Molecular Interactions

1
Molecular Interactions

• The most important to producing phases and
  interfaces in the materials

2
Background

• Atoms and molecules with complete valence shells
  can still interact with one another even though
  all of their valences are satisfied. They attract
  one another over a range of several atomic
  diameters and repel one another when pressed
  together.

3
Molecular interactions account for

• condensation of gases to liquids
• structures of molecular solids (surfaces)
• structural organisation of biological
  macromolecules as they pin molecular building
  blocks (polypeptides, polynucleotides, and
  lipids) together in the arrangement essential to
  their proper physiological function.

4
van der Waals interactions

• Interaction between partial charges in polar
  molecules
• Electric dipole moments or charge distribution
• Interactions between dipoles
• Induced dipole moments
• Dispersion interactions
• Interaction between species with neither a net
  charge nor a permanent electric dipole moment
  (e.g. two Xe atoms)

5
The total interaction

• Hydrogen bonding
• The hydrophobic effect
• Modelling the total interaction
• Molecules in motion

6
van der Waals interactions

• Interactions between molecules include the
  attractive and repulsive interactions between the
  partial electric charges of polar molecules and
  the repulsive interactions that prevent the
  complete collapse of matter to densities as high
  as those characteristic of atomic nuclei.

7
van der Waals interactions (contd.)

• Repulsive interactions arise from the exclusion
  of electrons from regions of space where the
  orbitals of closed-shell species overlap.
• Those interactions proportional to the inverse
  sixth power of the separation are called van der
  Waals interactions.

8
van der Waals interactions

• Typically one discusses the potential energy
  arising from the interaction.
• If the potential energy is denoted V, then the
  force is dV/dr. If V -C/r6
• the magnitude of the force is

9
Interactions between partial charges

• Atoms in molecules generally have partial
• charges.

10
Interactions between partial charges

• If these charges were separated by a vacuum, they
  would attract or repel one another according to
  Coulombs Law

where q1 and q2 are the partial charges and r is
their separation
11
Charges Interactions

• Coulombic Inteaction between q1 and q2
• Partial atomic ChargesApproximated distribution
  of electron in molecule

0.387 -0.387
12
Interactions between partial charges

• However, other parts of the molecule, or
• other molecules, lie between the charges, and
• decrease the strength of the interaction.
• Thus, we view the medium as a uniform
• continuum and we write

Where e is the permittivity of the medium lying
between the charges.
13

• The permittivity is usually expressed as a
  multiple of the vacuum permittivity by writing e
  ere0, where er is the relative permittivity
  (dielectric constant). The effect of the medium
  can be very large, for water at 250C, er 78.
• The PE of two charges separated by bulk water is
  reduced by nearly two orders of magnitude
  compared to that if the charges were separated by
  a vacuum.

14
Coulomb potential for two charges
vacuum
fluid
15
Ion-Ion interaction/Lattice Enthalpy

• Consider two ions in a lattice

16
Ion-Ion interaction/Lattice Enthalpy

• two ions in a lattice of charge numbers z1 and
• z2 with centres separated by a distance r12

where e0 is the vacuum permittivity.
17
Ion-Ion interaction/Lattice Enthalpy

• To calculate the total potential energy of all
  the ions in the crystal, we have to sum this
  expression over all the ions. Nearest neighbours
  attract, while second-nearest repel and
  contribute a slightly weaker negative term to the
  overall energy. Overall, there is a net
  attraction resulting in a negative contribution
  to the energy of the solid.

