AB₂ molecules like OF₂ and O₃

Further examples of molecules of point group C_2v are Oxygendiflouride OF₂ and the Sulfurdiflouride SF₂. The number of valence electrons is the same for both molecules. For a start, we do not introduce the complete number of electrons of the flourine atoms. Instead, we concentrate on those electrons appropriate for bonds of rotational symmetry. These electrons are found in the first and the second row of the table below.

Regarding only the pair of electrons in the σ-AO and the single electron in an pσ-AO of each flourine atom, the molecules OF₂ and SF₂ appear analogous to the previously dicussed water molecule. With this constrictions, we recieve the following series of molecular orbitals. The background color in the table signifies the role for molecular bonding: Blue for bonding, green for non-bonding and red for anti-bonding.

These eight orbitals harbour twelve electrons (6 of oxygen / sulfur and 3 from each flourine atom). Three bonding and two non-bonding orbitals accept a maximal number of ten electrons. For two electrons, only an antibonding orbital remains. Among the two antibonding orbitals, the 3a₁ is lower in energy and thus filled. With respect to molecular energy, 2a₁ and 3a₁ compensate each other. According to this approach, the formation and stability of the molecules OF₂ and SF₂ is based on two bonding molecular orbitals.

Now we want to introduce the electrons in π-AOs (or, more exactly, the electrons of pπ-orbitals) into our consideration. We then have the following series of molecular orbitals:

A number of five molecular orbitals are bonding and two are non-bonding. Together, they accept 14 electrons, but now, a total of 20 valence electrons (7 from both flourine atoms) are to be distributed. Therefore three antibonding MOs, namely 4a₁, 2b₁ and 3b₂ must harbour the six remaining electrons. We would expect the effects of five fully occupied bonding and three fully occupied antibonding orbitals to compensate each other partially. In fact, the molecules appear to be bound by only two molecular orbitals. Thus, the newly introduced electrons of flourine's &pi-AOs seem to be distributed equally among bonding and antibonding molecular orbital, having no overall effect.

We may use the same scheme of molecular orbitals to discuss the bonding within a molecule of ozone O₃ or sulfurdioxide SO₂. Flourine and oxygen differ by one valence electron. We therefore have 18 instead of 20 electrons and one more antibonding orbital remains empty. This would explain why ozone and sulfurdioxide are more stable than their flourine analogons.

Similar to diatomics, in molecules of the class AB_n, electrons in &sigma-; pσ- and pπ-states form bonds classified as σ- or π-MOs. Note that there is no true separation because the σ- and π-electrons and there are just a few symmetry groups where molecular orbitals are either formed from σ- or from π-orbitals. A table presents an overview. For example, such a separation

• is only found for molecules of point group D_∞h, i.e. for linear molecules.
• will not be found in point group D_3h. In the planar molecules AB₃ of this group orbitals of symmetry species a₁' harbour only σ-electrons and the orbitals of the symmetry species a₂', a₂" and e" only π-orbitals. But, to the orbitals of symmetry species e', orbitals of both σ and π-type contribute to the resulting molecular orbital of AB₃.
• will not be found for the bent molecules of point group C_2v. Here, a₂ and b₁ molecular orbitals are exclusively formed by π-type orbitals and a₁- and b₂-orbitals appear to be combinations of both types.

Let us get back to the example of ozone O₃ and sulfurdioxide SO₂. If we have one fully occupied bonding orbital of type 1b₁ and one empty antibonding orbital of symmetry species 2b₁, we would conclude that, among the remaining bonding orbitals, there is one of type π. A quantitative treatment shows that the other two molecular orbitals are mainly of σ-type. Therefore, in ozone and in sulfurdioxide are described as formed by two σ- and one π-bond.

In Oxygendifluoride OF₂ and Sulfurdiflouride SF₂, besides the 1b₁ the antibonding π-orbital 2b₁ is doubly occupied. Therefore there are two bonds of type σ and none of type π. The first simplified approach to this molecule which ignored the π-electrons led to the same picture.

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