The Forces between Molecules - Molecular Modelling - page 30

since all the attractive forces fall off as 1/ R 6 . This is known as the exp-6 potential. In the
Lennard-Jones 12-6 potential, we take a repulsive term proportional to 1/ R 12 and so

C 12
R 12

C 6
R 6

U L − J = − (2.20)

Once again the coefficients C 12 and C 6 have to be determined from experiments on the
species under study. The Lennard-Jones (L-J) potential is usually written in terms of the
well depth ε and the distance of closest approach σ as follows:

4ε σ
R

6 12 σ

R

U L − J =

−

(2.21)

The two L-J parameters σ and ε have been deduced for a range of atoms. The quantity ε/ k B
(which has dimensions of temperature) is usually recorded in the literature rather than ε.
Sample atomic parameters are listed in Table 2.2.

Table 2.2 Representative L-J atomic parameters

Atom ( ε/ k B )/K σ /pm

He 10.22 258

Ne 35.7 279

Ar 124 342

Xe 229 406

Over the years, people have extended these ideas to the interaction of simple molecules.
Some caution is needed; the interaction between two molecules will generally depend on
the precise details of their orientation, and the values given in Table 2.3 must be interpreted
as some kind of geometrical average.
Figure 2.6 shows a L-J 12-6 plot for argon.

Table 2.3 L-J parameters for simple molecules

Molecule ( ε/ k B )/K

σ /pm

H 2 33.3 297

O 2 113 343

N 2 91.5 368

Cl 2 357 412

Br 2 520 427

CO 2 190 400

CH 4 137 382

CCl 4 327 588

C 2 H 4 205 423

C 6 H 6 440 527

Source : Hirschfelder et al. (1954).