Valence Bond Theory
~6 min read · Tier toggle changes depth (T1 plain · T2 standard · T3 rigour)
You should be comfortable drawing Lewis structures and predicting molecular geometry using VSEPR theory. Familiarity with basic quantum numbers and the shapes of s and p orbitals is assumed.
Why this matters
Valence Bond Theory explains how atoms share electrons to form stable molecules.
While Lewis structures provide a useful bookkeeping method for electrons, they do not explain the directional nature of chemical bonds or the specific energies involved. Valence Bond (VB) Theory bridges the gap between simple electron counting and the quantum mechanical reality of bonding. It describes a covalent bond as the result of the overlap of atomic orbitals, each containing one unpaired electron. This overlap creates a region of high electron density between the nuclei, lowering the potential energy of the system and holding the atoms together. Understanding VB theory is essential for grasping why molecules have specific shapes and bond strengths, serving as a foundational step before exploring the more complex Molecular Orbital Theory.
The Core Idea: Overlap and Sharing
Imagine two hydrogen atoms approaching each other. Each has one electron in its 1s orbital. In Valence Bond Theory, a bond forms when these two orbitals overlap. The electrons are not fixed in one atom or the other; instead, they are shared in the space between the nuclei. This sharing is driven by electrostatic attraction: the electron density in the overlap region attracts both positive nuclei, pulling them closer together. The bond is strongest when the orbitals overlap as much as possible. This maximum overlap principle dictates that bonds are directional; atoms will orient themselves to maximise the spatial intersection of their orbitals. If the orbitals do not overlap effectively, no bond forms, or the bond is very weak. This simple concept of "overlap" replaces the vague idea of "sharing" with a physical, spatial mechanism that explains why bonds have specific lengths and angles.
Types of Covalent Bonds
Based on the geometry of the orbital overlap, covalent bonds are classified into two primary types: sigma (\(\sigma\)) and pi (\(\pi\)) bonds. A sigma bond is formed by the head-on, end-to-end overlap of atomic orbitals. The electron density is concentrated along the internuclear axis. Sigma bonds can be formed by the overlap of s-s, s-p, or p-p orbitals. Because the overlap is direct and substantial, sigma bonds are generally stronger than pi bonds. A pi bond, in contrast, is formed by the lateral, side-by-side overlap of parallel p orbitals. The electron density is concentrated above and below the internuclear axis, with a nodal plane containing the axis itself. Pi bonds are weaker than sigma bonds because the side-by-side overlap is less effective than head-on overlap. Furthermore, pi bonds restrict rotation around the bond axis, leading to the rigidity observed in double and triple bonds. For example, in a carbon-carbon double bond, one \(\sigma\) bond and one \(\pi\) bond exist, preventing free rotation and creating distinct cis and trans isomers.
Orbital Overlap and Bond Strength
The extent of orbital overlap directly correlates with bond strength and bond length. Greater overlap leads to a higher probability of finding electrons in the bonding region, which increases the electrostatic attraction between the nuclei and the shared electrons. This results in a shorter, stronger bond. For instance, the overlap of two 1s orbitals in H2 is significant relative to the size of the orbitals, creating a stable bond. However, if we consider the overlap of a 2s orbital with a 2p orbital, the shapes and sizes differ, affecting the efficiency of overlap. The concept of effective overlap is crucial. It is not just about touching; it is about the constructive interference of wave functions. When two atomic orbitals combine to form a bonding molecular orbital, their wave functions must have the same sign (phase). If the signs are opposite, destructive interference occurs, leading to an antibonding orbital with a node between the nuclei, which is energetically unfavorable. VB theory focuses on the constructive overlap that lowers the total energy of the system.
Limitations of Valence Bond Theory
While Valence Bond Theory successfully explains the formation and directionality of bonds, it has notable limitations. One major issue is its inability to fully account for the paramagnetism of the oxygen molecule (O2). VB theory predicts that all electrons in O2 are paired, implying diamagnetism, but experimental evidence shows O2 is paramagnetic. This discrepancy is resolved by Molecular Orbital Theory, which treats the molecule as a whole rather than a collection of localized bonds. Additionally, VB theory struggles with delocalized systems, such as benzene, where electrons are spread over the entire ring. In such cases, the concept of fixed single and double bonds is an approximation. VB theory also does not naturally explain the equal bond lengths in molecules like benzene without invoking resonance structures, which are a mathematical convenience rather than a physical reality. Therefore, while VB theory is intuitive and useful for understanding local bonding, it is often supplemented or replaced by Molecular Orbital Theory for a more comprehensive description of electronic structure.
A common misconception is that a double bond consists of two sigma bonds. In reality, a double bond always consists of one sigma bond and one pi bond. The sigma bond provides the primary connection and allows for the stability of the bond, while the pi bond adds extra electron density but restricts rotation. Confusing these leads to incorrect predictions about molecular flexibility and reactivity. C
Worked example
Problem. Consider the formation of a bond between two hydrogen atoms. The bond dissociation energy of H2 is \(436\ \mathrm{kJ\,mol^{-1}}\). If the bond length is \(74\ \mathrm{pm}\), calculate the average force required to break the bond, as an order-of-magnitude estimate, supposing the bond energy were supplied over a stretch equal to the bond length. Express the answer in Newtons.
- Convert the bond dissociation energy to Joules per molecule: \(E = \frac{436 \times 10^3\ \mathrm{J\,mol^{-1}}}{6.022 \times 10^{23}\ \mathrm{mol^{-1}}} = 7.24 \times 10^{-19}\ \mathrm{J}\).
- Convert the bond length to meters: \(d = 74\ \mathrm{pm} = 74 \times 10^{-12}\ \mathrm{m} = 7.4 \times 10^{-11}\ \mathrm{m}\).
- Use the relationship \(F = \frac{E}{d}\) to find the average force: \(F = \frac{7.24 \times 10^{-19}\ \mathrm{J}}{7.4 \times 10^{-11}\ \mathrm{m}}\).
- Calculate the value: \(F \approx 9.78 \times 10^{-9}\ \mathrm{N}\).
Units check. Joules are \(\mathrm{N\,m}\), so \(\frac{\mathrm{N\,m}}{\mathrm{m}} = \mathrm{N}\), which is correct for force.
Three quick tests
- What type of orbital overlap forms a sigma bond?
Answer
Head-on or end-to-end overlap of atomic orbitals. - Why is a pi bond weaker than a sigma bond?
Answer
Because the side-by-side overlap of p orbitals is less effective than the head-on overlap of sigma bonds. - Does Valence Bond Theory correctly predict the magnetic properties of O2?
Answer
No, it predicts diamagnetism, but O2 is paramagnetic, a limitation explained by Molecular Orbital Theory.
Back to CU-102 →
Every lecture and every result in this unit, with prerequisites and threads.
Lecture notes drafted with a local model and checked line by line by the editor; every number in the worked example was recomputed.