Molecular Interactions

1. Molecular Interactions The most important to producing phases and interfaces in the materials

2. Background Atoms and molecules with complete valence shells can still interact with one another even though all of their valences are satisfied. They attract one another over a range of several atomic diameters and repel one another when pressed together.

3. Molecular interactions account for: • condensation of gases to liquids • structures of molecular solids (surfaces) • structural organisation of biological macromolecules as they pin molecular building blocks (polypeptides, polynucleotides, and lipids) together in the arrangement essential to their proper physiological function.

4. van der Waals interactions • Interaction between partial charges in polar molecules • Electric dipole moments or charge distribution • Interactions between dipoles • Induced dipole moments • Dispersion interactions • Interaction between species with neither a net charge nor a permanent electric dipole moment (e.g. two Xe atoms)

5. The total interaction • Hydrogen bonding • The hydrophobic effect • Modelling the total interaction • Molecules in motion

6. van der Waals interactions Interactions between molecules include the attractive and repulsive interactions between the partial electric charges of polar molecules and the repulsive interactions that prevent the complete collapse of matter to densities as high as those characteristic of atomic nuclei.

7. van der Waals interactions (contd.) Repulsive interactions arise from the exclusion of electrons from regions of space where the orbitals of closed-shell species overlap. Those interactions proportional to the inverse sixth power of the separation are called van der Waals interactions.

8. van der Waals interactions • Typically one discusses the potential energy arising from the interaction. If the potential energy is denoted V, then the force is –dV/dr. If V = -C/r6 the magnitude of the force is:

9. Interactions between partial charges Atoms in molecules generally have partial charges.

10. Interactions between partial charges • If these charges were separated by a vacuum, they would attract or repel one another according to Coulomb’s Law: where q1 and q2 are the partial charges and r is their separation

11. Charges Interactions • Coulombic Inteaction between q1 and q2 • Partial atomic ChargesApproximated distribution of electron in molecule 0.387 -0.387

12. Interactions between partial charges However, other parts of the molecule, or other molecules, lie between the charges, and decrease the strength of the interaction. Thus, we view the medium as a uniform continuum and we write: Where e is the permittivity of the medium lying between the charges.

13. The permittivity is usually expressed as a multiple of the vacuum permittivity by writing e = ere0, where er is the relative permittivity (dielectric constant). The effect of the medium can be very large, for water at 250C, er = 78. The PE of two charges separated by bulk water is reduced by nearly two orders of magnitude compared to that if the charges were separated by a vacuum.

14. Coulomb potential for two charges vacuum fluid

15. Ion-Ion interaction/Lattice Enthalpy Consider two ions in a lattice

16. Ion-Ion interaction/Lattice Enthalpy two ions in a lattice of charge numbers z1 and z2 with centres separated by a distance r12: where e0 is the vacuum permittivity.

17. Ion-Ion interaction/Lattice Enthalpy To calculate the total potential energy of all the ions in the crystal, we have to sum this expression over all the ions. Nearest neighbours attract, while second-nearest repel and contribute a slightly weaker negative term to the overall energy. Overall, there is a net attraction resulting in a negative contribution to the energy of the solid.

18. For instance, for a uniformly spaced line of alternating cations and anions for which z1= +z and z2 = -z, with d the distance between the centres of adjacent ions, we find:

20. Born-Haber cycle for lattice enthalpy

21. Lattice Enthalpies, DHL0 / (kJ mol-1) Lattice Enthalpy ( ) is the standard enthalpy change accompanying the separation of the species that compose the solid per mole of formula units. e.g. MX (s) = M+(g) + X- (g)

22. Calculate the lattice enthalpy of KCl (s) using a Born-Haber cycle and the following information at 25oC: ProcessDH0 (kJ mol-1) Sublimation of K (s) +89 Ionization of K (g) +418 Dissociation of Cl2 (g) +244 Electron attachment to Cl (g) -349 Formation of KCl (s) -437

