MO Electron Filling Rules

Introduction

An MO energy diagram becomes useful only after electrons are placed correctly. Three familiar filling rules carry over from atomic orbital diagrams: use low levels first, allow at most two opposite-spin electrons in one orbital, and occupy equal-energy orbitals singly before pairing.

Core explanation

The Aufbau principle is a ground-state filling guide: place electrons in the available orbital of lowest energy, then work upward. For H₂, both electrons occupy σ1s with opposite spins before any enters σ1s . This gives a bonding occupation. For a molecular ion, adjust the total electron count first; H₂⁺ has only one electron in σ1s.

Pauli's exclusion principle prevents two electrons in the same spatial MO from having the same spin state. A box may contain ↑↓ but not ↑↑ as two electrons in one orbital. It does not forbid different orbitals from each having one ↑ electron. In a full MO diagram, each orbital has its own quantum state even if two orbitals share the same energy.

Hund's rule is crucial for degenerate π orbitals. A pair of π2p orbitals can have the same energy in a homonuclear diatomic's simple diagram. If two electrons reach a degenerate π pair, put one in each with parallel spins before pairing them in one box. Ground-state O₂ does this in the π orbitals, giving two unpaired electrons and paramagnetism. Pairing the two prematurely would give the wrong magnetic prediction even if the total electron count were correct.

Energy ordering for 2p-derived MOs is not identical across every second-period diatomic. B₂ through N₂ are commonly drawn with π2p below σ2p in the basic model because of s–p mixing, while O₂ and F₂ have σ2p below π2p. Use the ordering specified or appropriate for the species before filling. The same three rules then apply in either diagram.

Core 1s levels may be omitted from simplified valence MO diagrams because their bonding and antibonding occupations often cancel in bond-order calculations. If omitted, count valence electrons rather than total atomic electrons; mixing a valence-only diagram with a total-electron count overfills it.

The filling rules describe a chosen ground-state diagram. Excited states and electron correlation can be more complex. At this level, show every occupied box or a clear configuration and report both bond order and unpaired electron count.

Step-by-step reasoning

1. Count electrons for the neutral molecule or ion. 2. Select the correct orbital ordering and whether core levels are shown. 3. Fill lower-energy boxes first, at most two opposite-spin electrons per box. 4. In equal-energy sets, place single parallel spins before pairing. 5. Count bonding, antibonding and unpaired electrons.

Visual explanation

Draw two equal-height π boxes. Place one ↑ in each for two electrons, then show the incorrect alternative ↑↓ in one and an empty other with a cross through it. Below, write “two unpaired” versus the false “zero unpaired.”

Real-world analogy

People fill lower floors of a building before higher floors, but two people cannot occupy the same one-seat room in the same way; equal-floor rooms fill separately first under the model rule. The analogy helps remember ordering, capacity and degeneracy without explaining the quantum origin.

Real-world example

O₂'s paramagnetism can be demonstrated by its response to a magnetic field. Correct Hund-rule filling of its degenerate π orbitals predicts the unpaired electrons responsible for that observation.

Why?

Why is an equal-energy pair filled singly first? Hund's rule reflects the lower-energy arrangement of electrons with parallel spins in separate degenerate orbitals under the relevant quantum interactions. It is not a rule that electrons “dislike company” in a classical sense.

Common misconception

“Two electrons in two degenerate π orbitals must pair because there are two of them.” Hund's rule places one electron in each first. Premature pairing incorrectly removes predicted paramagnetism.

Worked example

Fill the simplest H₂⁺ and H₂ 1s MO levels. H₂⁺ has one electron: σ1s¹, no spin partner, one unpaired electron, bond order 0.5. H₂ has two: σ1s² with opposite spins, no unpaired electrons, bond order 1. Neither occupies σ1s . The difference follows electron count and Pauli filling, not a change in the orbital energy order.

Quick check

1. How do two electrons occupy a pair of equal-energy π orbitals in the ground-state filling model? Answer: One in each orbital with parallel spins before either orbital receives a second electron.

Exam focus

Show electron count and chosen MO order. Distinguish valence-only from all-electron diagrams. Use Pauli and Hund correctly before calculating bond order or declaring magnetic behaviour.

Advanced insight

Hund's rule arises from electron exchange and correlation effects in many-electron quantum states. The box-and-arrow representation is a compact ground-state approximation, not literal electrons sitting in drawn boxes.

Summary

MO filling uses lower-energy-first placement, Pauli's two-opposite-spin limit and Hund's single occupation of degenerate orbitals. Correct orbital ordering and electron count are prerequisites for bond order and magnetism predictions.

Practice questions

1. How many electrons can one spatial MO hold under Pauli's rule? Answer: Two with opposite spins. 2. How many unpaired electrons does H₂⁺ have in its simple ground-state MO diagram? Answer: One. 3. What goes wrong if O₂'s two π electrons are paired in one orbital? Answer: The diagram falsely predicts no unpaired electrons and misses paramagnetism. 4. Why must a valence-only diagram use a valence-electron count? Answer: Its omitted core orbitals cannot hold the core electrons in the displayed scheme.