Why Valence Bond Theory Was Needed
The Lewis approach helps in writing the structure of molecules, but it fails to explain how a chemical bond actually forms. It offers no reason for the wide difference in bond dissociation enthalpies and bond lengths of molecules that, on paper, look identical. Both $\ce{H2}$ and $\ce{F2}$ contain a single covalent bond formed by sharing one electron pair, yet their properties are very different.
| Molecule | Bond dissociation enthalpy | Bond length |
|---|---|---|
| $\ce{H2}$ | 435.8 kJ mol⁻¹ | 74 pm |
| $\ce{F2}$ | 155 kJ mol⁻¹ | 144 pm |
Lewis theory also gives no idea about the shapes of polyatomic molecules. The VSEPR theory does predict geometry, but only empirically; it does not explain why a particular geometry arises, and it has limited applications. To overcome these limitations, two theories rooted in quantum-mechanical principles were introduced: Valence Bond (VB) theory and molecular orbital theory.
Valence Bond Theory rests on the knowledge of atomic orbitals, electronic configurations of elements, the overlap criteria of atomic orbitals, the hybridisation of atomic orbitals, and the principles of variation and superposition. A rigorous mathematical treatment is beyond the NCERT scope, so the theory is presented qualitatively, beginning with the simplest molecule of all, $\ce{H2}$.
Formation of the H₂ Molecule
Consider two hydrogen atoms A and B approaching each other, with nuclei $N_A$ and $N_B$ and electrons $e_A$ and $e_B$. When the atoms are far apart there is no interaction. As they approach, new attractive and repulsive forces begin to operate simultaneously.
| Attractive forces (pull atoms together) | Repulsive forces (push atoms apart) |
|---|---|
| Nucleus and its own electron: $N_A\!-\!e_A$ and $N_B\!-\!e_B$ | Electron–electron: $e_A\!-\!e_B$ |
| Nucleus and the other atom's electron: $N_A\!-\!e_B$, $N_B\!-\!e_A$ | Nucleus–nucleus: $N_A\!-\!N_B$ |
Experimentally, the magnitude of the new attractive forces exceeds that of the new repulsive forces. As a result, the two atoms move closer and the potential energy of the system decreases. A stage is finally reached where the net attraction exactly balances the net repulsion and the system acquires its minimum energy. At this point the two atoms are bonded together into a stable molecule with a bond length of 74 pm.
Because energy is released when the bond forms, the $\ce{H2}$ molecule is more stable than the two isolated atoms. The energy released is the bond enthalpy, equal in magnitude to the minimum of the energy curve. Conversely, the same quantity of energy must be supplied to break the bond:
$\ce{H2(g) + 435.8\,kJ\,mol^{-1} -> H(g) + H(g)}$
The H₂ Potential-Energy Curve
The competition between attraction and repulsion is captured by the potential-energy curve, plotted against the internuclear distance. At large separation the energy is taken as zero. As the atoms approach, attraction dominates and the curve descends into a well; at very short distances nuclear and electronic repulsion shoot up steeply. The minimum sits at 74 pm, the bond length, and its depth below zero is the bond enthalpy of 435.8 kJ mol⁻¹.
The Orbital Overlap Concept
At the minimum-energy state, the two hydrogen atoms are so close that their atomic orbitals undergo partial interpenetration. This partial merging of atomic orbitals is called overlapping, and it results in the pairing of electrons. The covalent bond, in VB language, forms by the pairing of valence-shell electrons of opposite spin on the two atoms.
The single most important rule that follows is: the extent of overlap decides the strength of the covalent bond. In general, the greater the overlap, the stronger the bond. This one principle threads through the rest of the chapter, explaining the σ-versus-π hierarchy and, after hybridisation is introduced, the strengths of $sp$, $sp^2$ and $sp^3$ bonds.
Types of Overlap: s-s, s-p, p-p
When the orbitals of two atoms approach, the overlap may be positive, negative or zero, depending on the sign (phase) and the direction of the orbital wave-function amplitudes in space. For a bond to form, the overlapping lobes must have the same phase and be correctly oriented; this is positive overlap. Orbitals of opposite phase give negative overlap, and orthogonal orientations give zero net overlap. Three combinations build the axial (head-on) bonds.
Sigma and Pi Bonds
Depending on the mode of overlap, the covalent bond is classified into two types: the sigma ($\sigma$) bond and the pi ($\pi$) bond.
| Feature | Sigma (σ) bond | Pi (π) bond |
|---|---|---|
| Mode of overlap | End-to-end (head-on / axial) overlap along the internuclear axis | Sidewise (lateral) overlap, orbital axes parallel and perpendicular to the internuclear axis |
| Orbitals involved | s–s, s–p, or p–p (axial) | p–p (parallel), sidewise |
| Electron cloud | Symmetrical about the internuclear axis | Two saucer-shaped charge clouds above and below the plane of the atoms |
| Extent of overlap | Larger | Smaller |
| Strength | Stronger | Weaker |
| Occurrence | Present in every covalent bond, single or multiple | Only in multiple bonds, always in addition to a σ bond |
Strength of Sigma vs Pi Bonds
The strength of a bond depends on the extent of overlapping. In a sigma bond the orbitals overlap to a larger extent, so it is stronger; in a pi bond the sidewise overlap is smaller in extent, so it is weaker. This is why, in a multiple bond, the σ component is the more robust skeleton and the π component is comparatively easy to break, a fact that underpins the reactivity of double and triple bonds.
