10.6
Hybridization of Atomic Orbitals I
s and p orbitals overlapping to form covalent bonds cannot yield the various molecular shapes in the VSEPR model. Valence bond theory helps to explain this molecular geometry through the hybridization, or mixing, of atomic orbitals.
Some atomic orbitals involved in bonding recombine to form new orbitals whose shapes are a hybrid of the originals. The initial number of atomic orbitals and the number of hybrid orbitals generated is always the same.
Beryllium fluoride is a linear molecule. The beryllium atom has two valence electrons found in its 2s orbital in the ground state.
The s orbital mixes with one of the empty p orbitals to create orbitals that contain unpaired electrons available for bonding. This leaves two unhybridized p orbitals and produces two sp hybrid orbitals, named for the original atomic orbitals.
The hybrid orbitals have a different shape from their constituent atomic orbitals with one lobe that is significantly larger than the other. Thus, the electron probability density is highly concentrated in a directional lobe, which leads to a more effective overlap with the orbitals of other atoms. For clarity, these orbitals are often shown without the minor lobes.
The half-filled hybrid orbitals undergo end-to-end overlap with orbitals from the fluorine atoms to form two identical covalent bonds, which are also known as sigma (σ) bonds. Therefore, beryllium fluoride exhibits sp hybridization, is linear, and has a 180° bond angle.
The trigonal planar geometry boron trihydride can be explained by sp2 hybridization. Boron has one 2s and three 2p valence orbitals and three valence electrons.
Three of these orbitals, one s, and two p orbitals, mix to produce a set of three sp2 orbitals, each containing one unpaired electron, and one 2p orbital remains unhybridized.
Each of these overlap with a 1s orbital from a hydrogen atom to form three sigma bonds.
A molecule with sp2 hybridization has a trigonal planar geometry with 120° bond angles.
sp3 hybrid orbitals form the tetrahedral shape of a methane molecule. The carbon atom has four valence electrons. The mixing of the 2s and three 2p orbitals generates four equivalent sp3 hybrid orbitals that each can hold one unpaired electron.
The hybrid orbitals obtained through sp3 hybridization overlap with the 1s orbitals of the hydrogen atoms to produce a methane molecule that has tetrahedral geometry and 109.5° bond angles.
The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that result are called hybrid orbitals.
Understanding Atomic Orbital Hybridization
The following ideas are important in understanding hybridization:
- Hybrid orbitals do not exist in isolated atoms. They are formed only in covalently bonded atoms.
- Hybrid orbitals have shapes and orientations that are very different from those of the atomic orbitals in isolated atoms.
- A set of hybrid orbitals is generated by combining atomic orbitals. The number of hybrid orbitals in a set is equal to the number of atomic orbitals that were combined to produce the set.
- All orbitals in a set of hybrid orbitals are equivalent in shape and energy.
- The type of hybrid orbitals formed in a bonded atom depends on its electron-pair geometry, as predicted by the VSEPR theory.
- 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.
sp Hybridization
The beryllium atom in a gaseous BeCl2 molecule is an example of a central atom with no lone pairs of electrons in a linear arrangement of three atoms. There are two regions of valence electron density in the BeCl2 molecule that correspond to the two covalent Be–Cl bonds. To accommodate these two electron domains, two of the Be atom’s four valence orbitals will mix to yield two hybrid orbitals. This hybridization process involves the mixing of the valence s orbital with one of the valence p orbitals to yield two equivalent sp hybrid orbitals that are oriented in a linear geometry. The set of sp orbitals appears similar in shape to the original p orbital, but there is an important difference. The number of atomic orbitals combined always equals the number of hybrid orbitals formed. The p orbital is one orbital that can hold up to two electrons. The sp set is two equivalent orbitals that point 180° from each other. The two electrons that were originally in the s orbital are now distributed to the two sp orbitals, which are half-filled. In gaseous BeCl2, these half-filled hybrid orbitals will overlap with orbitals from the chlorine atoms to form two identical σ bonds.
When atomic orbitals hybridize, the valence electrons occupy the newly created orbitals. The Be atom had two valence electrons, so each of the sp orbitals gets one of these electrons. Each of these electrons pairs up with the unpaired electron on a chlorine atom when a hybrid orbital and a chlorine orbital overlap during the formation of the Be–Cl bonds.
Any central atom surrounded by just two regions of valence electron density in a molecule will exhibit sp hybridization. Other examples include the mercury atom in the linear HgCl2 molecule, the zinc atom in Zn(CH3)2, which contains a linear C–Zn–C arrangement, and the carbon atoms in HCCH and CO2.
sp2 Hybridization
The valence orbitals of a central atom surrounded by three regions of electron density consist of a set of three sp2 hybrid orbitals and one unhybridized p orbital. This arrangement results from sp2 hybridization, the mixing of one s orbital and two p orbitals to produce three identical hybrid orbitals oriented in a trigonal planar geometry.
