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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 B22-.

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.

Name of molecule

Boron

Chemical formula

B2

Electronic configuration

1s2 2s2 2p1

Molecular orbital electronic configuration

(σ1s2)(σ*1s2)(σ2s2)(σ*2s2) (π2px1)(π2py1)

Number of electrons in bonding MOs

6

Number of electrons in anti-bonding MOs

4

Bond order

1

Paramagnetic or Diamagnetic?

Paramagnetic

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.

formation of bonding and antibonding Molecular orbital diagram (MO) for B2

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 (π2px, π2py, and σ2pz) and three anti-bonding MOs (π*2px, π*2py, and σ*2pz).

You must note that the two p-orbitals overlapping end to end produce sigma bonding (σ2pz) and antibonding (σ*2pz) MOs.

Contrarily, the other four p-orbitals overlapping side by side in sets of two, produce the pi bonding (π2px and π2py ) and antibonding (π*2px and π*2py) MOs.

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

Energy level diagram of B2

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 π2px and π2py MOs, as shown in the completed Molecular orbital diagram of B2 drawn below.

Molecular orbital diagram (MO) of Boron (B2) and it's bond order

Is B2 diamagnetic or paramagnetic?

The presence of 2 unpaired electrons in the pi-bonding molecular orbitals of B2 (π2px and π2py) 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 formula for B2

∴ Bond order = (Nb –Na)/2

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

∴ Electrons in σ1s + σ2s + π2px + π2py = 2 + 2 + 1 + 1 = 6

  • Na= 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 B22-  

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.

B2+ Molecular orbital diagram (MO) and Bond order

In the above diagram, though the unpaired electron of π2py is removed, however, π2px still contains a single, unpaired electron. Therefore, B2+ is paramagnetic in nature.

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

MO electronic configuration of B2+: (σ1s2) (σ*1s2) (σ2s2) (σ*2s2) (π2px1)

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 π2px and π2py MOs of B2 are removed, producing the B22+ Molecular orbital diagram, containing no unpaired electron.

∴ Bond order of B22+ = (Nb –Na)/2 = (4 – 4)/2 = 0

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

Diamagnetic 

B22+ Molecular orbital diagram (MO) and Bond order

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 π2px, as shown in the MO diagram of B2 drawn below.

∴ Bond order of B2 = (Nb –Na)/2 = (7– 4)/2 = 1.5  

MO electronic configuration of B2: (σ1s2) (σ*1s2) (σ2s2) (σ*2s2) (π2px2) (π2py1)

Paramagnetic

B2- Molecular orbital diagram (MO) and Bond order

Finally, B22- 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 π2px and π2py are paired up, resulting in no unpaired electron in the Molecular orbital diagram of B22- i.e., a diamagnetic character.

 ∴ Bond order of B22- = (Nb –Na)/2 = (8 –4)/2 = 2

MO electronic configuration of B22-: (σ1s2) (σ*1s2) (σ2s2) (σ*2s2) (π2px2) (π2py2)

Paramagnetic

B22- Molecular orbital diagram (MO) and Bond order

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< B22-

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 > B22-

Also read:

FAQ

What is the molecular orbital (MO) diagram of B2?

The MO diagram of B2 is drawn below:

MO diagram for B2

The MO electronic configuration of B2 is (σ1s2) (σ*1s2) (σ2s2) (σ*2s2) (π2px1) (π2py1).

The presence of 2 unpaired electrons in the Molecular orbital diagram denotes B2 is a paramagnetic molecule.

The bond order of B2 is calculated as follows:

∴ Bond order of B2 = (Nb –Na)/2 = (6 – 4)/2 = 1

How many unpaired electrons are there in the Molecular orbital diagram of B2?

There are 2 unpaired electrons in the MO diagram of B2. These electrons are singly filled in the pi bonding (π2px and π2py) molecular orbitals of B2.

Which of the following options gives the correct ground state magnetic properties of B2 and C2 molecules?

  • A) B2 paramagnetic and C2 diamagnetic
  • B) B2 diamagnetic and C2 paramagnetic
  • C) Both are diamagnetic
  • D) Both are paramagnetic

Option A is the correct answer.

Total number of electrons in B2 = 10. As per the MO diagram shown below, there are two unpaired electrons, situated in the π2px and π2py molecular orbitals of B2, therefore, it is paramagnetic.

MO diagram of B2 is paramagnetic

Contrarily, the total number of electrons in C2 = 12, hence both the unpaired π2px and π2py electrons are paired up in the Molecular orbital diagram of C2, so it is a diamagnetic molecule. 

MO diagram of C2 is Diamagnetic

Which MOs are HOMO and LUMO in the molecular orbital diagram of B2?

HOMO stands for highest occupied molecular orbital while LUMO denotes lowest unoccupied molecular orbital.

In the Molecular orbital diagram of B2, π2px and π2py are HOMOs while σ2pz is LUMO.

How is the bond order of B2 different from that of B22-? Which of the two molecular ions possesses a greater bond length? 

The bond order of B22- (2) is higher than that of B2 (1.5) which means B22- is a more stable molecular ion.

However, as bond order is inversely proportional to bond length, therefore, the bond length of B2 is expected to be greater than that of B22-.

What is the difference between the Molecular orbital diagrams of B2+ and B2?

The MO electronic configuration of B2+ is (σ1s2) (σ*1s2) (σ2s2) (σ*2s2) (π2px1) while that of B2 is (σ1s2) (σ*1s2) (σ2s2) (σ*2s2) (π2px2) (π2py1).

This implies that the pi bonding (π2py) MO of B2+ is completely empty while in B2, π2px contains an electron pair while π2py contains a single unpaired electron.

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)(π2px1)(π2py1)
  • 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 B22- 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 < B22- i.e., 0, 0.5, 1, 1.5, and 2 respectively.
  • B2+ and B2 are both paramagnetic while B22+ and B22- are diamagnetic in nature.
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Vishal Goyal author of topblogtenz.com

Vishal Goyal is the founder of Topblogtenz, a comprehensive resource for students seeking guidance and support in their chemistry studies. He holds a degree in B.Tech (Chemical Engineering) and has four years of experience as a chemistry tutor. The team at Topblogtenz includes experts like experienced researchers, professors, and educators, with the goal of making complex subjects like chemistry accessible and understandable for all. A passion for sharing knowledge and a love for chemistry and science drives the team behind the website. Let's connect through LinkedIn: https://www.linkedin.com/in/vishal-goyal-2926a122b/

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