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• For instance, for a uniformly spaced line of
  alternating cations and anions for which z1 z
  and z2 -z, with d the distance between the
  centres of adjacent ions, we find

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Born-Haber cycle for lattice enthalpy
21
Lattice Enthalpies, DHL0 / (kJ mol-1)
Lattice Enthalpy ( ) is the standard
enthalpy change accompanying the separation of
the species that compose the solid per mole of
formula units. e.g. MX (s) M(g) X- (g)
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Calculate the lattice enthalpy of KCl (s) using a
Born-Haber cycle and the following information at
25oC

• Process DH0 (kJ mol-1)
• Sublimation of K (s) 89
• Ionization of K (g) 418
• Dissociation of Cl2 (g) 244
• Electron attachment to Cl (g) -349
• Formation of KCl (s) -437

23
Calculation of lattice enthalpy

• Process DH0 (kJ mol-1)
• KCl (s) K (s) ½ Cl2 (g) 437
• K (s) K (g) 89
• K (g) K (g) e- (g) 418
• ½ Cl2 (g) Cl (g) 122
• Cl (g) e- (g) Cl- (g) -349
• KCl (s) K (g) Cl- (g) 717 kJ
  mol-1

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Electric dipole moments

• When molecules are widely separated it is
  simpler to express the principal features of
  their interaction in terms of the dipole moments
  associated with the charge distributions rather
  than with each individual partial charge. An
  electric dipole consists of two charges q and q
  separated by a distance l. The product ql is
  called the electric dipole moment, m.

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Electric dipole moments

• We represent dipole moments by an arrow with a
  length proportional to m and pointing from the
  negative charge to the positive charge

m
d
d-
Because a dipole moment is the product of
a charge and a length the SI unit of dipole
moment is the coulomb-metre (C m)
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Electric dipole moments

• It is often much more convenient to report a
  dipole moment in debye, D, where
• 1D 3.335 64 x 10-30 C m

because the experimental values for molecules
are close to 1 D. The dipole moment of charges e
and e separated by 100 pm is 1.6 x 10-29 C m,
corresponding to 4.8 D.
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Electric dipole moments diatomic molecules

• A polar molecule has a permanent electric dipole
  moment arising from the partial charges on its
  atoms. All hetero-nuclear diatomic molecules are
  polar because the difference in
  electronegativities of their two atoms results in
  non-zero partial charges.

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Electric dipole moments
29
Electric dipole moments diatomic molecules

• More electronegative atom is usually the
  negative end of the dipole. There are exceptions,
  particularly when anti-bonding orbitals are
  occupied.
• CO dipole moment is small (0.12 D) but negative
  end is on C atom. Anti-bonding orbitals are
  occupied in CO and electrons in anti-bonding
  orbitals are closer to the less electronegative
  atom, contributing a negative partial charge to
  that atom. If this contribution is larger than
  the opposite contribution from the electrons in
  bonding orbitals, there is a small negative
  charge on the less electronegative atom.

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Electric dipole moments polyatomic molecules

• Molecular symmetry is of the greatest importance
  in deciding whether a polyatomic molecule is
  polar or not. Homo-nuclear polyatomic molecules
  may be polar if they have low symmetry
• in ozone, dipole moments associated with each
  bond make an angle with one another and do not
  cancel.

d
d
m
m
d-
d-
Ozone, O3
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Electric dipole moments polyatomic molecules

• Molecular symmetry is of the greatest importance
  in deciding whether a polyatomic molecule is
  polar or not.
• in carbon dioxide, dipole moments associated with
  each bond oppose one another and the two cancel.

m
m
d
d
d-
d-
Carbon dioxide, CO2
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Electric dipole moments polyatomic molecules

• It is possible to resolve the dipole moment of a
  polyatomic molecule into contributions from
  various groups of atoms in the molecule and the
  direction in which each of these contributions
  lie.

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Electric dipole moments polyatomic molecules

• 1,2-dichlorobenzene two chlorobenzene dipole
  moments arranged at 60o to each other. Using
  vector addition the resultant dipole moment
  (mres) of two dipole moments m1 and m2 that make
  an angle q with one another is approximately

mres
m1
q
m2
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Electric dipole moments polyatomic molecules
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Electric dipole moments polyatomic molecules

• Better to consider the locations and magnitudes
  of the partial charges on all the atoms. These
  partial charges are included in the output of
  many molecular structure software packages.
  Dipole moments are calculated considering a
  vector, m, with three components, mx, my, and mz.
  The direction of m shows the orientation of the
  dipole in the molecule and the length of the
  vector is the magnitude, m, of the dipole moment.

