Molecular orbital (MO) diagram for He2+, He2, He22+, He22-, He2-, and their bond order

Drawing molecular orbital (MO) diagrams can be a tricky task but not for He₂.

The Molecular orbital diagram of He₂ is quite simple. Using this MO diagram, we can calculate its bond order and comment on the bond length, bond stability, and magnetic properties of He₂ and its related ions such as He₂⁺, He₂^–, He₂²⁺, and He₂^2-.

Most importantly, we can find out whether He₂ (a dimer of a Noble gas element) actually exists or is it just an imaginary concept.   

However, to learn all that and much more, you need to do one thing and that is to continue reading this article. So, come along!

How to draw the molecular orbital (MO) diagram of He₂ 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 (BMO) is formed by the linear combination of two AOs in the same phase.

Contrarily, an antibonding molecular orbital (ABMO) 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 displayed schematically on an energy level diagram called the molecular orbital (MO) diagram.

The formula He₂ represents a homonuclear diatomic molecule i.e., a molecule containing two atoms from the same element, in this case, helium (He).

You can easily draw the MO diagram of He₂ following the simple steps given below.

Steps for drawing the molecular orbital (MO) diagram of He₂ with its bond order

1. Write down the electronic configuration of He₂ atoms

He₂ comprises two identical helium (He) atoms.

The electronic configuration of each He-atom is 1s².

2 He-atoms together make a total of 2(2) = 4 electrons available to be displayed in the Molecular orbital diagram of He₂.

2. Determine whether the molecule is homonuclear or heteronuclear

He₂ is a neutral molecule. It is homonuclear as it is formed by the combination of two atoms from the same element.

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

On the MO diagram, the bonding MO (σ1s) is placed at a lower energy level, below the 1s AOs of two He-atoms.

Contrarily, the antibonding MO (σ*1s) is situated at a higher energy level, above the 1s AOs of two He-atoms, as shown below.

3. Fill the molecular orbitals of He₂ with electrons following the energy and bonding principles

A total of 4 electrons are present in the 1s atomic orbitals of two helium atoms.

As per the Aufbau principle, the first electron is singly filled (Hund’s rule) in the lower energy σ1s BMO of He₂. The next electron is then paired up in the same MO in an opposite spin (Pauli Exclusion Principle).

The remaining two electrons are similarly placed as an electron pair in the high-energy σ*1s ABMO of He₂.

All 4 electrons consumed, result in a completely filled Molecular orbital diagram of He₂, as shown below.

As per the above MO diagram, the molecular orbital electronic configuration of He₂ is (σ1s²) (σ*1s²).

Is He₂ diamagnetic or paramagnetic?

The absence of any unpaired electrons in the Molecular orbital diagram of He₂ confirms its diamagnetic nature.

Diamagnetic substances possess no permanent dipole moment value; therefore they get repelled by an external magnetic field.

Bond order of He₂

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 = 2

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

∴ Electrons in σ*1s = 2

⇒ Bond order of He₂ = (2 – 2)/2 = 0/2 = 0.

A bond order of zero means that He₂ is an extremely unstable molecule. It is less stable than the isolated He-atoms. Therefore, He₂ is a hypothetical molecule that does not exist in real life.

Helium (He) is a Noble gas element, inert in nature. It does not react with itself or other elements to gain stability; rather it is very stable on its own possessing a full outer shell electronic configuration i.e., a complete duplet.  

MO diagrams and bond orders of He₂⁺, He₂^–, He₂²⁺ and He₂^2-  

He₂⁺ represents a cation of He₂, carrying a positive 1 charge which means it is formed by the loss of 1 valence electron from one of the two neutral He-atoms.

This results in a total of 4 -1 = 3 electrons available to be filled in the Molecular orbital diagram of He₂⁺. Thus, the electrons present in the higher-energy σ*1s MO of He₂ get unpaired, producing the He₂⁺ MO diagram as shown below.

