Intermolecular Forces:Electrostatics

1. Intermolecular Forces:Electrostatics • “Dielectrics • Different classical electrostatic interactions

2. 0= 8.85410-12 C2/ (N●m2) • This can change when not in vacuum Coulomb’s Law • Like charges repel, unlike charges attract • Force is directly along a line joining the two charges q1 q2 r ke= 8.988109 Nm2/C2

3. Dielectric The dielectric constant tells us about how electric fields are weakened due to mobility of dipoles. If we place a charge in a media with orientable/polarizable dipoles, the charge will be “solvated” by the dipoles Dielectric constants depend on mobility, size and polarizability of dipoles Not readily defined in a heterogenous flexible medium!

4. Dielectric In a homogenous material, a scale factor In a complex material, poisson’s equation

5. Multiple charges q3 r3 q2 r1 r2 q1 We can handle multiple charges by considering each on explicitly, or by a multipole expansion

6. Multipole expansion (qualitatively) When outside the charge distribution, consider a set of charges as being a decomposition of a monopole, a dipole { and higher order terms} The monopole term is the net charge at the center of the charges {often zero} The dipole moment has its positive head at the center of the positive changes, and its negative tail at the center of the negative charges

7. Multipole expansion The multipole expansion expands a potential in a complete set of functions: The significance is that we can study the different poles one by one, to understand any charge distribution Where might we have a significant dipole moment? Where might we have a significant quadrapole moment?

8. Charge-Charge Interaction r 0= 8.85410-12 C2/ (N●m2) When might we have charge-charge interactions?

9. Charge-Dipole Interaction + q - p + What is q?

10. Dipole-Dipole Interaction Since we have two different vectors, there are two angles, and so the angular component becomes complicated (see page20) + - + - The angular component is interesting when one has restricted motion, but otherwise only the radial component is essential Why is the angular component not interesting when one has unrestricted motion? When might restricted motion by interesting?

11. Npole-Mpole Interaction In general, when there are different “poles” interacting, the interaction energy has a r-dependence that increases with increasing order of the pole. Why are we only considering dipoles much? The decreasing range of the electrostatics is why higher order poles are less important, especially in biomolecules, where they many charges and dipoles {and quadrupoles around}

12. Induced Dipoles When a molecule is placed in an external field, the electron distribution is distorted For example: when a molecule is placed in water, the electric fields from the water molecules will change the electron distributions First approximation: with the polarizability being the coefficient

13. Induced Dipoles • When the field is due to a charge • When the molecule has a scalar polarizability, and there is a dipole: Proportionality constant depends on geometry if fixed; 2 if thermal motion

14. Induced Dipoles Precise calculation requires high-quality QM calc; form from radiation and matter Included as part of vdW interactions

15. Thermal Averaging: ion-dipole • Recall: At nonzero finite temperature, thermal energy can result in the • population of multiple states inside an ensemble • What does this mean? • We have to consider the statistical weight of each possible orientation • Integrate to determine the mean value of p in the direction of the field:

16. Thermal Averaging: Results • In the high T approximation: • What is the high T approximation? • When is the high T approximation realistic? • This means that the mean Energy is • This means that the mean Energy is:

17. Thermal Averaging: Dipole-Dipole • In the high T approximation: • Note the range! Why don’t I consider thermal motion with charge-charge interactions?

18. Hierarchy Fixed Thermal Ion-ion Charge-dipole Dipole-dipole Charge-molecule Dipole-molecule Induced dipole-induced dipole