The observed structure of the borane molecule, BH3, suggests sp2 hybridization for boron in this compound. The molecule is trigonal planar, and the boron atom is involved in three bonds to hydrogen atoms. The three valence electrons of the boron atom in the three sp2 hybrid orbitals are redistributed, and each boron electron pairs with a hydrogen electron when B–H bonds form.
Any central atom surrounded by three regions of electron density will exhibit sp2 hybridization. This includes molecules with a lone pair on the central atom, such as ClNO, or molecules with two single bonds and a double bond connected to the central atom, as in formaldehyde, CH2O, and ethene, H2CCH2.
sp3 Hybridization
The valence orbitals of an atom surrounded by a tetrahedral arrangement of bonding pairs and lone pairs consist of a set of four sp3 hybrid orbitals. The hybrids result from the mixing of one s orbital and all three p orbitals, which produces four identical sp3 hybrid orbitals. Each of these hybrid orbitals points toward a different corner of a tetrahedron.
A molecule of methane, CH4, consists of a carbon atom surrounded by four hydrogen atoms at the corners of a tetrahedron. The carbon atom in methane exhibits sp3 hybridization. The four valence electrons of the carbon atom are distributed equally in the hybrid orbitals, and each carbon electron pairs with a hydrogen electron when the C–H bonds form.
In a methane molecule, the 1s orbital of each of the four hydrogen atoms overlaps with one of the four sp3 orbitals of the carbon atom to form a sigma (σ) bond. This results in the formation of four strong, equivalent covalent bonds between the carbon atom and each of the hydrogen atoms to produce the methane molecule, CH4.
An sp3 hybrid orbital can also hold a lone pair of electrons. For example, the nitrogen atom in ammonia is surrounded by three bonding pairs and a lone pair of electrons directed to the four corners of a tetrahedron. The nitrogen atom is sp3 hybridized with one hybrid orbital occupied by the lone pair.
The molecular structure of water is consistent with a tetrahedral arrangement of two lone pairs and two bonding pairs of electrons. Thus we say that the oxygen atom is sp3 hybridized, with two of the hybrid orbitals occupied by lone pairs and two by bonding pairs. Since lone pairs occupy more space than bonding pairs, structures that contain lone pairs have bond angles slightly distorted from the ideal. Perfect tetrahedral structures have angles of 109.5°, but the observed angles in ammonia (107.3°) and water (104.5°) are slightly smaller. Other examples of sp3 hybridization include CCl4, PCl3, and NCl3.
This text has been adapted from Openstax, Chemistry 2e, Section 8.2: Hybrid Atomic Orbitals.
s and p orbitals overlapping to form covalent bonds cannot yield the various molecular shapes in the VSEPR model. Valence bond theory helps to explain this molecular geometry through the hybridization, or mixing, of atomic orbitals.
Some atomic orbitals involved in bonding recombine to form new orbitals whose shapes are a hybrid of the originals. The initial number of atomic orbitals and the number of hybrid orbitals generated is always the same.
Beryllium fluoride is a linear molecule. The beryllium atom has two valence electrons found in its 2s orbital in the ground state.
The s orbital mixes with one of the empty p orbitals to create orbitals that contain unpaired electrons available for bonding. This leaves two unhybridized p orbitals and produces two sp hybrid orbitals, named for the original atomic orbitals.
The hybrid orbitals have a different shape from their constituent atomic orbitals with one lobe that is significantly larger than the other. Thus, the electron probability density is highly concentrated in a directional lobe, which leads to a more effective overlap with the orbitals of other atoms. For clarity, these orbitals are often shown without the minor lobes.
The half-filled hybrid orbitals undergo end-to-end overlap with orbitals from the fluorine atoms to form two identical covalent bonds, which are also known as sigma (σ) bonds. Therefore, beryllium fluoride exhibits sp hybridization, is linear, and has a 180° bond angle.
The trigonal planar geometry boron trihydride can be explained by sp2 hybridization. Boron has one 2s and three 2p valence orbitals and three valence electrons.
Three of these orbitals, one s, and two p orbitals, mix to produce a set of three sp2 orbitals, each containing one unpaired electron, and one 2p orbital remains unhybridized.
Each of these overlap with a 1s orbital from a hydrogen atom to form three sigma bonds.
A molecule with sp2 hybridization has a trigonal planar geometry with 120° bond angles.
sp3 hybrid orbitals form the tetrahedral shape of a methane molecule. The carbon atom has four valence electrons. The mixing of the 2s and three 2p orbitals generates four equivalent sp3 hybrid orbitals that each can hold one unpaired electron.
The hybrid orbitals obtained through sp3 hybridization overlap with the 1s orbitals of the hydrogen atoms to produce a methane molecule that has tetrahedral geometry and 109.5° bond angles.
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