Construct and interpret pi-MO diagrams for benzene and polyenes

For a conjugated molecule, a good diagram links three things: the shape of each π molecular orbital, its relative energy and its occupancy.

GCE A-Level H3 Chemistry 9813-2027

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Learning objectives

Construct and interpret pi-MO diagrams for benzene and polyenes

Turn phase patterns into an energy diagram

For a conjugated molecule, a good diagram links three things: the shape of each π molecular orbital, its relative energy and its occupancy.

Construct the orbital set first by counting p orbitals and nodes. Then fill electrons and identify the HOMO and LUMO; do not guess them from a familiar molecule name.

What the diagram must show

For a linear polyene with N aligned p orbitals, draw N π molecular orbitals in order of increasing node count. More nodes place an orbital higher in energy.

For benzene, show the characteristic qualitative pattern of one lowest level, two degenerate levels, two higher degenerate levels and one highest level.

Each π molecular orbital holds at most two electrons. The HOMO and LUMO refer to occupancy after the correct number of π electrons has been placed.

Construct, fill and interpret

Buta-1,3-diene gives four levels. With four π electrons, ψ1 and ψ2 are occupied, ψ2 is the HOMO and ψ3 is the LUMO. The HOMO–LUMO gap is the energy separation relevant to the lowest simple π→π* excitation.

Benzene gives six levels in a 1–2–2–1 pattern. Six electrons fill the lowest level and the first degenerate pair. The occupied degenerate pair is the HOMO level and the next degenerate pair is the LUMO level.

A qualitative diagram does not require numerical energies or coefficients. It does require correct degeneracy, node order, electron filling and labels.

Worked example: buta-1,3-diene

Draw four horizontal levels and place them in order ψ1 < ψ2 < ψ3 < ψ4. Associate zero, one, two and three nodes with the four levels.

Place two electrons in ψ1 and two in ψ2. Label ψ2 as HOMO and ψ3 as LUMO, then draw the excitation arrow only if a transition is being discussed.

Try this

Construct the qualitative π-MO diagram for buta-1,3-diene and identify its frontier orbitals.

Check your answer

Four levels are required. ψ1 and ψ2 are doubly occupied; ψ2 is the HOMO and ψ3 is the LUMO.

Build the benzene diagram

Use six p orbitals to justify six levels. Draw the two equal-energy pairs on shared horizontal positions rather than as six evenly spaced single levels.

Place six electrons in the three bonding orbitals. Pauli filling gives two electrons per orbital; the occupied degenerate pair is not left singly occupied because four electrons remain after filling the lowest level.

Try this

Show the occupancy of benzene's 1–2–2–1 π-level pattern.

Check your answer

Place 2 electrons in the lowest level and 4 across the degenerate bonding pair. The degenerate antibonding pair and highest level are empty.

Transfer to hexa-1,3,5-triene

A six-carbon linear polyene has six π levels and six π electrons, but its level spacings and degeneracy pattern are not the same as benzene's cyclic pattern.

Draw six levels ordered by node count, fill the lowest three, and label the third and fourth levels HOMO and LUMO respectively.

Try this

Identify the occupied levels, HOMO and LUMO of ground-state hexa-1,3,5-triene.

Check your answer

The three lowest π levels are occupied. The third level is the HOMO and the fourth is the LUMO.

Common mistake: using electron count to invent levels

Four π electrons in butadiene do not mean four occupied orbitals: each orbital can hold two electrons. Conversely, six electrons in benzene do not all fit into its lowest orbital.

Do not give every benzene orbital a different energy. Symmetry produces the two degenerate pairs in the qualitative diagram.

Try this

Correct: ‘Benzene has six different π energies because it has six p orbitals.’

Check your answer

Benzene has six π molecular orbitals but only four qualitative energy positions: one level, a degenerate pair, another degenerate pair and one level.

Check your understanding

Before finishing a diagram, count parent p orbitals, resulting levels, π electrons, occupied orbitals and nodes. Then verify any required degeneracy and frontier labels.

Next, connect molecular energy gaps to photons and the electromagnetic spectrum.

Try this

List the construction order for a reliable conjugated π-MO diagram.

Check your answer

Count p orbitals, draw that many levels in node order, show required degeneracy, fill the π electrons, then label HOMO and LUMO.