Intermolecular Forces

1. Intermolecular Forces V(r) Repulsive region V(rm)=-ε, Fattr=Frep V(σ)=0, Vattr=Vrep r=σ rm r Attractive region εm

2. Repulsive region. Short range interactions. 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.

3. r r Hard-spheres potential V(r) σ r σ=2r Vrep(r≤σ)=∞ Vrep(r>σ)=0 Vatt=0

4. An analytical function reproducing the results of quantum calculations is: C = constant characteristic of the atom-atom pairwise interaction Van der Waalsradius = 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

5. 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.

7. Long range interactions. Electrostatic contributions 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:

8. Coulomb pair interaction 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).

9. - + Dipole moment 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

10. Which is the polarity of CO? δ-C—Oδ+

11. H2O: exp=1.85 D (OH) = 1.52D  = 2 (OH) cos(52.5°) O H H Isomers of dichlorobenzene: =0 =2.25D =1.48D

12. R12 μ2 q1 Ion-dipole interactions 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.

13. l q2 r q1 -q1

14. Per

15. - + Multipolar expansion Q = monopole. Ex. Na+ l μ dipole

16. Quadrupole CO2

17. Octupole

18. 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:

19. + + + - - + - - Dipole-dipole interaction 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):

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

21. Electric field Polarized molecule - - - - - - + + + - - - - - - + + + - - - - - - + + + Induced dipole interactions An apolar molecule under the effect of an external electric field could be polarized. hyperpolarizability polarizability

22. Molecular polarizability 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 : polarizability [C2m2J-1] Vacuum permittivity [C2m-1J-1] Volume polarizability [m3]

23. q = 0 p = 0 Q = -7.510-40 Cm2 // = 4.0510-24 cm3  = 2.0210-24 cm3 z x CO2 xx= // yy=zz=  p// = //E// p= E

24. Dipole-dipole induced interaction The electric field generated by a permanent dipole moment gives rise to a dipole moment (induced dipole moment) on a nearby apolar molecule. Cl H (HCl)= 1 Debye Benzene  = 110-29 m3 At 3Å ε≈ -0.8 kJ·mol-1

25. 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).

26. Induced dipole- induced dipole interaction 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 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.

27. Molecular polarizability Ionization energy For two CH4 molecules (=2.6·10-30 m3, I7 eV) separated by 3 Å: εint -2 kJ·mol-1.

30. 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 :

31. Hydrogen bond interaction 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:

32. 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: 1.03 Å O C N H 1.9-2.0 Å

33. Lennard-Jones potential (12,6)

35. The attractive force is maximum at : At this distance: Tipically around 10 pN.