THEORETICAL PHYSICAL CHEMISTRY TU DARMSTADT
Practical 2
Simulation of 300 SPC/E Water molecules with a Molecular
Dynamics Simulation Package (YASP)
Part A Running Water Simulation
Outline:
1. Introduction.
2. Getting the water-forcefield for the SPC/E model. How to
build a topology file.
3. Starting values for the atomic coordinates and velocities.
How to build a coordinates file.
4. Running molecular dynamics with all the input data using
YASP.
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THEORETICAL PHYSICAL CHEMISTRY TU DARMSTADT
Introduction
YASP is a molecular dynamics simulation package originally written by the Prof. Dr. Florian Müller-Plathe.
This simulation package is mainly used to study static and dynamical properties of a one component fluid or a
mixture of molecules set in a simulation cell at the atomistic scale. The Molecular Dynamics (MD) technique is
a scheme that allows one studying the time evolution of a classical system of N particles in the simulation cell of
volume V. In such simulations, the total energy E is a constant of motion. However, by modifying the equations
of motion, simulations in other statistical ensembles than NVE, namely NVT (constant volume-constant
temperature) or NPT (constant pressure-constant temperature) can be carried out. The YASP simulation package
is capable of handling all those ensembles.
After performing the MD simulations one needs to analyse the trajectory produced. The YASP simulation
package offers the possibility of analysing both the static and dynamical properties. In the second part of the
tutorial, you will have to calculate two important properties of water namely the radial distribution function
(structural property) and the diffusion coefficient (dynamical property). In a third part, you will study the
temperature effect on diffusion.
The MD program of YASP needs three different input files as it is illustrated in the sketch below: The topology
file that contains the force field parameters of a given molecule, the coordinates file that contains the initial
coordinates of the system’s particles and a file containing the simulation parameters (duration, statistical
ensemble…).
In the present tutorial, calculations deal with a system of 300 molecules of water at different temperatures and a
1 atmosphere pressure. Follow the instructions in order to carry out the MD simulations as well as the
subsequent analysis with the simulation package.
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THEORETICAL PHYSICAL CHEMISTRY TU DARMSTADT
How to build a topology file
The information regarding the topology file can be found in the following website
http://www.theo.chemie.tu-darmstadt.de/group/services/yaspdoc/yaspman/files_topology.html
We start with the force field parameters for the SPC/E model by Berendsen:
A water molecule is defined as depicted in the following picture:
The form of the potential is given by the addition of the Lennard-Jones potential and the Coulombic potential.
The equation for the interaction potential is given by the following function:
ε ij = The well depth of the Lennard Jones potential = ε i ε j .
σ ij =
σi + σ j
, where σ i and σ j are the radius of the atoms i and j.
2
qi and q j are the charges beared by atoms i and j.
ε = Dielectric constant.
ε 0 = Permitivity of vacuum.
rij = Distance between two atoms i and j.
rcutoff = Cutoff radius beyond which no explicit pair interactions are computed
The SPC/E model of water is a rigid water model, which means that the distances H-H and O-H are constrained.
Those distances are given in the above figure of the water model. The constraints are actually resolved by the
SHAKE algorithm in YASP-MD. In the SHAKE algorithm, the bond lengths are kept constant using an iterative
scheme.
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THEORETICAL PHYSICAL CHEMISTRY TU DARMSTADT
All the information dealing with the interaction parameters and the constraints are called topological
information and should be written in a topology file read by YASP-MD at the beginning of a simulation. The
information for one water molecule has to be saved in a file, say water.tp (.tp for topology). That file could
look like the following:
title:
water
atoms:
3
1 'H' 1.007825 0.0 0.0 0.4238
2 'H' 1.007825 0.0 0.0 0.4238
3 'O' 15.9949 0.65017 0.3166 -0.8476
constraints:
3
1 1 3 0.1
2 2 3 0.1
3 1 2 0.163
modified_nonbonded:
3
1 1 2 0 0 0 0
2 1 3 0 0 0 0
3 2 3 0 0 0 0
basta:
The first part “atoms” gives out the information of non-bonded parameters of each atom, the sequence of the
parameters in each line is:
atom index, atom type, molar mass(g/mol), ε (kJ/mol), σ(nm), partial charge.
