Chemical Bonding & Molecular Structure
Class 11 – CBSE (Advanced MIT‑style Notes)
Note: These notes are written for students who already possess a solid grounding in basic chemistry. They provide a rigorous, quantum‑mechanical treatment of chemical bonding, going well beyond the CBSE syllabus while staying tightly linked to the standard curriculum.
1. Introduction: From Classical to Quantum
| Classical view | Modern view |
|---|---|
| Bonds are “sticks” that hold atoms together. | Bonds are regions of high electron density generated by the overlap of atomic orbitals (AOs). |
| Ionic bonds arise from complete electron transfer. | Ionic bonds are the extreme limit of charge transfer; covalent bonds involve partial transfer (electron sharing). |
| Covalent bonds are simply “sharing” of electron pairs. | Covalent bonds are formed by constructive interference of orbitals, described by the Schrödinger equation. |
Why the quantum picture matters
- Explains the directionality of bonds (e.g., double bonds, aromaticity).
- Predicts bond lengths and bond strengths via the potential energy surface (PES).
- Provides a framework for electronic spectra and reactivity.
2. The Schrödinger Equation for Diatomic Molecules
For a two‑center, two‑electron system (e.g., H₂):
[ \hat H \Psi(\mathbf{r}_1,\mathbf{r}_2) = E \Psi(\mathbf{r}_1,\mathbf{r}_2) ]
[ \hat H = -\frac{\hbar^2}{2m}\nabla_1^2 -\frac{\hbar^2}{2m}\nabla_2^2 - \frac{e^2}{4\pi\varepsilon_0}\Bigl(\frac{1}{r_{1A}}+\frac{1}{r_{2A}}+\frac{1}{r_{1B}}+\frac{1}{r_{2B}}\Bigr) + \frac{e^2}{4\pi\varepsilon_0}\frac{1}{R} + \frac{e^2}{4\pi\varepsilon_0}\frac{1}{r_{12}} ]
- Hartree–Fock (HF) approximates the many‑body wavefunction as an antisymmetrized product of single‑particle orbitals (Slater determinant).
- Configuration Interaction (CI) adds excited determinants to capture electron correlation.
Key Insight: The shape of the resulting molecular orbital (MO) determines whether the bond is bonding (constructive interference) or antibonding (destructive interference).
3. Valence‑Bond (VB) Theory
| Concept | Formalism |
|---|---|
| Orbital Hybridisation | ( |
| Resonance | ( |
| Spin Coupling | Pauli principle: spin singlet vs triplet states. |
3.1 Hybrid Orbitals
- sp³: 4 × linear combination → tetrahedral (109.5°).
- sp²: 3 × linear combination → trigonal‑planar (120°).
- sp: 2 × linear combination → linear (180°).
Edge cases
- d‑orbital participation: e.g., ( \text{SF}_6 ) uses ( \text{sp}^3d^2 ).
- Hypervalency: molecules like ( \text{PCl}_5 ) exhibit "expanded octet" due to ( d )-orbitals or delocalized bonding.
3.2 Resonance Structures
- Canonical forms represent the same electron arrangement but differ in charge distribution.
- Resonance energy: the true state is lower in energy than any individual canonical form.
Caveat: Resonance is a conceptual tool, not a literal oscillation.
3.3 Edge Cases:
- Dative (coordinate) bonds: electron pair donated from one atom to an empty orbital of another (e.g., ( \text{NH}_3!+!Li^+ )).
- Three‑center two‑electron bonds: observed in boranes (e.g., ( \text{BH}_3 )).
4. Molecular Orbital (MO) Theory
4.1 Linear Combination of Atomic Orbitals (LCAO)
[ |\psi_{\text{MO}}\rangle = \sum_i c_i |n_i\ell_i m_i\rangle ]
- Constructive overlap → bonding MO (lower energy).
- Destructive overlap → antibonding MO (higher energy).
4.2 Bond Order
[ \text{BO} = \frac{(n_{\text{bonding}} - n_{\text{antibonding}})}{2} ]
- Example: ( \text{O}_2 ) → BO = 2 (two σ bonds + one π bond).
4.3 Symmetry & Group Theory
- Point groups (C₂v, D₃h, etc.) classify molecular symmetry.
- Character tables help predict allowed transitions and bonding patterns.
Deep Insight: The symmetry-adapted linear combinations (SALCs) of ligand orbitals determine the metal–ligand bonding in coordination complexes.