Molecular orbital (MO) diagram for C2 , C2-, C2+, C22+, C22-, and their bond order

If you are keen on learning how to draw the molecular orbital (MO) diagram of C₂ and calculate its bond order, then come along and continue reading the article.

In this article, we will discuss the Molecular orbital diagrams of C₂, C₂⁺, C₂^–, C₂²⁺, and C₂^2-, calculating their bond orders and determining some useful properties such as the bond strength, bond length, and magnetism of C₂ and its related ions.

How to draw the molecular orbital (MO) diagram of C₂ 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 C₂ represents a homonuclear diatomic molecule i.e., a molecule containing two atoms from the same element, in this case, carbon (C) from Group IV A (or 14) of the Periodic Table.

You can easily draw the MO diagram of C₂ following the simple steps given below.

Steps for drawing the molecular orbital (MO) diagram of C₂ with its bond order

1. Write down the electronic configuration of C₂ atoms

C₂ comprises two identical carbon (C) atoms.

The electronic configuration of each C-atom is 1s² 2s² 2p².

Usually, only the valence electrons are displayed in the MO diagram of a molecule, therefore, it is important to note that each C-atom contains 4 valence electrons.

2 C-atoms combined make a total of 2(6) = 12 electrons and 2(4) = 8 valence electrons to be filled in the Molecular orbital diagram of C₂.

2. Determine whether the molecule is homonuclear or heteronuclear

C₂ 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 carbon 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 C-atom overlap 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).

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

3. Fill the molecular orbitals of C₂ with electrons following the energy and bonding principles

A total of 4 electrons are present in the 1s atomic orbitals of two carbon 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 carbon, are uniformly distributed between σ2s and σ*2s molecular orbitals of C₂.

In contrast, there are a total of 2 + 2 = 4 electrons in the 2p atomic orbitals of two C-atoms.

2 out of the 4 electrons are first singly filled in the π2p_x and π2p_y MOs of C₂ (Hund’s rule). These are then paired up in an opposite spin (Pauli Exclusion Principle).

However, the rest of the 2p bonding and antibonding molecular orbitals stay entirely unoccupied in the MO diagram of C₂.  

Hence, we have successfully filled the Molecular orbital diagram of C₂ as shown below.

As per the above diagram, the Molecular orbital electronic configuration of C₂ is-

(σ1s²) (σ*1s²) (σ2s²) (σ*2s²) (π2p_x²) (π2p_y²)

Is C₂ diamagnetic or paramagnetic?

C₂ is a diamagnetic molecule as there are no unpaired electrons in its molecular orbital diagram.

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

Bond order of C₂

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 + 2 + 2 = 8

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

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

⇒ Bond order of C₂ = (8 – 4)/2 = 4/2 = 2. 

Bond order > 0 means C₂ is stable while a bond order value of 2 implies that there is ideally a double covalent bond (C=C) between two C-atoms in the diatomic C₂ molecule.

MO diagrams and bond orders of C₂⁺, C₂^–, C₂²⁺ and C₂^2-  

C₂⁺ represents a cation of the dicarbon molecule. It is a molecular ion formed by the loss of 1 valence electron from C₂.  

This valence electron is removed from one of the two 2p orbitals of an individual C-atom. Upon C₂⁺ formation, the electron present in π2p_y gets unpaired. As a result, C₂⁺ is paramagnetic and its Molecular orbital diagram is as shown below:

∴ Bond order of C₂⁺ = (N_b –N_a)/2 = (7 – 4)/2 = 1.5  

MO electronic configuration of C₂⁺: (σ1s²) (σ^*1s²) (σ2s²) (σ^*2s²) (π2p_x²) (π2p_y¹)

⇒ Paramagnetic

Conversely, C₂²⁺ is formed by removing two electrons, one from a 2p AO of each C-atom. Therefore, the electrons present in both π2p_x and π2p_y MOs get unpaired, producing the C₂²⁺ MO diagram. The presence of two unpaired electrons reveals the paramagnetic character of C₂²⁺.

∴ Bond order of C₂²⁺ = (N_b –N_a)/2 = (6 – 4)/2 = 1

MO electronic configuration of C₂²⁺: (σ1s²) (σ^*1s²) (σ2s²) (σ^*2s²) (π2p_x¹) (π2p_y¹)

⇒ Paramagnetic

C₂^– is a negatively charged ion (anion). 1 extra valence electron is gained by a parent C-atom. This extra valence electron singly occupies σ2p_z molecular orbital in the Molecular orbital diagram of C₂^–.

∴ Bond order of C₂^– = (N_b –N_a)/2 = (9 – 4)/2 = 2.5

MO electronic configuration of C₂^–: (σ1s²) (σ^*1s²) (σ2s²) (σ^*2s²) (π2p_x²) (π2p_y²) (σ2p_z¹)

⇒ Paramagnetic

Finally, C₂^2- is formed when 2 extra valence electrons are gained in the 2p AOs, one by each parent C-atom. These two electrons are accommodated as an electron pair in σ2p_z in the Molecular orbital diagram of C₂^2-.

The absence of any unpaired electron confirms the diamagnetic nature of C₂^2- unlike C₂⁺, C₂²⁺, and C₂^–.

 ∴ Bond order of C₂^2- = (N_b –N_a)/2 = (10 –4)/2 = 3

MO electronic configuration of C₂^2-: (σ1s²) (σ^*1s²) (σ2s²) (σ^*2s²) (π2p_x²) (π2p_y²) (σ2p_z²).

⇒ Diamagnetic

The bond order also signifies the strength of a bond. Therefore, for the C₂ family, the bond strength increases as follows:

C₂²⁺ < C₂⁺ < C₂ < C₂^– < C₂^2-

On the contrary, bond order is inversely proportional to bond length. The greater the bond strength, the closer the bonded atoms are to each other, i.e., possessing a shorter bond length.  

Therefore, the suspected bond lengths of the C₂ family decrease in the order:

C₂²⁺ > C₂⁺ > C₂ > C₂^– > C₂^2-

Also read:

• Molecular orbital diagram (MO) for Ne2, Ne2+, Ne22+, and Bond order
• Molecular orbital diagram (MO) for O2+, O2-, O22+, O22-, O2, 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 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

• C₂ represents a homonuclear diatomic molecule, containing two identical C-atoms.
• The MO electronic configuration of C₂ is (σ1s²) (σ^*1s²) (σ2s²) (σ^*2s²) (π2p_x²) (π2p_y²).
• The absence of any unpaired electron in the Molecular orbital diagram of C₂ predicts its diamagnetic nature.   
• The bond order of C₂ is 2 which means there is ideally a double covalent bond between two C-atoms in the C₂ molecule.
• C₂⁺, C₂^–, C₂²⁺, and C₂^2- are molecular ions formed by the loss or gain of electrons in the valence shell atomic orbitals of individual C-atoms.
• The bond order follows the ascending pattern: C₂²⁺ < C₂⁺ < C₂ < C₂^– < C₂^2- i.e., 1, 1.5, 2, 2.5, and 3 respectively.
• C₂⁺, C₂^–, and C₂²⁺ are paramagnetic while C₂^2- is a diamagnetic specie.