Molecular Orbital Theory is a model used in chemistry to describe the electronic structure of molecules. It explains the behavior of electrons in molecules in terms of molecular orbitals, which are constructed by combining atomic orbitals.

The Molecular Orbital Theory (often abbreviated to MOT) is a theory on chemical bonding developed at the beginning of the twentieth century by F. Hund and R. S. Mulliken to describe the structure and properties of different molecules. The valence-bond theory failed to adequately explain how certain molecules contain two or more equivalent bonds whose bond orders lie between that of a single bond and that of a double bond, such as the bonds in resonance-stabilized molecules. This is where the molecular orbital theory proved to be more powerful than the valence-bond theory (since the orbitals described by the MOT reflect the geometries of the molecules to which it is applied).

The Key Features of the Molecular Orbital Theory

1. Formation of molecular orbitals from atomic orbitals
2. Prediction of bond order and magnetic properties
3. Estimation of relative energies of molecular orbitals
4. Explanation of the observed shapes of molecules

The total number of molecular orbitals formed will always be equal to the total number of atomic orbitals offered by the bonding species.

Of the three types of molecular orbitals, bonding molecular orbitals have lower energy than the parent orbitals, whereas anti-bonding molecular orbitals have higher energy than the parent orbitals.

The molecular orbitals are filled with electrons in an ascending order of orbital energy (from the orbital with the lowest energy to the orbital with the highest energy).

The most effective combinations of atomic orbitals for the formation of molecular orbitals occur when the combining atomic orbitals have similar energies.

The Molecular Orbital Theory states that atoms tend to combine and form molecular orbitals, where electrons can be found in various atomic orbitals and are associated with different nuclei. In other words, an electron in a molecule can be present anywhere in the molecule.

The Molecular Orbital Theory, after its formulation, has had a major impact on our understanding of the bonding process. This theory works by combining atomic orbitals to form molecular orbitals, and further approximations are made using the Hartree–Fock (HF) or Density Functional Theory (DFT) models to the Schrödinger equation.

Table of Contents

Linear Combination of Atomic Orbitals

Conditions for Linear Combination of Atomic Orbitals

What are Molecular Orbitals?

Types of Molecular Orbitals

Formation of Molecular Orbitals

Bonding Molecular Orbitals

Anti-bonding Molecular Orbitals

Differences Between Bonding and Antibonding Molecular Orbitals

Features of Molecular Orbital Theory

The illustration of the molecular orbital theory approximation of the molecular orbitals as linear combinations of atomic orbitals is as follows:

It is essential to comprehend the concepts of atomic and molecular orbitals before delving deeper into the molecular orbital theory.

Video Lesson: Molecular Orbital Theory

Linear Combination of Atomic Orbitals (LCAO)

Molecular orbitals can generally be expressed as a Linear Combination of Atomic Orbitals (LCAO). These LCAOs are helpful in predicting the formation of these orbitals during the bonding of the atoms forming the molecule.

The Schrodinger equation used to describe the electron behaviour for molecular orbitals can be expressed in a manner analogous to that for atomic orbitals.

It is an approximate method for representing molecular orbitals which is a superimposition of two atomic wave functions. Constructive interference of these two wave functions produces a bonding molecular orbital while destructive interference of the same results in a non-bonding molecular orbital.

Read More

Chemical Bonding

Covalent Bond

Fajan’s Rule

VSEPR Theory

Crystal Field Theory

Conditions for Linear Combination of Atomic Orbitals

The conditions required for the linear combination of atomic orbitals are:

Same Energy of Combining Orbitals

The atomic orbitals that combine to form molecular orbitals should have comparable energy. This means that a 2p orbital of one atom can combine with the 2p orbital of another atom, but a 1s orbital and 2p orbital cannot combine together as they have an appreciable energy difference.

Same Symmetry Around Molecular Axis

The combining atoms should have the same symmetry around the molecular axis for proper combination; otherwise, the electron density will be sparse. For example, all the sub-orbitals of 2p have the same energy, but 2pz orbital of an atom can only combine with a 2pz orbital of another atom, not with 2px and 2py orbitals, as they have a different axis of symmetry. Generally, the z-axis is considered as the molecular axis of symmetry.

Proper Overlap between Atomic Orbitals

The combination of two atomic orbitals to form a molecular orbital is only possible when there is proper overlap. The greater the extent of overlap of the orbitals, the greater the nuclear density between the nuclei of the two atoms.

For the formation of a proper molecular orbital, two simple requirements must be met: the two atomic orbitals should have the same energy and proper overlap, and the same molecular axis of symmetry should be present.

Molecular Orbitals are atomic orbitals that overlap to form a single molecular orbital that is lower in energy than the original atomic orbitals.

The maximum probability of finding an electron in a molecule can be calculated using the molecular orbital function. Molecular orbitals are mathematical functions that describe the wave-like behavior of electrons in a given molecule.

Molecular orbital theory allows us to construct molecular orbitals from a combination of hybridized orbitals or atomic orbitals from each atom in the molecule. This model provides a great insight into the bonding of molecules.

