Draw the bonding orbital that results from the constructive overlap of the two p, orbitals shown below. node (higher energy) Px Px o antibonding MO

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### Constructive Overlap of \( \sigma \) Bonding Orbitals

When two \( p_x \) orbitals overlap constructively, they form a \( \sigma \) bonding orbital. This can be understood through the diagram provided below.

#### Visualization of \( p_x \) Orbital Overlap:

1. **Initial \( p_x \) Orbitals:**
   - The diagram starts with two \( p_x \) orbitals shown individually. Each orbital has a positive (+) and a negative (-) lobe, represented by different colors (green and blue).
   - The orbitals are placed adjacent to each other to indicate potential overlap.

2. **Constructive Overlap:**
   - When the \( p_x \) orbitals overlap constructively, their wavefunctions combine in phase (+ with + and - with -).
   - This constructive interference leads to the formation of a \( \sigma \) bonding orbital.

3. **Formation of \( \sigma \) Antibonding Molecular Orbital:**
   - The diagram depicts the two \( p_x \) orbitals overlapping and forming a bond where the areas of constructive overlap increase electron density along the axis connecting the two nuclei.
   - An antibonding molecular orbital (\( \sigma^* \)) is also illustrated. This orbital has a node, represented by a dashed magenta line, where there is zero electron probability.

4. **Energy Comparison:**
   - The diagram annotates that the \( \sigma^* \) antibonding molecular orbital is higher in energy compared to the \( \sigma \) bonding orbital.
  
### Summary

By tracing the progression from individual \( p_x \) orbitals to their combined \( \sigma \) antibonding molecular orbital, one can understand how atomic orbitals merge to form molecular orbitals. The key takeaway is recognizing how the constructive overlap leads to a bonding interaction, whereas destructive overlap results in a higher energy antibonding interaction with a node of zero electron density. This concept is fundamental in understanding molecular orbital theory and the formation of chemical bonds.
Transcribed Image Text:### Constructive Overlap of \( \sigma \) Bonding Orbitals When two \( p_x \) orbitals overlap constructively, they form a \( \sigma \) bonding orbital. This can be understood through the diagram provided below. #### Visualization of \( p_x \) Orbital Overlap: 1. **Initial \( p_x \) Orbitals:** - The diagram starts with two \( p_x \) orbitals shown individually. Each orbital has a positive (+) and a negative (-) lobe, represented by different colors (green and blue). - The orbitals are placed adjacent to each other to indicate potential overlap. 2. **Constructive Overlap:** - When the \( p_x \) orbitals overlap constructively, their wavefunctions combine in phase (+ with + and - with -). - This constructive interference leads to the formation of a \( \sigma \) bonding orbital. 3. **Formation of \( \sigma \) Antibonding Molecular Orbital:** - The diagram depicts the two \( p_x \) orbitals overlapping and forming a bond where the areas of constructive overlap increase electron density along the axis connecting the two nuclei. - An antibonding molecular orbital (\( \sigma^* \)) is also illustrated. This orbital has a node, represented by a dashed magenta line, where there is zero electron probability. 4. **Energy Comparison:** - The diagram annotates that the \( \sigma^* \) antibonding molecular orbital is higher in energy compared to the \( \sigma \) bonding orbital. ### Summary By tracing the progression from individual \( p_x \) orbitals to their combined \( \sigma \) antibonding molecular orbital, one can understand how atomic orbitals merge to form molecular orbitals. The key takeaway is recognizing how the constructive overlap leads to a bonding interaction, whereas destructive overlap results in a higher energy antibonding interaction with a node of zero electron density. This concept is fundamental in understanding molecular orbital theory and the formation of chemical bonds.
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