Molecular Dynamic Simulation of united atom liquid n-hexane

THEORETICAL PHYSICAL CHEMISTRY TU DARMSTADT
Questions
1. The torsion potential has the following analytic form:
K n
V ( τ ) =
τ
2
3
∑
n=
1
[ 1−
cos( n(
τ − ]
a. Plot the torsion energy as a function of the dihedral angle varying from 0 to 360 degree for
both the potential you used on the same graph (notice that τ0 is 180 for both the potentials). This can
be achieved by using the program gnuplot. Open a gnuplot session by typing:
gnuplot
then type
f ( x)
= K
K
3
And
1
* 0.
5*
( 1
+
cos( 3.
14159 / 180*
( x))
+ K
* 0.
5*
( 1+
cos( 3*
3.
14159 / 180*
( x)))
g(
x)
= K
K
'
3
'
1
* 0.
5*
( 1
* 0.
5*
( 1
+
+
plot [0:360] f(x), g(x)
cos( 3.
14159 / 180 * ( x))
+ K
cos( 3*
3.
14159 / 180 * ( x)))
Prepare a postscript file of your plot:
set terminal postscript color
set output ‘torsions.ps’
replot
If you need to go back to your plot
set terminal x11
Quit gnuplot by typing exit.
2
'
2
* 0.
5*
( 1
* 0.
5*
( 1
0 ))
−
−
cos( 2*
3.
14159 / 180*
( x)))
+
cos( 2 * 3.
14159 / 180 * ( x)))
+
b. What are a trans and a gauche conformations? Suppose the plot represents the torsion
potential of the central torsion angle of n-hexane. Use Newman projection to describe the
conformations corresponding to the maxima and the minima observed in the figure.
2. Did the two torsion potentials you used yield different angle distributions? Explain why by
considering the two plots of the torsion potential and especially the barrier energy to overcome to pass
form a trans configuration to a gauche configuration.
3. a. Plot the torsion state autocorrelation functions for 3 dihedral angles (head/tail and central) and the
two different potentials.
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