1. Crystal Binding (Bonding) Continued
More on Van der Waals
& Hydrogen Bonding

2. Van Der Waals Bonding
This WEAK dipole interaction is the origin of the van der Waals bond, which is therefore characterized by a LOW cohesive energy, and so LOW melting temperatures
Another type of van der Waals bonding is observed for certain POLAR molecules, that have a PERMANENT dipole moment
SPONTANEOUS DIPOLE FORMATION IN ONE ATOM
MAY INDUCE AN EQUAL AND OPPOSITE DIPOLE IN
ANOTHER ATOM NEARBY SO CAUSING ATTRACTION THIS IS THE VAN DER WAALS BOND

3. A DIPOLE CONSISTS OF EQUAL AND OPPOSITE CHARGES SEPARATED BY
Van Der Waals Bonding
Although IONIZED atoms are electrically NEUTRAL, electrons within them are in a CONSTANT state of motion, and so may MOMENTARILY form small charge DIPOLES
The direction and magnitude of this dipole CONSTANTLY fluctuates, but may INDUCE similarly fluctuating dipoles in other atoms
DIPOLE FORMS +e -e
A CHARGE DIPOLE MAY SPONTANEOUSLY FORM IN A NEUTRAL ATOM DUE TO THE MOTION OF ELECTRONS AROUND THE NUCLEUS
A DIPOLE CONSISTS OF EQUAL AND
OPPOSITE CHARGES SEPARATED BY
SOME DISTANCE

4. Van Der Waals Bonding typical values are n = 12, m = 6
Mathematically this potential energy variation can be APPROXIMATED as The CONSTANTS A and n are associated with REPULSIVE forces. The constants B and m are associated with ATTRACTIVE forces. At EQUILIBRIUM these forces BALANCE and we may write
 ro and E(ro) are the equilibrium SEPARATION and ENERGY  For a stable bond to form E(ro) must be NEGATIVE thus m < n
typical values are
n = 12, m = 6

5. Van Der Waals Bonding

6. Intermolecular Forces
The origin of intermolecular forces
The classification of intermolecular forces
Van der Waal’s force
Hydrogen bonding
Explore an example in depth to show the significance of existence of intermolecular forces.

7. The Origin of Intermolecular Forces
It is weak electrostatic force of attraction that exist an area of negative charge on one molecule and an area of positive charge on a second molecule.
What causes intermolecular forces?
Molecules are made up of charged particles: nuclei and electrons. When one molecule approaches another, there is a multitude of interactions between the particles in the two molecules. Each electron in one molecule is subject to forces from all the electrons and the nuclei in the other molecule.

8. Intermolecular force is weak compared to covalent bond
Intermolecular force is weak compared to covalent bond. It is relatively weak interactions that occur between molecules.
There are 2 types of intermolecular forces (both of them are electrostatic attraction between dipoles formed by uncharged molecules.)
1. Van der Waals' force
2. Hydrogen bonding
Van der waals’ force is formed by dipoles. There are 3 types of dipoles:
1. Permanent dipoles
2. Instantaneous dipoles
3. Induced dipoles

9. Permanent Dipole
These molecules have a permanent separation of positive and negative charge.
A simple example is HCl
 -
The pair of electrons in the covalent bond between hydroge and chlorine is
unequally shared due to the difference in electronegativity between hydrogen and
chlorine. Chlorine has a greater electronegativity compared to hydrogen and hence
Chlorine tends to attract the bonded electron pair to itself. chlorine becomes slightly
negatively charged (-), hydroge atom has a partial positive charged (+) .The
unsymmetrical distributed charge on the HCl molecule produces a permanent
dipole.

10. Instantaneous Dipole Induced Dipole
Instantaneous dipole is due to the fluctuation of electron clouds on non-polar molecules, positive and negative charges exist temporarily.
Induced Dipole
Induced dipole exists when a permanent dipole or instantaneous dipole comes close to a non-polar molecule, the non-polar molecule will be induced to form a dipole temporarily.

11. Classification diagram of intermolecular forces

12. Dipole-Dipole Interactions
Dipole-dipole interactions exist between molecules which are permanent dipole. They tend to orientate themselves that the attractive forces between molecules are maximized while repulsive forces are minimized.
In the illustration :
the H end of HCl is permanently slightly positive charge. The Cl end of HCl has a permanent slight negative charge, the "H" in one molecule is attracted to the "Cl" in a neighbor.

13. Instantaneous Dipole-Induced Dipole Interactions
Also known as London forces or Dispersion Forces
Instantaneous dipole-induced dipole Interactions exist in non-polar molecules. These forces result from temporary charge imbalances. The temporary charges exist because the electrons in a molecule or ion move randomly in the structure. The nucleus of one atom attracts electrons form the neighboring atom. At the same time, the electrons in one particle repel the electrons in the neighbor and create a short lived charge imbalance.
These temporary charges in one molecule or atom attract opposite charges in nearby molecules or atoms. A local slight positive charge + in one molecule will be attracted to a temporary slight - negative charge in a neighboring molecule.
Note: dispersion forces operate in all molecules whether they are polar or non-polar.

14. Dipole-Induced Dipole Interactions
Also known as induction force.
When a polar molecule approaches a nonpolar molecule, the permanent dipole on the polar molecule can distort the electron cloud of the nonpolar molecule, forming an induced dipole.

15. Van der Waals Radius & Covalent Radius
Van der Waals radius is one half of the distance between the nuclei of two atoms in adjacent molecules.
Covalent radius is one half of the distance between two atoms in the same molecules.
Van der Waals’ radius of a non-metal is always larger than the corresponding covalent radius because the covalent radius because covalent bond is much stronger than van der Waals’ forces.

