Chemistry Reference
In-Depth Information
work established that there are four rigorously defined fundamental compo-
nents that contribute to interactions between a pair of uncharged molecules
or atoms: electrostatic, induction (sometimes referred to as polarization), dis-
persion, and exchange-repulsion
83
(or simply exchange). The first two contri-
butions to the interaction energy were readily explained in terms of classical
electromagnetic theory. Interactions involving two permanent electrostatic
multipole moments (dipole, quadrupole, etc.) are relatively easy to understand
for anyone who has ever played with a pair of magnets; opposite poles (
þ=
)
attract each other, and like poles (
) repel each other. Similarly,
adhering a balloon to a wall with static electricity provides a macroscopic ana-
log for induction. However, quantum mechanics was required to rationalize
the dispersion and exchange energies. The latter is a simple consequence of
the Pauli exclusion principle, but an explanation of the dispersion energy is
more involved.
London was the first to describe the dispersion interaction.
81,82
Through
a quantum mechanical perturbation theory treatment of the interaction
energy, he demonstrated that, at second, order attractive terms can arise due
to the simultaneous electron correlation between two fragments even if they
possess no permanent electrostatic moment (e.g., a pair of rare gas atoms).
London dubbed the attraction
dispersion forces
because similar oscillator
strengths appear in equations describing the dispersion of electromagnetic
radiation (light). The attractive forces of these interactions are typically attrib-
uted to fluctuations (thermal or quantum mechanical) in the electron density
that give rise to an instantaneous dipole in one fragment that induces a dipole
in a neighbor. This semiclassical model was introduced after London's initial
work, and its physical significance is not manifest since there are no expres-
sions in the quantum mechanical derivation that can be interpreted as interac-
tions between instantaneous dipoles. At the very least, this fluctuating charge
or electrodynamic model provides a useful mnemonic.
As discussed in Paresegian's recent topic,
7
the modern view of dispersion
interactions has its roots in the the Casimir effect.
84
Rather than charge fluc-
tuations, the phenomenon can be viewed in terms of zero-point electromag-
netic-field fluctuations
þ=þ
and
=
in the vacuum as allowed by the Heisenberg
uncertainty principle
. Atoms and molecules can absorb
some of these frequencies, namely those frequencies that are resonant with
transitions between the quantum mechanical energy levels of the system as
determined by its electronic structure. This absorption of the electromagnetic
fluctuations gives rise to attractive forces between two bodies.
ð
E
t
h
=
2
p
Þ
We now recognize that ''empty space'' is a turmoil of electromagnetic waves of all
frequencies and wavelengths. They wash through and past us in ways familiar from
watching the two-dimensional version, a buoy or boat bobbing in rough water. We
can turn the dancing charges idea around. From the vacuum point of view, imagine
two bodies, such as two boats in rough water or a single boat near a dock, pushed
