Intermolecular Interactions: Understanding Molecular Forces and Properties

1. Everybody has a private space Chapter 21 Intermolecular Interactions I’m very social. I’m fine for being alone! I’m loving I have friends. How many intermolecular interactions? How (polar) molecules interact with (electric) field? How intermolecular interactions affect physical, chemical properties?

2. Electric properties of molecules Electric dipole moments, multipoles Polarizabilities Relative permittivity Refractive index Interaction between molecules (ions) Between charge and charge Between charge and permanent/induced electric dipole Interactions between permanent/induced dipoles Hydrogen bonding Repulsive (hydrophobic, ) and total interactions Liquids Molecular interactions, radial distribution, thermodynamics Liquid-vapour interface, capillary effect Condensation Contents

3. Intermolecular interactions:(general van der Walls forces) • Charge-charge • Electric dipole-dipole • Dipole-induced-dipole • Induced-dipole-induced dipole (London force) • Hydrogen bonding • Repulsive forces Model force fields

4. Charge-Charge Interaction

5. Electric dipole moments

7. Polar molecules

8. Addition of dipole moments

9. Addition of dipole moments

10. Addition of dipole moments

15. Polarization • The sum of the dipole moments of a sample: Dielectic sample: A medium that is polarizable but nonconducting. The energy of a dipole in an electric field is equal to the work done by recovering the two charges to the same point O (any point): This energy is highest if the dipole moment is opposite to the electric field. Therefore, a dipole moment tends to align with electric field.

16. Proof (Langevin function) At around or above room temperature:

17. Polarizabilities • Induced electric dipole moment by applied electric field: Polarizability Its unit? With very strong electric field: Hyperpolarizability

18. Polarizability volumes Unit: Polarizability volumes correlate with the HOMO-LUMO separation in atoms and molecules.

20. Justification (eq. 12.72)

21. Polarization at high frequencies

22. Relative permitivities (dielectric constant) In vacuum: In meidum: (Debye equation) (Clausius-Mossoti equation)

27. When Debye equation is invalid (selective) Using the permanent dipole moment (2.4 D) and polarizability of water, it’s easy to find that Debye equation fails seriously for water. The major reasons: (1) Debye equation was derived according to the so-called local field model. Essentially, the interactions between water molecules are not considered. (2) The water molecules are not freely rotating as the permanent dipole contribution term was derived. This free rotation assumption underestimates the contribution of the permanent dipole moment. • In liquid, because of mutual inducing effect, the permanent electric dipole moment of water is 2.5D, much larger than its gas phase value 1.85D. However, the third factor is much less important than the first and second one. Onsager and Kirkwood proposed corrections and their equations are much better than Debye equation, but still cannot fully account for the permittivity of water. Studies are going on today.

28. Permittivity is frequency dependent

32. Intermolecular interactions

33. Charge-Charge Interaction (when ions are present)

34. Charge-dipole interaction energy: a special case

35. From the perspective of q2, as its distance from the dipole increases, the dipole looks more and more like merged into a neutral point.

36. Charge-dipole interaction energy: general cases Example: water and a trivalent cation, distance 1 nm Very strong interaction! That’s why water can be so polarized by a trivalent cation (or anion) that a proton can be released from water and the solution is turned into an acid (by highly charged cation) or a base (by a highly charged anion)

37. Charge-induced dipole interaction energy r q A ‘hollow’ arrow denotes induced polarization (dipole moment) of a nonpolar molecule or a nonpolar group.

38. Dipole-dipole interaction energy: a simple case

39. Dipole-dipole interaction energy: a more general cases

43. Dipole-dipole interaction energy: the most general cases The electric field generated by at : The interaction energy of two dipoles is therefore:

44. Dipole-dipole interaction energy between two freely rotating molecules Is not averaged out to zero but is It is called Keesom interaction This is because the following calculation neglects the fact that molecules cannot rotate completely freely, the lower energy orientations are marginally favored.

45. Derivation of Keesom formula V << kT 

49. Dipole-induced dipole 1

50. Dipole-induced dipole interaction : Polarizability volume of the nonpolar molecule