Chemistry · Ch 4 — Chemical Bonding and Molecular Structure

Energy Level Diagram for Molecular Orbitals

4.7.4

Energy Level Diagram for Molecular Orbitals

From Atomic Orbitals to Molecular Orbitals

When two atoms approach each other, their atomic orbitals combine to form molecular orbitals. You already know that two 1s atomic orbitals give one bonding orbital ( $\sigma 1s$ ) and one antibonding orbital ( $\sigma^* 1s$ ). The same principle extends to the second shell.

For second-row elements (Li through Ne), each atom contributes one 2s orbital and three 2p orbitals — that is four atomic orbitals per atom, or eight in total for the diatomic molecule. These eight atomic orbitals combine to produce eight molecular orbitals:

Bonding MOs	Antibonding MOs
$\sigma 2s$	$\sigma^* 2s$
$\sigma 2p_z$	$\sigma^* 2p_z$
$\pi 2p_x$	$\pi^* 2p_x$
$\pi 2p_y$	$\pi^* 2p_y$

The labels tell you the symmetry: $\sigma$ orbitals are symmetric about the internuclear axis (end-on overlap), while $\pi$ orbitals have a nodal plane containing that axis (side-on overlap). The asterisk denotes antibonding character.

The Two Energy Sequences

The relative energies of these eight molecular orbitals are not the same for all homonuclear diatomic molecules of the second period. Experimental data from spectroscopy reveal two distinct sequences.

Sequence 1 — for O $_2$ and F $_2$ :

\sigma 1s < \sigma^* 1s < \sigma 2s < \sigma^* 2s < \sigma 2p_z < (\pi 2p_x = \pi 2p_y) < (\pi^* 2p_x = \pi^* 2p_y) < \sigma^* 2p_z

Notice that the $\sigma 2p_z$ orbital lies below the $\pi 2p$ pair. This is the order you will find for molecules with 8 or more valence electrons in the second shell (O $_2$ and F $_2$ ).

Sequence 2 — for Li $_2$ , Be $_2$ , B $_2$ , C $_2$ , N $_2$ :

\sigma 1s < \sigma^* 1s < \sigma 2s < \sigma^* 2s < (\pi 2p_x = \pi 2p_y) < \sigma 2p_z < (\pi^* 2p_x = \pi^* 2p_y) < \sigma^* 2p_z

Here the $\pi 2p$ orbitals are lower in energy than the $\sigma 2p_z$ orbital. This reversal occurs for lighter molecules (up to N $_2$ ).

Important

The key difference between the two sequences is the relative position of $\sigma 2p_z$ and the $\pi 2p$ pair. In O $_2$ /F $_2$ , $\sigma 2p_z$ is lower; in Li $_2$ –N $_2$ , the $\pi 2p$ orbitals are lower.

Why the Order Changes

The explanation lies in the energy gap between the 2s and 2p atomic orbitals. For oxygen and fluorine, the 2s–2p gap is large, so the $\sigma 2s$ and $\sigma^* 2s$ orbitals do not mix significantly with the $\sigma 2p_z$ orbitals. The $\sigma 2p_z$ orbital therefore remains relatively low in energy.

For lighter elements (Li through N), the 2s–2p gap is smaller. This allows substantial mixing (hybridisation) between the $\sigma 2s$ and $\sigma 2p_z$ orbitals. The mixing pushes the $\sigma 2p_z$ orbital up in energy, above the $\pi 2p$ pair. The $\pi$ orbitals, which have no $\sigma$ -type counterpart to mix with, are unaffected by this interaction and stay lower.

Note

The $\pi 2p_x$ and $\pi 2p_y$ orbitals are always degenerate (equal in energy) because they differ only in orientation, not in any physical property. The same holds for $\pi^* 2p_x$ and $\pi^* 2p_y$ .

A Practical Consequence …

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