Hybridisation

The Problem Hybridisation Solves

By the early 1930s, the valence bond theory could explain the formation of simple diatomic molecules like $\text{H}_2$ and $\text{F}_2$. But it failed spectacularly when faced with polyatomic molecules. Consider methane, $\text{CH}_4$: carbon has two half-filled $2p$ orbitals and one filled $2s$ orbital. If carbon used its pure $2p$ orbitals for bonding, it would form only two bonds — not four. Even if we promoted an electron from $2s$ to the empty $2p$ orbital, the resulting bonds would be of two different types (one from the $2s$ orbital and three from $2p$ orbitals), giving unequal bond lengths and angles. Yet experiment shows all four C–H bonds in methane are identical in length, strength, and energy, with bond angles of exactly $109.5^\circ$.

To resolve this contradiction, Linus Pauling introduced the concept of hybridisation in 1931. The central idea is that atomic orbitals on the same atom can mix — or hybridise — to form a new set of equivalent orbitals called hybrid orbitals. These hybrid orbitals, not the original pure atomic orbitals, are what actually participate in bond formation.

Definition of Hybridisation

Hybridisation is the process of intermixing atomic orbitals of slightly different energies (within the same atom) so as to redistribute their energies, resulting in the formation of a new set of orbitals of equivalent energies and identical shape.

For example, when one $2s$ orbital and three $2p$ orbitals of carbon undergo hybridisation, they produce four new $sp^3$ hybrid orbitals. Each $sp^3$ hybrid orbital has the same energy and the same shape — a lopsided dumbbell with one lobe much larger than the other.

Salient Features of Hybridisation

The textbook lists four key features that define the behaviour of hybrid orbitals. Each one has direct consequences for molecular structure.

1. The number of hybrid orbitals equals the number of atomic orbitals that get hybridised.

This is a conservation law for orbitals. If you mix $n$ atomic orbitals, you always get exactly $n$ hybrid orbitals — no more, no less. For carbon, mixing one $2s$ and three $2p$ orbitals (four atomic orbitals total) gives four $sp^3$ hybrid orbitals. If you mix one $s$ and two $p$ orbitals, you get three $sp^2$ hybrid orbitals. This rule is fundamental: it ensures that the total number of available orbitals for bonding is preserved.

2. The hybridised orbitals are always equivalent in energy and shape.

All hybrid orbitals produced from a given set of atomic orbitals have identical energy and identical shape. This is why all four C–H bonds in methane are identical — each bond uses an $sp^3$ hybrid orbital that is exactly like the other three. The equivalence is a direct consequence of the mathematical mixing process: the new wavefunctions are linear combinations of the original atomic orbitals, and the coefficients are chosen so that the resulting orbitals are as similar as possible.

3. The hybrid orbitals are more effective in forming stable bonds than the pure atomic orbitals.

Hybrid orbitals have a directional character — one lobe is much larger than the other. This asymmetry allows for greater overlap with the orbitals of other atoms. Greater overlap means stronger bonds. In methane, each $sp^3$ hybrid orbital of carbon overlaps more effectively with the $1s$ orbital of hydrogen than a pure $2p$ orbital would, resulting in stronger, more stable C–H bonds.

4. These hybrid orbitals are directed in space in some preferred direction to have minimum repulsion between electron pairs and thus a stable arrangement. Therefore, the type of hybridisation indicates the geometry of the molecules.

This is the most practically useful feature. Hybrid orbitals arrange themselves in space to minimise electron-pair repulsion — exactly the principle behind VSEPR theory. The geometry of the molecule is determined by the spatial arrangement of these hybrid orbitals. For example:

• $sp$ hybridisation gives a linear geometry ($180^\circ$ bond angle)
• $sp^2$ hybridisation gives a trigonal planar geometry ($120^\circ$ bond angle)
• $sp^3$ hybridisation gives a tetrahedral geometry ($109.5^\circ$ bond angle)

Important Conditions for Hybridisation

The textbook lists four conditions that must be satisfied for hybridisation to occur. These are not arbitrary — they follow from the underlying quantum mechanics.

1. The orbitals present in the valence shell of the atom are hybridised. Only orbitals in the outermost (valence) shell participate in hybridisation. Inner-shell orbitals are too low in energy and too tightly bound to the nucleus to mix effectively. For carbon, only the $2s$ and $2p$ orbitals (the valence orbitals) are involved; the $1s$ orbital remains unchanged.
2. The orbitals undergoing hybridisation should have almost equal energy. The energy difference between the mixing orbitals must be small. If the energies are too different, the mixing is inefficient and the resulting hybrid orbitals are not equivalent. This is why $s$ and $p$ orbitals in the same shell (which have similar energies) hybridise readily, but $s$ and $d$ orbitals from different shells generally do not.
3. Promotion of electron is not an essential condition prior to hybridisation. This is a subtle but important point. In the case of carbon, the ground-state electron configuration is $1s^2 2s^2 2p^2$. To form four bonds, one electron from the $2s$ orbital must be promoted to the empty $2p$ orbital, giving the configuration $1s^2 2s^1 2p^3$. This promotion requires energy. However, the energy gained from forming four strong bonds (using hybrid orbitals) more than compensates for the promotion energy. The key point is that promotion and hybridisation are separate steps — promotion can occur before hybridisation, but it is not a prerequisite for the mixing process itself.
4. It is not necessary that only half-filled orbitals participate in hybridisation. In some cases, even filled orbitals of valence shell take part in hybridisation. …