Explain discrete molecular-orbital energy levels

Read energy diagrams as allowed states

A molecular-orbital diagram is not a continuous ramp of possible energies. Each horizontal line represents one allowed molecular orbital with a definite energy.

Electrons can occupy these discrete levels according to the Aufbau principle, the Pauli exclusion principle and Hund's rule.

Discrete levels and electron filling

Discrete means that only particular stationary-state energies are allowed. An electron in the molecule cannot sit at an arbitrary energy between two molecular-orbital levels.

Each molecular orbital holds at most two electrons with opposite spins. Orbitals of equal energy are degenerate, and electrons occupy a degenerate set singly with parallel spins before pairing.

From levels to transitions

The vertical position of a level shows its energy; it is not a picture of where the orbital lies in the molecule. Spatial shape must be shown separately or encoded by the orbital label.

An electron moves between allowed levels only by gaining or losing the exact energy difference, ΔE. For a one-photon transition, ΔE = hf, so the spacing between levels determines the radiation frequency.

A level may be occupied, singly occupied, doubly occupied or empty. Occupancy changes the electron configuration, but it does not create new intermediate energy levels.

Worked example: filling a degenerate pair

Suppose a lower σ level contains two electrons and the next two π levels are degenerate. With two further electrons, place one electron in each π orbital with parallel spins.

Pairing both electrons in one π orbital would increase electron–electron repulsion and violate Hund's rule for the ground state.

Practise reading a level diagram

Move upward to higher energy and identify the highest occupied level and lowest unoccupied level. If either is degenerate, name the whole degenerate set.

For a transition, subtract the initial level energy from the final level energy; do not add their magnitudes simply because both values are printed.

Test the word ‘allowed’

If a diagram shows levels at −10 eV and −4 eV, −7 eV lies between them numerically but is not an allowed stationary level unless another line is shown there.

During a transition the system changes between states; it is not described as resting at every intermediate energy.

Common mistake: confusing height with position

A higher horizontal line means higher energy, not that the electron is physically farther above the molecule.

Electron arrows show occupancy and spin. They do not show a path travelled by an electron through space.

Check your understanding

You should be able to identify allowed levels, fill them using Pauli and Hund rules, and calculate a transition energy from a level spacing.

Next, use linear combinations of atomic orbitals to build the molecular levels of homonuclear diatomic molecules.