Molecular orbital (MO) diagram for B2, B2+, B22-, B2-, B22+, and their bond order

Are you here to learn how to draw the molecular orbital diagram of boron (B₂) and find its bond order? Then, what are you waiting for? Dive into the article and start reading!

In this article, we will teach you the simplest and most profound method for drawing the Molecular orbital diagram of B₂, B₂⁺, B₂^–, B₂²⁺, and B₂^2-.

You will also learn to calculate the bond order of this molecule and its molecular ions, which helps in predicting other useful properties such as bond strength, bond length, magnetism, etc.

How to draw the molecular orbital (MO) diagram of B₂ with its bond order?

As per the molecular orbital theory (MOT) of chemical bonding, after bond formation, the individual atomic orbitals cease to exist. Rather, the atomic orbitals of constituent atoms combine to form a unique set of molecular orbitals (MOs).

The electrons of the participant atoms are thus held in these MOs, belonging to the entire molecule in unison.

The linear combination of atomic orbitals (LCAO) produces two types of molecular orbitals:

• Bonding molecular orbitals
• Anti-bonding molecular orbitals

The number of MOs produced is exactly equal to the number of atomic orbitals coming together.

A bonding molecular orbital is formed by the linear combination of two AOs in the same phase.

Contrarily, an antibonding molecular orbital is produced by the linear combination of two AOs in the opposite phase, counteracting the cohesive forces of the combining nuclei.

This is why, a bonding MO always lies at a lower energy (greater stability) than the parent AOs while an antibonding MO occupies an energy level higher than that of parent AOs (higher instability).

The electrons are filled in these MOs following the three simple rules:

1. Aufbau Principle: Electrons first occupy the lower energy orbitals followed by their placement in the higher energy molecular orbitals.
2. Hund’s Rule: The incoming electrons are singly filled in the degenerate MOs before pairing occurs.
3. Pauli Exclusion Principle: Two electrons placed in the same MO exhibit an opposite spin (clockwise and anticlockwise).

The different numbers of electrons present in the bonding and/or antibonding MOs of a molecule are represented in the form of an energy level diagram called the molecular orbital (MO) diagram.

The MO diagram in turn helps in predicting other useful properties of molecules such as their bond order, bond stability, magnetic behavior, etc.

B₂ is a homonuclear diatomic molecule i.e., a molecule comprising two identical atoms from the same element i.e. boron (B).

We can easily draw the Molecular orbital diagram of B₂ following the steps given below.

Steps for drawing the molecular orbital (MO) diagram of B₂ with its bond order

1. Write down the electronic configuration of B₂ atoms

B₂ comprises two identical boron (B) atoms.

The electronic configuration of each B-atom is 1s² 2s² 2p¹.

Usually, only the valence electrons are displayed in the MO diagram of a molecule, therefore, it is important to note that each B-atom contains 3 valence electrons.

2 B-atoms together make a total of 2(5) = 10 electrons and 2(3) = 6 valence electrons in the B₂ molecule. 

2. Determine whether the molecule is homonuclear or heteronuclear

B₂ is a neutral molecule. It is homonuclear as it is formed by two atoms of the same element.

As per the rule of LCAO, the two 1s atomic orbitals of boron overlap to produce two molecular orbitals i.e., a bonding molecular orbital (σ1s) and an antibonding molecular orbital (σ*1s).

Similarly, two 2s atomic orbitals combine to form two MOs, σ2s and σ*2s.

Finally, the three 2p atomic orbitals from each B-atom combine to produce six MOs including three bonding MOs (π2p_x, π2p_y, and σ2p_z) and three anti-bonding MOs (π*2p_x, π*2p_y, and σ*2p_z).

You must note that the two p-orbitals overlapping end to end produce sigma bonding (σ2p_z) and antibonding (σ*2p_z) MOs.

Contrarily, the other four p-orbitals overlapping side by side in sets of two, produce the pi bonding (π2p_x and π2p_y ) and antibonding (π*2p_x and π*2p_y) MOs.

The MOs discussed above are located on the MO diagram in an increasing energy order.

3. Fill the molecular orbitals of B₂ with electrons following the energy and bonding principles

A total of 4 electrons are present in the 1s atomic orbitals of two boron atoms. Therefore, as per the Aufbau principle, the first two electrons go in the lowest energy σ1s MO, and the remaining two are accommodated in σ*1s.

Similarly, the 4 electrons in the 2s atomic orbitals of boron, are uniformly distributed between σ2s and σ*2s molecular orbitals of B₂.

8 electrons consumed out of the 10 initially available leaves behind only 2 electrons. Thus, these 2 valence electrons singly fill the π2p_x and π2p_y MOs, as shown in the completed Molecular orbital diagram of B₂ drawn below.

Is B₂ diamagnetic or paramagnetic?

The presence of 2 unpaired electrons in the pi-bonding molecular orbitals of B₂ (π2p_x and π2p_y) reveals the paramagnetic nature of B₂.  

Possessing unpaired electrons, paramagnetic substances when exposed to an external magnetic field, experience a magnetic pull and behave like magnets themselves. 

Bond order of B₂

The bond order formula is:

∴ Bond order = (N_b –N_a)/2

• N_b = Electrons present in the bonding MOs (Bonding electrons).

∴ Electrons in σ1s + σ2s + π2p_x + π2p_y = 2 + 2 + 1 + 1 = 6

• N_a= Electrons present in the anti-bonding MOs (Anti-bonding electrons).

∴ Electrons in σ*1s + σ*2s = 2 + 2 = 4

⇒ Bond order of B₂ = (6 – 4)/2 = 2/2 = 1.

