Unit 2: Chemical Bonding and Molecular Structure

Valence Bond Approach (VBT)

Introduced by Heitler and London, and later developed by Pauling, VBT describes chemical bonding as the overlap of atomic orbitals. A covalent bond is formed when two half-filled valence atomic orbitals from two different atoms overlap. The electrons in the overlapping region are shared and must have opposite spins.

Key Concepts:

• Overlap: The extent of overlap determines the strength of the bond. Greater overlap = stronger bond.
• Sigma (σ) bond: Formed by end-to-end (head-on) overlap of orbitals (e.g., s-s, s-p, p_z-p_z). This bond is symmetrical about the internuclear axis. All single bonds are sigma bonds.
• Pi (π) bond: Formed by sideways (lateral) overlap of p-orbitals (e.g., p_x-p_x, p_y-p_y). This bond has electron density above and below the internuclear axis. A π-bond is weaker than a σ-bond and only forms *after* a σ-bond is already present.

Example: In N₂ (a triple bond), there is one σ-bond and two π-bonds.

VSEPR Theory

The Valence Shell Electron Pair Repulsion (VSEPR) theory is a model used to predict the 3D geometry of individual molecules. It is based on a simple premise:

"The electron pairs (both bonding pairs and lone pairs) in the valence shell of a central atom will arrange themselves in space to be as far apart as possible, thereby minimizing repulsion."

Hierarchy of Repulsion:

The repulsion between electron pairs follows this order:

This is because lone pairs are only held by one nucleus and are more "spread out" (fatter) than bonding pairs, which are held by two nuclei.

Predicting Shapes:

1. Draw the Lewis structure to find the central atom.
2. Count the total number of electron domains (or "steric number") around the central atom. (A single bond, double bond, triple bond, or lone pair each counts as ONE domain).
3. This total number determines the electron geometry (the arrangement of all electron pairs).
4. The arrangement of *only the atoms* (ignoring the lone pairs) determines the molecular shape.

Hybridization

Hybridization is a concept within VBT, proposed by Pauling. It is the mixing of atomic orbitals of slightly different energies (e.g., one s and three p orbitals) to form a new set of hybrid orbitals of equivalent energy and shape.

These new hybrid orbitals are more effective at forming stable bonds and are oriented in space to match the geometries predicted by VSEPR theory.

Shapes of molecules and ions on the basis of VSEPR and hybridization

Concept of Resonance

Resonance is a VBT concept used when a single Lewis structure is insufficient to describe the bonding in a molecule or ion.
Example: In the carbonate ion (CO₃²⁻), a single Lewis structure would show one C=O double bond and two C-O single bonds. This is incorrect, as experiments show all three C-O bonds are identical in length (intermediate between a single and double bond).

Definition: The true structure is a resonance hybrid (an average) of all possible, valid Lewis structures (called canonical forms or resonance structures). The electrons in the π-system are delocalized (spread out) over the molecule.

Rules for Resonance:

• Only electrons (π-electrons or lone pairs) move, not atoms.
• All canonical forms must be valid Lewis structures.
• The true hybrid is more stable than any single canonical form. This increased stability is called resonance energy.

Molecular Orbital (MO) Approach

MO theory describes bonding in terms of molecular orbitals (MOs), which are delocalized over the entire molecule, rather than localized between two atoms (like in VBT).

Rules for the LCAO Method

MOs are formed by the Linear Combination of Atomic Orbitals (LCAO).

1. Atomic orbitals (AOs) must have similar energy to combine. (e.g., 1s combines with 1s, but not with 2s).
2. AOs must have the same symmetry relative to the molecular axis. (e.g., a p_z orbital can combine with another p_z, but not with a p_x).
3. AOs must overlap effectively.

When two AOs combine, they form two MOs:

• Bonding Molecular Orbital (BMO): Formed by constructive interference (addition) of AOs. It has lower energy than the original AOs, has high electron density between the nuclei, and stabilizes the molecule. (e.g., σ, π)
• Anti-bonding Molecular Orbital (ABMO): Formed by destructive interference (subtraction) of AOs. It has higher energy, has a node between the nuclei, and destabilizes the molecule. (e.g., σ*, π*)

MOs from s-s and p-p Overlap

• s-s overlap: 1s + 1s → σ1s (bonding) and σ*1s (anti-bonding)
• p-p overlap (end-on): p_z + p_z → σp (bonding) and σ*p (anti-bonding)
• p-p overlap (sideways): p_x + p_x → πp_x (bonding) and π*p_x (anti-bonding). Similarly, p_y + p_y → πp_y and π*p_y. The πp_x and πp_y orbitals are degenerate (same energy).

MO Diagrams of Homonuclear Diatomics (H₂ to Ne₂)

Electrons are filled into the resulting MOs using the Aufbau principle, Pauli exclusion principle, and Hund's rule, just like for atoms.

Energy Level Order (for O₂, F₂, Ne₂):
σ1s < σ*1s < σ2s < σ*2s < σ2p < π2p < π*2p < σ*2p

Energy Level Order (for B₂, C₂, N₂):
Due to s-p mixing, the σ2p orbital is pushed to a higher energy than the π2p orbitals.
σ1s < σ*1s < σ2s < σ*2s < π2p < σ2p < π*2p < σ*2p

Bond Order and Magnetic Properties

Bond Order = 1/2 · (No. of Bonding e⁻ - No. of Anti-bonding e⁻)

• Bond Order > 0: Molecule is stable (exists).
• Bond Order = 0: Molecule is unstable (does not exist, e.g., He₂).
• Higher bond order = stronger bond = shorter bond length.

Magnetic Properties:

• Paramagnetic: Has unpaired electrons. Attracted to a magnetic field. (e.g., O₂, B₂)
• Diamagnetic: All electrons are paired. Repelled by a magnetic field. (e.g., N₂, F₂)

Homonuclear vs. Heteronuclear Diatomics (CO, NO, NO⁺)

For heteronuclear diatomics, the AOs of the more electronegative atom are lower in energy. This creates an uneven (polar) distribution of electrons in the MOs.

• CO (14 e⁻, like N₂): Bond Order = 1/2(10-4) = 3. Diamagnetic.
• NO (15 e⁻): Bond Order = 1/2(10-5) = 2.5. Paramagnetic (1 unpaired e⁻ in π*).
• NO⁺ (14 e⁻, like N₂): Bond Order = 1/2(10-4) = 3. Diamagnetic.

Comparison of VB and MO theories