Molecular dynamics tutorial
with applications to aqueous systems
Garold Murdachaew
1400-1600, 13-14 October 2015
Chemicum A122
1
Outline
 Why should I learn about molecular simulations?
 Why should I learn about aqueous systems?
 CP2K package for molecular simulations
 VMD package for molecular visualization and analysis
 gnuplot and bash scripts and fortran codes for analysis of MD trajectories
 Hands-on MD exercises at CSC (taito) and on your local linux machine using
CP2K and VMD
2
Why should I learn about molecular simulations?
 Another tool in your toolbox to study systems more complex than clusters
 Simulations are computer experiments
 Simulations allow one to see atomic detail and discover reaction mechanisms
 Simulations allow one to model difficult conditions or processes:
 not possible in lab (e.g., high P, high T, etc.)
 too dangerous (e.g., deactivation/breakdown of nerve agents)
 too expensive
 Always keep in mind:
“The purpose of computing is insight, not numbers.”
– Richard Hamming, Numerical Methods for Scientists and Engineers
3
Why should I learn about aqueous systems?
 Water is ubiquitous
 Atmospheric and environmental
chemistries (one example: molecular
adsorption and chemical reactions on wet
and icy surfaces can lead to ozone holes)
 Catalysis
 Astrochemistry

Simulated production of biological precursors on
ice grains in the interstellar medium:
http://pubs.acs.org/doi/abs/10.1021/jp502738x
(see picture 1)
 Water is necessary for life
 Biochemistry and biology

Ion channels

Protein folding to native structure
(see picture 2):
http://www0.cs.ucl.ac.uk/staff/d.jones/t42morph.html
 “Liquid water is not a bit player in the
theatre of life, it’s the headline act.”
– Martin Chaplin, London South Bank University,
Water Structure and Science,
http://www1.lsbu.ac.uk/water/
4
The phase diagram of water is complex
5
http://www1.lsbu.ac.uk/water/water_phase_diagram.html
CP2K package for molecular simulations
 CP2K is free, open source (Fortran 2003), capable, and versatile package with a
large, active user and developer base
 Some key parts of CP2K (we will use the bolded capabilities in the exercises)
 FIST: classical molecular mechanics
 Quickstep: density functional calculations
 QM/MM: quantum mechanics and classical mechanics
 Molecular dynamics, Monte Carlo, and much more
 See: http://www.cp2k.org/
 Science with CP2K: http://www.cp2k.org/science
 Upcoming CECAM workshop: http://www.cecam.org/workshop-1122.html
 Previous CECAM workshop: http://www.cecam.org/workshop-273.html
 Tutorials: http://www.cp2k.org/tutorials
 Exercises: http://www.cp2k.org/exercises
 Input manual: http://manual.cp2k.org/trunk/CP2K_INPUT.html
 Google Groups: https://groups.google.com/forum/#!forum/cp2k
 On taito:
module load cp2k-env/2.5
sbatch cp2k_script.bash
6
VMD package for molecular visualization & analysis
 VMD is free to download
 Can be used for visualization and also analysis (gpu acceleration possible)
 Can handle large systems and long trajectories in many formats (xyz, etc.)
 Can produce publication quality snapshots and movies in many popular formats
 Can be run interactively or using a script
 See: http://www.ks.uiuc.edu/Research/vmd/
 Tutorials: http://www.ks.uiuc.edu/Research/vmd/current/docs.html#tutorials
 Documentation: http://www.ks.uiuc.edu/Research/vmd/current/docs.html
 Mailing list for questions: http://www.ks.uiuc.edu/Research/vmd/mailing_list/vmd-l/
 On taito:
module load vmd
vmd system.xyz
or
vmd -e vmd_script.vmd
7
Exercises
 Hands-on exercises at CSC (taito) and on your local linux machine (ask if you
wish to run locally) using CP2K and VMD. (Note that all examples are already
equilibrated but you should confirm this.)
 Structure and dynamics of ambient bulk liquid water using—
 Example 1: Classical potential (exercise4)
 Example 2: Density functional theory (exercise5)
 Calculate: Internal energy (enthalpy); Structure (RDFs); Diffusion coefficient (Einstein
relation); IR spectrum. Compare to experiment.
 Example 3: Rare instance of formic acid dissociation at the air-water
interface studied with DFT (exercise6)
 Timescale of deprotonation; Grotthus migration of the proton defect; Mechanisms; RDFs.
 Extra examples (ask if interested): Minimum energy structures of water
clusters (H2O)n=1-21 from density functional theory; Sulfuric acid deprotonation
on wet quartz surface using DFT; etc.
8
Important CP2K and theory references