16. Aided by polar or partial polar covalent bonds.
4) Van der Waals Bonds
Weakest bond
Usually between neutral molecules (even large ones like graphite sheets)
Aided by polar or partial polar covalent bonds.
Even stable A-A bonds like O2 or Cl2 will get slightly polar at low T & condense to liquid & ordered solid as vibration slows &  polarity
Weakness of the bond is apparent in graphite cleavage

17. Van der Waals Bonding
created by weak bonding of oppositely dipolarized electron clouds
commonly occurs around covalently bonded elements
produces solids that are soft, very poor conductors, have low melting points, low symmetry crystals

18. Hydrogen Bonding H+
Electrostatic bonding between an H+ ion with an anion or anionic complex or with a polarized molecules
Weaker than ionic or covalent; stronger than
Van der Waals
Close packing of
polarized molecules
Anions
polarized H2O
molecule
Ice

19. Intermolecular Forces
These intermolecular forces as a group are referred to as van der Waals forces.

20. van der Waals Forces Dipole-dipole interactions Hydrogen bonding
London dispersion forces

21. Ion-Dipole Interactions
A fourth type of force, ion-dipole interactions are an important force in solutions of ions.
The strength of these forces are what make it possible for ionic substances to dissolve in polar solvents.

22. Dipole-Dipole Interactions
Molecules that have permanent dipoles are attracted to each other.
The positive end of one is attracted to the negative end of the other and vice-versa.
These forces are only important when the molecules are close to each other.

23. Hydrogen Bonding
The dipole-dipole interactions experienced when H is bonded to N, O, or F are unusually strong.
We call these interactions hydrogen bonds.

24. Hydrogen Bonding
Hydrogen bonding arises in part from the high electronegativity of nitrogen, oxygen, and fluorine.
Also, when hydrogen is bonded to one of those very electronegative elements, the hydrogen nucleus is exposed.

25. Hydrogen Bonding
Hydrogen bond is a electrostatic force of attraction existing between polar hydrogen(+) and electronegative atom(-) of dipoles.
The hydrogen bond is weaker than the covalent bond, but relatively strong compared to van der Waals’ force.
Hydrogen bonding is a unique type of intermolecular molecular attraction. There are two requirements.  1. The first is a covalent bond between a H atom and either F, O, or N (These are the three most electronegative elements.) 2. The second is an interaction of the H atom in this kind of polar bond with a lone pair of electrons on a nearby atom of F, O, or N.

26. Hydrogen Bonding in an Ice Crystal
Ice has a lower density than water as ice has an open structure. In ice, each molecule is tetrahedral bonded to other molecules by hydrogen bond.

27. Hydrogen Bond in Water
Many other unique properties of water are due to the hydrogen bonds. For example, ice floats because hydrogen bonds hold water molecules further apart in a solid than in a liquid, where there is one less hydrogen bond per molecule. The unique physical properties, including a high heat of vaporization, strong surface tension, high specific heat, and nearly universal solvent properties of water are also due to hydrogen bonding.

28. Hydrogen Bonding in DNA
Hydrogen bonds play an important role in the ‘base-pairing’ duplication of DNA (A-T,C-G). Matching of the bases produces an accurate duplicate of the original DNA chain.

29. Lennard-Jones Potential
Attraction due to instantaneous dipole of molecules
Pair-wise non-bonded interactions O(N2)
Short range force
Use cut-off radius to reduce computations
Reduced complexity close to O(N)

30. Lennard-Jones Potential of Argon gas

31. Lennard Jones potentials
The Lennard-Jones potential
The truncated Lennard-Jones potential
The truncated and shifted Lennard-Jones potential

32. Lennard-Jones Potential

33. Minimum interaction energy and its distance
Some Lennard-Jones potential examples of application are listed in the Table. Even this crude interaction model has extensive applications. This model can explain many properties of gases, solids and liquids quite well.
Minimum interaction energy and its distance
r0(A)
(J) He
2.2
110 -22 H2
2.7 4 Ar
3.2 15 N2
3.7 13
CO2
4.5 40

34. The Lennard-Jones Potential
The short range 1/r12
repulsive term
The long range
1/r6 attractive term
Contributions:
Dipole-dipole (including H-bonding)
Induced dipole
London dispersion attraction
u(r)/ε ε
r/σ 1 2 3

35. Example – Lennard-Jones (LJ) clusters
21/6σ E
Two atoms: R R R ε
repulsion
dispersion (van der Waals)
Multiple atoms - assume pairwise additive: a 1 2 3
Isomers
different minima on potential energy surface
number of isomers grows exponentially with # of atoms
a and b – permutation-inversion isomers
Ea = Eb ≠ Ec b 1 3 2 c

36. Lennard-Jones Potential
physisorption
-DHads < 35 kJmol-1
potential energy
repulsive Coulombic interactions
Pauli repulsion
attractive van der Waals interactions z
DHads

37. Intermolecular Potentials
Electric dipole ~ r -3
2 dipoles ~ r -6
Repulsive nuclear forces ~ r -12
Total Potential = (Attractive) + (Repulsive)
“Lennard-Jones 6-12 Potential”
Dense Gases, Liquids and Solids
No long range interactions
Interact via elastic collisions
“Hard Sphere” Potential
Gases
Carey, V.P., Statistical Thermodynamics and Microscale Thermophysics, New York: Cambridge University Press, 1999.