8.1 Valence Bond Theory

Valence Bond Theory explains how atoms form covalent bonds through the overlap of atomic orbitals. It connects the quantum mechanical picture of electrons in orbitals to the real-world shapes and strengths of bonds you see in molecules.

Valence Bond Theory

Atomic orbital overlap in covalent bonds

A covalent bond forms when two atomic orbitals overlap, allowing a pair of electrons to be shared between two atoms. The shared electrons sit in the overlap region, where they're attracted to both nuclei simultaneously. That mutual attraction lowers the system's overall energy and stabilizes the bond.

For overlap to happen effectively, a few conditions need to be met:

• The orbitals must have compatible symmetry and orientation (for example, two p orbitals pointing toward each other along the bond axis).
• The orbitals should have comparable energies. A 1s orbital on hydrogen and a 2p orbital on fluorine can overlap well, but a huge energy mismatch between orbitals makes bonding much less favorable.
• Greater overlap produces a stronger bond. Orbital size and shape (s, p, d, f) affect how much overlap is possible.

The extent of overlap also influences molecular geometry. How orbitals point in space determines the angles between bonds, which is why Valence Bond Theory helps predict molecular shape.

Sigma vs pi bonds

Sigma ($\sigma$) bonds form through head-on (end-to-end) overlap of orbitals. The electron density is concentrated along the internuclear axis, directly between the two nuclei. This direct overlap is extensive, making sigma bonds the stronger of the two types.

Sigma bonds can involve several combinations of orbitals:

• s + s (as in $H_2$)
• s + p
• p + p (head-on)
• Hybrid orbitals like sp, $sp^2$, or $sp^3$ overlapping with each other or with s and p orbitals

Pi ($\pi$) bonds form through sideways (lateral) overlap of unhybridized p orbitals that are parallel to each other and perpendicular to the bond axis. The electron density sits above and below the internuclear axis rather than directly between the nuclei. Because this sideways overlap is less extensive, pi bonds are weaker than sigma bonds.

When atoms form multiple bonds, the first bond is always a sigma bond. Any additional bonds are pi bonds:

• Single bond: one $\sigma$ bond (e.g., C–C in ethane)
• Double bond: one $\sigma$ + one $\pi$ (e.g., C=C in ethene)
• Triple bond: one $\sigma$ + two $\pi$ (e.g., C≡C in ethyne)

The bond order (single, double, triple) directly affects bond strength and bond length. Higher bond order means a stronger, shorter bond.

Bond energy and orbital interactions

Bond energy is the energy required to break one mole of a particular bond in the gas phase. Greater orbital overlap produces a stronger bond with a higher bond energy.

Some reference values to know:

Notice that a C=C double bond is stronger than a C–C single bond, but it's not twice as strong. That's because the added pi bond contributes less strength than the sigma bond does.

A few key factors influence bond energy:

• Bond length: There's an optimal distance where attractive forces (nucleus-to-electron) and repulsive forces (nucleus-to-nucleus, electron-to-electron) are balanced. At this distance, orbital overlap and bond energy are maximized. Move the atoms farther apart and overlap decreases; push them too close and repulsion spikes.
• Electronegativity difference: Polar covalent bonds (like H–Cl) can actually be stronger than the average of the two corresponding homonuclear bonds (H–H and Cl–Cl) because the unequal sharing adds an ionic contribution to the bond strength.

You can estimate a molecule's overall bond energy by summing the average bond energies of all bonds present. For a molecule $AB_n$ with $n$ equivalent A–B bonds:

$D_0(AB_n) = \frac{1}{n}\sum D_0(A-B)$

where $D_0(A-B)$ is the average bond energy for each A–B bond. Keep in mind these are average values, so estimates won't perfectly match experimental measurements for every molecule.

Advanced concepts in bonding

These three ideas build directly on Valence Bond Theory and come up frequently alongside it:

• Hybridization is the mixing of atomic orbitals (say, one s and three p) to form new hybrid orbitals ($sp^3$) with intermediate shapes and energies. Hybridization explains why molecules like methane have equivalent bonds arranged tetrahedrally, even though carbon's native s and p orbitals aren't equivalent.
• VSEPR theory predicts molecular geometry by assuming that electron groups (bonding pairs and lone pairs) repel each other and arrange themselves as far apart as possible. It complements Valence Bond Theory by giving you a straightforward way to predict shapes.
• Resonance applies when more than one valid Lewis structure can be drawn for a molecule (like ozone or the nitrate ion). The actual electron distribution is a blend of all the resonance structures, not a flip between them. This "resonance hybrid" better represents where electrons really are.