.

NH3와 같은 강한 리간드는 큰 에너지 갭을 생성하여 강한 장 복합체를 만들고, H2O와 같은 약한 리간드는 작은 갭을 생성하여 약한 장 복합체를 만듭니다.

철(Fe)의 전자 구성은 리간드 강도에 따라 달라지므로 스핀 상태와 자기 특성이 달라집니다.

이 시스템은 t2g에 4개의 전자와 EG에 2개의 전자를 가지고 있어 상자성 및 고스핀 복합체입니다.

사면체 착물에서 NH3와 같은 강한 리간드는 궤도를 분할하여 t2g에는 양의 에너지 갭을, EG에는 음의 에너지 갭을 만듭니다.

H2O와 같은 약한 리간드는 두 궤도 세트 사이의 에너지 갭을 더 작게 만듭니다.

사면체 복합체의 전자는 어떤 궤도에 들어가느냐에 따라 높은 스핀 또는 낮은 스핀이 될 수 있습니다.

코발트가 H2O와 같은 약한 리간드와 반응하면 작은 에너지 갭이 발생하여 세 번째 전자가 t2g 궤도로 들어가 고스핀 착물이 생성됩니다.

이 복합체에서 짝을 이루지 않은 전자는 본질적으로 상자성을 띠게 됩니다.