Valence Bond Theory

Full Notes

Introduction: Forces Acting During Bond Formation

As two atoms approach each other to form a bond, attractive forces arise between the nucleus of one atom and the electrons of the other. At the same time, repulsive forces act between the two positively charged nuclei and between their electron clouds. The balance between these opposing forces determines whether a stable bond can form.

If the net attractive force outweighs the repulsion, the atoms form a stable bond and release energy in the process. This released energy is known as the bond enthalpy.

Potential Energy and Bond Formation

As two atoms bond, initially attraction dominates, pulling the atoms closer together. However, as the atoms get very close, repulsion increases sharply, causing instability.

The variation of potential energy with internuclear distance is illustrated in a potential energy diagram:

The depth of the energy well indicates bond strength, and the position of minimum energy shows bond length.

As atoms approach:

• Potential energy decreases, reaching a minimum at the equilibrium bond distance.
• This is the most stable configuration; bond formation is energetically favourable.

If atoms get closer than this optimum:

• Repulsive forces sharply increase, raising potential energy.
• The bond becomes unstable.

4.5.1 Orbital Overlap Concept

Valence Bond Theory (VBT), proposed by Heitler and London and extended by Pauling, suggests:

• A covalent bond forms when two half-filled atomic orbitals (each with one unpaired electron of opposite spin) overlap.
• The electron density between the nuclei increases, lowering potential energy and stabilizing the bond.
• Stronger overlap = stronger bond.

This model is localized, meaning bonds are considered as being between specific atom pairs (no delocalisation).

4.5.2 Directional Properties of Bonds

The strength and direction of bonds are determined by the orientation of the overlapping orbitals:

• s-orbitals are spherical and form non-directional bonds.
• p-orbitals and d-orbitals have specific orientations meaning they can form directional bonds.

Directional bonding explains fixed geometries (e.g., tetrahedral CH₄, linear BeCl₂).

4.5.3 Overlapping of Atomic Orbitals

The formation of a covalent bond depends on the overlap between atomic orbitals.

Depending on how the orbitals combine, the overlap can be positive, negative, or zero, each affecting bond strength differently.

Positive and Negative Overlap

Positive Overlap:
Occurs when the lobes of orbitals with the same sign (same phase) interact constructively. This leads to increased electron density between nuclei, resulting in strong, stable bond formation.
Example: s–s or p–p overlap in H₂, Cl₂.

Negative Overlap:
Occurs when lobes of opposite signs (opposite phase) overlap. This leads to destructive interference, lowering electron density and weakening the interaction. Such overlap does not favor bond formation and is considered unstable.

Zero Overlap

Zero overlap happens when orbitals do not point towards each other or are perpendicular. No effective overlap occurs, so no bond forms.
Example: 2p_x of one atom and 2p_y of another oriented perpendicularly.

These distinctions help explain why not all orbital interactions lead to bond formation – only positive, effective overlaps result in stable covalent bonds.

4.5.4 Types of Overlapping and Nature of Covalent Bonds

There are two main types of covalent bond, sigma and pi:

Sigma (σ) Bond

Formed by end-to-end (head-on) overlap of orbitals.

Electron density is cylindrically symmetrical around the bond axis.

Involves s–s, s–p, and p–p (head-on) orbital overlap.

Allows free rotation around the bond axis.

Pi (π) Bond

Formed by sidewise overlap of two parallel p-orbitals.

Electron density lies above and below the internuclear axis. Present in double and triple bonds (as the second and third bonds). Involves p–p (sideways) orbital overlap.

Does not allow free rotation.

4.5.5 Strength of Sigma and Pi Bonds

• σ-bonds are stronger because of greater orbital overlap along the bond axis.
• π-bonds are weaker and less stable individually.
• This means a double bond isn’t twice as strong as a single bond (since the π bond is weaker than the σ bond that makes it up).

In multiple bonds:

• First bond = σ
• Others = π

Example: C≡C (ethyne) has 1 σ + 2 π bonds.

Summary

• Bond formation results from a balance between attractive and repulsive forces.
• Valence Bond Theory explains covalent bonds through orbital overlap and electron pairing.
• Positive (constructive) overlap forms stable bonds; zero or negative overlap does not.
• σ-bonds form by head-on overlap; π-bonds form by sidewise overlap.
• σ-bonds are stronger, while π-bonds restrict rotation and add rigidity to molecules.