Quickstep: http://www.sciencedirect.com/science/article/pii/S0010465505000615 (paper1)

Performance of BLYP-D2 for water and effectiveness in reproducing the hydrogen bond:
http://pubs.acs.org/doi/abstract/10.1021/jp901990u (paper2); see also:
https://en.wikipedia.org/wiki/Hydrogen_bond ; https://en.wikipedia.org/wiki/Water_model

Grotthuss mechanism: http://www.sciencedirect.com/science/article/pii/000926149500905J (paper3); see also:
https://en.wikipedia.org/wiki/Grotthuss_mechanism

Grimme’s DFT-D2: http://onlinelibrary.wiley.com/doi/10.1002/jcc.20495/abstract (paper4) or see:
https://en.wikipedia.org/wiki/London_dispersion_force

Books:

M. P. Allen, D. J. Tildesley, Computer Simulation of Liquids (1989)

Donald McQuarrie, Statistical Mechanics (1976, 2000)

Dominik Marx, Jürg Hutter, Ab Initio Molecular Dynamics: Basic Theory and Advanced Methods (2009)

Mark Tuckerman, Statistical Mechanics: Theory and Molecular Simulation (2010)
View the wiki links; then download and start reading these papers, starting with the Quickstep paper (paper1), while
you are waiting for calculations to finish. Finish the reading at home. papers5,6,7 (see next page) may also be helpful.
Some of you may already have backgrounds in these areas, some do not. Thus I included the wiki links to give a quick
flavor.
9
Recent publications from Halonen group using CP2K
Relevant papers:

Relevant to Examples 1 and 2: Simulated with semiempirical method (NDDO): “Semiempirical
Self-Consistent Polarization Description of Bulk Water, the Liquid-Vapor Interface, and Cubic Ice”
http://pubs.acs.org/doi/abs/10.1021/jp110481m (paper5)

Relevant to Example 3: Simulated with DFT and shows acid deprotonation and Grotthus
mechanism: “Dissociation of HCl into Ions on Wet Hydroxylated (0001) α-Quartz”
http://pubs.acs.org/doi/abs/10.1021/jz4017969 (paper6)

Relevant to Example 3: Simulated with classical potentials and shows molecular scattering :
“Nitrogen dioxide at the air–water interface: trapping, absorption, and solvation in the bulk and at
the surface” http://pubs.rsc.org/en/content/articlehtml/2012/cp/c2cp42810e (paper7)
Other papers:
10

Ice slab and proton hopping example using DFT from Sampsa Riikonen: “Ionization of Acids on the
Quasi-Liquid Layer of Ice” http://pubs.acs.org/doi/abs/10.1021/jp505627n

