11.7 Weak Molecular Interactions
533
11.7.6 Dipole Induced-Dipole Interactions
A molecule with an electric dipole moment δ can induce another nearby molecule
with no natural dipole to get one. The electric field of the first acts on the electrons
and nuclei of the second, pushing opposite charges apart. The interaction energy V
for the pair is given by
V = −kαδ
2 /r
6 .
(11.32)
The factor α is called the ‘polarizability’ of the second molecule.
11.7.7 Induced-Dipole Induced-Dipole Interaction
Quantum theory requires all bound particles to have some uncertainty in their
motion. 13 A bound particle cannot be at rest. Electrons bound in space must jiggle,
even in their lowest quantum state. 14 As a result, fluctuating electric fields must
also be created around molecules. These fluctuating fields act on charges in nearby
molecules, forcing them to jiggle in unison. In turn, the coherent jiggles of these
charges act back on the original charges. The result is force, always attractive, that
depends on how easily the charges can be accelerated in their bound states. Electrons
can be forced to accelerate by a given field far more easily than the nuclei of atoms,
so the charge fluctuation forces are dominated by the jiggling of electrons. The ease
with which electrons in a given atom or molecule (labeled by an index ‘i’) can be
so jiggled is measured by its induced polarizability, α i . The interaction energy V αα
due to charge-fluctuations in each of two interacting molecules with polarizabilities
of α i , α j is found to be
V αα (r) = −K(T )
α i α j
r 6 ,
(11.33)
where the coefficient K(T ) is always positive and may depend on the temperature
T of the surrounding solution and on the excitation energies available to the
molecules. The resulting force, is called the ‘London dispersion force’, a pure
quantum effect. 15 There are a number of ways to which the dispersion force
13 Quantum theory gives the Heisenberg uncertainty principle, p x x ≥ ¯
h/2, where p x is
the uncertainty in a particle’s momentum, and x the uncertainty in its position, both along any
direction, such as the x axis. Thus, neither can be zero.
14 The potential energy for a confined electron can be expanded as a power series about its
minimum: V = V o + (1/2)
3
1 k j (x j − x j 0 ) 2 + · · · . The lowest electron energy state will be well
approximated by that of a harmonic oscillator, for which E 0 = (1/2)hf , where f =
3
1
k j /m e .
15 F. London, Zur Theorie und Systematik der Molekularkräfte, Zeitschrift für Physik 63:3–4, 245
(1930).
533
11.7.6 Dipole Induced-Dipole Interactions
A molecule with an electric dipole moment δ can induce another nearby molecule
with no natural dipole to get one. The electric field of the first acts on the electrons
and nuclei of the second, pushing opposite charges apart. The interaction energy V
for the pair is given by
V = −kαδ
2 /r
6 .
(11.32)
The factor α is called the ‘polarizability’ of the second molecule.
11.7.7 Induced-Dipole Induced-Dipole Interaction
Quantum theory requires all bound particles to have some uncertainty in their
motion. 13 A bound particle cannot be at rest. Electrons bound in space must jiggle,
even in their lowest quantum state. 14 As a result, fluctuating electric fields must
also be created around molecules. These fluctuating fields act on charges in nearby
molecules, forcing them to jiggle in unison. In turn, the coherent jiggles of these
charges act back on the original charges. The result is force, always attractive, that
depends on how easily the charges can be accelerated in their bound states. Electrons
can be forced to accelerate by a given field far more easily than the nuclei of atoms,
so the charge fluctuation forces are dominated by the jiggling of electrons. The ease
with which electrons in a given atom or molecule (labeled by an index ‘i’) can be
so jiggled is measured by its induced polarizability, α i . The interaction energy V αα
due to charge-fluctuations in each of two interacting molecules with polarizabilities
of α i , α j is found to be
V αα (r) = −K(T )
α i α j
r 6 ,
(11.33)
where the coefficient K(T ) is always positive and may depend on the temperature
T of the surrounding solution and on the excitation energies available to the
molecules. The resulting force, is called the ‘London dispersion force’, a pure
quantum effect. 15 There are a number of ways to which the dispersion force
13 Quantum theory gives the Heisenberg uncertainty principle, p x x ≥ ¯
h/2, where p x is
the uncertainty in a particle’s momentum, and x the uncertainty in its position, both along any
direction, such as the x axis. Thus, neither can be zero.
14 The potential energy for a confined electron can be expanded as a power series about its
minimum: V = V o + (1/2)
3
1 k j (x j − x j 0 ) 2 + · · · . The lowest electron energy state will be well
approximated by that of a harmonic oscillator, for which E 0 = (1/2)hf , where f =
3
1
k j /m e .
15 F. London, Zur Theorie und Systematik der Molekularkräfte, Zeitschrift für Physik 63:3–4, 245
(1930).