Physical Chemistry Third Edition

846 20 The Electronic States of Diatomic Molecules

Table 20.2 Ground-State Electron Configurations of Homonuclear Diatomic Molecules

Electron Configuration Bond Order

H 2 :(σg 1 s)^21

He 2 :(σg 1 s)^2 (σ∗u 1 s)^20

Li 2 :(σg 1 s)^2 (σ∗u 1 s)^2 (σg 2 s)^21

Be 2 :(σg 1 s)^2 (σ∗u 1 s)^2 (σg 2 s)^2 (σ∗u 2 s)^20

B 2 :(σg 1 s)^2 (σ∗u 1 s)^2 (σg 2 s)^2 (σ∗u 2 s)^2 (πu 2 px)(πu 2 py)1

C 2 :(σg 1 s)^2 (σ∗u 1 s)^2 (σg 2 s)^2 (σ∗u 2 s)^2 (πu 2 px)^2 (πu 2 py)^22

N 2 :(σg 1 s)^2 (σ∗u 1 s)^2 (σg 2 s)^2 (σ∗u 2 s)^2 (πu 2 px)^2 (πu 2 py)^2 (σg 2 pz)^23

O 2 :(σg 1 s)^2 (σ∗u 1 s)^2 (σg 2 s)^2 (σ∗u 2 s)^2 (σg 2 pz)^2 (πu 2 px)^2 (πu 2 py)^2 (π∗g 2 px)(π∗g 2 py)2

F 2 :(σg 1 s)^2 (σ∗u 1 s)^2 (σg 2 s)^2 (σ∗u 2 s)^2 (σg 2 pz)^2 (πu 2 px)^2 (πu 2 py)^2 (π∗g 2 px)^2 (π∗g 2 py)^21

Ne 2 :(σg 1 s)^2 (σ∗u 1 s)^2 (σg 2 s)^2 (σ∗u 2 s)^2 (σg 2 pz)^2 (πu 2 px)^2 (πu 2 py)^2 (π∗g 2 px)^2 (π∗g 2 py)^2 (σ∗u 2 pz)^20

EXAMPLE20.5

Write an orbital wave function without antisymmetrization or normalization for the diatomic

boron molecule in its ground level.

Solution

Ψψσg (^1) s(1)α(1)ψσg 1 s(2)β(2)ψσ∗u 1 s(3)α(3)ψσ∗u 1 s(4)β(4)
×ψσg 2 s(5)α(5)ψσg (^2) s(6)β(6)ψσ∗u 2 s(7)α(7)ψσ∗u 2 s(8)β(8)
×ψπu 2 px(9)α(9)ψπu 2 py(10)α(10)
This wave function is one of the three triplet wave functions making up the ground level.
Another triplet function contains twoβspin functions instead ofαfactors for electrons 9 and 10
and the third triplet function contains the symmetric spin factor
√
1
2
[α(9)β(10)+β(9)α(10)].
There is also a singlet function containing the antisymmetric spin factor
√
1
2
[α(9)β(10)−
β(9)α(10)].
Exercise 20.10
Write an orbital wave function without antisymmetrization or normalization for
a.Diatomic oxygen in its ground level.
b.Diatomic helium in the excited-state electron configuration (σg 1 s)^2 (σu∗ 1 s)(σg 2 s).
What is the bond order for this molecule? Do you think it could exist?