Physical Chemistry Third Edition

21.6 Delocalized Bonding 885

ammonias bonded to the platinum atom with the chlorines

adjacent to each other and the ammonias adjacent to

each other, explaining thecisdesignation. Describe

the bonding in cisplatin, using appropriate hybrid

orbitals.

21.22It was once thought that the inert gases could not form
chemical bonds, but it is not difficult to form compounds
of xenon with fluorine and oxygen. Describe the bonding

in XeF 4 , using appropriate hybrid orbitals. You can use

the VSEPR theory to determine the electron geometry

and the molecular geometry.

21.23Describe the bonding in XeOF 4 , using appropriate

hybrid orbitals. You can use the VSEPR theory to

establish the electron geometry and the molecular

geometry.

21.6 Delocalized Bonding

In our qualitative descriptions of chemical bonding we have used LCAOMOs made

from two atomic orbitals and valence-bond factors containing two atomic orbitals. In

this section we discuss molecules for which this description is unsatisfactory.

The Valence-Bond Method and Resonance

We consider the benzene molecule (C 6 H 6 ) as an example. A simple valence-bond wave

function for benzene has alternating single C–C bonds and double CC bonds. It is

an experimental fact that double bonds are shorter than single bonds, so this wave

function conflicts with the experimental fact that the benzene molecule is hexagonal

in shape with six C–C bonds of the same length. This deficiency is remedied in the

valence-bond method by the use ofresonance. To illustrate this method we place the

benzene molecule in thexyplane and orient the coordinate system at each carbon so

that its 2sp^2 orbital regions point in the directions of the C–C bond and the C–H bonds.

We first construct a simple valence-bond wave function with alternating single bonds

and double bonds between the carbon atoms. The single bonds are sigma bonds made

from two 2sp^2 hybrids, and each double bond consists of a sigma bond made from 2sp^2

hybrids and a pi bond made from unhybridized 2pzorbitals.

To obtain a better representation of benzene, we construct another valence-bond

wave function with the double bonds in the other locations. We represent the two

structures by abbreviated structural formulas as follows:

I II

where the carbon atoms are located at the corners of the hexagons and the hydro-

gen atoms have been omitted. These structures are calledresonance structures.Itis

customary to write a double-headed arrow between resonance structures.

We construct a wave function that is a linear combination:

ΨcIΨI+cIIΨII (21.6-1)

where the valence-bond wave functions corresponding to structures I and II are called

ΨIandΨII. This representation of the wave function as a linear combination of wave