Intermolecular Forces

36
V(r) r r m ε m r=σ Attractive region Attractive region Repulsive region Repulsive region V(r m )=-ε, F attr =F rep V(σ)=0, V attr =V rep

description

Intermolecular Forces. V(r). Repulsive region. V(r m )=- ε , F attr =F rep V( σ )=0, V attr =V rep. r= σ. r m. r. Attractive region. ε m. Repulsive region. Short range interactions. - PowerPoint PPT Presentation

Transcript of Intermolecular Forces

Page 1: Intermolecular Forces

V(r)

rrm

εm

r=σ

Attractive regionAttractive region

Repulsive regionRepulsive region V(rm)=-ε, Fattr=Frep

V(σ)=0, Vattr=Vrep

Page 2: Intermolecular Forces

Short range interactions are dominated by interelectronic repulsion, The quantitative treatment of such interactions necessarily requires QM description (Pauli effects).

These interactions substantiate the concept of sterical hindrance.

Page 3: Intermolecular Forces

r

r

V(r)

Vrep(r≤σ)=∞

Vrep(r>σ)=0

σ=2r

Vatt=0

Page 4: Intermolecular Forces

An analytical function reproducing the results of quantum calculations is:

10,12n )( nR

CRV

C = constant characteristic of the atom-atom pairwise interaction

Van der Waals radius = it represents the minimum contact distance between two atoms. It can be approximately considered as the interatomic distance beyond the repulsive energy rapidly rises

rVdW ≈ σ

Page 5: Intermolecular Forces

The Van der Waals radius also defines a Van der Waals area (SVdW) and volume (VVdW). They represent areas and volumes that cannot be penetrated (excluded areas and volumes).

The Van der Waals volume of a molecule is approximately given by the sum of of the Van der Waals volumes of the atoms or groups of atoms forming the molecule.

3

4 3 2 VdWVdW VS

Page 6: Intermolecular Forces

Contact interatomic distances

Atom pair Average distance (Å)

Minimum distance (Å)

C - - C 3.2 3.0

C - - O 2.8 2.7

C - - N 2.9 2.8

C - - H 2.4 2.2

O - - O 2.8 2.7

O - - N 2.7 2.6

O - - H 2.4 2.2

N - - N 2.7 2.6

N - - H 2.4 2.2

H - - H 2.0 1.9

Page 7: Intermolecular Forces

At long range intermolecular distances we can approximately neglect quantum effects and describe nuclei and electrons as point charges following the laws of classical electrostatics (Coulomb law).

The interaction energy between a charge qi and a charge distribution qj is simply given by the sum of the pair coulomb contributions:

j ij

jii R

qq = V

Page 8: Intermolecular Forces

12

21

02

21

0coul R

q

4

1 V

R

q

4

1 F

12

qq

The energy of coulomb interaction between ions is of the order of 250 kJ·mol-1. q = electric charge = 1.60·10-19 C = 4.8·10-10 ues

1 ues = 1 electrostatic unit. It is the charge that at 1 cm of distance from an other unit charge exerts 1 dyne force (CGS units).

782 )OH( 2)esano(

Page 9: Intermolecular Forces

The dipole moment is a vector measuring the distance between the center of the positive and negative charge distributions:

- +

l

μ

Unit positive and negative charges separated by a 1 Å distance: = q · l = 4.8·10-10·1·10-8 = 4.8·10-18 ues·cm = 4.8 D (Debye)

1 Debye = 10-18 ues·cm=3.336·10-30C·m

rq

Page 10: Intermolecular Forces

Dipole moment of some molecular bond

bond (D) bond (D)

H-F 1.9 C-F 1.4

H-Cl 1.1 C-Cl 1.5

H-N 1.3 C-N 0.2

H-O 1.5 C-O 0.1

Which is the polarity of CO?

δδ--C—OC—Oδδ++

Page 11: Intermolecular Forces

H2O: exp=1.85 D (OH) = 1.52D = 2 (OH) cos(52.5°)

O

H H

=0 =2.25D =1.48D

Isomers of dichlorobenzene:

Page 12: Intermolecular Forces

q1μ2

R12

212

2 1

0 R

q

4

1 -= V

The order of magnitude of this interaction is 15 kJ·mol-1. The interaction can be attractive or repulsive depending on the nature of the charge q1 and the charge–dipole relative orientation.

Page 13: Intermolecular Forces

l

rq1 -q1q2

x

x

r

q ql

r

q ql

r

q q

1

1

1

1

422

4

1= V

0

212121

0

r

lx =

2

Page 14: Intermolecular Forces

Per 12

r

l

......xxx

211

1......xx

x

21

1

1

22

0

21

0

21 1141

1

1

1

4= V xxxx

r

q q

x

x

r

q q

2

0

212

0

21

0

21

442

4=

r

q

r

lq qx

r

q q

Page 15: Intermolecular Forces

Q = monopole. Ex. Na+

- +

l

μ

dipole

Page 16: Intermolecular Forces

Quadrupole

CO2

Page 17: Intermolecular Forces

Octupole

Page 18: Intermolecular Forces

The interaction energy decreases with the distance as faster as the order of the multipolar interaction increases.