The second part “constraints” gives out the bonded parameters of each pair of atoms bonded, the sequence of
the parameters in each line is:
Index, atom1, atom2, bonded-length between atom1 and atom2
The third part “modified_nonbonded” gives out modified non-bonded parameters for a pair of atoms. The nonbonded potential between these two atoms are calculated with the parameter listed in this part, not those in the
first part (“atoms” part) any more. In most situations, the non-bonded parameters need to be modified when the
two atoms belong to the same molecule, and their distance is close enough, mostly less than or equal to 3 bonds.
The sequence of the parameters in each line is:
Index, atom1, atom2, ε12 (kJ/mol), σ12(nm), partial charge of atom1, partial charge of atom2.
Now we have created the topology of a single molecule. But YASP-MD needs information about all the
molecules of the sample we aim simulating. Thus we have to multiply the information of the water.tp file by
using the program jointp:
jointp 300 water.tp > md.tp
This will generate a file md.tp containing the topology of 300 SPC/E water molecules. This file must be edited
in order to add two lines so that the reaction field methodology would be applied. According to that method, a
cavity with explicitly handled coulomb-forces is surrounded by a continuum having the dielectric constant
epsilon = 72 of water at normal conditions:
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THEORETICAL PHYSICAL CHEMISTRY TU DARMSTADT
# topology file cobbled together by:
# jointp 300 water.tp
reaction_field_dielectric:
72
atoms:
900
1 'H' 1.007825 0 0 0.4238
2 'H' 1.007825 0 0 0.4238
3 'O' 15.9949 0.65017 0.3166 -0.8476
4 'H' 1.007825 0 0 0.4238
.
.
.
How to build a coordinates file
http://www.theo.chemie.tu-darmstadt.de/group/services/yaspdoc/yaspman/files_coordinate.html
The topology file is now ready. In order to start the simulation we should provide YASP-MD with an initial
configuration of the water system. This will be realized by setting 300 water molecules on a cubic lattice. If one
assumes we want to simulate a sample having a density of 1000 kg/m3, the box dimension will be approximately
of 2.1 nm. Before we create the final sample by replicating a water molecule, we first have to write the file
water.co as input for the tool position of the YASP package. This file gives information about the
coordinates of a single water molecule and the simulation box size. The title: keyword holds a comment, the
box: the lengths of the cubic box vectors x, y and z. In the coordinates: section the integer number of
atoms per molecule precedes the data lines. Each line has the running atom number, the label and the xyz
coordinates of the atoms in nm. The file is closed with the word basta:
title:
water
box:
+2.100000e+00
coordinates:
3
1
'H'
2
'H'
3
'O'
basta:
+2.100000e+00
+2.100000e+00
+1.000000e-01
-3.255681e-02
+0.000000e+00
+0.000000e+00
+9.455185e-02
+0.000000e+00
+0.000000e+00
+0.000000e+00
+0.000000e+00
Now replicate the water molecule from water.co 300 times to create md.co:
position 300 water.co md.co
The program prompts for the cubic box-dimension (in nm):
Create lattice coordinate file
-----------------------------Number of molecules: 300
Atom coordinate file: water.co
Lattice coordinate file: md.co
Box size: 2.1
This gives a cubic lattice of 300 water molecules.
