Molecular Orbital Theory

In molecular orbital theory, electrons in a molecule are not assigned to individual chemical bonds between atoms but are treated as moving under the influence of the atomic nuclei in the whole molecule. The molecular orbital model is by far the most prolific of the various different chemical bonding models, and it serves as the foundation for the majority of quantitative calculations. Although molecular orbital theory has a lot of complicated mathematics in its entire form, the essential idea behind it is relatively simple to understand. However, in order to fully understand the molecular orbital theory more clearly and thoroughly, it is necessary to first understand what atomic and molecular orbitals are.

Characteristics of Molecular Orbital Theory

• Molecular orbitals are formed from the linear combination of atomic orbitals with almost equal energies.
• In a molecule, molecular orbitals are associated with the nuclei of the bonded atoms.
• The number of created molecular orbitals equals the number of combining atomic orbitals.
• When two atomic orbitals combine, they generate two new orbitals known as bonding and antibonding molecular orbitals. The bonding molecular orbital has less energy than the atomic orbitals, whereas the anti-bonding molecular orbital has more energy than the atomic orbitals.
• The shapes of the produced molecular orbitals are determined by the type of combining atomic orbitals.

Linear Combination of Atomic Orbitals (LCAO)

In quantum chemistry, a linear combination of atomic orbitals (LCAO) is a quantum superposition of atomic orbitals and a method for computing molecular orbitals. In quantum mechanics, wave functions are used to explain electron configurations in atoms. In a mathematical sense, these wave functions are the fundamental functions that define the electrons of a given atom. 

One of LCAO’s basic assumptions is that the number of molecular orbitals equals the number of atomic orbitals included in the linear expansion. Essentially, n atomic orbitals are combined to form n molecular orbitals.

Conditions for Linear Combination of Atomic Orbitals

• Same symmetry: For an appropriate combination, the combining atoms must have the same symmetry around the molecular axis; otherwise, the electron density would be sparse. For example, all sub-orbitals of 2p have the same energy, but an atom’s 2pz orbital can only combine with another atom’s 2pz orbital; it cannot combine with 2px or 2py orbitals as they have a different axis of symmetry.

• Same Energy: The combining atomic orbitals must have the same or nearly the same energy. This indicates that an atom’s 2p orbital can combine with another atom’s 2p orbital, but 1s and 2p cannot since they have a significant energy difference.

• Proper Overlap-If the overlap between the atomic orbitals is appropriate, the two atomic orbitals will combine to produce a molecular orbital. The nuclear density between the nuclei of the two atoms will be higher if their orbitals overlap to a greater extent.

What are Molecular Orbitals?

A molecular orbital is a mathematical function in chemistry that describes the location and wavelike behavior of an electron in a molecule. This function may be used to calculate chemical and physical characteristics like the probability of finding an electron in a given region. In 1932, Robert S. Mulliken used the terms atomic orbital and molecular orbital to refer to one-electron orbital wave functions. 

The location of orbital electrons in an isolated atom is defined by functions known as atomic orbitals. When several atoms combine chemically to create a molecule, the electrons’ positions are decided by the molecule as a whole. Hence, atomic orbitals combine to create molecular orbitals. The molecular orbitals are occupied by electrons from the constituent atoms.

Types of Molecular Orbitals

The different types of Molecular Orbitals are:

1. Bonding Molecular Orbitals: Bonding orbitals place the majority of the electron density between the nuclei of the bonded atoms. Electrons in bonding orbitals help to stabilize the molecule because they are between the nuclei. 

1. Anti-Bonding Molecular Orbitals: Antibonding orbitals place the majority of the electron density outside the nuclei. They also have lower energy due to their proximity to the nuclei.

1. Non-Bonding Molecular Orbitals: The occupation of electrons in a non-bonding orbital, also known as a non-bonding molecular orbital, does neither increase nor decrease the bond order between the participating atoms.

Characteristics of Bonding Molecular Orbitals

• The cumulative impact of atomic orbitals creates bonding molecular orbitals.

• The likelihood of finding an electron in the bonding molecular orbital’s internuclear region is larger than that of the combining atomic orbitals.

• The electrons in the bonding molecular orbitals cause attraction between the two nuclei of bound atoms.

• As a result of attraction, the bonding molecular orbital has less energy than the atomic orbitals from which it is created. This explains why molecular orbitals are stable.

Characteristics of Anti-bonding Molecular Orbitals

• The subtractive effect of the atomic orbitals results in the formation of antibonding molecular orbitals.

• The electron density reduces near the nuclei of the atoms, while the density increases away from the internuclear region.

• The electrons in the antibonding molecular orbital cause the two atoms to repel each other.

• Due to the repulsive force, the antibonding molecular orbital has more energy and less stability than the atomic orbitals from which it is formed. It does not encourage bond formation.

Conclusion

Molecular orbital theory focuses on the assumption that atomic orbitals are combined to form molecular orbitals. Because the electron density from each atom is spread out throughout the span of the whole molecule, the electrons have significantly decreased in energy. This accounts for the stability that happens during bonding. The degree of the stabilization depends upon the amount of overlap between atomic orbitals and the difference in energy between them. Atomic orbitals that overlap efficiently form stable molecular orbitals. One condition for overlap is that the overlapping atomic orbitals must be of equal energies.