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Electric dipole moments polyatomic molecules

• To calculate the x-component we need to know the
  partial charge on each atom and the atoms
  x-coordinate relative to a point in the molecule
  and from the sum

mz
m
where qJ is the partial charge of atom J, xJ is
the x coordinate of atom J, and the sum is over
all atoms in molecule
mx
my
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Partial charges in polypeptides
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Calculating a Molecular dipole moment
H
0.18
(182,-87,0)
(0,0,0)
m
C
-0.36
N
0.45
(132,0,0)
O
-0.38
(-62,107,0)
mx (-0.36e) x (132 pm) (0.45e) x (0 pm)
(0.18e) x (182 pm) (-0.38e) x (-62 pm)
8.8e pm 8.8 x (1.602 x 10-19 C) x (10-12
m) 1.4 x 10-30 C m 0.42 D
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Calculating a Molecular dipole moment
my (-0.36e) x (0 pm) (0.45e) x (0 pm)
(0.18e) x (-86.6 pm) (-0.38e) x (107 pm)
-56e pm -9.1 x 10-30 C m -2.7 D mz 0
m (0.42 D)2 (-2.7 D)21/2 2.7 D
Thus, we can find the orientation of the
dipole moment by arranging an arrow 2.7 units of
length (magnitude) to have x, y, and z components
of 0.42, -2.7, 0 units (Exercise calculate m
for formaldehyde)
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Interactions between dipoles

• The potential energy of a dipole m1 in the
  presence of a charge q2 is calculated taking into
  account the interaction of the charge with the
  two partial charges of the dipole, one a
  repulsion the other an attraction.

l
q2
-q1
q1
r
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Interactions between Dipoles

• The potential energy between a point dipole and
  the point charge q (lgtgtr)

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Interactions between dipoles
A similar calculation for the more general
orientation is given as
q2
r
l
q
-q1
q1
If q2 is positive, the energy is lowest when q
0 (and cos q 1), as the partial negative charge
of the dipole lies closer than the partial
positive charge to the point charge and the
attraction outweighs the repulsion.
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Interactions between dipoles

• The interaction energy decreases more rapidly
  with distance than that between two point charges
  (as 1/r2 rather than 1/r), because from the
  viewpoint of the point charge, the partial
  charges on the dipole seem to merge and cancel as
  the distance r increases.

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• Increasing the distance, the potentials of the
  charges decrease and the two charges appear to
  merge.
• These combined effect approaches zero more
  rapidly than by the distance effect alone.

l
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Interactions between dipoles
Interaction energy between two dipoles m1 and m2
l2
q2
-q2
r
l1
q
-q1
q1
For dipole-dipole interaction the potential
energy decreases as 1/r3 (instead of 1/r2 for
point-dipole) because the charges of both dipoles
seem to merge as the separation of the dipoles
increases.
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• The potential energy between two parallel dipoles

This applies to polar molecules in a fixed,
parallel, orientation in a solid.
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Interactions between dipoles

• The angular factor takes into account how the
  like or opposite charges come closer to one
  another as the relative orientations of the
  dipoles is changed.
• The energy is lowest when q 0 or 180o (when 1
  3 cos2q -2), because opposite partial charges
  then lie closer together than like partial
  charges.
• The energy is negative (attractive) when q lt
  54.7o (the angle when 1 3 cos2q 0) because
  opposite charges are closer than like charges.
• The energy is positive (repulsive) when q gt 54.7o
  because like charges are then closer than
  opposite charges.
• The energy is zero on the lines at 54.7o and (180
  54.7) 123.3o because at those angles the two
  attractions and repulsions cancel.