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THEORETICAL PHYSICAL CHEMISTRY TU DARMSTADT
Running molecular dynamics with YASP
At this point the force-field and the initial configuration are ready to use. Now YASP-MD needs to know about
some parameters to determine the course of the simulation. This can be done with the script mkmdinput. (For
almost all questions you can use the default value by pressing return
.) Type:
mkmdinput
file name [md.in]:
#
# YASP/MD input file generated by mkmdinput (Thu May 14 20:24:09 MET DST 1998)
#
title (anything up to 72 characters): SPC/E water_300K
number of atoms (no default): 900
cutoff for nonbonded interactions [0.9 nm]:
cutoff to which the neighbour list is calculated [1.0 nm]:
neighbour-list update frequency [every 15 steps]:
set the neighbour list size manually?
(not necessary for systems of uniform density) [n/y]:
time step [0.002 ps]:
number of time steps [1000]: 10000
temperature, used
1. to initialise velocities (ignored for continuation runs)
2. as bath temperature in constant temperature simulations,
if selected [300 K]:
use constant-temperature MD (weak-coupling)? [y/n]: y
temperature coupling time [0.2] :
temperature increment [0 K / time step] :
use constant-pressure MD (weak-coupling)? [n/y]: y
1. couple isotropically to total pressure
2. couple to pressure in x,y,z separately
enter number: 1
bath pressure [101.3 kPa] :
pressure increment [0 kPa / time step] :
coupling time [0.5 ps] :
isothermal compressibility [1.0e-6 1/kPa] :
printout frequency [every 100 steps]: 50
sample properties for averages [every 100 steps]: 50
calculate rolling averages [every 100 steps]: 50
verbose level (min:0, max:5, default:1): 5
write a trajectory file? [y/n]: y
write trajectory frame [every 100 steps]: 50
dump restart file [every 100 steps]: 500
stop centre-of-mass translation [every 1000 steps]:
set a time limit [n/y]: y
maximum cpu time [360000 seconds]:
basta:
To carry out the molecular dynamics with YASP, you need use command mkmdjob to build a script file, say,
named as “run”:
mkmdjob
file name [run]:
MD input file: md.in
input coordinates file: md.co
topology file: md.tp
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THEORETICAL PHYSICAL CHEMISTRY TU DARMSTADT
external field specification file (cr for no external field file):
position restraints file (cr for no position restraints file):
output coordinates file: mdout.co
MD output file: md.out
trajectory file: md.trj
save job script ? (yes: give filename /no: '<cr>'): run
submit job ? (y/n): n (note: if you type “y”, job will be submitted directly)
NOTICE: Once one already has “md.in” and “run” files, there is no need for running
commands “mkmdinput” and “mkmdjob” again and again to obtain new “md.in” and
“run” files. What one needs to do is only to modify the old “md.in” and “run” files with
“kate” or “vi”, changing some of the parameters (md.in) or file names (run) to what is
needed.
If you read the run file created, the format will be
#!/bin/csh
# MD job script generated by mdjob
rm -f fort.* >& /dev/null
ln -s md.tp
fort.3
ln -s md.in
fort.4
ln -s md.out
fort.7
ln -s md.trj
fort.8
yaspmd < md.co | proper > mdout.co
rm -f fort.* >& /dev/null
By typing ./run & , you will run the molecular dynamics in the background directly on the workstation. You
can check it by typing top.
When the program finished the 10000 steps (this should take only some minutes) you can have a look at a first
and simple result. Use the program yasp2xyz to transfer the file format from *.co to *.xyz, which is the
format needed for visualization programs. Transfer the file md.co and mdout.co to xyz format and see how
the molecule positions have changed during the simulation.
yasp2xyz < file.co > file.xyz
you can find the manual of yasp commands in
http://www.theo.chemie.tu-darmstadt.de/group/services/yaspdoc/manfiles/index.html
The configurations may appear as below:
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THEORETICAL PHYSICAL CHEMISTRY TU DARMSTADT
If you check the mdout.co file with “kate” or “more”, two lines of data are listed for each atom. The first line
indicates coordinates, the second one shows velocities in x, y, z direction separately. The initial file md.co does
not exhibit velocities, which will be randomly taken from a Gaussian distribution appropriate for the selected
temperature by the YASP-MD program while starting the run.
