Page 128 - Bruno Linder Elementary Physical Chemistry

August 18, 2010 11:37 9in x 6in b985-ch10 Elementary Physical Chemistry

Quantum Theory. The Chemical Bond 113

where c H =0.33 and c F =0.94 in bonding and c H =0.94 and c F =0.33 in
anti-bonding orbitals. Thus,

Ψ bnd =0.33ψ(H) + 0.94ψ(F) (10.13a)
Ψ antb =0.94ψ(H) − 0.33ψ(F) (10.13b)

10.7. Structure of Polyatomic Molecules
In the molecular orbital approach (LCAO-MO), each molecular orbital is a
linear combination of all the atomic orbitals.
2
In benzene (C 6H 6 ), the six C atomic orbitals are sp hybrids, forming
◦
σ bonds at 120 angles. The p orbitals form π bonds that spread over the
entire molecule. The π bonds are delocalized and each pair helps to bind
several atoms. Delocalization is an important feature of MO bonding.

10.8. Normalization. Normal Constants
The wave-functions of all systems should be normalized, meaning that the
square wave-function should integrate to 1. For example,
Particle-in-a–box:

ψ = N sin nπx/L (10.14)

2 L 2
Normalization, N ∫ 0 dx sin nπ/L =1, gives

N = 2/L (10.15)

It is customary to include the normalization factor in atoms with the
wave-function. Thus, the ground state wave-function for H, for example, is
√ 3 −(Z/a)r
ψ 1s =(1/ π)(Z/a) 2 e which includes the normalization factor.

10.9. Normalization Molecules (MO)

Assuming that the atomic orbitals are already normalized, we can write

Ψ= ψ A + ψ B

2
2
2
N 2 Ψ dv = N 2 ψ dv + ψ dv +2 ψ Aψ B dv
B
A
2
= N [1+1+2S] = 1 (10.16a)