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Interactions between dipoles

• Calculate the molar potential energy of the
  dipolar interaction between two peptide links
  separated by 3.0 nm in different regions of a
  polypeptide chain with q 180o, m1 m2 2.7 D,
  corresponding to 9.1 x 10-30 C m

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• Freely rotating dipoles Liquid, Gas
• The interaction energy of two freely rotating
  dipoles is zero.
• Real molecules do not rotate completely freely
  due to the fact that their orientations are
  controlled partially by their mutual interaction.
  

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Interactions between dipoles
When a pair of molecules can adopt all relative
orientations with equal probability, the
favourable orientations (a) and the unfavourable
ones (b) cancel, and the average interaction is
zero. In an actual fluid (a) predominates
slightly.
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Interactions between dipoles
E a 1/r6 gt van der Waals interaction E a 1/T gt
greater thermal motion overcomes the mutual
orientating effects of the dipoles at higher T
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• The average interaction energy of two polar
  molecules rotating at a fixed separation r
• Probability that a particular orientation is
  given by Boltzmann distribution
• Keesom Interaction

Average interaction is attractive.
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Interactions between dipoles

• At 25oC the average interaction energy for pairs
  of molecules with m 1 D is about -1.4 kJ mol-1
  when the separation is 0.3 nm.
• This energy is comparable to average molar
  kinetic energy of 3/2RT 3.7 kJ mol-1 at 25oC.
• These are similar but much less than the energies
  involved in the making and breaking of chemical
  bonds.

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Induced dipole moments

• A non-polar molecule may acquire a temporary
  induced dipole moment m as a result of the
  influence of an electric field generated by a
  nearby ion or polar molecule. The field distorts
  the electron distribution of the molecule and
  gives rise to an electric dipole. The molecule is
  said to be polarizable.
• The magnitude of the induced dipole moment is
  proportional to the strength of the electric
  field, E, giving
• m a E
• where a is the polarizability of the molecule.

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Induced dipole moments

• The larger the polarizability of the molecule the
  greater is the distortion caused by a given
  strength of electric field.
• If a molecule has few electrons (N2) they are
  tightly controlled by the nuclear charges and the
  polarizability is low.
• If the molecule contains large atoms with
  electrons some distance from the nucleus (I2)
  nuclear control is low and polarizability is high.

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Induced dipole moments

• Polarizability also depends on the orientation
  of the molecule toward the electric field unless
  the molecule is tetrahedral (CCl4), octahedral
  (SF6), or icosahedral (C60).
• Atoms and tetrahedral, octahedral, and
  icosahedral molecules have isotropic
  (orientation-independent) polarizabilities
• All other molecules have anisotropic
  (orientation-dependent) polarizabilities

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Polarizability volume

• The polarizability volume has the dimensions of
  volume and is comparable in magnitude to the
  volume of the molecule

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Polarizability volumes
59
Polarizability volume
What strength of electric field is required to
induce an electric dipole moment of 1 mD in a
molecule of polarizability volume 1.1 x 10-31 m3?
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Dipole-induced dipole moments

• A polar molecule with dipole
• moment m1 can induce a dipole
• moment in a polarizable
• molecule

the induced dipole interacts with the permanent
dipole of the first molecule and the two are
attracted together
the induced dipole (light arrows) follows the
changing orientation of the permanent dipole
(yellow arrows)
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Dipole-induced dipole moments

• For a molecule with m 1 D (HCl) near a
  molecule of polarizability volume a 1.0 x
  10-31 m3 (benzene), the average interaction
  energy is about -0.8 kJ mol-1 when the separation
  is 0.3 nm.
• E a 1/r6 gt van der Waals interaction

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Dispersion interactions

• Interactions between species with neither a net
  charge nor a permanent electric dipole moment
• uncharged non-polar species can interact because
  they form condensed phases such as benzene,
  liquid hydrogen and liquid xenon
• The dispersion interaction (London Force) between
  non-polar species arises from transient dipoles
  which result from fluctuations in the
  instantaneous positions of their electrons

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Dispersion interactions
Electrons from one molecule may flicker into an
arrangement that results in partial positive and
negative charges and thus gives an
instantaneous dipole moment m1. This dipole can
polarize another molecule and induce in it an
instantaneous dipole moment m2. Although the
first dipole will go on to change the size and
direction of its dipole ( 10-16 s) the second
dipole will follow it the two dipoles are
correlated in direction, with the positive
charge on one molecule close to a negative
partial charge on the other molecule and vice
versa.