Now we are almost finished with the first part of the water-simulation tutorial. After 10000 steps the system
should have reached equilibrium. Conserve the md.out file for a further analysis during Part B by copying this
file in md1.out. This can be achieved by:
cp md.out md1.out.
Since the system is equilibrated, a production run can be initiated. It will be analysed in Part B. This run will be
80ps long. So, edit the file md.in and change the number_of_time_steps: keyword to 40000, copy the file
mdout.co to md.co and run the program again. Check the status and progress of the simulation by doing
tail -f md.out
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THEORETICAL PHYSICAL CHEMISTRY TU DARMSTADT
Practical 2
Part B Water Simulation Analysis
Outline:
5. Gaining Equilibrium
6. Radial Distribution Functions (RDF)
7. Diffusion Coefficient
8. Temperature dependence
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THEORETICAL PHYSICAL CHEMISTRY TU DARMSTADT
5. Gaining Equilibrium
The 20 picosecond long equilibration run should be analyzed. The tool plot_values allows one to visualize
the temperature's or other's time progressions using gnuplot. The keywords avalaible are:
temp
Temperature
dens
Mass density
etot
Total energy
pot
Potential energy
press
Pressure
nonbond
Nonbonded energy
box
Box volume
nonbondinter
Nonbonded inter energy.
You can type
plot_values temp md1.out
to get a plot of the temperature time-dependence, for example. The plot below shows a relaxation toward the
adjusted 300K temperature. Note that the plot displays the temperature in K versus recorded steps.
A relevant quantity to “see” how molecules interact from the initial configuration and to decide whether the
system has reached an equilibrium configuration is the total energy. Plot the total energy of the equilibration run
using the plot_values tool and estimate in real time (not in number of records) the time required by the total
energy to stabilise around an averaged minimum value.
Once the system is equilibrated, it is possible to get average quantities from the 80ps long production run. The
production trajectory will be used in the present part of the practical.
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THEORETICAL PHYSICAL CHEMISTRY TU DARMSTADT
6. Radial Distribution Functions (RDF)
In order to analyse the structure of a system, one is interested in quantifying the distribution of particles over
space and especially how the positions of those particles are correlated. The quantity g(r), which is called radial
distribution function (RDF), is referred to as a pair correlation function or pair distribution function, and the
product ρg(r) (ρ being the density of the system) gives the conditional probability density that a particle will be
found at a distance r from another.
Now the tutorial explains some ways to get simple structural and dynamical information about the 300 water
molecules system. Firstly, we start with the calculation of the radial distribution functions (RDF) or g(r). The
tool mixed_rdf will be used to calculate them.
mixed_rdf uses a template file, called for example rdf.tpl, with two sorted sets of atoms. The rdf is
calculated for every combination of atoms from the two sets and written as an output. One needs to pay attention
to the syntax:
N1 = number of atoms in set 1
atom nr 1 of set 1
atom nr 2 of set 1
.
.
atom nr N1
N2 = number of atoms in set 2
atom nr 1 of set 2
atom nr 2 of set 2
.
.
.
atom nr N2
You can use command lines, such as echo and awk to prepare the rdf.tpl file from the md.tp file. Follow
the example to produce the rdf.tpl file for oxygen-oxygen pairs of 300 molecules:
#write number of atoms in first set, remember to change 300 to 600 when rdf of “H” is
calculated instead of “O”.
echo 300 > rdf.tpl
# print atom bin numbers of Oxgen for first set
awk '/O/ {print $1}' md.tp >> rdf.tpl
#write number of atoms in second set, remember to change 300 to 600 when rdf of “H” is
calculated instead of “O”.
