Molecular Orbital Theory Diagrams

Why This Matters

Molecular orbital (MO) theory is one of the most powerful tools you'll encounter in General Chemistry II because it explains why molecules behave the way they do—not just their shapes, but their stability, magnetic properties, and reactivity. While Lewis structures give you a quick sketch, MO diagrams reveal the deeper electronic architecture that determines whether a molecule will form at all, how strong its bonds are, and whether it's attracted to a magnetic field.

You're being tested on your ability to construct and interpret MO diagrams, calculate bond order, predict paramagnetism vs. diamagnetism, and explain how orbital mixing affects energy levels. Exam questions love to ask you to compare molecules like $O_2$ and $N_2$, or explain why $CO$ is unusually stable. Don't just memorize electron configurations—know what each orbital filling means for molecular properties.

---

Foundational Concepts: Bonding vs. Antibonding

Before diving into specific molecules, you need to understand the core principle: when atomic orbitals combine, they form bonding orbitals (lower energy, stabilizing) and antibonding orbitals (higher energy, destabilizing). The balance between these determines everything.

Bonding and Antibonding Orbitals

• Bonding orbitals (σ, π)—formed from constructive interference of atomic orbitals, concentrating electron density between nuclei
• Antibonding orbitals (σ, π)**—formed from destructive interference, with a node between nuclei that reduces stability
• Bond order formula: $\text{Bond Order} = \frac{(\text{bonding electrons}) - (\text{antibonding electrons})}{2}$—higher bond order means stronger, shorter bonds

MO Energy Level Diagrams

• Aufbau filling—electrons fill lowest-energy orbitals first, following Hund's rule and the Pauli exclusion principle
• Orbital ordering shifts—for $Z \leq 7$ homonuclear diatomics, the $\sigma_{2p}$ orbital is higher in energy than $\pi_{2p}$ due to s-p mixing
• Diagram interpretation—unpaired electrons indicate paramagnetism; bond order predicts stability and bond strength

---

Homonuclear Diatomics: Symmetric Orbital Combinations

When two identical atoms combine, their atomic orbitals have equal energies, creating perfectly symmetric MO diagrams. The key challenge is knowing when orbital ordering changes.

Homonuclear Diatomic Molecules ($H_2$, $N_2$, $O_2$, $F_2$)

• Symmetrical MO diagrams—identical atoms mean bonding and antibonding orbitals form from equivalent atomic orbital contributions
• Bond order varies: $H_2$ has bond order 1, $N_2$ has bond order 3 (triple bond), $O_2$ has bond order 2—directly correlating with bond strength
• $O_2$ is paramagnetic—its MO diagram shows two unpaired electrons in the $\pi^*_{2p}$ orbitals, a fact Lewis structures completely miss

Orbital Ordering in Homonuclear Diatomics

• For $B_2$, $C_2$, $N_2$—s-p mixing raises $\sigma_{2p}$ above $\pi_{2p}$, so $\pi_{2p}$ fills first
• For $O_2$, $F_2$—minimal s-p mixing means $\sigma_{2p}$ is lower than $\pi_{2p}$, following the "expected" order
• Why it matters—getting the orbital order wrong changes your electron configuration and magnetism predictions entirely

---

Heteronuclear Diatomics: Unequal Contributions

When two different atoms bond, their atomic orbitals have different energies due to electronegativity differences. This asymmetry shifts electron density and creates polarity.

Heteronuclear Diatomic Molecules ($CO$, $NO$)

• Asymmetric energy levels—the more electronegative atom contributes more to bonding orbitals, pulling electron density toward itself
• $CO$ has bond order 3—despite being heteronuclear, it's isoelectronic with $N_2$ and has exceptional stability (stronger than most triple bonds)
• $NO$ has bond order 2.5—one unpaired electron in a $\pi^*$ orbital makes it paramagnetic and highly reactive as a free radical

---

Polyatomic Molecules: Geometry Meets MO Theory

For molecules with three or more atoms, MO theory combines with hybridization and VSEPR to explain geometry. The shape depends on how orbitals mix and how lone pairs arrange themselves.

Linear Triatomic Molecules ($BeH_2$, $CO_2$)

• 180° bond angles—result from sp hybridization of the central atom, creating two equivalent orbitals pointing in opposite directions
• $CO_2$ double bonds—each C=O bond consists of one σ bond and one π bond, with delocalized π electrons across the molecule
• No lone pairs on central atom—in both $BeH_2$ and $CO_2$, all valence electrons participate in bonding, maintaining linear geometry

Angular Triatomic Molecules ($H_2O$)

• 104.5° bond angle—sp³ hybridization with two lone pairs compressing the H-O-H angle below the ideal tetrahedral 109.5°
• Lone pair repulsion—lone pairs occupy more space than bonding pairs, pushing bonded atoms closer together
• Polar molecule—the bent geometry creates a net dipole moment, enabling hydrogen bonding and water's unique properties

---

Larger Molecular Geometries: Expanding the Octet

Molecules with central atoms from period 3 and beyond can accommodate more than eight electrons, leading to geometries that require d-orbital participation in hybridization.

Tetrahedral Molecules ($CH_4$)

• 109.5° bond angles—sp³ hybridization creates four equivalent orbitals arranged tetrahedrally around carbon
• Four σ bonds—each C-H bond forms from overlap of an sp³ hybrid orbital with hydrogen's 1s orbital
• Nonpolar and symmetric—the symmetrical arrangement cancels all bond dipoles, making methane nonpolar

Octahedral Molecules ($SF_6$)

• 90° bond angles—sp³d² hybridization creates six equivalent orbitals pointing toward vertices of an octahedron
• Six σ bonds—sulfur expands its octet using 3d orbitals to accommodate six fluorine atoms
• Nonpolar despite polar bonds—perfect octahedral symmetry cancels all S-F dipoles

Square Planar Molecules ($XeF_4$)

• 90° bond angles in a plane—dsp² hybridization with two lone pairs occupying axial positions to minimize repulsion
• Four σ bonds plus two lone pairs—the six electron domains start octahedral, but lone pairs create square planar geometry
• Nonpolar overall—the symmetric arrangement of fluorine atoms cancels dipoles (despite what you might expect)

---

Pi Bonding and Delocalization

Pi bonds form from side-by-side overlap of p orbitals and are weaker than sigma bonds but crucial for understanding reactivity, especially in organic molecules.

Pi-Bonding in Organic Molecules (Ethylene, Benzene)

• Ethylene ($C_2H_4$)—the C=C double bond has one σ bond (sp² overlap) and one π bond (unhybridized p orbital overlap), restricting rotation
• Benzene ($C_6H_6$)—six π electrons are delocalized across the ring in a continuous molecular orbital, creating exceptional stability (aromaticity)
• sp² hybridization in both—planar geometry allows p orbitals to align for π bonding; bond angles are approximately 120°

---

Quick Reference Table

---

Self-Check Questions

1. Why does $O_2$ exhibit paramagnetism while $N_2$ is diamagnetic, even though both are homonuclear diatomic molecules? Draw the MO diagrams to support your answer.

2. Calculate the bond order for $NO$. Based on this value, would you predict $NO$ to be more or less stable than $N_2$? Explain.

3. Compare the molecular geometries of $CO_2$ and $H_2O$. Both have three atoms—why does one end up linear and the other bent?

4. If an FRQ asks you to explain why $CO$ has an unusually strong bond despite being heteronuclear, what concepts from MO theory would you use in your response?

5. How does the MO diagram for $N_2$ differ from that of $O_2$ in terms of orbital ordering, and what causes this difference?