Types of Molecular Orbitals

According to the molecular orbital theory, there are three primary types of molecular orbitals that are formed from the linear combination of atomic orbitals. These orbitals are as follows:

Anti-Bonding Molecular Orbitals

The electron density concentrates behind the nuclei of the two bonding atoms in anti-bonding molecular orbitals, resulting in the repulsion of the nuclei of the two atoms. This weakens the bond between the two atoms.

Non-Bonding Molecular Orbitals

In the case of non-bonding molecular orbitals, there is a complete lack of symmetry in the compatibility of two bonding atomic orbitals, resulting in no positive or negative interactions between the molecular orbitals formed. Consequently, these types of orbitals do not affect the bond between the two atoms.

Formation of Molecular Orbitals

Two atomic orbitals, $\Psi_A$ and $\Psi_B$, represent the amplitude of the electron wave of atoms A and B, respectively. These waves may be in phase or out of phase.

Case 1: When the two waves are in phase so that they add up, the amplitude of the wave amplitude of the wave is given by Φ = ΨA + ΨB.

Case 2: When the two waves are out of phase, the amplitude of the new wave is calculated as Φ ´= ΨA – ΨB, where the waves are subtracted from each other.

Characteristics of Bonding Molecular Orbitals

The probability of finding the electron in the internuclear region of the bonding molecular orbital is higher than that of combining atomic orbitals. link to Probability

The attraction between the two atoms is a result of the electrons present in the bonding molecular orbital.

The bonding molecular orbital has lower energy due to the attraction between the combining atomic orbitals, making it more stable than the combining atomic orbitals.

They are formed by the additive effect of the atomic orbitals so that the amplitude of the new wave is given by Φ = ΨA + ΨB

They are represented by σ, π, and δ.

Characteristics of Anti-Bonding Molecular Orbitals

The probability of finding the electron in the internuclear region decreases in the anti-bonding molecular orbitals.

The electrons present in the anti-bonding molecular orbital cause repulsion between the two atoms.

The anti-bonding molecular orbitals have higher energy due to the repulsive forces and lower stability.

They are formed by the subtractive effect of the atomic orbitals. The amplitude of the new wave is given by Φ’ = ΨA - ΨB

They are represented by σ∗, π∗, and δ∗

What Causes Antibonding Orbitals to be Higher in Energy?

The energy levels of bonding molecular orbitals are always lower than those of anti-bonding molecular orbitals. This is because the electrons in the orbital are attracted by the nuclei in the case of bonding Molecular Orbitals whereas the nuclei repel each other in the case of the anti-bonding Molecular Orbitals.

Difference between Bonding and Antibonding Molecular Orbitals

Bonding molecular orbitals (MOs) are those in which the electron density is concentrated between the two nuclei, leading to a lower energy and increased stability. Antibonding MOs are those in which the electron density is concentrated outside the internuclear region, leading to a higher energy and decreased stability.

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| Molecular Orbital Theory |

| Bonding Molecular Orbitals | Anti-Bonding Molecular Orbitals |

| Bonding molecular orbitals are formed by the additive effect of atomic orbitals | Anti-bonding molecular orbitals are formed by the subtractive effect of atomic orbitals |

| Probability of finding electrons is more in bonding molecular orbitals, while probability of finding electrons is less in antibonding molecular orbitals. There is also a node between the anti-bonding molecular orbital between two nuclei where the electron density is zero. |

| These are formed by the overlap of + with - part of the electron waves |

The electron density in the bonding molecular orbital in the internuclear region is high, resulting in the nuclei being shielded from each other and thus the repulsion is very low. Conversely, the electron density in the antibonding molecular orbital in the internuclear region is very low, causing the nuclei to be less shielded from each other.

| The bonding molecular orbitals are represented by σ, π, δ. | The corresponding anti-bonding molecular orbitals are represented by σ, π, δ^*. |

Stabilization energy is the term used to describe the decrease in energy of the bonding molecular orbital when compared to the combining atomic orbitals, while destabilization energy is the term used to describe the increase in energy of the anti-bonding molecular orbitals.

Try this: Determine whether the following molecules are paramagnetic or diamagnetic by constructing a molecular orbital picture for each: Paramagnetic materials, those with unpaired electrons, are attracted by magnetic fields whereas diamagnetic materials, those with no unpaired electrons, are weakly repelled by such fields.

B2

C2

O2

NO

CO

Features of Molecular Orbital Theory

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When two atomic orbitals overlap, they lose their individual identities and combine to form new orbitals known as molecular orbitals.

The electrons in the molecules are filled in the new energy states called the Molecular orbitals, similar to the way electrons in an atom are filled in an energy state called atomic orbitals.

The probability of finding an electron around a molecule’s group of nuclei is determined by the molecular orbital.

The two combining atomic orbitals should have energies that are similar and orientations that are comparable. For instance, 1s can combine with 1s but not with 2s.

The number of molecular orbitals formed is equal to the number of atomic orbitals combining.

The shape of molecular orbitals formed is dependent on the shape of the combining atomic orbitals.

The Filling of Orbitals According to Molecular Orbital Theory Follows These Rules:

Aufbau’s Principle: Molecular orbitals are filled in an ascending order of energy levels.

Pauli’s Exclusion Principle: In an atom or a molecule, no two electrons can possess the same set of four quantum numbers.

Hund’s Rule of Maximum Multiplicity: Electron pairing does not occur until all atomic or molecular orbitals are filled with a single electron each.