23. Calculation of lattice enthalpy ProcessDH0 (kJ mol-1) KCl (s) K (s) + ½ Cl2 (g) +437 K (s) K (g) +89 K (g) K+ (g) + e- (g) +418 ½ Cl2 (g) Cl (g) +122 Cl (g) + e- (g) Cl- (g) -349 KCl (s) K+ (g) + Cl- (g) +717 kJ mol-1

24. Electric dipole moments When molecules are widely separated it is simpler to express the principal features of their interaction in terms of the dipole moments associated with the charge distributions rather than with each individual partial charge. An electric dipole consists of two charges q and –q separated by a distance l. The product ql is called the electric dipole moment, m.

25. Electric dipole moments We represent dipole moments by an arrow with a length proportional to m and pointing from the negative charge to the positive charge: m d+ d- Because a dipole moment is the product of a charge and a length the SI unit of dipole moment is the coulomb-metre (C m)

26. Electric dipole moments It is often much more convenient to report a dipole moment in debye, D, where: 1D = 3.335 64 x 10-30 C m because the experimental values for molecules are close to 1 D. The dipole moment of charges e and –e separated by 100 pm is 1.6 x 10-29 C m, corresponding to 4.8 D.

27. Electric dipole moments: diatomic molecules A polar molecule has a permanent electric dipole moment arising from the partial charges on its atoms. All hetero-nuclear diatomic molecules are polar because the difference in electronegativities of their two atoms results in non-zero partial charges.

28. Electric dipole moments

29. Electric dipole moments: diatomic molecules More electronegative atom is usually the negative end of the dipole. There are exceptions, particularly when anti-bonding orbitals are occupied. • CO dipole moment is small (0.12 D) but negative end is on C atom. Anti-bonding orbitals are occupied in CO and electrons in anti-bonding orbitals are closer to the less electronegative atom, contributing a negative partial charge to that atom. If this contribution is larger than the opposite contribution from the electrons in bonding orbitals, there is a small negative charge on the less electronegative atom.

30. Electric dipole moments: polyatomic molecules • Molecular symmetry is of the greatest importance in deciding whether a polyatomic molecule is polar or not. Homo-nuclear polyatomic molecules may be polar if they have low symmetry • in ozone, dipole moments associated with each bond make an angle with one another and do not cancel. d+ d+ m m d- d- Ozone, O3

31. Electric dipole moments: polyatomic molecules • Molecular symmetry is of the greatest importance in deciding whether a polyatomic molecule is polar or not. • in carbon dioxide, dipole moments associated with each bond oppose one another and the two cancel. m m d+ d+ d- d- Carbon dioxide, CO2

32. Electric dipole moments: polyatomic molecules It is possible to resolve the dipole moment of a polyatomic molecule into contributions from various groups of atoms in the molecule and the direction in which each of these contributions lie.

33. Electric dipole moments: polyatomic molecules 1,2-dichlorobenzene: two chlorobenzene dipole moments arranged at 60o to each other. Using vector addition the resultant dipole moment (mres) of two dipole moments m1 and m2 that make an angle q with one another is approximately: mres m1 q m2

34. Electric dipole moments: polyatomic molecules

35. Electric dipole moments: polyatomic molecules Better to consider the locations and magnitudes of the partial charges on all the atoms. These partial charges are included in the output of many molecular structure software packages. Dipole moments are calculated considering a vector, m, with three components, mx, my, and mz. The direction of mshows the orientation of the dipole in the molecule and the length of the vector is the magnitude, m, of the dipole moment.

