Transcript Lecture #3

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
q1
q2
r
ke q1q2
Fe 
2
r
ke = 8.988109 Nm2/C2
-12 C2/ (N●m2)
q1q2

=
8.85410
0
ˆ
Fe 
r
2
4 0 r
•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
+ +
– ––
+ +
+
F
Small test
charge q
E  F /q
Potential Energy of charges
charge q
•Suppose we have an electric field
•If we move a charge within this
field, work is being done
•Electric Fields are doing work on Electric Field E
the charge
W  F  s  qE  s

U  W  qE  s  q E  s

•If path is not a straight line, or electric field varies you can
rewrite this as an integral
U   q  E  ds
Electric Potential
Point A
•Path you choose does not matter.
(conservative)
B
U  q  E  ds
A
•Factor out the charge – then you
have electric potential V
Electric Field E
Point B
U
V 
   E  ds
q
A
B
E  F /q
•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!
q2 = -1 C
10 cm
Dipole moment is qd.
It is a vector!
5 cm
q1 = +1 C
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
+
d
If we place the dipole in an external field, then there is a torque
on the dipole.
q
-
+
Each charge has a force of
magnitude qE on it, and a
lever arm of size d/2 .
Electric Dipoles and torque
q
  Fd sin q
+
-
F=qE
p
The dipole rotates to increase the alignment Therefore,
with the field.
p=dq
  pE sin q
So the torque vector is:
~
~
~
  pE
Electric Dipoles and Energy
q
+
~
~
~
  pE
-
p
Work is required to rotate the dipole
against the field.
So,
dW  dq  pE sin qdq
The work is transformed into potential energy, so
Pick a convention for qi and,,
q
f
U 
q pE sin qdq  pE (cos q
i
i
 cos q f )
~
~
U   pE cos q   p  E
Multiple charges
q3
r3
r1
q1
q2
r2
ke qi
V 
ri
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:


Pi (cos q )  

4 0 i 0
r
q

i
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
q1q2
Ep 
2
4 0 r
0 = 8.85410-12 C2/ (N●m2)
When might we have charge-charge interactions?