Title: Molecular Interactions
1Molecular Interactions
- The most important to producing phases and
interfaces in the materials
2Background
- 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.
3Molecular 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.
4van 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)
5The total interaction
- Hydrogen bonding
- The hydrophobic effect
- Modelling the total interaction
- Molecules in motion
6van 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.
7van 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.
8van 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
9Interactions between partial charges
- Atoms in molecules generally have partial
- charges.
10Interactions 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
11Charges Interactions
- Coulombic Inteaction between q1 and q2
- Partial atomic ChargesApproximated distribution
of electron in molecule
0.387 -0.387
12Interactions 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.
14Coulomb potential for two charges
vacuum
fluid
15Ion-Ion interaction/Lattice Enthalpy
- Consider two ions in a lattice
16Ion-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.
17Ion-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.
18- 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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20Born-Haber cycle for lattice enthalpy
21Lattice 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)
22Calculate 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
23Calculation 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
24Electric 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.
25Electric 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)
26Electric 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.
27Electric 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.
28Electric dipole moments
29Electric 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.
30Electric 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
31Electric 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
32Electric 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.
33Electric 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
34Electric dipole moments polyatomic molecules
35Electric 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.
36Electric 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
37Partial charges in polypeptides
38Calculating 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
39Calculating 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)
40Interactions 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
41Interactions between Dipoles
- The potential energy between a point dipole and
the point charge q (lgtgtr)
42Interactions 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.
43Interactions 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.
44- 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
45Interactions 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.
46- The potential energy between two parallel dipoles
This applies to polar molecules in a fixed,
parallel, orientation in a solid.
47Interactions 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.
48Interactions 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
49- 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.
50Interactions 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.
51Interactions 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
52- 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.
53Interactions 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.
54Induced 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.
55Induced 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.
56Induced 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
57Polarizability volume
- The polarizability volume has the dimensions of
volume and is comparable in magnitude to the
volume of the molecule
58Polarizability volumes
59Polarizability 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?
60Dipole-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)
61Dipole-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
62Dispersion 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
63Dispersion 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.
64Dispersion 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
65Dispersion 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)
66Total 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
67Hydrogen 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.
68- 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.
69Hydrogen 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
70Interaction potential energies
71The 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).
72The 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.
73The 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.
74The 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.
75The 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.
76Modelling 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.
77Modelling 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.
78Modelling 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
79Modelling 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.
80Modelling 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
81Modelling 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.
82Modelling 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
83Modelling 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
84Modelling 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
85Modelling 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
86THE END
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