Absolutely Small - Michael D. Fayer [124]
FIGURE 18.3. Top: Benzene σ bonding. Each carbon makes three bonds using three sp2orbitals that lie in the xy plane. Each carbon has a pzorbital perpendicular to the plane of the benzene ring. Bottom: The carbon pzorbitals have positive and negative lobes that are above and below the plane of the ring. The bond lengths are exaggerated and the pzlobes are made small for clarity of presentation. The lobes of adjacent pzorbitals overlap.
The Bonding and Antibonding Molecular Orbitals
In benzene, six pz atomic orbitals combine to form three bonding MOs and three antibonding MOs, as shown in Figure 18.4. The six carbon 2pz orbitals, one on each carbon atom, have identical energy. This is indicated by the six closely spaced lines on the left-hand side of Figure 18.4. These combine to form six MOs with energy levels shown on the right-hand side of the figure. Three of the MOs have energies lower than the pz atomic orbital energy. These are the bonding MOs. Three of the MOs have energies higher than the atomic orbital energy. These are the antibonding MOs. Figure 18.5 shows the bonding and antibonding energy levels with the six electrons, one from each carbon, placed in the appropriate energy levels. We place the electrons in the lowest energy level consistent with the Pauli Principle. The Pauli Principle (Chapter 11) states that at most two electrons can be in a single orbital, and they must have opposite spin states (one up arrow and one down arrow). The first two electrons go into the lowest energy MO. The next two MOs have the identical energy indicated by two closely spaced lines. Two electrons will go into each of these MOs. The three MOs filled by the six electrons are all π bonding MOs. The π antibonding MOs are empty.
FIGURE 18.4. Left: Benzene has six carbon atoms, each with a 2pzorbital. These have identical energy, which is indicated by the six closely spaced lines. Right: The six pzorbitals combine to form six π molecular orbitals, three bonding (b) and three antibonding (*) MOs.
FIGURE 18.5. Benzene π molecular orbital energy levels with the six electrons placed in the appropriate MOs in the lowest possible energy levels consistent with the Pauli Principle.
The Carbon-Carbon Bond Order is 1.5
Figure 18.5 shows that the six carbon pz electrons occupy three π bonding MOs. Therefore, there are three π bonds shared by six carbons. These three π bonds are in addition to the σ bonds that connect each carbon to its two nearest carbon neighbors. The net result is that each carbon has 1.5 bonds to other carbons. The three π bonds shared by the six carbon atoms contribute a half of a bond joining adjacent carbons. The bonds between carbon atoms are shorter and stronger than a carbon-carbon single bond, but not as short or as strong as a full double bond. The π bonding keeps the molecule rigorously planar. Twisting the ring away from planarity reduces the overlap of the pz orbitals and raises the energy. Figure 18.6 shows a chemical diagram of benzene. A carbon is represented by a vertex. A hydrogen atom is at the end of each line that emanates from a carbon. The circle represents the delocalized π electron system.
FIGURE 18.6. Benzene chemical diagram. A carbon atom is at each vertex, and a hydrogen is at the end of each line from a carbon. The circle represents the delocalized π molecular orbitals.
Many molecules have carbon rings with delocalized π bonding. Another example is naphthalene, which is shown in Figure 18.7. Naphthalene has 10 carbons forming two six-membered rings with eight hydrogens. The two circles represent the delocalized π molecular orbitals. Like benzene, naphthalene is planar and each carbon has 1.5 bonds to the adjacent carbons.
FIGURE 18.7. Naphthalene chemical diagram. Naphthalene has 10 carbons and eight hydrogens. The circles represent