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a molecular orbital (MO) is a mathematical function describing the wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of finding an electron in any specific region.

Molecular bonds are formed by sharing of electrons. A chemical bond is the sharing of two electrons by two atoms. Atoms can form single, double or triple bonds by sharing the respective amount of electrons.

The molecular orbital is a mathematical function that depicts electron in a molecule in its wave like behaviour. This is used for calculating the chemical physical properties of an electron in any specified region.

In 1932, Robert S. Mulliken gave the term orbital which was short for one-electron orbital wave function. Molecular orbitals are formed by combining the hybrid or the atomic orbitals from each of the atom of a molecule or some other molecular orbitals from a group of atoms.

Electrons are present in the orbitals of varied energy levels like 1s, 2s, 3d etc. These orbitals can easily predict the location an electron anywhere around an atom. The molecular orbital theory states that the electrons present in the molecules have their existence in varied orbitals, giving the probability of being able to find that electron at a specific point around the molecule.

Molecular orbitals are formed by the interaction between the atomic orbitals (when the atomic orbitals are compatible with each other).



For producing the set of orbitals for a molecule, the valence atomic wave functions for the bonded atoms in a molecule are added together. For example, let us take the example of the bonds present in the molecules of formula A2- an example of the bonding present in homonuclear diatomic molecules.

Hydrogen or H2 contains the presence of hydrogen atom in 1s orbital and hence we add up the two 1s wave functions.

The in-phase (Since the value of wave functions can either be positive or negative, we can add the wave functions in either in-phase (taking both plus or both minus) or out-of-phase (taking one minus and one plus)) overlap leads to the production of electron density between the two nuclei resulting in an orbital having a low energy.

The other molecular orbital s H-H depicts a decline the electron density existent between the two nuclei. Electron density is zero at the nodal plane between the nuclei. It is also termed as anti-bonding molecular orbital owing to the decrease in the bonding between the two nuclei.

The anti-bonding molecular orbital has higher energy than the bonding orbital or the hydrogen 1s orbital. In H2 molecule, there are no electrons present in the anti-bonding orbital.