• An instantaneous dipole on one molecule induces
  a dipole on another molecule, and the two dipoles
  attract thus lowering the energy.

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Dispersion interactions

• Overall, net attractive interaction
• Polar molecules interact by
• dispersion interactions and dipole-dipole
  interactions
• dispersion interactions often dominant
• Dispersion interaction strength depends on
• polarizability of first molecule which is decided
  by nulcear control
• loose gt large fluctuations in e- distribution
• polarizability of second molecule

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Dispersion interactions
London formula
I1, I2 are the ionization energies of the two
molecules Potential energy of interaction is
proportional to 1/r6 so this too is a
contribution to the van der Waals interaction.
For two CH4 molecules, V -5 kJ mol-1 (r 0.3
nm)
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Total interaction- Hydrogen bonding
The coulombic interaction between the partly
exposed positive charge of a proton bound to an
electron withdrawing X atom (in XH) and the
negative charge of a lone pair on the second atom
Y, as in d-XHd Yd-

• Strongest intermolecular interaction
• Denoted XHY, with X and Y being N, O, or F
• only molecules with these atoms
• Contact interaction
• turns on when XH group is in contact with Y atom

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Hydrogen Bonding

• A dipole-dipole force with a hydrogen atom bonded
  to nitrogen, oxygen or fluorine.
• The energy of a hydrogen bond is typically 5 to
  30 kJ/mole.
• These bonds can occur between molecules or within
  different parts of a single molecule.
• The hydrogen bond is a very strong fixed
  dipole-dipole van der Waals-Keesom force, but
  weaker than covalent, ionic and metallic bonds.

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• A hydrogen atom attached to a relatively
  electronegative atom (usually fluorine, oxygen,
  or nitrogen) is a hydrogen bond donor.
• An electronegative atom such as fluorine, oxygen,
  or nitrogen is a hydrogen bond acceptor,
  regardless of whether it is bonded to a hydrogen
  atom or not.

Hydrogen bond Strength
FH...F 40 kcal/mol OH...N 6.9 kcal/mol OH...O 5.0 kcal/mol NH...N 3.1 kcal/mol NH...O 1.9 kcal/mol HOH...OH3 4.3 kcal/mol

• The length of hydrogen bonds depends on bond
  strength, temperature, and pressure.
• The typical length of a hydrogen bond in water is
  1.97 Å.

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Hydrogen bonding

• Leads to
• rigidity of molecular solids (sucrose, ice)
• low vapour pressure (water)
• high viscosity (water)
• high surface tension (water)
• secondary structure of proteins (helices)
• attachment of drugs to receptor sites in proteins

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Interaction potential energies
71
The Hydrophobic effect

• An apparent force that influences the shape of a
  macromolecule mediated by the properties of the
  solvent, water.
• Why dont HC molecules dissolve appreciably in
  water?
• Experiments show that the transfer of a
  hydrocarbon molecule from a non-polar solvent
  into water is often exothermic (DH lt 0)
• The fact that dissolving is not spontaneous must
  mean that entropy change is negative
• (DS lt 0).

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The Hydrophobic effect

• For example, the process
• CH4 (in CCl4) CH4 (aq)
• has DH - 10 kJ mol-1, DS - 75 J K-1 mol-1,
  and DG 12 kJ mol-1 at 298 K.
• Substances characterized by a positive Gibbs
  energy of transfer from a non-polar to a polar
  solvent are classified as hydrophobic.

