Briefly describe the valence bond theory of covalent bond formation by taking an example of hydrogen. How can

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Q. Briefly describe the valence bond theory of covalent bond formation by taking an example of hydrogen. How can you interpret energy changes taking place in the formation of dihydrogen?

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Concept understanding — Orbital Hybridization Theory

Orbital Hybridization Theory – From Intuition to Precision

The Problem That Started It All

Imagine you are looking at a methane molecule, $\text{CH}_4$ . Carbon has four valence electrons: two in the $2s$ orbital and two in the $2p$ orbitals. If carbon used its pure atomic orbitals to bond, you would expect two bonds from the $2s$ (identical, but one direction) and two from the $2p$ (at $90^\circ$ to each other). That would give you three different bond types and bond angles of $90^\circ$ and something else.

But experiment says methane is perfectly tetrahedral: all four bonds are identical in length, strength, and energy, and the bond angle is $109.5^\circ$ , not $90^\circ$ . Something is fundamentally wrong with the "pure orbital" picture.

This is the puzzle that hybridization theory solves.

The Core Intuition

Think of atomic orbitals as shapes that an electron can occupy. The $s$ orbital is a sphere. The $p$ orbitals are dumbbells along the $x$ , $y$ , and $z$ axes. When an atom forms bonds, it wants to mix these shapes together to create new, hybrid shapes that point in directions that maximise bond strength and minimise repulsion.

It is like mixing primary colours to get new colours. You don't have to use red, blue, and yellow separately — you can blend them to get green, orange, or purple. Similarly, an atom can blend its $s$ and $p$ orbitals to get new hybrid orbitals that are better suited for bonding.

The key insight: hybridization is a mathematical mixing of atomic orbitals on the same atom to produce an equal number of new, equivalent hybrid orbitals. The number of hybrid orbitals formed always equals the number of atomic orbitals mixed.

The Precise Statement

s

The theory rests on three pillars:

Conservation of orbitals: Mixing $n$ atomic orbitals gives exactly $n$ hybrid orbitals. No orbitals are created or destroyed.
Energy averaging: The hybrid orbitals have energies that are intermediate between the original $s$ and $p$ energies.
Directionality: Hybrid orbitals point in specific directions to minimise electron pair repulsion, which directly determines molecular shape.

The Three Common Hybridizations

Hybridization	Orbitals Mixed	Number of Hybrids	Geometry	Bond Angle	Example
$sp$	one $s$ + one $p$	2	Linear	$180^\circ$	$\text{BeCl}_2$
$sp^2$	one $s$ + two $p$	3	Trigonal planar	$120^\circ$	$\text{BF}_3$
$sp^3$	one $s$ + three $p$	4	Tetrahedral	$109.5^\circ$	$\text{CH}_4$

Note

The superscript in $sp^2$ or $sp^3$ tells you how many $p$ orbitals were mixed. $sp^3$ means one $s$ and three $p$ orbitals were blended. It does not mean there are three $s$ orbitals — there is only one $s$ orbital per shell.

How It Works: The Methane Example

Carbon in its ground state has the configuration $1s^2 2s^2 2p_x^1 2p_y^1$ . Only two unpaired electrons — it should form only two bonds. But we know carbon forms four bonds.

Step 1: Promotion. One electron from the $2s$ orbital is promoted (excited) to the empty $2p_z$ orbital. This costs a small amount of energy, but it is more than compensated by the energy released when four strong bonds form instead of two.

Step 2: Hybridization. The one $2s$ orbital and three $2p$ orbitals mix to form four equivalent $sp^3$ hybrid orbitals. Each hybrid has 25% $s$ character and 75% $p$ character.

Step 3: Bonding. Each $sp^3$ hybrid overlaps with the $1s$ orbital of a hydrogen atom, forming four identical $\sigma$ bonds. The hybrids point to the corners of a tetrahedron, giving the $109.5^\circ$ angle. …

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Valence Bond Theory explains covalent bond formation as the overlap of atomic orbitals containing unpaired electrons, leading to electron pairing and energy stabilization; for dihydrogen, two hydrogen 1s orbitals overlap, and the system's potential energy decreases to a minimum at the bond length, signifying bond formation and energy release.

Valence Bond Theory (VBT) is a fundamental concept in chemistry that explains the formation of covalent bonds based on the overlap of atomic orbitals. The core idea is that a covalent bond forms when two atomic orbitals, each containing an unpaired electron, overlap. This overlap allows the electrons to pair up, leading to a region of increased electron density between the nuclei, which stabilizes the molecule. The greater the overlap, the stronger the bond.

Valence Bond Theory of Covalent Bond Formation (Example: Hydrogen)

Let's use the formation of a dihydrogen molecule ( $\text{H}_2$ ) from two hydrogen atoms to understand VBT and the associated energy changes.

Isolated Hydrogen Atoms:

Each hydrogen atom has one electron in its 1s atomic orbital. The electron configuration is $1s^1$ . The 1s orbital is spherical. When two hydrogen atoms are far apart, they do not interact, and their potential energy is considered zero (a reference point).
Approach of Hydrogen Atoms:

As two hydrogen atoms begin to approach each other, several forces come into play:
- Attractive Forces: The nucleus of one hydrogen atom is attracted to the electron of the other hydrogen atom, and vice-versa.
- Repulsive Forces: The two nuclei repel each other, and the two electrons repel each other.
Initially, as the atoms get closer, the attractive forces are stronger than the repulsive forces.
Orbital Overlap and Bond Formation:

When the two hydrogen atoms come close enough, their 1s atomic orbitals begin to overlap. This overlap allows the two unpaired electrons (one from each hydrogen atom) to pair up and occupy the overlapping region. This pairing of electrons in the overlapping orbitals is the essence of covalent bond formation according to VBT. The bond formed by the direct, head-on overlap of atomic orbitals along the internuclear axis is called a sigma ( $\sigma$ ) bond.

Important

A covalent bond forms when atomic orbitals containing unpaired electrons overlap, and the electrons in the overlapping region become paired, leading to a decrease in the system's potential energy.

Interpretation of Energy Changes in Dihydrogen Formation

The energy changes during the formation of $\text{H}_2$ can be visualized by plotting the potential energy of the system against the internuclear distance between the two hydrogen atoms.

Initial State (Infinite Separation):

When the two hydrogen atoms are infinitely far apart, there is no interaction between them. The potential energy of the system is conventionally taken as zero.
Decreasing Potential Energy (Attraction Dominates):

As the two hydrogen atoms approach each other, the attractive forces (nucleus-electron attractions) start to dominate over the repulsive forces (nucleus-nucleus and electron-electron repulsions). This net attraction leads to a decrease in the potential energy of the system. The system becomes more stable as energy is released.
Minimum Potential Energy (Equilibrium Bond Length): …

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Q.Briefly describe the valence bond theory of covalent bond formation by taking an example of hydrogen. How can you interpret energy changes taking place in the formation of dihydrogen?

Valence Bond Theory of Covalent Bond Formation (Example: Hydrogen)

Interpretation of Energy Changes in Dihydrogen Formation

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