Physical Chemistry Third Edition

20.3 Homonuclear Diatomic Molecules 849

Exercise 20.12

a.Using as many nonbonding orbitals as possible give the ground-state electron configuration

of B 2. Write the corresponding orbital wave function without antisymmetrization.

b.Using as many nonbonding orbitals as possible give the ground-state electron configuration

of O 2. Write the corresponding orbital wave function without antisymmetrization.

Homonuclear Diatomic Molecules in the

Valence-Bond Approximation

For the ground states of some homonuclear diatomic molecules satisfactory simple

valence-bond wave functions can be constructed. In this approximation each pair of

bonding electrons occupies a bonding factor constructed from two atomic orbitals on

different nuclei as in Eq. (20.3-7). All other electrons occupy nonbonding orbitals since

the valence-bond theory has nothing analogous to antibonding orbitals. The resulting

wave function is very similar to LCAOMO wave functions that employ nonbonding

orbitals as in Example 20.6. We make no attempt to describe the ground states of

diatomic boron and diatomic oxygen since the bonding factors do not accommodate

unpaired electrons.

EXAMPLE20.7

Write a simple valence bond wave function for C 2 in its ground state.

Solution

Ψψ 1 sA(1)α(1)ψ 1 sA(2)β(2)ψ 1 sB(3)α(3)ψ 1 sB(4)β(4)

×ψ 2 sA(5)α(5)ψ 2 sA(6)β(6)ψ 2 sB(7)α(7)ψ 2 sB(8)β(8)

×

√

1

2

[ψ 2 pxA(9)ψ 2 pxB(10)+ψ 2 pxB(9)ψ 2 pxA(10)]

×[α(9)β(10)−β(9)α(10)]

×

√

1

2

[ψ 2 pyA(11)ψ 2 pyB(12)+ψ 2 pyB(11)ψ 2 pyA(12)]

×[α(11)β(12)−β(11)α(12)] (20.3-20)

Exercise 20.13

Write the wave function corresponding to the configuration of C 2 in Example 20.6 without

antisymmetrization and compare it with the wave function in Eq. (20.3-20).

A bonding factor corresponds to a single covalent bond, so the bond order for the

C^2 wave function in Example 20.7 is equal to 2, as in the LCAOMO description of

Example 20.6. This wave function does not include ionic terms, but ionic terms can be

added to each bonding factor in the wave function to make an improved valence-bond

function.