Chapter 10, Problem 41P

If one were to try to draw the simplest Lewis structure fur molecular oxygen, the result might be the following

However, it is known from the properties of molecular oxygen and experiments that $O_2$ contains two unpaired electrons, and therefore, the Lewis structure above is incorrect. To understand the structure of $O_2$, it is necessary to employ a molecular orbital representation. To do so, we will need to recall (1) the shapes of bonding and antibonding $\sigma$ and $\pi$ molecular orbitals, (2) that each orbital can con rain a maximum of two electrons, (3) that molecular oxygen has 16 electrons in total, and (4) that the two unpaired electrons in oxygen occupy separate degenerate (equal-energy) orbitals. Now, open the molecular model on the book’s website for oxygen and examine its molecular orbitals in sequence from the HOMO-7 orbital to the LUMO, [HOMO-7 means the seventh orbital in energy below the highest occupied molecular orbital (HOMO), HOMO-6 means the sixth below the HOMO, and so forth.) Orbitals HOMO-7 through HOMO-4 represent the $\sigma 1\text{s},\sigma 1{\text{s}}^{\text{*}},\sigma 2\text{s},$ and $\sigma 2\text{s*},$ orbitals, respectively, each containing a pair of electrons.

(a) What type of orbital is represented by HOMO-3 and HOMO-2? (Hint: What types of orbitals are possible for second-row elements like oxygen, and which orbitals have already been used?)

(b) What type of orbital is HOMO-1? [Hint: The $\sigma 2s^{*}$ and $\sigma 2{\text{s}}^{\text{*}}$ orbitals are already filled, as are the HOMO-3 and HOMO-2 orbitals identified in part (a). What bonding orbital remains?)

(c) The orbitals designated HOMO and LUMO in $O_2$ have the same energy (they are degenerate), and each contains one of the unpaired electrons of the oxygen molecule. What type of orbitals are these?