echo 300 >> rdf.tpl
# print atom bin numbers of Oxgen for second set
awk '/O/ {print $1}' md.tp >> rdf.tpl
here “>>” means to write continuously in the file, and would not replace the contents which already existed in
the file. Run the program:
mixed_rdf 300 0.8 md.trj < rdf.tpl > gofr.dat
With 300 as the number of points, on which g(r) is evaluated on the interval [0,0.8]. Have a look at gofr.dat with
xmgrace and compare your curve to the one below. Here we show the oxygen-oxygen pair distribution (solid
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THEORETICAL PHYSICAL CHEMISTRY TU DARMSTADT
line and column 2 in the gofr.dat file) together with its spatial integral (dashed line, column 3). Actually, the
spatial integral is computed as:
Where gOO(r) is the RDF for oxygen-oxygen correlation.
What is the meaning of that integral? What quantity does it give if ρ is a number density? (Hint: What kind of
operation does one do while integrating?)
To make a plot of the datafile gofr.dat with xmgrace, there is to type:
xmgrace –block gofr.dat –bxy 1:2 –bxy 1:3 –world xmin ymin xmax ymax
The whole sentence means that “plot column1 of the datafile as x, column2 as y1, column3 as y2, with x
ranging from xmin (for example, here can be 0.2) to xmax (here can be 0.8), y ranging from ymin (here can be
0) to ymax (here can be 4).
NOTICE: xmin, xmax, ymin, ymax are specific data denoting the minimum and maximum numbers on
the x and y axis
.
7. Diffusion Coefficient
In this part, we quantitatively characterize water diffusion under equilibrium conditions by computing its selfdiffusion coefficient. We use the following definition (first derived by Einstein):
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THEORETICAL PHYSICAL CHEMISTRY TU DARMSTADT
The quantity
is called mean squared displacement (MSD) and is calculated as
It should be noticed that we proceed by measuring the distance travelled in time t for every particle i considered
independently and we finally compute an average over the whole set of N water molecules.
A subscript “1” is written in the MSD definition because we compute the diffusion of a labelled molecule
among otherwise identical molecules and finally average over the whole set. For this reason too, we call the
diffusion coefficient self-diffusion coefficient.
The asymptotic limit
in the definition means that MSD and time are proportional after an initial transient time of which we a priori
ignore the duration. This time is actually the time required to relax an initial regime and install the diffusion one.
At short time, a particle does not encounter its neighbours, and it moves freely from its initial direction of
motion. The motion is then inertial and a displacement during t will be
such that the MSD would write
But it takes a finite amount of time for a force to alter the initial velocity of a particle. The diffusive motion is
characterized by the particle experiencing random fluctuating forces due to its environment. This is valid for a
longer time scale and the MSD is then proportional to time. Such behaviours can be illustrated on a full
logarithmic plot reporting the MSD with respect to time.
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THEORETICAL PHYSICAL CHEMISTRY TU DARMSTADT
The time at which the MSD becomes parallel to the slope 1 can be considered as the beginning of the
asymptotic limit, in other words, the diffusion regime.
To assess the diffusion coefficient of water, we first calculate the mean-square-displacement of all oxygens in
our sample. This does not give us exactly the value of water diffusion but is rather close to our aim, if we
neglect the contribution of the hydrogen to the centre of mass.
We make use of the program msd which needs again a template file. This is rather simple, and can be made by
echo 1 3 > msd.tpl
The first integer is the number of sites (one, only the oxygen) the second number the site index in a molecule.
