198 Topics in Current Chemistry Editorial Board: A. de Meijere KN ...

8 J.P. Glusker
other induced, will interact in the same way as two dipoles. The strength of this
interaction depends on the magnitude of the permanent dipole moment of the
polar molecule, and on the polarizability of the second molecule. Even if the two
molecules are nonpolar, there can be attractive, low-energy molecular interactions
between them. These are induced dipole-induced dipole interactions, also
called London dispersion forces, in which a nonpolar molecule induces a small
instantaneous dipole in another nearby polar molecule. The force F (in dynes)
between two charges q and q¢ (in electrostatic units) is expressed by Coulomb’s
equation:
F = /q q¢)/(er 2 )
where r is the distance (in cm) between the charges and e is the dielectric constant
of a medium (such as solvent). The higher the dielectric constant of the
medium, the more the force between the two groups interacting with each other
is reduced. For example, hydrogen chloride exists as H + and Cl – in water, which
has a high dielectric constant of 80, while in vacuo, where the dielectric constant
is unity, the two components combine directly to give HCl. Thus water is an
excellent solvent because Coulombic interactions in it are sufficiently weak to
allow ions to remain separated.
4
Directed Organic Interactions
Analyses of packing in crystals have, in many cases, shown that there are directional
preferences of binding. The nature of this directionality appears to
depend on the partial charges developed on the interacting atoms. Some examples
will now be described.
4.1
Intermolecular Interactions in Hydrocarbons
The nature of intermolecular interactions is exemplified by the crystal structures
of polycyclic aromatic hydrocarbons (PAHs) which contain only carbon
and hydrogen atoms. Analyses of crystal structures have led to the derivation of
numerical constants describing the forces between pairs of atoms [11, 12]. Thus
the potential energy expression involves an equation of the form
V = ∑ j, k[–A jkr jk –6 +Bjk exp (–C jkr jk) + q jq kr jk –1 ] . (1)
In this equation r jk is a nonbonded interatomic distance between atoms j and k,
q is the point electrostatic charge on an atom, and A jk B jk and C jk are adjustable
parameters that have been obtained from experimental measurements of unit
cell dimensions, interatomic distances, and packing arrangements in crystal
structures. A jk represents the coefficient of the London dispersion attraction
term between atoms j and k, while B jk and C jk are short-range repulsive energy
terms. The summation is over all interatomic interactions (between all j atoms
and all k atoms). For PAHs the terms in Eq. (1) represent forces between pairs of