Simulated with DFT and shows acid deprotonation and Grotthus mechanism: “First and second
deprotonation of H2SO4 on wet hydroxylated (0001) α-quartz”
http://pubs.rsc.org/en/content/articlehtml/2014/cp/c4cp02752c
CP2K example 1: Water with classical potential
@SET BASE_NAME run
@SET ID 01
&NONBONDED
&LENNARD-JONES
&GLOBAL
PROJECT liq
ATOMS O O
PREFERRED_FFT_LIBRARY FFTW
EPSILON 78.198 ! this is K, = 0.155 kcal/mol = 0.650 kJ/mol
PRINT_LEVEL LOW
SIGMA 3.166
RCUT 11.4
RUN_TYPE GEOMETRY_OPTIMIZATION
&END LENNARD-JONES
&END GLOBAL
&LENNARD-JONES
ATOMS O H
&MOTION
EPSILON 0.0
&GEO_OPT
SIGMA 3.6705
TYPE minimization
RCUT 11.4
OPTIMIZER BFGS
&END LENNARD-JONES
MAX_ITER 400 ! 200 is default
&LENNARD-JONES
&END GEO_OPT
ATOMS H H
&END MOTION
EPSILON 0.0
SIGMA 3.30523
&FORCE_EVAL
RCUT 11.4
METHOD FIST
&END LENNARD-JONES
&MM
&END NONBONDED
&POISSON
&END FORCEFIELD
&EWALD
&END MM
EWALD_TYPE spme
ALPHA .44
&SUBSYS
GMAX 25 25 25
&SUBSYS
&CELL
O_SPLINE 6
ABC 12.4138 12.4138 12.4138
&END EWALD
&END CELL
&END POISSON
&COORD
&FORCEFIELD
O
12.25967785390
1.34872474190
12.42975017890 H2O
EMAX_ACCURACY 500.0
H
12.28658481340
1.45497852510
11.43794042330 H2O
EMAX_SPLINE 1.0E15 ! 10000000000.0
H
12.12685964540
2.28501721350
12.78165108500 H2O
EPS_SPLINE 1.0E-9
...
10.52064998830
9.65806143920
9.70630308870 H2O
&SPLINE
&END SPLINE
H
&END COORD
&BEND
&TOPOLOGY
ATOMS H O H
&GENERATE
K 0.
THETA0 1.8
&END BEND
&BEND
!
BONDLENGTH_MAX 2.0
BONDPARM_FACTOR 0.9
&END GENERATE
ATOMS O H H
&END TOPOLOGY
K 0.
&KIND O
THETA0 1.8
ELEMENT O
&END BEND
&END KIND
&BOND
&KIND H
ATOMS O H
ELEMENT H
K 0.
&END KIND
R0 1.8
&PRINT
&END BOND
&BOND
ATOMS H H
&CELL
&END CELL
&END PRINT
K 0.
&END SUBSYS
R0 1.8
&PRINT
&END BOND
&CHARGE
ATOM O
CHARGE -0.8476
&GRID_INFORMATION
&END GRID_INFORMATION
&END PRINT
&END FORCE_EVAL
&END CHARGE
&CHARGE
! RESTART_FILE_NAME ./run-01.restart
CHARGE 0.4238
!&END EXT_RESTART
&END CHARGE
11
!&EXT_RESTART
ATOM H
CP2K example 1: Water with classical potential
As you can see, the cp2k input file can have four
major sections (order of the sections is not
important). Note that ”!” or ”#” comments out the
line.
&FORCE_EVAL
METHOD FIST
&MM
&POISSON
&EWALD
…
&END MM
&SUBSYS
&CELL
&GLOBAL
ABC 12.4138 12.4138 12.4138
PROJECT liq
&END CELL
PREFERRED_FFT_LIBRARY FFTW
&COORD
PRINT_LEVEL LOW
O
12.25967785390
1.34872474190
12.42975017890 H2O
RUN_TYPE GEOMETRY_OPTIMIZATION
H
12.28658481340
1.45497852510
11.43794042330 H2O
H
12.12685964540
2.28501721350
12.78165108500 H2O
&END GLOBAL
…
&MOTION
&GEO_OPT
TYPE minimization
&END COORD
….
&END FORCE_EVAL
OPTIMIZER BFGS
MAX_ITER 400 ! 200 is default
&END GEO_OPT
&END MOTION
12
!&EXT_RESTART
! RESTART_FILE_NAME ./run-01.restart
!&END EXT_RESTART
Running example 1
1. login to taito (you are going to be doing calculations in the queue, thus have open in a web
browser for reference: https://research.csc.fi/taito-user-guide)
2. cd $WRKDIR