We can run the program:
msd 300 md.trj < msd.tpl > msd.dat
300 is the number of molecules, and data are read from md.trj. This generates msd.dat. Notice that there are 5
columns in msd.dat, with column 1 as time, column 2, 3, 4 as mean squared displacement in x, y, and z direction
separately, column 5 as the sum of the msd in x, y, and z direction. Thus you can plot msd vs. time using
column 1 as x, column 5 as y:
The diffusion coefficient can be obtained by using the tool diffcoeff. By It is necessary to indicate which part
of the MSD should be eliminated from the computation bu using the –l option. For instance here, we will
remove the 5 first picoseconds in order to fit the curve in the diffusion regime and we get the results by typing:
diffcoeff -l 5 < msd.dat
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THEORETICAL PHYSICAL CHEMISTRY TU DARMSTADT
Diffusion coefficients (cm^2/s)
# Dxx: 2.1886e-05 intercept: 0.046335 nm
# Dyy: 2.24329e-05 intercept: 0.0491062 nm
# Dzz: 2.38824e-05 intercept: 0.0402674 nm
# mean(Dxx,Dyy,Dzz): 2.27338e-05 stddev(Dxx,Dyy,Dzz): 1.03164e-06
# <D>: 2.27338e-05 intercept: 0.0786116 nm
2.27338e-05 1.03164e-06
Thus the diffusion coefficient is about 2.3e-05 cm^2/s.
Now try a different template file:
echo 1 1 > msd2.tpl
Here the first integer (the number of sites) is one the second number 1 the site index corresponding to the
hydrogen. We can run the program again:
msd 300 md.trj < msd2.tpl > msd2.dat
and compare the results with the previous ones.
It is also possible to plot the time evolution of the MSD logarithm with respect to the time logarithm. This can
be achieved by transforming the time in its logarithm and the MSD in its logarithm too by the command:
awk
‘{print log($1),log($2)}’
msd.dat > msd-log.dat
One is then able to check that the “long” time behaviour of the MSD is linear with a slope of 1 and follows the
Einstein law of diffusion.
The previous awk line command will be successful only if one tries to compute the logarithm of strictly
positive numbers. Check that the first line of your msd.dat file does not contain any zero value. In case there is
one, simply remove that first line.
8. The diffusion as an activated process
The diffusion can be modelled as an activation process where molecules have to overcome an energy barrier
related to intermolecular interactions in order to diffuse among others in the liquid. Therefore, the temperature
dependence of the diffusion coefficient may be modelled with an Arrhenius law:
 E 
D = D0 exp − a 
 RT 
It is assumed here that the activation energy Ea is independent of temperature. This is not strictly correct;
however, this assumption can be valid if we restrict ourselves to a limited range of temperature. Furthermore,
by computing the temperature dependence of the diffusion coefficient, it is possible to obtain the activation
energy for diffusion in the temperature range sampled.
You have now to use the experience you gained during the last parts of the practical. You have to compute the
diffusion coefficient of water at three other temperatures, namely 285K, 307K and 315K. In order to minimize
your own task and let the computational power work, create three new directories corresponding to each
temperature. Write a common script that you will copy in each of the directories. The script should carry out the
following tasks:
1. Run an equilibration simulation of 20ps.
2. Using the final configuration of the equilibration stage as an input, produce a 80ps long simulation.
3. Compute the water oxygen diffusion coefficient and put the result in a file named diff-coeff-Txxx.dat
where xxx is the temperature corresponding to the working directory.
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THEORETICAL PHYSICAL CHEMISTRY TU DARMSTADT
It is advised to make a draft of your script and write it after. Note that you will have to change by hand the
reference temperature in the input file for each temperature.
The computational time required to achieve the set of three simulations is approximately one hour.
Gather your results in a file named D-T.dat where the first column will be the temperature, the second one
will be the diffusion coefficient and the third one the error bar to the diffusion coefficient.
Once finished, you are asked to produce 2 plots: A first one where the diffusion coefficient is reported with its
error bars with respect to temperature.
