Molecular orbital (MO) diagram for H2, H2-, H2+, H22-, H22+, and their bond order
The molecular orbital (MO) diagram of H2 reveals the secrets behind the bonding principles of hydrogen- a low-density, high-reactivity, explosive gas, packed with exceptional energy content.
In this article, we will teach you how to draw the Molecular orbital diagram of H2 and its related ions i.e., H2+, H2–, H22+, and H22-.You will also learn to calculate the bond orders, predicting the stability, bond lengths, and magnetic properties of all the aforementioned.
How to draw the molecular orbital (MO) diagram of H2 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:
Aufbau Principle: Electrons first occupy the lower energy orbitals followed by their placement in the higher energy molecular orbitals.
Hund’s Rule: The incoming electrons are singly filled in the degenerate MOs before pairing occurs.
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.
H2 is a homonuclear diatomic molecule i.e., a molecule containing two identical atoms from the same element i.e. hydrogen (H).
Drawing the Molecular orbital diagram of H2 is a super easy task if you follow the simple steps given below.
Steps for drawing the molecular orbital (MO) diagram of H2 with its bond order
1. Write down the electronic configuration of H2 atoms
H2 comprises two identical hydrogen (H) atoms.
The electronic configuration of each H-atom is 1s1.
2 H-atoms together make a total of 2(1) = 2 electrons to be displayed in the Molecular orbital diagram of H2.
2. Determine whether the molecule is homonuclear or heteronuclear
H2 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 hydrogen 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 H-atoms.
Contrarily, the antibonding MO (σ*1s) is situated at a higher energy level, above the 1s AOs of two H-atoms, as shown below.
3. Fill the molecular orbitals of H2 with electrons following the energy and bonding principles
A total of 2 electrons are present in the 1s atomic orbitals of two hydrogen atoms.
As per the Aufbau principle, the first electron is singly filled (Hund’s rule) in the lower energy σ1s MO of H2. The next electron is then paired up in the same MO in an opposite spin (Pauli Exclusion Principle).
This successfully completes the H2 Molecular orbital diagram shown below in which the σ*1s MO stays empty.
MO electronic configuration of H2: (σ1s2)
Is H2 diamagnetic or paramagnetic?
The absence of any unpaired electrons in the Molecular orbital diagram of H2 confirms its diamagnetic nature.
Diamagnetic substances possess no permanent dipole moment value; therefore they get repelled by an external magnetic field.
Bond order of H2
The bond order formula is:
∴ Bond order = (Nb –Na)/2
Nb = Electrons present in the bonding MOs (Bonding electrons).
∴ Electrons in σ1s = 2
Na= Electrons present in the anti-bonding MOs (Anti-bonding electrons).
∴ Electrons in σ*1s = 0
⇒ Bond order of H2 = (2 – 0)/2 = 2/2 = 1.
A bond order of 1 means that there is a single covalent bond between two H-atoms in H2.
MO diagrams and bond orders of H2+, H2–, H22+ and H22-
H2+ represents a cation of H2, carrying a positive 1 charge which means it is formed by the loss of 1 valence electron from one of the two neutral H-atoms.
An H+ ion (proton) is produced by removing the single valence electron possessed by an H-atom.
This results in only 2 -1 = 1 electron available to be filled in the Molecular orbital diagram of H2+. Thus, the electrons present in σ1s MO get unpaired, as shown below.
The presence of an unpaired electron means H2+ is paramagnetic, unlike H2.
∴ Bond order of H2+ = (Nb –Na)/2 = (1-0)/2 = 0.5
MO electronic configuration of H2+: (σ1s1)
⇒ Paramagnetic
Conversely, H22+ is formed by removing two electrons, one from each H-atom.
2– 2 = 0 electrons available to be filled in the MO diagram. Therefore, both the electrons present in σ1s MO of H2 are removed, resulting in an empty H2 Molecular orbital diagram. The absence of any unpaired electrons implies that H22+ is diamagnetic.
∴ Bond order of H22+ = (Nb –Na)/2 = (0 – 0)/2 = 0
MO electronic configuration of H22+: (σ1s0)
⇒ Diamagnetic
A bond order of zero denotes that H22+ is less stable than the isolated H-atom. It is thus a hypothetical molecular ion that does not exist in real life.
H2– is a negatively charged ion (anion). 1 extra valence electron is gained by an H-atom.
This makes a total of 2 + 1 = 3 electrons available to be filled in the Molecular orbital diagram of H2–. This extra valence electron is accommodated in the high-energy sigma antibonding MO (σ*1s) as shown below.