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The Hydrophobic effect

• When a HC molecule is surrounded by water, the
  water molecules form a clathrate cage. As a
  result of this acquisition of structure, the
  entropy of the water decreases, so the dispersal
  of the HC into water is entropy-opposed.
• The coalescence of the HC into a single large
  blob is entropy-favoured.

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The Hydrophobic effect

• The formation of the clathrate cage decreases the
  entropy of the system because the water molecules
  must adopt a less disordered arrangement than in
  the bulk liquid.
• However, when many solute molecules cluster
  together fewer (but larger) cages are required
  and more solvent molecules are free to move.
• This leads to a net decrease in the organization
  of the solvent and thus a net increase in the
  entropy of the system.

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The Hydrophobic effect

• This increase in entropy of the solvent is large
  enough to render spontaneous the association of
  hydrophobic molecules in a polar solvent.
• The increase in entropy that results in the
  decrease in structural demands on the solvent is
  the origin of the hydrophobic effect.
• The presence of hydrophobic groups in
  polypeptides results in an increase in structure
  of the surrounding water molecules and a decrease
  in entropy.

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Modelling the total interaction

• The total attractive interaction energy between
  rotating molecules that cannot participate in
  hydrogen bonding is the sum of the contributions
  from the dipole-dipole, dipole-induced-dipole,
  and dispersion interactions.
• Only the dispersion interaction contributes if
  both molecules are non-polar.

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Modelling the total interaction

• All three interactions vary as the inverse sixth
  power of the separation. Thus the total van der
  Waals interaction energy is
• where C is a coefficient that depends on the
  identity of the molecules and the type of
  interaction between them.

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Modelling the total interaction

• The attractive (negative) contribution has a
  long range, but the repulsive (positive)
  interaction increases more sharply once the
  molecules come into contact.
• Repulsive terms become important and begin to
  dominate the attractive forces when molecules are
  squeezed together.

graph of the potential energy of two
closed-shell species as the distance between them
is changed
79
Modelling the total interaction

• These repulsive interactions arise primarily from
  the Pauli exclusion principle, which forbids
  pairs of electrons being in the same region of
  space.
• The repulsions increase steeply in a way that can
  be deduced only by very extensive, complicated,
  molecular structure calculations.

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Modelling the total interaction

• In many cases one may use a greatly simplified
  representation of the potential energy.
• details ignored
• general features expressed using a few adjustable
  parameters
• Hard-Sphere potential (approximation)
• Assume potential energy rises abruptly to
  infinity as soon as the particles come within
  some separation s

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Modelling the total interaction

• V 8 for r s
• V 0 for r gt s
• There is no potential energy of interaction
  until the two molecules are separated by a
  distance s when the potential energy rises
  abruptly to infinity

s
This very simple assumption is surprisingly
useful in assessing a number of properties.
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Modelling the total interaction

• Another approximation is to express the
  short-range repulsive potential energy as
  inversely proportional to a high power of r
• where C is another constant (the star signifies
  repulsion). Typically, n is set to 12, in which
  case the repulsion dominates the 1/r6 attractions
  strongly at short separations as
• C/r12 gtgt C/r6

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Modelling the total interaction

• The sum of the repulsive interaction with n 12
  and the attractive interaction given by
• is called the Lennard-Jones (12,6)-potential. It
  is normally written in the form

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Modelling the total interaction

• The two parameters are e, the depth of the well,
  and s, the separation at which V 0.

The Lennard-Jones potential models the
attractive component by a contribution that is
proportional to 1/r6, and a repulsive component
by a contribution proportional to 1/r12
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Modelling the total interaction
Species e/ kJ mol-1 s / pm
Ar 128 342
Br2 536 427
C6H6 454 527
Cl2 368 412
H2 34 297
He 11 258
Xe 236 406
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THE END
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