Crystal Binding

(Bonding) Continued

More on Van der Waals

& Hydrogen 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

Van Der Waals Bonding

+ -+ -SPONTANEOUS DIPOLE FORMATION IN ONE ATOM

MAY INDUCE AN EQUAL AND OPPOSITE DIPOLE IN

ANOTHER ATOM NEARBY SO CAUSING ATTRACTIONTHIS IS THE VAN DER WAALS BOND

•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

Van Der Waals Bonding

+e -e

A DIPOLE CONSISTS OF EQUAL ANDOPPOSITE CHARGES SEPARATED BY

SOME DISTANCE

A CHARGE DIPOLE MAY SPONTANEOUSLYFORM IN A NEUTRAL ATOM DUE TO THE MOTION

OF ELECTRONS AROUND THE NUCLEUS

+ -

DIPOLE

FORMS

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

mn rB

rA

rE )(

1)(&0

1

nm

rB

rEmBnA

rdrdE

mo

o

mn

orr o

Van Der Waals Bonding

typical values aren = 12, m = 6

Van Der Waals Bonding

mn rB

rA

rE )(

1)(&

1

n

m

r

BrE

mB

nAr

mo

o

mn

o

nA

mBr

r

mB

r

nA

r

mB

r

nA

dr

dE

nmmn

mnrr o

11

110

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.

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.

• 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' force2. Hydrogen bonding

• Van der waals’ force is formed by dipoles. There are 3 types of dipoles:1. Permanent dipoles2. Instantaneous dipoles3. Induced dipoles

Permanent DipoleThese 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 permanentdipole.

Instantaneous 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.

Classification diagram of intermolecular forces

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.

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.

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.

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.

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

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

Hydrogen Bonding

Electrostatic bonding Electrostatic bonding between an H+ ion between an H+ ion with an anion or with an anion or anionic complex or anionic complex or with a polarized with a polarized moleculesmoleculesWeaker than ionic or Weaker than ionic or covalent; stronger than covalent; stronger than Van der WaalsVan der Waals polarized H2O

moleculeIce

Close packing of polarized molecules

Anions

H+

Intermolecular Forces

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

van der Waals Forces

• Dipole-dipole interactions

• Hydrogen bonding

• London dispersion forces

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.

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.

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.

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.

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.

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.

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.

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.

Lennard-Jones PotentialAttraction due to instantaneous dipole of

moleculesPair-wise non-bonded interactions O(N2)Short range forceUse cut-off radius to reduce computationsReduced complexity close to O(N)

Lennard-Jones Potential of Argon gas

-150

-100

-50

0

50

100

150

200

250

300

0.3 0.5 0.7 0.9 1.1 1.3 1.5

r (nm)

v(r)

/kb

(K

)

612

4rr

U LJ

Lennard Jones potentials

uLJ r 4r

12

r

6

u r uLJ r r rc

0 r rc

u r uLJ r uLJ rc r rc

0 r rc

•The truncated and shifted Lennard-Jones potential

•The truncated Lennard-Jones potential

•The Lennard-Jones potential

Lennard-Jones Potential

Minimum interaction energy and its distance  r0(A) (J)

He 2.2 110 -22

H2 2.7 4

Ar 3.2 15

N2 3.7 13

CO2 4.5 40

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.

The Lennard-Jones Potential

612

4rr

ru

The long range 1/r6 attractive term

The short range 1/r12 repulsive term

u(r)/ε

r/σ

0

10 2 3

Contributions:Dipole-dipole (including H-bonding)Induced dipoleLondon dispersion attraction

ε

Example – Lennard-Jones (LJ) clusters

R

Isomers• different minima on potential energy surface• number of isomers grows exponentially

with # of atoms• a and b – permutation-inversion isomers• Ea = Eb ≠ Ec

612

RR4

E

ji

E

6

ij

12

ij RR4

Two atoms:

Multiple atoms - assume pairwise additive:

a

b

c

dispersion (van der Waals)repulsion

1 2 3

1 3 2

R

E

R

ε

21/6σ

Lennard-Jones Potentialphysisorption

z

pote

ntia

l en e

rgy

ads < 35 kJmol-1

attractive van der Waals interactions

repulsive Coulombic interactionsPauli repulsion

ads

0

Carey, V.P., Statistical Thermodynamics and Microscale Thermophysics, New York: Cambridge University Press, 1999.

• No long range interactions

• Interact via elastic collisions

“Hard Sphere” Potential

Gases• 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

Intermolecular PotentialsIntermolecular Potentials