Molecular orbital (MO) diagram for F2, F2+, F2-, F22+, F22-, and their bond order

The chemical formula F₂ represents fluorine, a pale-yellow gas formed by the combination of two identical halogen atoms of exceptional reactivity and electronegativity in the Periodic Table of Elements.

In this article, we will teach you the step-by-step construction of the molecular orbital (MO) diagram of fluorine (F₂) that provides insight into the bond order, bond length, strength, and magnetic properties of the fluorine molecule. You will also learn to draw the MO diagrams of related molecular ions i.e., F₂⁺, F₂^–, F₂²⁺, and F₂^2-.

So let’s take a deep dive into this intricate but super fun realm of Chemistry.

How to draw the molecular orbital (MO) diagram of F₂ 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.

Fluorine (F₂) is a homonuclear diatomic molecule. Two identical F-atoms combine to form an F₂ molecule.

We can easily draw the Molecular orbital diagram of F₂ following the steps given below.

Steps for drawing the molecular orbital (MO) diagram of F₂ with its bond order

1. Write down the electronic configuration of F₂ atoms

F₂ consists of two fluorine (F) atoms.

The electronic configuration of each F-atom is 1s² 2s² 2p_x² 2p_y² 2p_z¹.

Usually, only the valence electrons are displayed in the MO diagram of a molecule, therefore, it is important to note that each F-atom contains 7 valence electrons.

2 F-atoms combined make a total of 18 electrons and 14 valence electrons in F₂.

2. Determine whether the molecule is homonuclear or heteronuclear

F₂ is a neutral molecule. It is homonuclear as it is formed by two atoms of the same element. Thus the individual AOs of two F-atoms lie at the same energy level.

As per the rule of LCAO, the two 1s atomic orbitals of fluorine 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 F-atom overlap to produce six MOs including three bonding MOs (σ2p_z, π2p_x, and  π2p_y) 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 F₂ with electrons following the energy and bonding principles

A total of 4 electrons are present in the 1s atomic orbitals of two fluorine 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 fluorine, are uniformly distributed between σ2s and σ*2s molecular orbitals of F₂.

In contrast, there are a total of 5 + 5 = 10 electrons in the 2p atomic orbitals of two F-atoms. Thus, the first two electrons are placed in σ2p_z while the next two are situated in π2p_x and π2p_y and consequently paired up.

2 + 2 + 2 = 6 leaves behind 10 – 6 = 4 valence electrons which are finally placed in the high energy antibonding MOs (π*2p_x and π*2p_y), one in each (Hund’s rule) and then paired up in opposite spins (Pauli Exclusion Principle).  

This successfully completes the molecular orbital diagram of F₂ as shown below.

Is F₂ diamagnetic or paramagnetic?

F₂ is a diamagnetic molecule as there are no unpaired electrons in its molecular orbital diagram. Rather, even the electrons in the high-energy antibonding MOs (π*2p_x and π*2p_y) are paired up.

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

Bond order of F₂

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 + σ2p_z + π2p_x + π2p_y = 2 + 2 + 2 + 2 + 2 = 10

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

∴ Electrons in σ*1s + σ*2s + π*2p_x + π*2p_y = 2 + 2 + 2 + 2 = 8

⇒ Bond order of F₂ = (10 – 8)/2 = 2/2 = 1.  

A bond order of 1 implies that there is a single covalent bond (F-F) between two F-atoms in an F₂ molecule.

MO diagrams and bond orders of F₂⁺, F₂^–, F₂²⁺ and F₂^2-  

F₂⁺ represents a cation of fluorine. It is a molecular ion formed by the loss of 1 valence electron from the fluorine molecule.

This valence electron is removed from the least stable, high-energy 2p atomic orbital of an F-atom. As a result, the Molecular orbital diagram of fluorine is transformed as shown below:

∴ Bond order of F₂⁺ = (N_b –N_a)/2 = (10 – 7)/2 = 1.5

⇒ Paramagnetic

Similarly, F₂²⁺ is formed by removing two electrons, one from a 2p AO of each F-atom. Therefore, the electrons present in both π^*2p_x and π^*2p_y MOs get unpaired to produce the F₂²⁺ Molecular orbital diagram.

∴ Bond order of F₂²⁺ = (N_b –N_a)/2 = (10 – 6)/2 = 2

⇒ Paramagnetic

Contrarily, F₂^– is a negatively charged anion. 1 extra valence electron is gained by an F-atom. This extra electron singly fills σ*2p_z in the Molecular orbital diagram of F₂^–.

∴ Bond order of F₂^– = (N_b –N_a)/2 = (10 – 9)/2 = 0.5

⇒ Paramagnetic

Finally, F₂^2- is formed when 2 extra valence electrons are gained, one by each parent F-atom. Consequently, these 2 electrons are accommodated as an electron pair in the highest energy antibonding MO i.e., σ*2p_z, resulting in an F₂^2- Molecular orbital diagram, completely filled with electrons.   

∴ Bond order of F₂^2- = (N_b –N_a)/2 = (10 –10)/2 = 0

⇒ Diamagnetic

F₂^2- is an exception. It is the only diamagnetic molecular ion out of all those discussed above.

However, a bond order of zero implies that the formation of F₂^2- ion is extremely unlikely in real life. Rather, it is a hypothetical ion only.

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

F₂^2- < F₂^– < F₂ < F₂⁺ < F₂²⁺

However, bond order is inversely proportional to bond length. The greater the bond strength, the closer the bonded atoms are to each other.

Therefore, the bond lengths of the fluorine family decrease in the order:

F₂^2- > F₂^– > F₂ > F₂⁺ > F₂²⁺

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 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 O2+, O2-, O22+, O22-, O2, 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

• Fluorine (F₂) is a homonuclear diatomic molecule. Two identical F-atoms combine to form F₂.
• As per MOT, 10 atomic orbitals of individual fluorine atoms combine to form 10 molecular orbitals including 5 bonding and 5 antibonding MOs.
• The MO electronic configuration of F₂ is (σ1s²)(σ^*1s²)(σ2s²)(σ^*2s²) (σ 2p_z²) (π2p_x²)(π2p_y²)(π^*2p_x²) (π^*2p_y²).
• The absence of any unpaired electrons in the Molecular orbital diagram of F₂ denotes it is a diamagnetic substance.
• The bond order of F₂ is 1 which means there is a single covalent bond between two F-atoms in the F₂ molecule.
• F₂⁺, F₂^–, F₂²⁺, and F₂^2- are molecular ions formed by the loss or gain of electrons in the valence shell atomic orbitals of individual F-atoms.
• The bond order follows the ascending pattern: F₂^2- < F₂^– < F₂ < F₂⁺ < F₂²⁺ i.e., 0, 0.5, 1, 1.5, and 2 respectively.
• F₂⁺, F₂^– and F₂²⁺ are all paramagnetic while F₂^2- is diamagnetic in nature.