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Molecular Orbital Theory

oxygen as predicted by molecular orbital theory

Core Concepts

In this article, we learn about Molecular Orbital Theory, an important concept in quantum mechanics, as well as its application in understanding molecular bonds and antibonds.

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What is Molecular Orbital Theory?

Molecular orbital theory (MOT) is one of two fundamental bonding theories, along with valence bond theory (VBT), that help explain the formation of bonds between atoms. In particular, molecular orbital theory is useful in explaining how bonding chemically changes atomic behavior. Additionally, the theory accounts for phenomena not explained by valence bond theory, such as the paramagnetic nature of diatomic oxygen

At its most basic, molecular orbital theory states that the formation of bonds involves the mixing of atomic valence orbitals to form molecular orbitals. This differs from valence bond theory, which states that bonds form from shared valence electrons which stay in their atomic orbitals

Forming a Molecular Orbital

In essence, a chemical bond involves the nuclei of two atoms attracted to one another’s electrons. As two nuclei approach one another, this attractive force increases. However, the two atoms also increasingly repel each other at shorter distances, due to the like charges of the nuclei and electrons. Ultimately, there exists some distance where the atoms are most attracted to each other before the repulsive forces dominate the interaction. When two atoms reach this perfect attractive distance, they are considered chemically bonded. This distance is denoted by the minimum (3) in the following graph:

internuclear distance graph

Under molecular orbital theory, the valence orbitals of both atoms mix to form molecular orbitals. As the valence electrons fill these new molecular orbitals, they consequently behave differently than when occupying atomic orbitals. Thus, bonding under molecular orbital theory inherently changes the chemical behavior of the involved atoms.

molecular orbital formation, consistent with theory
The electron orbitals of two atoms mixing to form a molecular bonding orbital.

 According to the laws of quantum mechanics, the number of valence orbitals must remain constant for each atom. Thus, if the two s valence orbitals of two hydrogens mix, two molecular orbitals form: the sigma bonding orbital and sigma antibonding orbital. When electrons occupy the bonding orbital, the atoms’ potential energy drops as a sigma bond of mutual attraction forms. But what exactly is an antibonding orbital?

Bonds and Antibonds

Spatially, for two nuclei to have attractive forces between valence electrons, those electrons must occupy some space between the two nuclei. This space is the bonding orbital.

We can also imagine that the nuclei approach with their electrons occupying the space on the other side of the nuclei. In this case, the attraction of the nuclei to their electrons draws the nuclei apart from each other, preventing a bond. This space is the antibonding orbital.

Further, remembering that electrons count as waves, like sound or light, we can think of a bond as a constructive interaction between the waves of the shared electrons. The combination of the atomic orbitals when they’re “in-phase”, meaning that the electrons both occupy the space between the nuclei, the interaction reinforces itself, forming a bond. However, if the electrons are “out-of-phase”, meaning that both do not occupy the space between the nuclei, the interaction is destructive, preventing further attractive forces between the nuclei.

sigma antibonding and bonding orbital as predicted by molecular orbital theory
Antibonding (top) and bonding (bottom) s molecular orbitals. The dots correspond to nuclei or “nodes”/”antinodes” while the circles correspond to electron clouds.

Differences between Valence Bond Theory and Molecular Orbital Theory

The following table summarizes the differences between valence bond theory and molecular orbital theory.

PhenomenonValence Bond TheoryMolecular Orbital Theory
Bonding OrbitalsElectrons involved in bonding remain in atomic valence orbitals.Electrons involved in bonding enter a newly created molecular bonding orbital.
Individual Atomic ChemistryAtoms maintain their characteristic chemical nature.Atoms chemically change, due to the movement of their electrons into molecular orbitals.
Use of Valence ElectronsGenerally, not all of an atom’s valence electrons are involved in bonding.All of the atom’s valence electrons shift into molecular bonding orbitals, and thus each takes part in bonding.
ResonanceAcknowledges that resonant molecules are chemically distinct.Does not take the resonance of molecules into account.
Molecular BondingOnly accounts for the bonding relationship between two atoms at a time.Accounts for the bonding of the entire molecule.
HybridizationDefines and characterizes hybridization.Does not illustrate hybridization.

 Bonding Examples in Molecular Orbital Theory

Now that we understand both bonds and antibonds, let’s look at some examples.

H2 Bond Formation

When we have two neutrally-charged hydrogens, both atoms individually have one valence electron in the 1s orbital. As the hydrogens approach, their valence orbitals mix, forming the sigma bonding and antibonding orbitals. We can express these orbital formations using a molecular orbital diagram.

dihydrogen molecular orbital diagram as predicted by molecular orbital theory

As mentioned before, the bonding orbital involves a drop in potential energy. Conversely, antibonding involves an increase in potential energy, as the atoms resist approaching. The molecular orbital diagram reflects these energy changes. Specifically, it displays the sigma bonding and antibonding orbitals respectively below and above the valence orbitals.

Because the atoms seek to lower their potential energy, their single valence electrons fill the sigma bonding orbital, forming a bond.

dihydrogen molecule

O2 Bond Formation

With two neutrally-charged oxygens, both atoms have six total valence electrons across four orbitals 2and 2p energy levels. Since all valence orbitals form molecular orbitals, the eight total valence orbitals between both molecules mix to form eight molecular orbitals. Like with hydrogen, the 2s orbitals form a sigma bonding and a sigma antibonding orbital. The two sets of three 2p orbitals form the same sigma orbitals, as well as two pi-bonding and antibonding orbitals.

dioxygen orbital diagram as dictated by molecular orbital theory
Top: p molecular orbitals. Bottom: s molecular orbitals

Both 2s orbitals of the oxygen hold two electrons, which fill the sigma bonding and antibonding orbitals. Both 2p orbitals have four electrons, for eight total between both oxygens. Since the lowest energy orbitals fill first, the sigma and pi orbitals fill, leaving two electrons to occupy the pi antibonding orbitals. Due to Hund’s Rule, the electrons each occupy a separate antibonding orbital.

In sum, O2 has two sigma bonds and one sigma antibond, which nets one sigma bond. Additionally, the molecule has two pi bonds and two half-filled pi antibonds, which ultimately nets one pi bond. With one sigma and one pi bond, molecular bond theory predicts that oxygen has a double bond, consistent with valence bond theory.

dioxygen molecule

Additionally, as mentioned previously, the placement of the two electrons in the separate antibonds makes O2 paramagnetic. You can observe this paramagnetism when you pour liquid O2 between the poles of a strong magnet. As a result, the liquid oxygen becomes trapped in the magnetic field.

paramagnetic nature of water