Why are there no \(s p^{4}\) or \(s p^{5}\) hybrid orbitals?

Hybridization is a concept in molecular orbital theory that explains how atomic orbitals in an atom mix to form new hybrid orbitals. These hybrid orbitals are then involved in the formation of chemical bonds with other atoms. The number of hybrid orbitals formed is equal to the number of atomic orbitals that are mixed in the process. For example, when an s orbital mixes with a p orbital, an sp hybrid orbital is formed, and when an s orbital mixes with two p orbitals, an sp^2 hybrid orbital is created.

In order to understand why there are no sp^4 or sp^5 hybrid orbitals, we need to consider the number of available atomic orbitals that can participate in hybridization in an atom. For formation of hybrid orbitals, the central atom can use its s orbital, and the three p orbitals found in its outer shell. Thus, there can only be a maximum of 4 hybrid orbitals formed by combining these orbitals – and these include: sp (1 s and 1 p), sp^2 (1 s and 2 p), sp^3 (1 s and 3 p), and dsp^3 (1 d, 1 s and 3 p) where a d orbital from a lower shell or an excited state is involved.

As described in step 2, there are only 4 available orbitals (1 s and 3 p orbitals) in the outer shell of an atom that can participate in hybridization. Therefore, an sp^4 hybridization would require the mixing of 1 s orbital with 4 p orbitals. Similarly, an sp^5 hybridization would involve the mixing of 1 s orbital with 5 p orbitals. However, only 3 p orbitals are present in each energy level of an atom, making it impossible for 4 or 5 p orbitals to combine with an s orbital to form sp^4 or sp^5 hybrids. In conclusion, the reason there are no sp^4 or sp^5 hybrid orbitals is because the number of available p orbitals in each energy level of an atom is limited to 3, making it impossible to form hybrids with more than 3 p orbitals.