The Forces between Molecules - Molecular Modelling - page 23

We now need to investigate more closely the precise form of this pair potential. The
potential comprises a repulsive part (important for small R ) and an attractive part (important
for large R ). It turns out that there are three major contributions to the attractive part, as we
will see below.
2.2 Multipole Expansion
Suppose that we have two molecules with centres a distance R apart (Figure 2.2). The
distance R is taken to be large compared with a molecular dimension.
Molecule A
R
Molecule B
Figure 2.2 Two interacting molecules
Each molecule consists of a number of charged particles, and in principle we can write
down an expression for the mutual potential energy of these two molecules in terms of the
pair potentials between the various point charges. The basic physical idea of the multipole
expansion is to make use of the fact that several of these particles go to form molecule A,
and the remainder to form molecule B, each of which has a distinct chemical identity. We
therefore seek to write the mutual potential energy of A and B in terms of properties of the
two molecular charge distributions and their separation.
2.3 Charge-Dipole Interaction
I can illustrate the ideas by considering an elementary textbook problem, the mutual
potential energy of a simple small electric dipole and a point charge (Figure 2.3).
Suppose then that we have a simple dipole consisting of a pair of charges Q A and Q B
aligned along the horizontal axis and equally separated from the coordinate origin by
distance d . We introduce a third charge Q as shown, with the scalar distance R from the
origin. This point charge makes an angle θ with the electric dipole, as shown.