give answer in 2 step with explanation at the end of each step and final answer at the end:2. (15 points) Consider the incomplete MO diagram for square planar XeF « below.
Answer the questions that s

Question

give answer in 2 step with explanation at the end of each step and final answer at the end:2. (15 points) Consider the incomplete MO diagram for square planar XeF « below.
Answer the questions that start on the following page.
Note that there are parts A-E for this question.
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A) (2 points) Box A comesponds 10 a certain number of non-bonding orbitals.
"How many non-bonding orbitals are Box A and what are thes symmetries?
8) (3 points) Box B comesponds 10 a certain number of noN-bonding orbitals. How
‘many non-bonding orbitals are in Box B and what are their symmetries?
Hint: one e, representation of LGOS is non-bonding due to poor overap.

VIPSolutions · Accepted Answer

Let's answer parts (A) and (B) step-by-step as requested.

---

## **A) Box A: Non-bonding Orbitals and Symmetries**

### **Step 1: Identify Non-bonding Orbitals in Box A**
- Box A is at the energy level of the F 2s orbitals.
- In a square planar XeF₄ molecule, the F 2s orbitals generally do **not** mix significantly with any Xe orbitals (because of symmetry and energy mismatch).
- Thus, each of the four F atoms contributes a non-bonding 2s orbital.

**Explanation:**  
Each F atom brings a 2s orbital, and these do not interact with the Xe orbitals, remaining as non-bonding molecular orbitals.

---

### **Step 2: Symmetries of Non-bonding Orbitals in Box A**
- The linear combinations of four F 2s orbitals transform as $ a_{1g} $, $ b_{1g} $, $ e_u $, and $ b_{2g} $ in $ D_{4h} $ symmetry.
- However, the **non-bonding** ones are those that do not significantly interact with Xe, which for F 2s are all four.

**Final Answer for A:**  
**There are 4 non-bonding orbitals in Box A, with symmetries:**  
$ a_{1g}, b_{1g}, e_u, $ and $ b_{2g} $.

---

## **B) Box B: Non-bonding Orbitals and Symmetries**

### **Step 1: Identify Non-bonding Orbitals in Box B**
- Box B is at the energy level between Xe 5p and F 2p orbitals.
- The question hints that "one $ e_u $ representation of LGOs is non-bonding due to poor overlap."
- Generally, when symmetry or energy prevents effective mixing, some combinations remain non-bonding.

**Explanation:**  
The $ e_u $ combination of the F 2p orbitals does not interact well with Xe orbitals due to poor spatial overlap, so this set remains non-bonding.

---

### **Step 2: Symmetries of Non-bonding Orbitals in Box B**
- The non-bonding orbitals in Box B are thus the $ e_u $ set (which is doubly degenerate, so **2 non-bonding orbitals**).

**Final Answer for B:**  
**There are 2 non-bonding orbitals in Box B, both with $ e_u $ symmetry.**

---

## **Summary Table**

| Box   | No. of Non-bonding Orbitals | Symmetries             |
|-------|-----------------------------|------------------------|
| A     | 4                           | $ a_{1g}, b_{1g}, e_u, b_{2g} $ |
| B     | 2                           | $ e_u $              |

VIPSolutions · Answer

## **A) Box A: Non-bonding Orbitals and Symmetries**

### **Step 1: Identify Non-bonding Orbitals in Box A**
- Box A corresponds to the energy level of the F 2s orbitals.
- Each of the four F atoms contributes a 2s orbital that does not significantly mix with Xe orbitals due to symmetry and energy differences.

**Explanation:**  
These F 2s orbitals remain non-bonding because they do not interact effectively with the Xe orbitals.

---

### **Step 2: Symmetries of Non-bonding Orbitals in Box A**
- The contributions of the F 2s orbitals can be described in terms of symmetry representations in the $ D_{4h} $ point group.
- The symmetries of the four non-bonding orbitals are $ a_{1g}, b_{1g}, e_u, $ and $ b_{2g} $.

**Final Answer for A:**  
**There are 4 non-bonding orbitals in Box A, with symmetries:**  
$ a_{1g}, b_{1g}, e_u, $ and $ b_{2g} $.

---

## **B) Box B: Non-bonding Orbitals and Symmetries**

### **Step 1: Identify Non-bonding Orbitals in Box B**
- Box B is at the energy level between Xe 5p and F 2p orbitals.
- The hint indicates that one $ e_u $ representation of local Gaussian orbitals (LGOs) is non-bonding due to poor overlap.

**Explanation:**  
The $ e_u $ combination of the F 2p orbitals does not effectively overlap with Xe orbitals, resulting in non-bonding characteristics.

---

### **Step 2: Symmetries of Non-bonding Orbitals in Box B**
- The non-bonding orbitals in Box B consist of the $ e_u $ set, which is doubly degenerate.
- Therefore, there are **2 non-bonding orbitals** in Box B.

**Final Answer for B:**  
**There are 2 non-bonding orbitals in Box B, both with $ e_u $ symmetry.**

---

## **Summary Table**

| Box   | No. of Non-bonding Orbitals | Symmetries                       |
|-------|-----------------------------|----------------------------------|
| A     | 4                           | $ a_{1g}, b_{1g}, e_u, b_{2g} $ |
| B     | 2                           | $ e_u $                        |

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