The presence of an unpaired electron denotes the paramagnetic nature of the anion.
∴ Bond order of H2– = (Nb –Na)/2 = (2– 1)/2 = 0.5
MO electronic configuration of H2–: (σ1s2) (σ*1s1)
⇒ Paramagnetic
Finally, H22- is formed when 2 extra valence electrons are gained, one by each H-atom in its 1s atomic orbital.
2 + 2 = 4 electrons available to be filled in the Molecular orbital diagram of H22-. Thus, the two extra valence electrons are accommodated as an electron pair in σ*1s MO as shown below.
The absence of any unpaired electron makes H22- a diamagnetic molecular ion.
∴ Bond order of H22- = (Nb –Na)/2 = (4 –4)/2 = 0
MO electronic configuration of H22-: (σ1s2) (σ*1s2)
⇒ Diamagnetic
Again, a bond order of zero implies that H22- just like H22+ is extremely unstable and thus non-existent.
To sum up the information discussed above, for the H2 family, the bond order increases as follows:
H22+ = H22- < H2+ = H2– < H2
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 value, increases as shown below:
H22- < H22+ < H2– < H2+ < H2
As bond length is inversely proportional to bond strength, therefore, the suspected bond lengths of the H2 family can ideally be arranged in the descending order shown below:
The molecular orbital diagram of H2 is shown below.
The MO electronic configuration of H2 is σ1s2.
The absence of any unpaired electron in the above MO diagram reveals the diamagnetic character of H2.
The bond order of H2 is calculated as follows:
Bond order = (Nb-Na)/2 = (2-0)/2 = 1
How is the Molecular orbital diagram of H2– different from that of H2?
There are a total of 3 electrons to be filled in the Molecular orbital diagram of H2–. Therefore, its MO electronic configuration is (σ1s2) (σ*1s1). The extra valence electron is singly filled in the high-energy sigma antibonding MO.
Therefore, H2– is paramagnetic in nature. Contrarily, the MO electronic configuration of H2 is σ1s2. The absence of any unpaired electron reveals the diamagnetic behavior of H2.
Discuss the relative stabilities of H2, H2+, and H2– w.r.t their molecular orbital diagrams.
The stability of a molecule or molecular ion is generally related to its bond order. The higher the bond order, the greater the molecular stability.
The bond orders of the above-mentioned species are:
H2 (1), H2+ (0.5) and H2– (0.5).
This means H2 is the most stable. H2+ and H2– possess the same bond order; however, H2+ is slightly more stable than H2– because the latter contains electrons in the less stable sigma antibonding MO while H2+ contains its only electron in the relatively more stable sigma bonding MO.
Therefore, stability increases in the order:
H2–< H2+< H2
Which of the following possess the strongest bond H2, H2+, H2–, H22+, or H22-?
The higher the bond order value, the greater the bond strength. The bond orders of the above-mentioned species are:
Thus, H2 possesses the strongest bond out of all five.
Which out of H2+ and H2 possess a longer bond length as per MOT?
Bond length is inversely proportional to bond order. As the bond order of H2+ (0.5) is less than that of H2 (1), therefore, H2+ possesses a higher bond length.
It is also experimentally proven that the bond length of H2+ (106 pm) > the bond length of H2 (74 pm).
What is the MO electronic configuration of H22-? Is this a stable species?
The Molecular orbital electronic configuration of H22- is (σ1s2) (σ*1s2). Its bond order is calculated as follows:
Bond order = (Nb-Na)/2 = (2-2)/2 = 0
An equal number of bonding and antibonding electrons and a bond order of zero means that H22- is extremely unstable. Rather, it is only a hypothetical (imaginary) anion.
Summary
H2 is a homonuclear diatomic molecule. Two identical hydrogen atoms combine to form H2.
The MO electronic configuration of H2 is (σ1s2).
The absence of any unpaired electrons in the Molecular orbital diagram of H2 denotes it is a diamagnetic molecule.
The bond order of H2 is 1, which means there is a single covalent bond between two hydrogen atoms in H2.
H2+, H2–, H22+, and H22- are molecular ions formed by the loss or gain of electrons in the valence shell atomic orbitals of individual H-atoms.
The bond order follows the ascending pattern: H22+ = H22- < H2+ = H2– < H2i.e., 0, 0.5, and 1 respectively.
H2+ and H2– are both paramagnetic while H22+ and H22- are diamagnetic molecular ions.
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/
Topblogtenz is a website dedicated to providing informative and engaging content related to the field of chemistry and science. We aim to make complex subjects, like chemistry, approachable and enjoyable for everyone.
