# D6.4 MOs for Second-row Diatomic Molecules

Let’s consider some slightly more complex examples of molecular orbitals. F_{2}, O_{2}, and N_{2} are diatomic molecules formed by elements from the second row of the periodic table. These molecules contain many more electrons than H_{2}, and their molecular orbitals are derived from *p* atomic orbitals as well as *s* atomic orbitals.

**Activity: Shapes and Phases of p Atomic Orbitals
**

**Additional Practice**

Now think about what happens when two atoms containing 2*p* atomic orbitals approach each other. Assume that the internuclear axis is the *z* axis. This means that the 2*p _{z}* atomic orbitals are aligned along the internuclear axis while the 2

*p*and 2

_{x}*p*atomic orbitals are oriented perpendicular to the internuclear axis.

_{y}When the two atoms approach, the bonding and antibonding overlap of the two 2*p _{z}* atomic orbitals occurs along the internuclear axis (

*z*axis):

MOs derived from these two combinations are labeled σ_{2pz} and σ^{*}_{2pz}. *If you don’t understand why these MOs are have the label σ, review the section on MO diagrams.*

It is also possible to make bonding and antibonding combinations from the two 2*p _{x}* AOs and from the two 2

*p*AOs. Here is a diagram for the two ways the 2

_{y}*p*AOs can overlap. Notice that the orbitals overlap side-by-side, not end-on, because the 2

_{x}*p*AOs are aligned perpendicular to the internuclear axis (

_{x}*z*axis).

**Activity: Molecular Orbitals Involving p Atomic Orbitals
**

**Additional Practice**

When two 2*p* AOs overlap side-by-side, the bonding MO formed is not symmetric with respect to rotation around the internuclear axis. Thus, the bond formed is not a σ bond. If you look down the internuclear (bond) axis, the “side view” of the MO looks similar to a 2*p* atomic orbital; this MO is called a π orbital.

Think about all atomic orbitals that are occupied in a fluorine atom, F: 1*s*, 2*s*, 2*p*_{z}, 2*p*_{x}, and 2*p*_{y}. For each pair of AOs (such as *2s* on atom A with 2*s* on atom B), overlap produces one bonding and one antibonding MO. There is σ and σ^{*} for 1*s – 1s*, 2*s – 2s*, and 2*p*_{z} – 2*p*_{z} overlaps. There is π and π^{*} for 2*p*_{x} – 2*p*_{x}, and 2*p*_{y} – 2*p*_{y} overlaps. These ideas result in the MO energy-level diagram shown here:

From the ten AOs (five from each F atom), ten MOs are formed in F_{2}. Note that whether a MO is bonding or antibonding is dependent on whether it is lower or higher in energy than the AOs from which it is derived. Hence, even though σ^{*}_{2s} is lower in energy than σ_{2pz}, it is still an antibonding MO.

The y-axis in the above figure only shows qualitative relative energy ordering. If you consider the actual energy values, the core electrons are much much lower in energy than the valence electrons. For example, the energy difference between the 1*s* and 2*s* atomic orbitals in F is 62,000 kJ/mol while the difference between 2*s* and 2*p* is only 1,800 kJ/mol. The core electrons also occupy orbitals that are much smaller (closer to their nucleus) than valence electrons. Hence, the core electrons from two atoms will not overlap in any significant way even as their valence electrons overlap to form covalent bonds. This is why you will often see the core electrons omitted from MO diagrams. (Such omission will not hinder your analysis of the molecule. For example, results from bond order calculations will be the same with or without core electrons.)

We also see in Figure: MO Energies for F_{2} that the two π bonding MOs, π_{2px} and π_{2py}, are degenerate (have the same energy). This is because the side-by-side overlap of two 2*p** _{x}* AOs is identical to the side-by-side overlap of two 2

*p*AOs. They differ only in that π

_{y}_{2px}and π

_{2py}are perpendicular to each other, because the 2

*p*

*AO is perpendicular to the 2*

_{x}*p*

*AO. Similar reasoning leads to the conclusion that the π*

_{y}^{*}

_{2px}and π

^{*}

_{2py}MOs are also degenerate. Recognizing degenerate MOs is important when applying Hund’s rule to determine molecular electron configurations.

Figure: Pi-Bond MOs (below) shows the formation of the two perpendicular π bonds as two N atoms approach each other. (The two molecular depictions in the figure represent the same N_{2} molecule: one shows the 2*p*_{x} – 2*p*_{x} orbital overlap and the other shows the 2*p*_{y} – 2*p*_{y} orbital overlap.)

**Exercise: Molecular Orbital Electron Configurations
**

**Additional Practice**

Based on the electron configuration for the F_{2} molecule, the π and π^{*} MOs are all filled; there is no net π bond in the molecule. This is reflected in the bond order calculation: F_{2} has a bond order of 1, corresponding to a single σ bond.

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