Physical Chemistry Third Edition

21.6 Delocalized Bonding 889

Figure 21.9 The Orbital Regions of the Delocalized Pi Orbitals in Benzene by the Hückel Method.Positive regions are in black and
negative regions are in gray.

There are six electrons to occupy the delocalized space orbitals. By the Aufbau

principle, in the ground-state each of the three lowest-energy space orbitals is occupied

by two electrons with opposite spins, as depicted by arrows in Figure 21.8. Although

these orbitals do not have simple angular momentum properties, we refer to them as pi

orbitals.

In the first excited state, an electron in one of the highest occupied molecular orbitals

(HOMOs) is promoted to one of the lowest unoccupied molecular orbitals (LUMOs),

increasing the energy of the molecule by 2|β|. This transition can be observed spectro-

scopically, and the value ofβcan be determined.

EXAMPLE21.10

From the fact that benzene absorbs strongly at wavelengths near 180 nm, estimate the

value ofβ.

Solution

2 |β|

hc

λ



(6. 6261 × 10 −^34 J s)(2. 9979 × 108 ms−^1 )

180 × 10 −^9 m

 1. 10 × 10 −^18 J

β− 5. 5 × 10 −^19 J, which is equivalent to –3.4 eV or –330 kJ mol−^1