Conditions for Linear Combination of Atomic Orbitals

The molecular orbital hypothesis describes how two atoms create a chemical link by overlapping their atomic orbitals. This hypothesis was established by Robert Mulliken and Friedrich Hund around the twentieth century. The overlapping of 2 or more atomic orbitals results in the generation of an equal number of molecular orbitals. A mathematical method called the linear combination of atomic orbitals (LCAO) is used to express molecular orbitals. The below article will briefly discuss the LCAO and the prerequisites for the linear combination of atomic orbitals. 

What are atomic orbitals?

According to the atomic orbital definition, it is the quantum state of an individual electron in a single atom’s electron cloud. 

The chance of locating a specific atom’s electron in a certain region of space is described by atomic orbitals. It also depicts the wave-like behaviour of electrons. Atomic orbitals are the fundamental building blocks of the atomic orbital model. This model is also known as the wave mechanics or electron cloud model. It is an advanced framework for visualising the electron’s submicroscopic behaviour in matter. 

The Schrodinger equation solutions can calculate an atom’s electron density. A total of two electrons can be found in an atomic orbital. Sublevels of atomic orbitals are designated as s, p, d, and f. The shapes of atomic orbitals vary from one sublevel to the other. For example, the sublevel s is a sphere. The p sublevel is dumbbell-shaped, and the shapes of d and f orbitals are pretty complex.

What are molecular orbitals?

A molecular orbital is a mathematical function that specifies the location of an electron in a molecule. R.S. Mulliken and F. Hund proposed it for the first time in 1932. A molecular orbital can calculate physical and chemical parameters like the probability of finding an electron in a specific location. It also depicts the wave-like behaviour of electrons.

The region of space where a molecule’s valence electron is most usually present is known as a molecular orbital (MO). The MO can be classified into three types, namely non-bonding, bonding and antibonding molecular orbitals. 

Linear combinations of atomic orbitals

A linear combination of atomic orbitals (LCAO) can be employed to express molecular orbitals. It is the mathematical process of merging atomic orbitals to form molecular orbitals. The orbital formation from the interaction between the atoms that form a molecule can be predicted using the LCAO. It’s basically a superimposition, or overlapping approach wherein constructive interference of 2 atomic wave functions produces a BMO (bonding molecular orbital), and destructive interference produces an ABMO (antibonding molecular orbital)

Conditions for the linear combination of atomic orbitals

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

• Adequate overlapping of atomic orbitals

Sufficient overlapping is required when merging two atomic orbitals to form molecular orbitals. The extent of overlap determines the density of electrons among molecular orbital nuclei. To generate the proper molecular orbital, you need the correct orientation and the right amount of energy. For proper overlapping, the atomic orbitals must have identical orbital energies. A molecule’s orbitals are filled with electrons from its constituent atoms. In addition, the atomic orbitals must adequately overlap and have the same molecular axis of symmetry for proper orientation.

• Symmetry around the molecular axis

The merging atoms must have the same symmetry around the molecular axis to successfully combine. For example, one atom’s 1pz orbital will only combine with another atom’s 1pz orbital. You might be wondering why, given that all of the 1p sub-orbitals have the same energy. It’s worth mentioning that atomic orbitals with the same or roughly the same energy levels will not merge if their symmetry differs. For example, because of their different axis of symmetry, an atom’s 1pz orbital cannot merge with 1px and 1py orbitals.

• Atomic orbital energies

The atomic orbitals that combine to form molecular orbitals should have the same or approximately the same energy levels. Let’s have a look at an example. Because their energy levels are comparable, the 1s orbital can merge with another 1s orbital. The 1s orbital, on the other hand, cannot be combined with a 2s orbital. The reason for this is that the latter’s energy level is substantially higher than the 1s orbital. 

Conclusion

A mathematical process known as the linear combination of atomic orbitals can be used to anticipate the orbital production from atomic interactions that form molecules. The atomic orbitals must fulfil certain requirements to merge and produce molecular orbitals. The energy levels and symmetry of the interacting atoms around the molecular axis, for example, should be the same. The efficiency of atomic orbital interactions is also determined by the sufficient overlapping of the atomic orbitals.