How To Draw Molecular Orbital Diagram

How to Draw Molecular Orbital Diagram
Learning how to draw molecular orbital diagram is a fundamental skill for students of chemistry, physics, and materials science. This visual tool reveals how atomic orbitals combine to form bonding and antibonding molecular orbitals, predicts molecular stability, and explains magnetic properties. By mastering the step‑by‑step procedure, you can confidently construct diagrams for diatomic and polyatomic species, interpret experimental data, and deepen your understanding of quantum‑chemical concepts.

Understanding Molecular Orbital Theory

Before putting pen to paper (or cursor to screen), grasp the core ideas behind molecular orbital (MO) theory:

• Linear Combination of Atomic Orbitals (LCAO): Molecular orbitals are formed by the constructive or destructive interference of atomic wavefunctions (ψ).
• Bonding vs. Antibonding: In‑phase overlap lowers energy (bonding MO), while out‑of‑phase overlap raises energy (antibonding MO, denoted with an asterisk *).
• Symmetry and Node Count: The number of nodes in an MO increases with its energy; symmetry labels (σ, π, δ, etc.) describe the orbital’s shape relative to the internuclear axis.
• Aufbau Principle, Pauli Exclusion, Hund’s Rule: Electrons fill MOs from lowest to highest energy, two per orbital with opposite spins, and degenerate orbitals are singly occupied before pairing.

These principles guide every decision when you draw a molecular orbital diagram.

Step‑by‑Step Guide to Drawing MO Diagrams

Follow this systematic workflow to produce accurate diagrams for any homonuclear or heteronuclear diatomic molecule.

1. Determine the Valence Electron Count

Identify the total number of valence electrons contributed by each atom. For example, O₂ has 6 valence electrons per oxygen atom → 12 total.

2. Choose the Appropriate Energy Ordering

• For second‑period homonuclear diatomics (Li₂ to N₂), the σ₂p orbital lies below the π₂p set.
• For O₂ and beyond, the π₂p orbitals drop below σ₂p due to s‑p mixing reduction.
  Write the generic sequence: σ₁s < σ₁s < σ₂s < σ₂s < (π₂pₓ = π₂p_y) < σ₂p_z < (π₂pₓ = π₂p_y) < σ*₂p_z. Adjust as needed.

3. Draw the Atomic Orbital Columns

Create two vertical columns labeled with the constituent atoms (A and B). Inside each column, sketch the relevant atomic orbitals (usually s and p) in order of increasing energy. Use bold lines for the orbitals and label them (e.g., 2s, 2pₓ).

4. Connect with Molecular Orbitals

Between the columns, draw a third set of orbitals representing the MOs. For each pair of atomic orbitals of the same symmetry, draw one bonding (lower) and one antibonding (higher) MO. Connect them with dashed lines to show the LCAO origin.

5. Populate Electrons

Fill the MOs following Aufbau, Pauli, and Hund’s rules. Use upward arrows (↑) for spin‑up electrons and downward arrows (↓) for spin‑down. Degenerate orbitals receive single electrons before any pairing.

6. Label Bond Order and Magnetic Properties Calculate bond order:

[ \text{Bond order} = \frac{N_{\text{bonding}} - N_{\text{antibonding}}}{2} ]

State whether the molecule is diamagnetic (all electrons paired) or paramagnetic (unpaired electrons present).

7. Add Symmetry Notations (Optional)

For advanced work, append symmetry labels (σ_g, σ_u*, π_u, π_g*, etc.) to each MO, especially when discussing selection rules for spectroscopy.

Common Examples

H₂ (Hydrogen)

• Valence electrons: 2
• Energy order: σ₁s < σ*₁s
• Diagram: Two electrons fill σ₁s (bonding), bond order = 1, diamagnetic.

N₂ (Nitrogen)

• Valence electrons: 10
• Energy order (N₂ and earlier): σ₂s < σ₂s < π₂pₓ = π₂p_y < σ₂p_z < π₂pₓ = π₂p_y < σ₂p_z - Filling yields: (σ₂s)² (σ*₂s)² (π₂pₓ)² (π₂p_y)² (σ₂p_z)² → bond order = 3, diamagnetic.

O₂ (Oxygen)

• Valence electrons: 12
• Energy order (O₂ onward): σ₂s < σ₂s < σ₂p_z < π₂pₓ = π₂p_y < π₂pₓ = π₂p_y < σ₂p_z
• Filling: (σ₂s)² (σ₂s)² (σ₂p_z)² (π₂pₓ)² (π₂p_y)² (π₂pₓ)¹ (π*₂p_y)¹ → bond order = 2, paramagnetic (two unpaired electrons).

CO (Carbon Monoxide – Heteronuclear)

• Treat as isoelectronic with N₂ but shift energies due to electronegativity difference; the σ₂p_z is slightly lower than π₂p set. - Result: bond order = 3, diamagnetic, with a slight dipole moment.

Tips and Pitfalls

• Check s‑p mixing: For B₂, C₂, and N₂, the σ₂p orbital is raised above the π₂p set; forgetting this leads to incorrect bond orders.
• Maintain symmetry: Degenerate π orbitals must be drawn at the same horizontal level; otherwise, electron filling becomes ambiguous.
• Use consistent arrow direction: Always place spin‑up arrows first in degenerate sets to obey Hund’s rule.
• Label clearly: Small, legible labels prevent confusion when revisiting the diagram for calculations or explanations. - Practice with isomers: Drawing both cis‑ and trans‑ isomers of simple polyatomics (e.g., O₃) helps reinforce how geometry influences orbital overlap