The theory

Linear combination of atomic orbitals

Understanding and applying the concept of hybridization is one of the topics that many students have difficulty with. It is only a theory and builds upon the simpler theory of the linear combination of atomic orbitals from different atoms to form covalent bonds. Possibly the difficulty with hybridization may be due to the fact that students do not really understand how molecular orbitals form from atomic orbitals as the topic is not clearly covered by the IB in sub-topic 14.1 Further aspects of covalent bonding. This is because the 'understandings' in the IB chemistry guide refers to "overlap" rather than the combination of atomic orbitals and does not include the existence of anti-bonding orbitals. To understand this consider the simplest case of the combination of two s orbitals (one from each atom) to form a sigma (σ) bond.  When two s orbitals combine together they form two molecular orbitals. One of these molecular orbitals is at a lower energy level than the atomic orbitals and is known as a sigma (σ) bonding orbital. It is formed when the two s atomic orbitals combine constructively. The other, formed when the two s orbitals combine destructively, is at a higher energy and is known as a sigma antibonding orbital denoted by σ*. Overall there is no energy change as the average energy of the bonding and antibonding molecular orbitals is the same as that of the atomic orbitals.

This can be used to explain the bonding in hydrogen. Each hydrogen atom contains one electron in an s orbital. When two hydrogen atoms are brought into contact with each other the orbitals combine to give the two molecular orbitals, each of which can contain two electrons.

According to the aufbau principle both of the electrons from the two hydrogen atoms will go into the molecular orbital with the lowest energy, i.e. the bonding orbital, and a sigma bond is formed as it is more energetically favourable than if the two electrons remain in their separate atomic orbitals. Consider if two helium atoms are brought into close contact. Each contains two electrons (1s²) so two will go into the bonding orbital and two will go into the antibonding orbital so that there is no net gain in energy and so no bond is formed between the helium atoms. An analogous compound to hydrogen is the helium hydride ion HHe⁺,  which is the strongest acid known. It is formed when H (1s¹) and He⁺ (1s¹) combine.. The compound He₂⁺ , formed by the combination of He (1s²) with He⁺ (Is¹), contains two electrons in the bonding molecular orbital and one in the antibonding molecular orbital so overall forms a weak ‘half’ covalent bond (described as having a bond order of ½) which is longer and weaker than the bond in H₂.

When an s atomic orbital on one atom combines with a p orbital on another atom a sigma bonding and a sigma antibonding molecular orbital are formed. Similarly p_x and p_x atomic orbitals combine ‘head on’ to give sigma molecular bonding and antibonding orbitals but the combinations of p_y and p_y and p_z and p_z both involve ‘sideways on’ combinations and pi (π) bonding and antibonding molecular orbitals (π*) are formed.

Hybridization

To understand hybridization it is best to start by considering the bonding in methane. Each of the four hydrogen atoms has the electron configuration 1s¹ and the electron configuration of carbon is 1s²2s²2p². Carbon contains four outer electrons, two paired together in the 2s orbital and one each in two of the three 2p orbitals. It is not easy to see how these can form four sigma bonds without the unpairing of the two 2s electrons nor why the shape of methane is tetrahedral as the p orbitals are orthogonal (at right angles) to each other.  The mixing of atomic orbitals to form new hybrid orbitals with their own properties (e.g. energy and shape) is known as hybridization. When the carbon atom bonds in methane the 2s orbital and the three 2p orbitals hybridize to form four new hybrid orbitals. This is known as sp³ hybridization and the four new hybrid orbitals, which each contain one unpaired electron, point towards the corners of a tetrahedron giving a bond angle of 109.5^o. The electron in each of the sp³ hybrid orbitals is able to combine with an electron in the s orbital of a hydrogen atom to fill the four bonding sigma molecular orbitals leaving the antibonding orbitals empty resulting in four equal C−H sigma bonds. This is shown in slide 1 the gallery below which can also be found on the page on the sub-topic on 14.2 Hybridization.

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Slide 2 in the gallery explains why organic compounds containing three electron domains have a bond angle of 120^o as now the hybridization is sp², i.e. three hybrid orbitals are formed from the s and two of the three p orbitals. The remaining p orbital is free to form a π bond with the p orbital of the bonding atom at right angles to the plane of the sigma bonds. This occurs in alkenes and carbonyl compounds such as aldehydes and ketones. In compounds where  the central carbon atom has two electron domains the bond angle will be 180^o and the two hybrid orbitals are formed from one s and one p orbital to give sp hybridization. This leaves two p orbitals which can each form a π bond with the p orbitals on the bonding atom. This occurs in carbon dioxide, alkynes and nitriles (see Slide 3). It also occurs in carbon monoxide where one of the sp hybrid orbitals on both the carbon and oxygen atoms contains a non-bonding pair of electrons and the other forms a σ bond between the carbon and oxygen atoms along with two π bonds to form the triple bond.

Hybridization and bonding in carbon monoxide

(both the C and O atom are sp hybridized with the triple bond consisting of one σ and two π bonds)

The gallery then goes on to explain the structure of benzene (Slide 5). Delocalization will occur whenever there are alternate C=C and C−C bonds as each of the carbon atoms will be sp² hybridized so the electrons in the resulting π bonds can be spread over all the bonds equally. This results in an increase in electrical conductivity. The electron transition between the bonding and non-bonding orbitals is of lower energy in compounds containing much delocalization (also known as conjugation) than those where the bonding is localized. Hence when they are excited highly conjugated compounds tend to absorb light at a lower wavelength than compounds containing just localized bonds resulting in coloured compounds. Examples of highly conjugated molecules include porphyrins and carotenes (see for example the structure of β-carotene given below and the structures of chlorophyll, heme and α-carotene given in Section 35 of the IB data booklet).

The IB limits the types of hybridization to sp³, sp² and sp and most examples relate to organic compounds but the concept can also be applied to other simple compounds such as NH₃, NH₄⁺ and H₂O for sp³, BF₃ and CO₃²⁻ for sp² and BeCl₂ for sp. Other types of hybridization exist, e.g. d²sp³ for octahedral complexes, but these are beyond the IB syllabus.

Practice quiz

You should now be in a position to answer all of the ten questions which can be found in the quiz on the hybridization page.