Intermolecular Forces “Review” of electrostatics -> today Force, field, potentials, and energy Dipoles and multipoles Discussion of types of classical electrostatic interactions Dr. Fetrow will do hydrogen bond and inclusion in force fields

Electromagnetic force One of the four fundamental forces of nature Responsible for the vast majority of what we observe around us The best-understood and best-tested of the forces of nature Almost* all interactions we care about in biology come from electrons Intermolecular forces can be divided into three types: Direct charge interactions Van der Waals interactions -> interactions between fluctuating charge distributions Pauli interactions -> electrons don’t like to be onto of each other

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

Electric Fields Electric Field is the ability to exert a force at a distance on a charge It is defined as force on a test charge divided by the charge – – –Small test charge q

Potential Energy of charges Suppose we have an electric field If we move a charge within this field, work is being done Electric Field E charge q Electric Fields are doing work on the charge If path is not a straight line, or electric field varies you can rewrite this as an integral

Electric Potential Electric Field E Point A Point B Path you choose does not matter. (conservative) Factor out the charge – then you have electric potential V Electric potential, and the electrostatic energy have the same relation as do the force and electric field

Dipoles A dipole is a postive and negative charge separated by a distance d Commonly found in molecules! Though the distances and charges are much smaller! q 1 = +1  C 5 cm 10 cm q 2 = -1  C Dipole moment is qd. It is a vector! Why don’t the charge fly together?

Electric Dipoles The electric dipole moment, p, of a pair of charges is the vector directed from –q to +q and has magnitude d*q If we place the dipole in an external field, then there is a torque on the dipole. - + Each charge has a force of magnitude qE on it, and a lever arm of size d/2.  - + d

Electric Dipoles and torque - +  F=qE p p=dq Therefore, The dipole rotates to increase the alignment with the field. So the torque vector is:

Electric Dipoles and Energy - +  p So, Work is required to rotate the dipole against the field. The work is transformed into potential energy, so Pick a convention for  i and,,

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?