The presence of an unpaired electron means He₂⁺ is paramagnetic, unlike He₂.

∴ Bond order of He₂⁺ = (N_b –N_a)/2 = (2-1)/2 = 0.5    

Molecular orbital electronic configuration of He₂⁺: (σ1s²) (σ*1s¹)

⇒ Paramagnetic

Conversely, He₂²⁺ is formed by removing two electrons, one from each He-atom.

4 – 2 = 2 electrons available to be filled in the MO diagram of He₂²⁺. Therefore, both the electrons present in σ*1s MO of He₂ are removed, yielding the He₂²⁺ Molecular orbital diagram.

The absence of any unpaired electron implies that He₂²⁺ is diamagnetic.

∴ Bond order of He₂²⁺ = (N_b –N_a)/2 = (2 – 0)/2 = 1

MO electronic configuration of He₂²⁺: (σ1s²)

⇒ Diamagnetic

Contrarily, He₂^– is a negatively charged ion (anion). 1 extra valence electron is gained by a He-atom.

This makes a total of 4 + 1 = 5 electrons available to be filled in the Molecular orbital diagram of He₂^–. This leads to an extra electron singly filled in the σ2s MO of He₂^– (previously empty in the case of He₂).

The σ2s (BMO) and σ*2s (ABMO) molecular orbitals of He₂ or He₂^– are produced by the linear combination of the 2s atomic orbitals of individual He-atoms.

The presence of an unpaired electron denotes the paramagnetic nature of the anion.  

∴ Bond order of He₂^– = (N_b –N_a)/2 = (3– 2)/2 = 0.5  

Molecular orbital electronic configuration of He₂^–: (σ1s²) (σ^*1s²) (σ2s¹)

⇒ Paramagnetic

Finally, He₂^2- is formed when 2 extra valence electrons are gained, one by each He-atom in its 1s atomic orbital. 

4 + 2 = 6 electrons available to be filled in the Molecular orbital diagram of He₂^2-. Thus, the two extra valence electrons are accommodated as an electron pair in the σ2s MO as shown below.

The absence of any unpaired electron makes He₂^2- a diamagnetic molecular ion.

 ∴ Bond order of He₂^2- = (N_b –N_a)/2 = (4 –2)/2 = 1

MO electronic configuration of He₂^2-: (σ1s²) (σ^*1s²) (σ2s²)

⇒ Diamagnetic

To sum up the information discussed above, for the He₂ family, the bond order increases as follows:

He₂  < He₂⁺ = He₂^– < He₂²⁺ = He₂^2-

However, the strength and stability of a bond, which depends on the placement of electrons in the bonding and antibonding MOs in addition to their respective bond order values, increases as shown below:

He₂ < He₂^– < He₂⁺ < He₂^2- < He₂²⁺

As bond length is inversely proportional to bond strength, therefore, the suspected bond lengths of the He₂ family can ideally be arranged in the descending order shown below:

He₂ > He₂^– > He₂⁺ > He₂^2- > He₂²⁺

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 O2+, O2-, O22+, O22-, O2, 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 B2, B2+, B22-, B2-, B22+, 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

• He₂ is a homonuclear diatomic molecule, containing two identical He-atoms.
• The MO electronic configuration of He₂ is (σ1s²) (σ*1s²).
• The absence of any unpaired electron in the Molecular orbital diagram of He₂ denotes it is a diamagnetic molecule. 
• The bond order of He₂ is 0, which means it is extremely unstable and does not exist in real life.
• He₂⁺, He₂^–, He₂²⁺, and He₂^2- are molecular ions formed by the loss or gain of electrons in the valence shell atomic orbitals of individual He-atoms.
• The bond order follows the ascending pattern: He₂ < He₂⁺ = He₂^– < He₂²⁺ = He₂^2- i.e., 0, 0.5, and 1 respectively.
• He₂⁺ and He₂^– are both paramagnetic while He₂²⁺ and He₂^2- are diamagnetic molecular ions.