882 21 The Electronic Structure of Polyatomic Molecules
Exercise 21.8
Write the expression forΨIin Eq. (21.5-2).The ionic character of a bond can also be represented by placing an ionic term in
each bonding factor instead of making an ionic term for the entire wave function. The
space factor of the first bonding factor in the water molecule wave function would
become[ψ 2 sp (^3) (2)(7)ψ 1 sA(8)+ψ 1 sA(7)ψ 2 sp (^3) (2)(8)+cψ 2 sp (^3) (2)(7)ψ 2 sp (^3) (2)(8)] (21.5-3)
with a similar factor for the other bond. An optimum value for the coefficientcwould
be obtained by minimizing the variational energy of the molecule.
Exercise 21.9
Using the valence-bond method, give a description of the bonding in
a.Ammonia
b.Methane
c.Hydrogen fluoride
The simple wave functions for diatomic molecules obtained in Chapter 20 can be
improved by using hybrid orbitals, both in the LCAOMO method and the valence-bond
method.
EXAMPLE21.6
Write a simple valence-bond wave function for the ground-state of diatomic F 2 using 2sp^3
hybrid orbitals.
Solution
Orient the coordinate axes so that each atom has a hybrid orbital region pointing at the other
atom. Make the bonding factor with one of the hybrid orbitals on each atom and use the other
three for lone pairs. Denote the hybrids involved in the bond as 2sp^3 (1)A and 2sp^3 (1)B. We
omit the spin factors. Use the 1sand the other 2sp^3 orbitals as nonbonding orbitals. Without
complete antisymmetrization, the wave function isΨψ 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 sp (^3) (2)A(5)α(5)
×ψ (^2) sp (^3) (2)A(6)β(6)ψ 2 sp (^3) (3)A(7)α(7)ψ 2 sp (^3) (3)A(8)β(8)ψ 2 sp (^3) (4)A(9)α(9)
×ψ (^2) sp (^3) (4)A(10)β(10)ψ 2 sp (^3) (2)B(11)α(11)ψ 2 sp (^3) (2)B(12)β(12)
×ψ (^2) sp (^3) (3)B(13)α(13)ψ 2 sp (^3) (3)B(14)β(14)ψ 2 sp (^3) (4)B(15)α(15)ψ 2 sp (^3) (4)B(16)β(16)
×[ψ 2 sp (^3) (1)A(17)ψ 2 sp (^3) (1)B(18)+ψ 2 sp (^3) (1)B(17)ψ 2 sp (^3) (1)A(18)]
×[α(17)β(18)−β(17)α(18)]