# Force Field Exercise

```Conformational Energy and Force Fields
MOBIL Summer School, Aarhus University, August 13 2009
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Propene
Energy
Conformational energy
Molecular Subparts
Atomgroups and –types
Potential Energy Function
Bonding Interactions
Non-bonding Interactions
Parameters
Energy => Force
Force Field
Potential Energy Surface
Force Field Exercise
8
7
4
3
1
9
2
5
6
Force Field Exercise
Q1 – Bond Stretch
The contribution from bond stretching to the potential energy function can be described as
Ebond  12 k  r  r0 
2
Four bond stretching functions are seen on the graph. The solid line represents the stretching of the single
C-C bond in propene. Double bonds are typically shorter and stronger than single bonds.
Which of the other three lines represent the stretching of the double C=C bond in propene and why?
4
2
Energy
3
3
2
1
1
0
1.2
1.3
1.4
1.5
r/Å
1.6
1.7
Q2 – Bond Rotation
The contribution from bond rotation to the potential energy function can be described as
Ebondrot   12 Vn 1  cos n 
n
where n is the number of energy minima encountered during a 360° rotation around the bond.
Two bond rotation functions are seen on the graph. One of them represents the H6-C2-C3-H9 contribution
to the rotation around the single bond in propene, the other represents the H5-C1-C2-H6 contribution to
the rotation around the double bond.
Which line represents the single bond, which represents the double bond and why?
12
2
Energy
8
4
1
0
0
60
120
180
240
ω/°
300
360
Advanced follow up: Here was shown only one contribution to the potential energy profile for rotating
around the bonds. How many interactions contribute in fact to the rotation around the single and the
double bonds?
Q3 – VdW Interactions
The contribution from Van der Waals interactions to the potential energy function can be described as
EvdW
6
  Rmin 12
 Rmin  
  
 2
 
  r 
r

 

The graphs represent the vdW interaction between two hydrogens and between a hydrogen and a carbon
(sp3).
Which line represents the H-H interaction, which represents the C-H interaction and why?
0.25
0.2
Energy
0.15
2
0.1
0.05
0
-0.05
1
2
3
4
5
r/Å
Q4 – Force Field
What constitutes a force field, and why does it make sense to call it a ”force field”?
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