For an n-pole interacting with an m-pole:

1

1V

mnr

Page 19: Intermolecular Forces

The interaction energy can be attractive or repulsive depending on the relative orientation between the two molecular dipoles:

+ + +

+- -

-

-

For two non-rotating dipoles (fixed orientation, like in solids):

3120

21

R4

- = V

-1

int molkJ2

Page 20: Intermolecular Forces

For rotating dipoles (solution, gas) the interaction energy should be averaged among all possible orientations following the Boltzmann distribution.

Because attractive energy orientations are slightly favoured with respect to orientations giving rise to repulsive interactions, dipole-dipole interactions in solution or in gas phases are attractive, depending on the temperature:

612R kT

C - =V

22

21

-1int molkJ .070

At 25°C for two HCl molecules (μ=1D) at 5Å:

Page 21: Intermolecular Forces

An apolar molecule under the effect of an external electric field could be polarized.

- - - - - - + + +

- - - - - -

+ + + - - - - - -

+ + +

Electric fieldElectric field

Polarized molecule

......E: 2indotto 2

1E

βα

polarizability hyperpolarizability

Page 22: Intermolecular Forces

potential)on I(ionizati

number) (atomic Z

Polarizability is a molecular property that increases with the number of electrons belonging to the molecule and decreases with the increase of the ionization potential :

04 '

Volume polarizability[m3]

polarizability [C2m2J-1]

Vacuum permittivity [C2m-1J-1]

Page 23: Intermolecular Forces

CO2

q = 0

p = 0

Q = -7.510-40 Cm2

// = 4.0510-24 cm3

= 2.0210-24 cm3

yy=zz= xx= //

z

x

p// = //E// p= E

Page 24: Intermolecular Forces

The electric field generated by a permanent dipole moment gives rise to a dipole moment (induced dipole moment) on a nearby apolar molecule.

(HCl)= 1 Debye Benzene = 110-29 m3

H

Cl

At 3Å ε ≈ -0.8 kJ·mol-1

Page 25: Intermolecular Forces

60

221

12R4

- = V

-1

int molkJ .80

As the orientation of the induced dipole depends on the orientation of the inducing dipole, the dipole-induced dipole interaction does not depend on the thermal energy (kT).

Page 26: Intermolecular Forces

A pure quantistic effect arising from the correlation between the electron motions of the interacting atoms at large distances.

These interactions, named dispersion or London interactionsdispersion or London interactions, occur in all systems, even between apolar molecules.

They are always attractive. Semiclassically can be described as the interaction between istantaneous dipoles arising from the fluctuations of electronic charge distributions.

Page 27: Intermolecular Forces

21

2121

II

II

R

C

R

C - =V

66

22

21

1212

Molecular polarizabilityMolecular polarizability Ionization energyIonization energy

For two CH4 molecules (=2.6·10-30 m3, I7 eV) separated by 3 Å: εint -2 kJ·mol-1.

Page 28: Intermolecular Forces
Page 29: Intermolecular Forces

Interaction Distance dependence

Energy(kJ mol-1)

Type

Ion-ion R-1 250 ion

Ion-dipole R-2 15

Dipole-dipole R-3 2 Fixed dipoles

R-6 0.3 Rotating dipoles

Dipole-induced dipole

R-6 0.3

Dispersion(London)

R-6 2 All the molecules

Page 30: Intermolecular Forces

In basence of ions and for rotating systems in solution, dipolar interactions are attractive nad depend on the sixth inverse power of the distance.

These contributions to the potential energy can be described by an analytical finction as :

6R

C - =V

Page 31: Intermolecular Forces

The electrostatic origin of H-bond interaction is emphasized by the involvement of strong electronegative atoms in competition with the same H-atom:

D-(donor) H+ - - - -A-(acceptor)

H-bond interaction can de described as a dipole-dipole interaction between fixed dipoles:

3A-H-D

HBR

C - = V

Page 32: Intermolecular Forces

The order of magnitude of H-bond interaction is 20 kJ·mol-1 (R 2Å).Length and strenght of H-bond depend on the electronegativity of the donor-acceptor pair and on the geometry of the atomic groups:

N H O C1.03 Å

1.9-2.0 Å

Page 33: Intermolecular Forces

46

0

12

0

r

r

r

r)r(V

Page 34: Intermolecular Forces
Page 35: Intermolecular Forces

224

7

0

13

0

0

r

r

r

r

rr

)r(VF

The attractive force is maximum at :

1.244r7

2600

6 rr

At this distance: r

-2.3970

maxF

Tipically around 10 pN.

Page 36: Intermolecular Forces