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# Molecular Orbital Theory

• Difficulty Level : Medium
• Last Updated : 20 Nov, 2021

The Molecular Orbital Theory is a chemical bonding theory developed at the turn of the twentieth century by F. R. Hund and R. S. Mulliken to explain the structure and properties of various molecules. The valence-bond theory failed to adequately explain how certain molecules, such as resonance-stabilized molecules, contain two or more equivalent bonds with bond orders that fall between that of a single bond and that of a double bond. This is where the molecular orbital theory outperformed the valence-bond theory (since the orbitals described by the MOT reflect the geometries of the molecules to which it is applied).

### Molecular Orbital Theory

In a nutshell, the molecular orbital theory states that each atom tends to combine and form molecular orbitals. As a result of this arrangement, electrons can be found in a variety of atomic orbitals and are typically associated with various nuclei. In a nutshell, an electron in a molecule can be found anywhere within the molecule.

The molecular orbital theory offered a new way of understanding the bonding process after its formulation, which was one of its most significant impacts. According to this theory, molecular orbitals are essentially considered to be linear combinations of atomic orbitals. Approximations to the SchrÃ¶dinger equation are then made using the Hartreeâ€“Fock or density functional theory models.

Features of Molecular Orbital Theory

• The atomic orbitals overlap to form new orbitals known as molecular orbitals. When two atomic orbitals collide, they lose their identity and merge to form new orbitals known as molecular orbitals.
• Similar to how electrons in an atom are filled in an energy state called atomic orbitals, electrons in molecules are filled in new energy states called Molecular orbitals.
• The molecular orbital expresses the probability of finding the electronic distribution in a molecule around its group of nuclei.
• The two combining atomic orbitals should have comparable energies and orientations. 1s, for example, can combine with other 1s but not with 2s.
• The number of formed molecular orbitals equals the number of atomic orbitals combined.
• The shape of the formed molecular orbitals is determined by the shape of the combining atomic orbitals.

### Linear Combination of Atomic Orbitals

A linear combination of atomic orbitals can be used to express molecular orbitals. These LCAOs can be used to predict the formation of these orbitals in the bonding between the atoms that make up a molecule. The Schrodinger equation used to describe electron behaviour in molecular orbitals can be written in a manner similar to that used to describe electron behaviour in atomic orbitals.

It is a rough way of representing molecular orbitals. It’s more of a superimposition method in which constructive interference of two atomic wave functions results in a bonding molecular orbital and destructive interference results in a non-bonding molecular orbital.

Conditions for Linear Combination of Atomic Orbitals

1. Same Energy of Combining Orbitals: The energy levels of the atomic orbitals that combine to form molecular orbitals should be comparable. This means that an atom’s 2p orbital can combine with another atom’s 2p orbital, but 1s and 2p cannot combine because they have a significant energy difference.
2. Same Symmetry about Molecular Axis: For proper combination, the combining atoms must have the same symmetry around the molecular axis; otherwise, the electron density will be sparse. For example, all sub-orbitals of 2p have the same energy, but a 2pz orbital of an atom can only combine with another atom’s 2pz orbital and cannot combine with 2px and 2py orbitals because they have a different axis of symmetry. The z-axis is generally regarded as the molecular axis of symmetry.
3. Proper Overlap between Atomic Orbitals: If the overlap is sufficient, the two atomic orbitals will combine to form a molecular orbital. The greater the extent of orbital overlap, the greater the nuclear density between the nuclei of the two atoms. Two simple requirements can help you understand the condition. Proper energy and orientation are required for the formation of proper molecular orbitals. The two atomic orbitals should have the same energy for proper energy, and the atomic orbitals should have proper overlap and the same molecular axis of symmetry for proper orientation.

### Molecular Orbitals

The molecular orbital function can be used to calculate the space in a molecule where the probability of finding an electron is greatest. Molecular orbitals are mathematical functions that describe the wave nature of electrons in a particular molecule.

These orbitals can be constructed by combining hybridized orbitals of atomic orbitals from each atom in the molecule. Molecular orbitals provide a great model for demonstrating molecule bonding via molecular orbital theory.

Types of Molecular Orbitals

According to molecular orbital theory, some types of molecular orbitals are formed by the linear combination of atomic orbitals. These orbitals are described in more detail below.

• Anti Bonding Molecular Orbitals: In anti-bonding molecular orbitals, the electron density is concentrated behind the nuclei of the two bonding atoms. As a result, the nuclei of the two atoms are pulled apart from each other. These orbitals erode the bond between two atoms.
• Non-Bonding Molecular Orbitals: In the case of non-bonded molecular orbitals, the molecular orbitals created have no positive or negative interactions with each other due to a complete lack of symmetry in the compatibility of two bonding atomic orbitals. These orbitals have no effect on the bond between the two atoms.

Characteristics of Bonding Molecular Orbitals

1. The probability of finding the electron in the bonding molecular orbital’s internuclear region is greater than that of combining atomic orbitals.
2. The electrons in the bonding molecular orbital cause the two atoms to be attracted to one another.
3. Because of attraction, the bonding molecular orbital has lower energy and thus greater stability than the combining atomic orbitals.
4. They are formed as a result of the additive effect of atomic orbitals.

Characteristics of Anti-bonding Molecular Orbitals

1. In the anti-bonding molecular orbitals, the probability of finding an electron in the internuclear region decreases.
2. The electrons in the anti-bonding molecular orbital cause the two atoms to repel each other.
3. Because of the repulsive forces, the anti-bonding molecular orbitals have more energy and less stability.
4. They are formed by the atomic orbitals’ subtractive effect.

Antibonding Orbitals and High Energy: Bonding molecular orbitals always have lower energy levels than anti-bonding molecular orbitals. This is due to the fact that in the case of bonding Molecular Orbitals, the electrons in the orbital are attracted by the nuclei, whereas in the case of anti-bonding Molecular Orbitals, the nuclei repel each other.

### Sample Problems

Question 1: What is a molecular orbital theory?

The Molecular Orbital Theory is a chemical bonding theory established by F. Hund and R. S. Mulliken at the turn of the twentieth century to describe the structure and behaviour of various molecules.

Question 2: Elaborate on Molecular orbital theory.

According to molecular orbital theory, each atom tends to combine and form molecular orbitals. Electrons are found in distinct atomic orbitals as a result of this arrangement, and they are frequently connected with different nuclei. In a molecule, an electron can be found anywhere in the molecule.

Question 3: How is Linear Combination of Atomic orbitals useful?