# 3.6 Valence Bond Theory Valence Bond Theory (VBT), proposed by Heitler and London in 1927 and later developed by Pauling, provides a quantum mechanical explanation for the formation of covalent bonds. It successfully explains key molecular properties like bond energies, bond lengths, and the shapes of covalent molecules. The core idea of VBT is that covalent bonds are formed by the **overlapping of partially filled atomic orbitals** from two different atoms. The two overlapping orbitals share a common region in space, but otherwise retain their individual identities. --- ## Main Points of VBT 1. A covalent bond is formed by the overlap of two **half-filled** atomic orbitals, one from each of the bonding atoms. 2. The electrons in the overlapping orbitals must have **opposite spins**. 3. The number of covalent bonds an atom can form is typically equal to the number of **unpaired electrons** in its outermost (valence) shell. 4. The first bond formed by the direct overlap of two orbitals is a **sigma ($\sigma$)** bond. Subsequent bonds (in double or triple bonds) are **pi ($\pi$)** bonds, formed by the overlap of additional orbitals. 5. For a bond to form, the overlapping orbitals must have the same symmetry with respect to the **bond axis** (the imaginary line joining the nuclei of the two bonded atoms). 6. The process of orbital overlap releases energy. The greater the extent of the overlap, the more energy is released, and the stronger the resulting bond. ## Types of Overlapping and Nature of Covalent Bonds The way atomic orbitals overlap determines the type of covalent bond formed. The two main types are sigma ($\sigma$) and pi ($\pi$) bonds. ### Sigma ($\sigma$) Bond A sigma bond is formed by the **direct, head-on overlap** of atomic orbitals along the internuclear axis. The electron density in a sigma bond is concentrated directly between the two nuclei. All single bonds are sigma bonds. *Types of Overlap:* - $s-s$ overlap (e.g., in $\mathrm{H_2}$) - $s-p$ overlap (e.g., in $\mathrm{HF}$) - $p-p$ head-on overlap (e.g., in $\mathrm{F_2}$) ### Pi ($\pi$) Bond A pi bond is formed by the **sideways or parallel overlap** of atomic orbitals (typically p-orbitals) above and below the internuclear axis. The electron density in a pi bond is located in two regions, one above and one below the plane of the sigma bond. *Types of Overlap:* - $p_y-p_y$ parallel overlap - $p_z-p_z$ parallel overlap ### Multiple Bonds - A **double bond** consists of one sigma ($\sigma$) bond and one pi ($\pi$) bond (e.g., Ethene, $\mathrm{C_2H_4}$). - A **triple bond** consists of one sigma ($\sigma$) bond and two pi ($\pi$) bonds (e.g., Acetylene, $\mathrm{C_2H_2}$). ## Strength of Sigma and Pi Bonds A **sigma ($\sigma$) bond is stronger than a pi ($\pi$) bond**. This is because the head-on overlap in a sigma bond is more effective and results in a higher electron density concentrated between the nuclei, leading to a stronger attraction. The sideways overlap of a pi bond is less effective, and its electron density is more diffuse (spread out), making it a weaker and more easily broken bond. ## Single Bond Formation #### a) Formation of the $\mathrm{H_2}$ Molecule The electron configuration of a hydrogen atom is $1s^1$. A covalent bond forms when the half-filled $1s$ orbital of one hydrogen atom overlaps head-on with the half-filled $1s$ orbital of another hydrogen atom. This $s-s$ overlap creates a sigma ($\sigma$) bond. $$ \mathrm{H}(1s^1) + \mathrm{H}(1s^1) \rightarrow \mathrm{H-H} \text{ (\sigma bond)} $$ #### b) Formation of the $\mathrm{F_2}$ Molecule The electron configuration of fluorine is $1s^2 2s^2 2p^5$. It has one half-filled orbital, the $2p_z$ orbital. The head-on overlap of the $2p_z$ orbital from each fluorine atom forms a $p-p$ sigma ($\sigma$) bond. $$ \mathrm{F}(2p_z^1) + \mathrm{F}(2p_z^1) \rightarrow \mathrm{F-F} \text{ (\sigma bond)} $$ *Figure 3.6.6: Orbital diagram for the formation of the $\mathrm{F_2}$ molecule.* #### c) Formation of the $\mathrm{HF}$ Molecule In the hydrogen fluoride molecule, the half-filled $1s$ orbital of the hydrogen atom overlaps with the half-filled $2p_z$ orbital of the fluorine atom. This $s-p$ head-on overlap results in a sigma ($\sigma$) bond. ## Multiple Bond Formation #### a) Formation of the $\mathrm{O_2}$ Molecule (Double Bond) An oxygen atom ($1s^2 2s^2 2p^4$) has two half-filled p-orbitals ($2p_y^1, 2p_z^1$). 1. One pair of p-orbitals (e.g., $2p_z$) overlaps head-on to form a **sigma ($\sigma$) bond**. 2. The other pair of p-orbitals ($2p_y$) overlaps sideways (parallel) to form a **pi ($\pi$) bond**. The combination results in a double bond ($\mathrm{O=O}$) between the two oxygen atoms. #### b) Formation of the $\mathrm{N_2}$ Molecule (Triple Bond) A nitrogen atom ($1s^2 2s^2 2p^3$) has three half-filled p-orbitals ($2p_x^1, 2p_y^1, 2p_z^1$). 1. The $2p_x$ orbitals from each nitrogen atom overlap head-on to form a **sigma ($\sigma$) bond**. 2. The $2p_y$ orbitals from each atom overlap sideways to form the first **pi ($\pi$) bond**. 3. The $2p_z$ orbitals from each atom also overlap sideways to form the second **pi ($\pi$) bond**. This results in a triple bond ($\mathrm{N \equiv N}$) between the two nitrogen atoms. --- | Bond Type | Composition | |-------------|----------------------------| | Single Bond | 1 $\sigma$ bond | | Double Bond | 1 $\sigma$ + 1 $\pi$ bond | | Triple Bond | 1 $\sigma$ + 2 $\pi$ bonds | For related concepts, see , , and [Molecular Orbital Theory](/note/chemistry-11/310-molecular-orbital-theory).