Two consequences are worth fixing in memory before the bond-counting drills. First, a single bond is always a pure σ bond. Second, in any multiple bond the first bond is the σ bond and every additional bond is a π bond formed in addition to it.
Simple orbital overlap predicts the wrong bond angles for $\ce{CH4}$, $\ce{NH3}$ and $\ce{H2O}$. Pauling's fix is the next chapter section — see Hybridisation.
Counting Sigma and Pi Bonds
This is the highest-frequency skill NEET tests from this section. The recipe is mechanical once the rule is internalised:
- Every single bond = 1 σ.
- Every double bond = 1 σ + 1 π.
- Every triple bond = 1 σ + 2 π.
- Count every bond in the molecule, including all C–H and C–C bonds — not just the multiple bonds.
| Molecule | Bonds present | σ bonds | π bonds |
|---|---|---|---|
| $\ce{N2}$ (N≡N) | one triple bond | 1 | 2 |
| $\ce{C2H4}$ ethene | 4 C–H + 1 C=C | 4 + 1 = 5 | 1 |
| $\ce{C2H2}$ ethyne | 2 C–H + 1 C≡C | 2 + 1 = 3 | 2 |
| $\ce{C2H6}$ ethane | 6 C–H + 1 C–C | 7 | 0 |
| $\ce{CO2}$ (O=C=O) | two C=O double bonds | 2 | 2 |
Count the σ and π bonds in ethyne, $\ce{C2H2}$ (H–C≡C–H).
Walk through every bond. The two C–H bonds are single bonds: 2 σ. The carbon–carbon link is a triple bond: it contributes 1 σ + 2 π. Adding the σ contributions: $2 + 1 = 3$ σ bonds. The π count comes only from the triple bond: 2 π bonds. Result: 3 σ and 2 π.
Don't forget the C–H sigma bonds
The most common error is counting only the σ bond hidden inside a double or triple bond and ignoring every single bond around it. In $\ce{C2H4}$, students often write "1 σ" because they see one C=C; the correct answer is 5 σ (four C–H plus one C–C σ) and 1 π. Every line in the structural formula is at least one σ bond.
Rule: total σ = total number of bonds (single + multiple counted once each); total π = (number of double bonds) + 2 × (number of triple bonds).
Directional Properties and Limitations
Valence Bond Theory accounts for the directional nature of bonds: $\ce{H2}$ forms by overlap of two 1s orbitals, and in polyatomic molecules the geometry matters as much as bond formation. But simple atomic-orbital overlap runs into trouble with shape. Carbon's ground-state configuration $\text{[He]}2s^2 2p^2$ becomes $\text{[He]}2s^1 2p_x^1 2p_y^1 2p_z^1$ on excitation, giving four half-filled orbitals to overlap with four hydrogen 1s orbitals.
The catch is direction. The three 2p orbitals lie at 90° to one another, so pure p-overlap would force three of the H–C–H angles to 90°, while the spherical 2s orbital can overlap in any direction, leaving the fourth bond undefined. This does not match the observed tetrahedral angle of 109.5° in $\ce{CH4}$. The same flaw predicts 90° angles for $\ce{NH3}$ and $\ce{H2O}$, against the real values of 107° and 104.5°.
| Molecule | VBT (pure overlap) predicts | Observed angle |
|---|---|---|
| $\ce{CH4}$ | 90° | 109.5° |
| $\ce{NH3}$ | 90° | 107° |
| $\ce{H2O}$ | 90° | 104.5° |
To repair this directional failure, Pauling introduced the concept of hybridisation, in which atomic orbitals of slightly different energies intermix to form an equivalent set of hybrid orbitals that point in the correct directions. Valence Bond Theory also cannot explain the paramagnetism of $\ce{O2}$, a gap filled by molecular orbital theory. Despite these limits, VBT remains the working language of the covalent bond and the foundation for everything that follows.
Valence Bond Theory in one screen
- Introduced by Heitler and London (1927); developed by Pauling. A covalent bond forms when half-filled valence orbitals of opposite-spin electrons overlap.
- The extent of overlap decides bond strength: greater overlap → stronger bond.
- The $\ce{H2}$ energy curve minimum lies at 74 pm (bond length); its depth is the bond enthalpy 435.8 kJ mol⁻¹.
- σ bond = axial (head-on) overlap (s–s, s–p, p–p), stronger; π bond = sidewise overlap of parallel p-orbitals, weaker.
- Single bond = 1 σ; double = 1 σ + 1 π; triple = 1 σ + 2 π. Count every bond. ($\ce{N2}$: 1 σ, 2 π · $\ce{C2H4}$: 5 σ, 1 π · $\ce{C2H2}$: 3 σ, 2 π.)
- Limitation: pure overlap predicts 90° angles for $\ce{CH4}$, $\ce{NH3}$, $\ce{H2O}$ — solved by hybridisation; paramagnetism of $\ce{O2}$ needs MO theory.