This can be done by using the program gnuplot. Type:
gnuplot
Then type:
plot “D-T.dat” u 1:2:3 w errorbars
Label the axis using the commands set xlabel and set ylabel
set xlabel ‘Type here the label of xaxis’
set ylabel ‘Type here the label of yaxis’
It is also possible to modify the ranges of each axis by using the commands set xrange and set yrange:
set xrange [xmin;xmax]
set yrange [ymin;ymax]
In order to confirm and view the last modifications, always type
replot
Type the following commands in order to produce a Postscript file that you will include in your report:
set term postscript color
set output ‘filename.ps’
replot
set term x11
To quit gnuplot:
exit
In order to compute the activation energy to diffusion, the Arrhenius-type law described above can be written:
ln D = ln D0 −
Ea
RT
Therefore the activation energy can be obtained from a linear regression of the plot where the logarithm of D is
plotted against the inverse of the temperature 1/T.
Write a file D-T-log.dat where the first column will be 1/T and the second lnD.
The linear regression can be achieved by gnuplot. Open a gnuplot session. Do the plot by typing:
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THEORETICAL PHYSICAL CHEMISTRY TU DARMSTADT
plot “D-T-log.dat”
Carry out the linear regression typing :
fit a*x+b ‘D-T-log.dat’ via a,b
Collect the results and compute the activation energy from the slope of the regression. Plot the result of the
regression:
plot a*x+b, ‘D-T-log.dat’
Produce a Postscript file of your result.
The activation energy to diffusion is related to the strength of intermolecular forces. A well-defined quantity that
is also related to intermolecular forces is the heat of vaporization. Molecular dynamics simulations allow one to
obtain such a thermodynamic quantity. It can be extracted from the md.out file by the tool vapor:
vapor md.out 300
where 300 is the number of water molecules. The result is given in kJ/mol.
Compute the heat of vaporization at each temperature. Which one would you choose to be the closest to the
experimental one? Why? Compare the result of your computation to an experimental value.
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THEORETICAL PHYSICAL CHEMISTRY TU DARMSTADT
REPORT (Max. 2 pages)
1.
Plot the total energy of the equilibration run at 300K with respect to time. Give an estimate of the time
required to stabilize this quantity around an average minimum value. Is that time shorter than the
equilibration length?
2.
Use the production run to give the average density of the system at 300K.
3.
Plot the intermolecular part of the following radial distribution functions (RDFs):
Oxygen-oxygen
Oxygen-hydrogen
Hydrogen-hydrogen
4.
At which distance is located the first peak of the oxygen-oxygen RDF? Compare it to the Lennard-Jones
radius of the model of oxygen used here.
5.
An important length of water as a physical system can be estimated from the oxygen-hydrogen pair
distribution function (O-H RDF). Which one is it? At which value of the distance oxygen-hydrogen do you
locate it?
6. What kind of information is available from the plot of the spatial integral from the oxygen-oxygen RDF?
How many neighbors does a water molecule have in its first neighbor shell?
7.
Taking into account the number of first neighbors you found, the existence of hydrogen bonds and the
distances you can extract from the RDFs, imagine and draw a 3-dimension sketch of the structure of the
immediate surrounding of a water molecule.
8. Plot the mean-squared-displacement (MSD) of oxygen with respect to time in linear axis at 300K. Plot the
logarithm of MSD with respect to the logarithm of time.
At which time will you begin to fit the MSD curve you obtained to compute the diffusion coefficient?
Compute the diffusion coefficient of hydrogen atoms at 300K and oxygen atoms at 285K, 300K, 307K and
315K. Discuss the results at 300K.
Plot the diffusion coefficient of water oxygen with respect to temperature.
Plot the curve of the variation of lnD with respect to 1/T and the result of your linear regression.
Which value of the activation energy to diffusion do you obtain?
Which estimate of the value of the heat of vaporization do you obtain? Justify your choice.
Compare the two last quantities and discuss their ordering.
Compare qualitatively the diffusion activation energy you would expect in the liquid phase in a range of
temperature close to the melting point to the one obtained at a temperature higher than the standard one?
Summarize your results below:
300K
Density (Water)
Diffusion Coefficient (Water oxygen)
Diffusion Coefficient (Water hydrogen)
Temperature
Simulation
Exp.
Water diffusion coefficient (simulation)
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