Absolutely Small - Michael D. Fayer [82]
SIGMA MOLECULAR ORBITALS
When the orbitals are brought sufficiently close together, they can form bonding and antibonding molecular orbits. First we will look at molecular orbitals formed from s and p atomic orbitals that give σ bonding and antibonding MOs. A σ MO has electron density along the line joining the nuclei. As discussed above, s orbitals can only form σ orbitals because of their spherical shape. p orbitals can also form σ MOs. Figure 13.2 shows σ bonding and antibonding MOs formed from both s and p orbitals. The upper part of the figure depicts the two possible ways that a pair of s orbitals can be combined. The s orbitals are waves and can have either a + or - sign associated with them. In the top portion, both s orbitals have + signs. When they combine, the s orbital waves constructively interfere to produce a σ bonding MO. In the second line of the figure, one s orbital is + and the other is -. When they combine, they destructively interfere to form an antibonding MO. The bonding MO concentrates the electron density between the nuclei, while the antibonding MO pushes the electron density to the outside, reducing the negative electron density between the nuclei. The positively charged nuclei repel each other more strongly, making this configuration antibonding.
The bottom portion of Figure 13.2 shows the results of combining two p orbitals to form σ molecular orbitals. The σ p bonding MO is generated by overlapping the + lobe of one p orbital with the + lobe of the other p orbital. There is constructive interference between the + lobes, resulting in high electron density between the atomic nuclei. There are two nodal planes that are perpendicular to the page. These are the two nodal planes that came from the two atomic p orbitals. In contrast, in the bottom line of the figure, the positive lobe of one p orbital is overlapped with the negative lobe of the other p orbital. The result is destructive interference, producing the antibonding MO. The electron density is pushed to the outside, and it is greatly reduced between the two nuclei. In addition to the two nodal planes that come from the atomic orbitals, there is a third nodal plane that arises because there is complete destructive interference between the positive and negative lobes of the two atomic p orbitals. In these bonding and antibonding MOs formed from atomic p orbitals, there is electron density along the line connecting the nuclei. Therefore, these are σ MOs.
FIGURE 13.2. Upper portion: a pair of s orbitals are overlapped in two ways to give σ bonding (constructive interference) and σ antibonding (destructive interference) molecular orbitals. Lower portion: a pair of p orbitals are overlapped in two ways to give σ bonding (constructive interference) and σ antibonding (destructive interference) molecular orbitals. In all cases, there is electron density along the line through the nuclei.
PI MOLECULAR ORBITALS
s orbitals can only form σ MOs, but p orbitals can form σ MOs and another type of molecular orbital called π (the Greek letter pi) MOs. When p atomic orbitals come together end to end, they form σ MOs. When they come together side to side, they form π MOs, as shown in Figure 13.3. The upper portion of the figure shows two p orbitals forming a bonding molecular orbital. The positive lobe of one atomic orbital overlaps the positive lobe of the other, and the negative lobes overlap. There is constructive interference for both the positive and negative lobes. As can be seen in the figure, there is a great deal of electron density in the area between the two nuclei. However, there is no electron density directly along the line connecting the nuclei. There is a nodal plane that is perpendicular to the plane of the page because each atomic orbital has a nodal plane perpendicular to the page. The nodal plane contains the nuclei. In spite of the nodal plane, all of that electron density immediately