A bond order of 1 means there is a single covalent bond between two B-atoms in B₂. Also, a positive bond order value implies that B₂ exists as a stable molecule.

MO diagrams and bond orders of B₂⁺, B₂^–, B₂²⁺ and B₂^2-  

B₂⁺ represents a cation of boron, carrying a positive 1 charge which means it is formed by the loss of 1 valence electron from one of the two neutral B-atoms of B₂. 

This valence electron is removed from the highest energy 2p atomic orbital of a B-atom. This makes a total of 10-1 = 9 electrons available to be filled in the MO diagram of B₂⁺. Thus, the Molecular orbital diagram of B₂⁺ is drawn as shown below.

In the above diagram, though the unpaired electron of π2p_y is removed, however, π2p_x still contains a single, unpaired electron. Therefore, B₂⁺ is paramagnetic in nature.

∴ Bond order of B₂⁺ = (N_b –N_a)/2 = (5-4)/2 = 0.5   

MO electronic configuration of B₂⁺: (σ1s²) (σ^*1s²) (σ2s²) (σ^*2s²) (π2p_x¹)

⇒ Paramagnetic

Conversely, B₂²⁺ is formed by removing two electrons. 10 – 2 = 8 electrons available to be filled in the MO diagram.

Therefore, the electrons present in both π2p_x and π2p_y MOs of B₂ are removed, producing the B₂²⁺ Molecular orbital diagram, containing no unpaired electron.

∴ Bond order of B₂²⁺ = (N_b –N_a)/2 = (4 – 4)/2 = 0

MO electronic configuration of B₂²⁺: (σ1s²) (σ^*1s²) (σ2s²) (σ^*2s²)

⇒ Diamagnetic 

A bond order of zero implies that B₂²⁺ is almost non-existent and its formation is only an imaginary idea devised by scientists to explain certain concepts.

Contrarily, B₂^– is a negatively charged anion. 1 extra valence electron is gained by a B-atom.

10 + 1 = 11 electrons available to be filled in the MO diagram. Thus, as per the Pauli Exclusion Principle, this extra electron is paired up in π2p_x, as shown in the MO diagram of B₂^– drawn below.

∴ Bond order of B₂^– = (N_b –N_a)/2 = (7– 4)/2 = 1.5  

MO electronic configuration of B₂^–: (σ1s²) (σ^*1s²) (σ2s²) (σ^*2s²) (π2p_x²) (π2p_y¹)

⇒ Paramagnetic

Finally, B₂^2- is formed when 2 extra valence electrons are gained in the 2p AOs, one by each parent B-atom.

10 + 2 = 12 electrons available to be filled in the MO diagram. Thus, both π2p_x and π2p_y are paired up, resulting in no unpaired electron in the Molecular orbital diagram of B₂^2- i.e., a diamagnetic character.

 ∴ Bond order of B₂^2- = (N_b –N_a)/2 = (8 –4)/2 = 2

MO electronic configuration of B₂^2-: (σ1s²) (σ^*1s²) (σ2s²) (σ^*2s²) (π2p_x²) (π2p_y²)

⇒ Paramagnetic

The bond order signifies the strength of a bond. Therefore, for the B₂ family, the bond strength increases in the order:

B₂²⁺ < B₂⁺ < B₂ < B₂^– < B₂^2-

However, an increasing bond order in turn means a decreasing bond length. Therefore, the bond lengths of the B₂ family follow the order:

B₂²⁺ > B₂⁺ > B₂ > B₂^– > B₂^2-

Also read:

• Molecular orbital diagram (MO) for Ne2, Ne2+, Ne22+, and Bond order
• Molecular orbital diagram (MO) for C2, C2-, C2+, C22+, C22-, and Bond order
• Molecular orbital diagram (MO) for He2+, He2, He22+, He22-, He2-, and Bond order
• Molecular orbital diagram (MO) for H2, H2-, H2+, H22-, H22+, and Bond order
• Molecular orbital diagram (MO) for Li2, Li2+, Li2-, Li22-, Li22+, and Bond order
• Molecular orbital diagram (MO) for Be2, Be2+, Be22-, Be2-, Be22+, and Bond order
• Molecular orbital diagram (MO) for O2+, O2-, O22+, O22-, O2, and Bond order
• Molecular orbital diagram (MO) for N2, N2+, N22-, N22+, N2-, and Bond order
• Molecular orbital diagram (MO) for F2, F2+, F2-, F22+, F22-, and Bond order
• Molecular orbital diagram (MO) for NF+, NF, NF-, and Bond order
• Molecular orbital diagram (MO) for NO, NO+, NO-, and Bond order
• H2O Molecular orbital diagram (MO), Bond order
• HF Molecular orbital diagram (MO), Bond order

FAQ

Summary

• B₂ is a homonuclear diatomic molecule. Two identical boron atoms combine to form B₂.
• The MO electronic configuration of B₂ is (σ1s²)(σ^*1s²)(σ2s²)(σ^*2s²)(π2p_x¹)(π2p_y¹)
• The absence of any unpaired electrons in the Molecular orbital diagram of B₂ denotes it is a diamagnetic molecule. 
• The bond order of B₂ is 1 which means there is a single covalent bond between two B-atoms in the B₂ molecule.
• B₂⁺, B₂^–, B₂²⁺, and B₂^2- are molecular ions formed by the loss or gain of electrons in the valence shell atomic orbitals of individual B-atoms.
• The bond order follows the ascending pattern: B₂²⁺ < B₂⁺ < B₂ < B₂^– < B₂^2- i.e., 0, 0.5, 1, 1.5, and 2 respectively.
• B₂⁺ and B₂^– are both paramagnetic while B₂²⁺ and B₂^2- are diamagnetic in nature.