Same Energy of Combining Orbitals

Around the 20th century, Robert Mulliken and Friedrich Hund established the Molecular Orbital Theory to describe the behaviour and geometry of numerous molecules. The molecular orbital model describes how two atoms create a chemical linkage by overlapping their atomic orbitals. The overlapping of more than one orbital results in the generation of molecular orbitals. A mathematical method is used to express molecular orbitals, called the linear combination of atomic orbitals. In the article below, we will discuss the LCAO and the conditions for the combination of atomic orbitals in detail. 

Molecular Orbitals

A molecular orbital, in chemistry, is a mathematical function that describes where an electron in a molecule is located. It also describes the electron’s wave-like behaviour. A molecular orbital can be used to determine the physical and chemical parameters, such as the likelihood of locating an electron in a certain region. 

The activity of a molecule’s electron is represented by ψ, a wave function in quantum mechanics, similar to the behaviour of an atom’s electrons. Electrons surrounding atoms in molecules have discrete energy levels. A molecular orbital depicted by Ψ2 is the region of space where a molecule’s valence electron is most commonly present. Similar to atomic orbitals, a molecular orbital is filled when it has 2 electrons with opposite spins.

Features of molecular orbital

A molecular orbital is formed by the union of 2 or more atomic orbitals. Some of the important features of the molecular orbital are as follows:

• Molecular orbitals are created by the linear combination of atomic orbitals of the same or almost similar energies. 
• The merging atomic orbitals determine the shapes of the molecular orbitals generated.
• The total count of molecular and atomic orbitals is always equal. So, when two atomic orbitals combine, they form two molecular orbitals. 
• The antibonding molecular orbital and bonding molecular orbital are two significant forms of molecular orbitals. The bonding molecular orbital has lower energy than the atomic orbitals. On the contrary, the antibonding molecular orbital possesses higher energy than the atomic orbitals.
• In a molecule, molecular orbitals are related to the nuclei of a bonded atom.
• The molecular orbital filling uses the same rules as the filling of atomic orbitals. These are the following:
  • Aufbau principle: The filling of Molecular Orbitals is done in the sequence of their ascending energy levels 
  • Pauli’s exclusion principle: The maximum number of electrons in a molecular orbital is two, and they must exhibit opposite or reverse spins. 
  • Hund’s rule of maximum multiplicity: The electron pairing in 2 molecular orbitals with the same levels of energy occurs whenever the orbital has one electron. 

Linear Combinations of Atomic Orbitals

The linear combination of atomic orbitals (LCAO) is the mathematical process of merging atomic orbitals to form molecular orbitals. A linear combination of atomic orbitals can be employed to express molecular orbitals. The creation of orbitals from the interaction between the atoms that form a molecule can be predicted using these LCAOs. The Schrodinger equation for the behaviour of molecular orbital electrons can be stated similarly to the Schrodinger equation for the behaviour of atomic orbital electrons. 

Prerequisites for the combination of atomic orbitals

There are certain conditions for combinations of atomic orbitals to merge and generate molecular orbitals. These conditions or prerequisites are mentioned below. 

• The energy of the atomic orbitals

The energy levels of the atomic orbitals combining to generate molecular orbitals should be the same or nearly the same. Let’s look into an example. The 1s orbital can merge with another 1s orbital since their energy levels are comparable. However, the 1s orbital cannot unite with a 2s orbital. Why? The reason being the energy level of the latter is much higher compared to that of the 1s orbital. 

• Appropriate atomic orbital overlapping

The merging of 2 atomic orbitals to generate molecular orbitals requires adequate overlapping. The density of electrons among the molecular orbital nuclei is proportional to the extent of overlap. Orientation and optimal energy are necessary to create the appropriate molecular orbital. Both atomic orbitals must have similar orbital energy for appropriate overlapping. Electrons from their constituent atoms occupy the orbitals of a molecule. Additionally, the atomic orbitals must appropriately overlap and have the same molecular axis of symmetry for proper orientation.

• Same symmetry 

The merging atoms should share the same symmetry around the molecular axis to combine properly. For instance, the 1pz orbital of one atom will only merge with the 1pz orbital of another atom. You may wonder why since all the sub-orbitals of 1p have the same energy. It’s worth noting that atomic orbitals with the same or nearly the same levels of energy won’t merge if their symmetry isn’t the same. Therefore, an atom’s 1pz orbital can only join with another atom’s 1pz orbital and cannot merge with 1px and 1py

orbitals due to their distinct axis of symmetry.

Conclusion

Whenever 2 or more than 2 atoms of the same or nearly the same energy levels merge, molecular orbitals are formed. The creation of orbitals from the atomic interaction that forms a molecule can be predicted using a mathematical process called the linear combination of atomic orbitals. The atomic orbitals follow certain conditions to merge and form molecular orbitals. For example, the energy levels and symmetry around the molecular axis of the participating atoms should be the same. Also, the overlap between the atomic orbitals determines the efficacy of atomic orbital interactions.