36. Electric dipole moments: polyatomic molecules To calculate the x-component we need to know the partial charge on each atom and the atom’s x-coordinate relative to a point in the molecule and from the sum: mz m where qJ is the partial charge of atom J, xJ is the x coordinate of atom J, and the sum is over all atoms in molecule mx my

37. Partial charges in polypeptides

38. Calculating a Molecular dipole moment H (182,-87,0) +0.18 (0,0,0) m C -0.36 N +0.45 (132,0,0) O -0.38 (-62,107,0) mx = (-0.36e) x (132 pm) + (0.45e) x (0 pm) +(0.18e) x (182 pm) + (-0.38e) x (-62 pm) = 8.8e pm = 8.8 x (1.602 x 10-19 C) x (10-12 m) = 1.4 x 10-30 C m = 0.42 D

39. Calculating a Molecular dipole moment my = (-0.36e) x (0 pm) + (0.45e) x (0 pm) +(0.18e) x (-86.6 pm) + (-0.38e) x (107 pm) = -56e pm = -9.1 x 10-30 C m = -2.7 D mz = 0 m =[(0.42 D)2 + (-2.7 D)2]1/2 = 2.7 D Thus, we can find the orientation of the dipole moment by arranging an arrow 2.7 units of length (magnitude) to have x, y, and z components of 0.42, -2.7, 0 units (Exercise: calculate m for formaldehyde)

40. Interactions between dipoles The potential energy of a dipole m1 in the presence of a charge q2 is calculated taking into account the interaction of the charge with the two partial charges of the dipole, one a repulsion the other an attraction. l q2 -q1 q1 r

41. r -q1 +q1 q2 l Interactions between Dipoles • The potential energy between a point dipole and the point charge q (l>>r)

42. Interactions between dipoles A similar calculation for the more general orientation is given as: q2 r l q -q1 q1 If q2 is positive, the energy is lowest when q = 0 (and cos q = 1), as the partial negative charge of the dipole lies closer than the partial positive charge to the point charge and the attraction outweighs the repulsion.

43. Interactions between dipoles The interaction energy decreases more rapidly with distance than that between two point charges (as 1/r2 rather than 1/r), because from the viewpoint of the point charge, the partial charges on the dipole seem to merge and cancel as the distance r increases.

44. r r r l -q1 +q1 q2 q2 q2 l • Increasing the distance, the potentials of the charges decrease and the two charges appear to merge. • These combined effect approaches zero more rapidly than by the distance effect alone. l

45. Interactions between dipoles Interaction energy between two dipoles m1 and m2: l2 q2 -q2 l1 r q -q1 q1 For dipole-dipole interaction the potential energy decreases as 1/r3 (instead of 1/r2 for point-dipole) because the charges of both dipoles seem to merge as the separation of the dipoles increases.

46. r -q1 -q2 +q1 +q2 +q2 -q2 q r l l l l +q1 -q1 • The potential energy between two parallel dipoles This applies to polar molecules in a fixed, parallel, orientation in a solid.

47. Interactions between dipoles The angular factor takes into account how the like or opposite charges come closer to one another as the relative orientations of the dipoles is changed. • The energy is lowest when q = 0 or 180o (when 1 – 3 cos2q = -2), because opposite partial charges then lie closer together than like partial charges. • The energy is negative (attractive) when q < 54.7o (the angle when 1 – 3 cos2q = 0) because opposite charges are closer than like charges. • The energy is positive (repulsive) when q > 54.7o because like charges are then closer than opposite charges. • The energy is zero on the lines at 54.7o and (180 – 54.7) = 123.3o because at those angles the two attractions and repulsions cancel.

48. Interactions between dipoles Calculate the molar potential energy of the dipolar interaction between two peptide links separated by 3.0 nm in different regions of a polypeptide chain with q = 180o, m1 = m2 = 2.7 D, corresponding to 9.1 x 10-30 C m

49. Freely rotating dipoles: Liquid, Gas • The interaction energy of two freely rotating dipoles is zero. • Real molecules do not rotate completely freely due to the fact that their orientations are controlled partially by their mutual interaction.

50. Interactions between dipoles When a pair of molecules can adopt all relative orientations with equal probability, the favourable orientations (a) and the unfavourable ones (b) cancel, and the average interaction is zero. In an actual fluid (a) predominates slightly.