Download 7. Molecular interactions

7. Molecular interactions
7.1 Polar molecules
A polar molecule is a molecule with a permanent dipole moment
(stemming from partial charges due to electronegativity and other
features of bonding). Non-polar molecules acquire a (temporary)
induced dipole moment in an electric field.
Electric dipole moment:
  qR
7.2 Dipole moments
All heteronuclear diatomic
molecules are polar
(unit: 1D=3.335 10-30 Cm)
a’ is the polarizability
volume of the molecule:
'

4 0
with a the polarizability
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7.3 Interaction energy of charge and dipole
V 
1q2
4 0 r 2
Potential energy between two
charges in a vacuum:
The potential energy of the
interaction between a
dipole m1 and a point
charge q2 is the sum of the
repulsion of like charges
and the attraction of
opposite charges. For a
‘point’ dipole: l<<r.
V
q1q2
4 0 r
7.3.1 Interaction energy of dipoles
There are two contributions to
the diminishing field of an electric
dipole with distance (here seen
from the side). The potentials of
the charges decreases (shown
by fading intensity) and the two
charges appear to merge, so
their combined effect approaches
zero more rapidly than by the
distance effect alone.
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7.4 Interaction energy of two dipoles
The interaction energy of two dipoles is the sum of the repulsions of
like charges and the attractions of opposite charges.
(a) Collinear
arrangement of dipoles.
V 
(b) Parallel
arrangement of
electric dipoles.
V
1 2
2 0 r 3
1 2
4 0 r 3
7.5 The electric field generated by a dipole
E monopole
q

4 0 r 2
E dipole 

2 0 r 3
Strength of the electric
field generated by an
electric point charge
The electric field of a dipole is
the sum of the opposing fields
from the positive and the
negative charges, each of
which is proportional to 1/r2.
The difference, the net field, is
proportional to 1/r3!
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7.6 Dipole-dipole interactions
The potential energy of interaction between two polar molecules is
a complicated function of their relative orientation. When the two
dipoles are parallel as shown, the potential energy is
V
1 2 f ( )
4 0 r 3
f ( )  1  3 cos 2 ( )
This expression applies to polar molecules in a fixed, parallel
orientation in a solid.
7.6.1 Dipole-dipole interactions
In a fluid of freely rotating molecules, the interaction between
dipoles averages to zero. However, because their mutual potential
energy depends on their relative orientation, the molecules do not in
fact rotate completely freely, even in a gas. In fact, the lower energy
configurations are marginally favoured, and a nonzero(!) average
interaction results:
C
V  6
r
2 1  2
C
3(4 0 ) 2 k BT
2
2
attractive interaction; temperature dependent
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7.7 Dipole-induced-dipole interactions
(a) A polar molecule with dipole
moment m1 (brown arrow) can induce
a dipole m2*(white arrow) in a nonpolar
molecule, and (b) the latter’s
orientation follows the former’s, so the
interaction does not average to zero.
The average interaction energy when
the separation of the molecules is r is:
C
V  6
r
 
C 1 2
4 0
2
'
a2’ is the polarizability
volume of molecule 2
The interaction is independent of the temperature!
7.8 Induced-dipole-induced-dipole interactions
(a) In the dispersion interaction an
instantaneous dipole on one
molecule induces a dipole on
another molecule, and the two
dipoles then interact to lower the
energy.
(b) The two instantaneous dipoles
are correlated and, although they
occur in different orientations at
different instants, the interaction
does not average to zero.
V 
C
r6
3 ' ' II
C  1  2 1 2
2
I1  I 2
I1, I2 are the ionisation
energies of the two molecules
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7.8.1 Induced-dipole-induced-dipole interactions
Nonpolar molecules (including closed shell atoms, such as Ar)
attract one another even though neither has a permanent dipole
moment.
Examples are the condensation of Ar at low temperatures
and the fact that benzene is a liquid at normal temperatures.
Induced-dipole-induced-dipole interactions are called
dispersion interaction or London interaction.
7.9 Hydrogen bonding
A hydrogen bond is an attractive interaction between two species
that arises from a link of the form A–H · · B , where A and B are highly
electronegative elements and B possesses a lone pair of electrons.
It is conventionally regarded as being limited to N, O, and F, but if B
is an ionic species (such as Cl-), it may also participate in hydrogen
bonding.
The formation of such a bond can be regarded either as the approach
between a partial positive charge of H and a partial negative charge of
B or as a particular example of delocalized molecular orbital formation
in which A, H, and B each supply one atomic orbital from which three
molecular orbitals are constructed.
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7.9.1 Hydrogen bonding
The molecular orbital interpretation of
the formation of an A–H · · B
hydrogen bond. From the three, A, H,
and B orbitals, three molecular orbitals
can be formed (their relative
contributions are represented by the
sizes of the spheres). Only the two
lower energy orbitals are occupied, and
there may therefore be a net lowering
of energy compared with the separate
AH and B species.
7.10 The total attractive interaction
In the following we consider molecules that are unable to participate
in hydrogen bond formation. The total attractive interaction between
rotating molecules is then the sum of the three van der Waals
contributions discussed earlier. If both molecules are nonpolar only
the dispersion interaction contributes. In a fluid phase all three
contributions to the potential energy vary as 1/r6 so:
V 
C6
r6
C6 is a coefficient that depends on the identity of the molecules
Limitations:
• only dipolar interactions are taken into account;
• assumption is that molecules can rotate reasonably freely;
• equation relates to the interaction of pairs of molecules.
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7.11 Repulsive and total interactions
When molecules are squeezed together, the
nuclear and electronic repulsions and the
rising electronic kinetic energy begin to
dominate the attractive forces. The
repulsions increase steeply with decreasing
separation. Simple model: hard sphere
potential: V= for rd; V=0 for rd
(compare to QM I, particle in a box)
The general form of an intermolecular
potential energy curve. At long range
the interaction is attractive, but at
close range the repulsion dominates.
7.11.1 Repulsive and total interactions
Lennard-Jones potential
Another widely used approximation is V 
Cn Cm

rn rm
with n>m.
Special case: Lennard-Jones potential:
n=12, m=6.
 r0 12  r0  6 
V  4      
 r 
 r  
e is the depth of the well and r0 the
separation at which V=0. The well
minimum occurs at 21/6 r0.
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7.11.2 Lennard-Jones potential examples
Another widely used approximation is
V
Cn Cm

rn rm
with n>m.
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