Second-Period MO Energy Ordering

Introduction

The standard 2p orbital ordering in introductory MO diagrams changes across the second-period homonuclear diatomics. B₂, C₂ and N₂ commonly use π2p below σ2p, while O₂ and F₂ use σ2p below π2p. This switch matters for filling, bond order and magnetism.

Core explanation

After the 2s-derived σ2s and σ2s levels, three 2p atomic orbitals on each atom combine into a σ2p pair and two degenerate π2p pairs, bonding and antibonding. The exact relative energies of bonding σ2p and bonding π2p are not fixed by the labels alone. In the common B₂–N₂ diagram, π2p lies below σ2p. In the common O₂–F₂ diagram, σ2p lies below π2p. The antibonding π2p levels follow above the bonding 2p levels in these basic schemes.

The switch is usually explained through s–p mixing. MOs with the same appropriate symmetry and reasonably close energies can interact, shifting their energies. For lighter second-period molecules, 2s and 2p atomic energies are closer, so mixing of sigma-symmetry levels is more significant and raises the σ2p level relative to π2p. For O₂ and F₂, the 2s–2p separation is larger, so the mixing effect is weaker and the more intuitive σ2p-below-π2p order applies.

Mixing does not create extra electrons or additional independent orbitals. The number of molecular orbitals remains equal to the number of atomic orbitals combined in the chosen basis. It changes the energies and character of compatible levels. Simply memorising the switch without this concept can lead to filling B₂ like O₂ and predicting its magnetism incorrectly.

For B₂, two electrons beyond filled 2s-derived levels enter the two degenerate π2p bonding orbitals separately, giving two unpaired electrons in the basic model. If σ2p were incorrectly placed below π2p, those two would pair in one σ box and a false diamagnetic result would follow. For N₂, both π2p orbitals and σ2p are filled, producing a closed-shell diamagnetic state and bond order three.

Some diagrams include 1s core levels; others omit them. The energy-order switch discussed here concerns the valence 2p levels. When using a diagram, match its labels and electron count rather than copying an ordering from memory without identifying the molecule.

Step-by-step reasoning

1. Identify the diatomic molecule and its valence-electron count. 2. Choose the B₂–N₂ or O₂–F₂ qualitative ordering. 3. Fill 2s-derived levels, then the appropriate 2p sequence. 4. Apply Hund's rule to degenerate π pairs. 5. Count bond order and unpaired electrons from the filled diagram.

Visual explanation

Draw two side-by-side energy ladders. Left B₂–N₂ has π2p below σ2p; right O₂–F₂ reverses those two levels. Mark an arrow showing sigma levels shift due to s–p mixing, while the number of boxes remains unchanged.

Real-world analogy

Two runners can swap finishing order when one is affected more strongly by track conditions. The runners are still the same two; their relative energies change. s–p mixing shifts orbital levels without inventing extra orbitals.

Real-world example

MO diagrams explain the observed paramagnetism of B₂ and O₂ through different parts of their filling patterns. Choosing the correct 2p order is essential for B₂, where the lower π pair gives two unpaired electrons.

Why?

Why does sigma mixing affect π less in the elementary explanation? Orbitals interact strongly only when their symmetry permits. Sigma-symmetry levels can mix with one another, while the differently symmetric π pair does not mix with those sigma levels in the same way.

Common misconception

“s–p mixing adds new MOs to the diagram.” It shifts and blends existing compatible orbital levels. The total number of MOs still matches the atomic-orbital basis used.

Worked example

Place B₂'s six valence electrons in the common light-diatomic order. σ2s² and σ2s ² take four. The remaining two occupy the two degenerate π2p bonding orbitals singly under Hund's rule. There are two unpaired electrons. Bonding valence electrons total four (σ2s two and π2p two), antibonding total two (σ2s ), so bond order (4 − 2)/2 = 1. Using the wrong 2p order would incorrectly pair the last two in σ2p.

Quick check

1. Which lies lower in the common N₂ valence diagram, π2p or σ2p? Answer: π2p lies below σ2p in the standard light-diatomic ordering.

Exam focus

Write the orbital order before filling and use the correct species group. Apply Hund's rule to π degeneracy. Explain s–p mixing as energy interaction among compatible levels, not new-orbital creation.

Advanced insight

The ordering change is gradual across the period rather than a magical abrupt switch at an element boundary. Introductory diagrams discretise it into two standard patterns useful for common diatomic species.

Summary

B₂–N₂ commonly have π2p below σ2p due to stronger s–p mixing; O₂–F₂ commonly have σ2p below π2p. Correct ordering and Hund filling are necessary for bond-order and magnetic predictions.

Practice questions

1. Which level lies lower for O₂ in the common simple diagram, σ2p or π2p? Answer: σ2p. 2. How many unpaired electrons does the basic B₂ diagram predict? Answer: Two, one in each degenerate π2p bonding orbital. 3. Does s–p mixing create extra orbital boxes? Answer: No. It changes energies and characters of existing compatible orbitals. 4. Why must Hund's rule be used for B₂'s last two valence electrons? Answer: They enter a degenerate π pair and occupy separate orbitals before pairing.