Intermolecular Forces:Electrostatics “Dielectrics Different classical electrostatic interactions

Coulomb’s Law Like charges repel, unlike charges attract Force is directly along a line joining the two charges k e =  10 9 N  m 2 /C 2 q1q1 q2q2 r  0 =  C 2 / (N●m 2 ) This can change when not in vacuum

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

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

Multiple charges q1q1 q2q2 q3q3 r1r1 r2r2 r3r3 We can handle multiple charges by considering each on explicitly, or by a multipole expansion

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

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?

Charge-Charge Interaction r  0 =  C 2 / (N●m 2 ) When might we have charge-charge interactions?

Charge-Dipole Interaction - +  p + What is  ?

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 When might restricted motion by interesting? Why is the angular component not interesting when one has unrestricted motion?

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. 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} Why are we only considering dipoles much?

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

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

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

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:

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

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

Hierarchy FixedThermal Ion-ion Charge-dipole Dipole-dipole Charge-molecule Dipole-molecule Induced dipole-induced dipole