4.2 Hybrid Atomic Orbitals

Objectives

By the end of this section, you will be able to:

• Explain the concept of atomic orbital hybridization
• Determine the hybrid orbitals associated with various molecular geometries

Thinking in terms of overlapping atomic orbitals is one way for us to explain how chemical bonds form in diatomic molecules. However, to understand how molecules with more than two atoms form stable bonds, we require a more detailed model.

As an example, let us consider the water molecule, in which we have one oxygen atom bonding to two hydrogen atoms. Oxygen has the electron configuration 1s²2s²2p⁴, with two unpaired electrons (one in each of the two 2p orbitals). Valence bond theory would predict that the two O–H bonds form from the overlap of these two 2p orbitals with the 1s orbitals of the hydrogen atoms. If this were the case, the bond angle would be 90°, as shown in Figure 1 below, because p orbitals are perpendicular to each other. Experimental evidence shows that the bond angle is 104.5°, not 90°. The predictions of the valence bond theory model do not match real-world observations of a water molecule. As a result, researchers need a different model.

Hybridization and Wave Functions

Quantum-mechanical calculations explain why the observed bond angles in H₂O differ from those predicted by the overlap of the 1s orbital of the hydrogen atoms with the 2p orbitals of the oxygen atom. The wave function, ψ, serves as a mathematical expression that provides information about each orbital. It describes the wavelike properties of electrons in an isolated atom. Together, these factors help clarify the discrepancies in bond angle predictions. When atoms bond together in a molecule, their wave functions combine to produce new mathematical descriptions that have different shapes.

Researchers refer to this process of combining wave functions as hybridization. They mathematically achieve this through the linear combination of atomic orbitals (LCAO), a technique that will reappear later. The new orbitals resulting from hybridization are called hybrid orbitals.

Characteristics of Hybrid Orbitals

In an isolated oxygen atom, the valence orbitals consist of a 2s orbital and three 2p orbitals. In contrast, the valence orbitals in an oxygen atom within a water molecule form four equivalent hybrid orbitals that point approximately toward the corners of a tetrahedron. Consequently, the overlap of the O and H orbitals should yield a tetrahedral bond angle of 109.5°. However, the observed angle is 104.5°, which provides experimental evidence supporting the need for hybridization in valence bond theory to make accurate predictions.

The following ideas are important in understanding hybridization:

1. Hybrid orbitals do not exist in isolated atoms. They are formed only in covalently bonded atoms.
2. Hybrid orbitals have shapes and orientations that are very different from those of the atomic orbitals in isolated atoms.
3. Combining atomic orbitals generates a set of hybrid orbitals. The number of hybrid orbitals in the set equals the number of atomic orbitals that were combined to create it.
4. All orbitals in a set of hybrid orbitals are equivalent in shape and energy.
5. The type of hybrid orbitals formed in a bonded atom depends on its electron-pair geometry. This geometry is predicted by VSEPR theory.
6. Hybrid orbitals overlap to form σ bonds. Unhybridized orbitals overlap to form π bonds.

In the following sections, we shall discuss the common types of hybrid orbitals.