Orbital hybridisation

(Note: The 1s orbital is lower in energy than the 2s orbital, and the 2s orbital is lower in energy than the 2p orbitals)

The valence bond theory would predict, based on the existence of two half filled p-type orbitals (the designations p_x p_y or p_z are meaningless at this point, as they do not fill in any particular order), that C forms two covalent bonds. CH₂, however, is known as a methylene group and cannot exist outside of a molecular system. Therefore, this theory alone cannot explain the existence of CH₄.

Furthermore, ground state orbitals cannot be used for bonding in CH₄. While exciting a 2s electron into a 2p orbital would theoretically allow for four bonds, according to the valence bond theory which has been proved experimentally correct for systems like O₂ this would imply that the various bonds of CH₄ would have differing energies due to differing levels of orbital overlap. Once again, this has been experimentally disproved: any hydrogen can be removed from a carbon with equal ease.

To summarise, to explain the existence of CH₄ and many other molecules a method by which as many as 12 bonds (for transition metals) of equal strength (and therefore equal length) can be created is required.

The answer is the theory of hybridisation. At this time it is important to note that orbitals are, and always will be, a model. They are not real. They are derived from specialised solutions of the Schrödinger equation and therefore to hybridise, to mix an orbital, is simply to change the mathematical function governing where that electron should be. It is not altering the structure of the atom in any way.

The first step in hybridisation is the excitation of one (or more) electrons. From this point of the explanation on, it can be assumed that the subject of study is carbon in the context of methane, for simplicity. The proton that forms the nucleus of a hydrogen atom attracts one of the valence electrons on carbon. This causes an excitation, moving a 2s electron into a 2p orbital. This, however, increases the influence of the carbon nucleus on the valence electrons by increasing the effective core potential (the amount of charge the nucleus exerts on a given electron = Charge of Core - Charge of all electrons closer to the nucleus).

The combination of these forces creates new mathematical functions known as hybridised orbitals. In the case of carbon attempting to bond with four hydrogens, four orbitals are required. Therefore, the 2s orbital (core orbitals are almost never involved in bonding) mixes with the three 2p orbitals to form four sp³ hybrids (read as s p three). See graphical summary below.

becomes
In CH₄, four sp³ hybridised orbitals are overlapped by hydrogen's 1s orbitals, yielding four sigma (σ) bonds. The four bonds are of the same length and strength, and there are four of them. This theory fits our requirements.

translates into

Similarly, other C-compounds and other molecules may be explained, for example ethene (C₂H₄). Carbon will never form any less than four bonds unless it is given no other choice, which only seldom occurs. Therefore, ethene has two double bonds between the carbons. The Lewis structure looks like this:

Carbon will sp² hybridise, because hybrid orbitals will form only sigma bonds and one pi bond is required for the double bond between the carbons. The hydrogen-carbon bonds are all of equal strength and length, which agrees with experimental data.

Molecule shape

• AX₂ (eg, BeCl₂): sp hybridisation; linear or digonal shape
• AX₃ (eg, BCl₃): sp² hybridisation; trigonal planar shape
• AX₄ (eg, CCl₄): sp³ hybridisation; tetrahedral shape
• AX₅ (eg, PCl₅): sp³d hybridisation; trigonal bipyramidal shape
• AX₆ (eg, SF₆): sp³d² hybridisation; octahedral (or square bipyramidal) shape