2.19 Appendices
47
Interaction energies (in kJ mol
−1 ) for some molecules
Molecule
μ/D a
α b
E Keesom
E Debye
E London
Ar
0.00
1.85
0.00
0.00
8.5
CO
0.11
2.20
0.00
0.01
8.8
HI
0.40
6.06
0.03
0.11
25.9
HCl
1.08
2.93
3.31
1.0
16.8
H 2 O
1.85
1.65
36.4
1.9
9.0
a 1 D = 3.3356×10 −30 Cm
b Unit: C 2 m 2 J −1
2.19.5.4 Lennard-Jones Potential (or 6–12 Potential)
When the distance between the molecules is large, the attractive forces are dominant
and they vary all as r
−6 but when the molecules are close to each other, appears
a short-range repulsive force due to the Pauli exclusion principle that prevents the
collapse of molecules. Its interaction energy can be approximated by
E repulsion =
A
r n
(2.66)
where A is a positive constant and n a number between 9 and 12. Lennard-Jones
found that the best fit for most substances is n = 12. This gives the Lennard-Jones
potential
E LJ = ε
r m
r
12 − 2
r m
r
6
(2.67)
where ε is the depth of the potential well and r m the distance at which the potential
reaches its minimum (Fig. 2.2).