Chapter 4.35 - Formation of Molecular orbitals from p-orbitals

• In the previous section 4.34, we saw the properties of Li₂ and Be₂. In this section we will see B₂
• The details related to B₂ can be written in 11 steps:
1. B has the electronic configuration: 1s²2s²2p¹
• So when two B atoms combine to form the B₂ molecule, the following mergers will take place:
(i) The 1s orbital of one B atom merges with the 1s orbital of the other B atom
          ✰ This results in the formation of bonding and anti-bonding orbitals: σ_1s and σ*_1s 
(ii) The 2s orbital of one B atom merges with the 2s orbital of the other B atom
          ✰ This results in the formation of bonding and anti-bonding orbitals: σ_2s and σ*_2s
(iii) The 2p orbital of one B atom  merges with the 2p orbital of the other B atom
          ✰ This results in the formation of various bonding and anti-bonding orbitals
• We are familiar with (i) and (ii)
• But we have not seen any merger between p-orbitals yet
• So the B₂ molecule gives us a chance to learn about the merger of p-orbitals
• The following steps from (2) to (10) will help us to learn about that merger
2. We have three p-orbitals. They are: p_x, p_y and p_z
• The p_x of one B atom merges with the p_x of the other B atom
    ♦ During the merger, both constructive and destructive additions take place
          ✰ The constructive addition results in a bonding orbital
          ✰ The destructive addition results in a anti-bonding orbital
• The p_y of one B atom merges with the p_y of the other B atom
    ♦ During the merger, both constructive and destructive additions take place
          ✰ The constructive addition results in a bonding orbital
          ✰ The destructive addition results in a anti-bonding orbital
• The p_z of one B atom merges with the p_z of the other B atom
    ♦ During the merger, both constructive and destructive additions take place
          ✰ The constructive addition results in a bonding orbital
          ✰ The destructive addition results in a anti-bonding orbital
3. Counting the number of '✰'s in (2), we see that:
■ A total of six molecular orbitals will be produced when the two p-orbitals merge
• We need to learn the details about each one of them
4. Let us see the initial stage when the two B atoms are independent
This is shown in the fig.4.195 below:

Fig.4.195

• The p-orbitals of both the B atoms are shown in the fig.4.195
    ♦ The p_x orbitals are shown in green color
    ♦ The p_y orbitals are shown in blue color
    ♦ The p_z orbitals are shown in red color
• The nuclei are shown as small yellow spheres
• The z-axis is assumed to be the 'inter-nuclear axis'
    ♦ 'Inter-nuclear axis' is the axis which passes through the nuclei of the combining atoms
5. First we will see the merger of 2p_z orbitals
(We choose p_z first because, they lie along the inter-nuclear axis)
A. Bonding orbital
• This can be explained in 7 steps
(i) Assume that, p_x and p_y are removed from the above fig.4.195
    ♦ Then we will be able to understand the 'merger of p_z' more easily
• The constructive addition is shown in fig.4.196 below:

Fig.4.196

(ii) We see that, the resulting molecular orbital has:
    ♦ A thicker middle portion
    ♦ Two thinner portions, one on either sides
(iii) We have to give it a suitable name
    ♦ We see that, the two 2p orbitals add 'in a end-to-end manner' along the inter-nuclear axis
    ♦ So the resulting molecular orbital is denoted by the symbol 'σ' 
    ♦ Recall the ‘formation of σ bonds’ in the topic of hybridization (See fig.4.142 of section 4.25)
(iv) In our present case, the molecular orbital is formed by the merger of two 2p_z orbitals
    ♦ So we call the resulting molecular orbital as: σ_2pz
(v) The above fig.4.196 is a 3D view. Such a view helps us to understand the actual shapes
• But in the present case, a 2D view will give us some extra details. It is shown in fig.4.197 below:

Fig.4.197

(vi) In fig.4.197, consider the shape of σ_2pz
    ♦ Consider the region between the two nuclei
          ✰ This region is thicker
          ✰ This thicker region is at the exact middle portion between the two nuclei 
(vii) That means, the electrons will be spending more time in the middle portion between the two nuclei
    ♦ So both the nuclei has a strong influence on the electrons
    ♦ This gives rise to a strong bond between the two nuclei
• Since the addition is constructive, σ_2pz is a bonding orbital
B. Anti-bonding orbital
• This can be explained in 8 steps
(i) The destructive addition resulting in the formation of anti-bonding orbital is shown in fig.4.198 below:

Fig.4.198

(ii) The resulting molecular orbital has two separate parts
• Each part has a larger lobe and a smaller lobe
    ♦ We have to give it a suitable name
    ♦ We see that, the two 2p_z orbitals add 'in a end-to-end manner' along the inter-nuclear axis
    ♦ So the resulting molecular orbital is denoted by the 'σ' symbol 
    ♦ Recall the ‘formation of σ bonds’ in the topic of hybridization (See fig.4.142 of section 4.25)
(iii) In or present case, the molecular orbital is formed by the merger of two 2p_z orbitals
    ♦ But the resulting molecular orbital is an anti-bonding orbital
    ♦ We have to distinguish it from the bonding orbital. For that, we give an extra '*' symbol
    ♦ So we call the resulting anti-bonding molecular orbital as: σ*_2pz
(iv) The above fig.4.198 is a 3D view. Such a view helps us to understand the actual shapes
• But in the present case, a 2D view will give us some extra details. It is shown in fig.4.199 below:

Fig.4.199

(v) In fig.4.199, consider the shape of σ*_2pz 
    ♦ Consider the region between the two nuclei
          ✰ This region is thinner
          ✰ This thinner region is at the exact middle portion between the two nuclei 
(In the 3D view, we will not recognize the fact that, the thinner portion is at the exact middle portion)
(vi) In fig.4.199, consider the shape of σ*_2pz 
    ♦ Consider the regions on the left and right sides of the two nuclei
          ✰ Those regions are thicker
          ✰ Those thicker regions are symmetrically distributed on either sides of the two nuclei 
(In the 3D view, we will not recognize the fact that, the thicker portions are symmetrically distributed)  
(vii) That means, the electrons will be spending more time away from the two nuclei
• It is clear that, in the σ*_2pz,
    ♦ The left side nucleus has no influence on the right side electron
    ♦ The right side nucleus has no effect on the left side electron
• The two 2p_z orbitals were independent before bond formation
• Now, even after the formation of the anti-bond, they are trying to separate away from each other
• This is because of the repulsion between the two nuclei
(viii) In fact, there is a definite plane between the two nuclei in the σ*_2pz
• This plane can be clearly marked in the 3D view. This is shown in the fig.4.200 below:

Fig.4.200

• In this plane, we will never find any electrons.  It is a nodal plane.
6. In this step we will see the merger of 2p_x orbitals
A. Bonding orbital
• This can be explained in 7 steps
(i) Assume that, p_y and p_z are removed from the earlier fig.4.195
    ♦ Then we will be able to understand the 'merger of p_x' more easily
• The constructive addition is shown in fig.4.201 below:

Fig.4.201

(ii) The resulting molecular orbital has two 'U' shaped clouds:
    ♦ One on either side of the z-axis
(iii) We have to give it a suitable name
    ♦ We see that, the two 2p orbitals add 'in a side-wise manner'
    ♦ So the resulting molecular orbital is denoted by the symbol '𝞹' 
    ♦ Recall the ‘formation of 𝞹 bonds’ in the topic of hybridization (See fig.4.148 of section 4.26)
(iv) In our present case, the molecular orbital is formed by the merger of two 2p_x orbitals
    ♦ So we call the resulting molecular orbital as: 𝞹2px
(v) The above fig.4.201 is a 3D view. Such a view helps us to understand the actual shapes
• But in the present case, a 2D view will give us some extra details. It is shown in fig.4.202 below:

Fig.4.202

(vi) In fig.4.202, consider the shape of 𝞹2px
    ♦ Consider the region between the two nuclei
          ✰ This region is thicker
(vii) That means, the electrons will be spending more time in the middle portion between the two nuclei
    ♦ So both the nuclei has a strong influence on the electrons
    ♦ This gives rise to a strong bond between the two nuclei
(But it will not be as strong as a 'end-to-end' bond. 'Side-wise' bonding will be weaker than 'end-to-end' bonding) 
• Since the addition is constructive, 𝞹2px is a bonding orbital

B. Anti-bonding orbital
• This can be explained in 8 steps
(i) The destructive addition resulting in the formation of anti-bonding orbital is shown in fig.4.203 below:

Fig.4.203

(ii) The resulting molecular orbital has two separate parts
• Each part has two equal lobes, one on either side of the z-axis
    ♦ We have to give it a suitable name
    ♦ We see that, the two 2p_x orbitals add 'in a side-wise manner'
    ♦ So the resulting molecular orbital is denoted by the '𝞹' symbol 
    ♦ Recall the ‘formation of 𝞹 bonds’ in the topic of hybridization (See fig.4.148 of section 4.26)
(iii) In or present case, the molecular orbital is formed by the merger of two 2p_x orbitals
    ♦ But the resulting molecular orbital is an anti-bonding orbital
    ♦ We have to distinguish it from the bonding orbital. For that, we give an extra '*' symbol
    ♦ So we call the resulting anti-bonding molecular orbital as: 𝞹*_2px
(iv) The above fig.4.203 is a 3D view. Such a view helps us to understand the actual shapes
• But in the present case, a 2D view will give us some extra details. It is shown in fig.4.204 below:

Fig.4.204

(v) In fig.4.204, consider the shape of 𝞹*_2px
    ♦ Consider the region between the two nuclei
          ✰ This region is has very low density of electrons
(vi) Again in fig.4.204, consider the shape of 𝞹*_2px
    ♦ Consider the regions on the left and right sides of the two nuclei
          ✰ Those regions are thicker
          ✰ Those thicker regions are symmetrically distributed on either sides of the two nuclei 
(In the 3D view, we will not recognize the fact that, the thicker portions are symmetrically distributed)  
(vii) That means, the electrons will be spending more time away from the two nuclei
• It is clear that, in the 𝞹*_2px
    ♦ The left side nucleus has no influence on the right side electron
    ♦ The right side nucleus has no effect on the left side electron
• The two 2p_x orbitals were independent before bond formation
• Now, even after the formation of the anti-bond, they are trying to separate away from each other
• This is because of the repulsion between the two nuclei
(viii) In fact, there is a definite plane between the two nuclei in the 𝞹*_2px
• This plane can be clearly marked in the 3D view. This is shown in the fig.4.205 below:

Fig.4.205

• In this plane, we will never find any electrons. It is a nodal plane.

---

• So we have completed 6 steps in the discussion on B₂ molecule
• In the discussion, we have seen:
    ♦ Merger between two p_z orbitals
    ♦ Merger between two p_x orbitals
• In the next section, we will see the following merger:
    ♦ Merger between two p_y orbitals

PREVIOUS           CONTENTS          NEXT


Copyright©2020 Higher Secondary Chemistry. blogspot.in - All Rights Reserved