3. cp –pr /wrk/murdacha/md_class . (copy directories with fortran analysis codes and examples to
your WRKDIR)
4. cd md_class/ANALYZE_PROGRAMS (compile two simple fortran-2003 analysis programs; later try
to understand these programs since you may run them)
5. module load gcc
6. cd src-analyze-water
7. make analyze.x
8. cd ../src-rdf-water
9. make rdf.x
10. cd $WRKDIR/liq_spce (this is the input we just went over = Exercise4 for the class)
11. sbatch runit.bash
1.
But first: edit if needed the input and script; module load vmd; vmd geometry.xyz or vmd –e liq.vmd to see the starting
geometry
12. Examine the output:
13
1.
Use gnuplot on the *.ener file to check energy conservation (plot column 2 versus 4, then column 2 versus 5 and 6)
2.
Use vmd to view the trajectory: module load vmd; vmd run-01.xyz or use the vmd script (may need to edit)
Running example 1
13. Now do the short MD NVE run but first clean
the directory (rm some files), and edit liq.inp
replacing:
1.
RUN_TYPE GEOMETRY_OPTIMIZATION by RUN_TYPE
MD (this means GEO_OPT stuff will be ignored)
2.
Add these lines (see file md_lines) after the line
&END GEO_OPT :
&MD
ENSEMBLE NVT ! NVE
STEPS 1000
TIMESTEP 1.0
&PRINT
&TRAJECTORY ON
&EACH
MD 10
TEMPERATURE 300.0
&END EACH
&THERMOSTAT
FILENAME =${BASE_NAME}-${ID}.xyz
TYPE NOSE
FORMAT XYZ
REGION MOLECULE
&END TRAJECTORY
&NOSE
&VELOCITIES ON
LENGTH 3
YOSHIDA 3
&EACH
MD 10
TIMECON 100
&END EACH
MTS 2
FILENAME =${BASE_NAME}-${ID}_vel.xyz
&END NOSE
FORMAT XYZ
&END THERMOSTAT
&END VELOCITIES
&PRINT ON
&FORCES ON
&ENERGY
&EACH
MD 1
&END EACH
FILENAME =${BASE_NAME}-${ID}.ener
&END ENERGY
&END PRINT
&END MD
&EACH
MD 10
3. Do the run: sbatch runit.bash
4. Examine the output:
1.
Use gnuplot on the *.ener file to check energy
conservation (plot column 2 versus 4, then column 2
versus 5 and 6)
2.
Use vmd to view the trajectory: module load vmd;
vmd run-01.xyz or use the vmd script (may need to
edit)
3.
How does an MD run at 300 K differ from a GEO_OPT
run (at 0K)?
&END EACH
FILENAME =${BASE_NAME}-${ID}_force.xyz
FORMAT XYZ
&END FORCES
&RESTART_HISTORY
&EACH
MD 1000
&END EACH
&END RESTART_HISTORY
&RESTART ON
BACKUP_COPIES 1
&EACH
MD 1
&END EACH
FILENAME =${BASE_NAME}-${ID}.restart
&END RESTART
&END PRINT
14
Running example 1
14. Now do the MD NVT production run, first clean the directory (rm some files), and edit liq.inp
replacing:
1.
ENSEMBLE NVE by ENSEMBLE NVT
2.
STEPS 1000 by STEPS 100000 (100 ps run)
3.
VELOCITIES ON by VELOCITIES OFF
4.
FORCES ON by FORCES OFF
15. Do the run and then examine the output:
1.
Use gnuplot on the *.ener file to check energy conservation (plot column 2 versus 4, then column 2 versus 5 and 6)
2.
Use vmd to view the trajectory: module load vmd; vmd run-01.xyz or use the vmd script (may need to edit)
3.
Is the energy conserved? This the canonical ensemble (NVT). Should energy be conserved? Do you see oscillations?
4.
Is your water liquid? How can you tell? Is it equilibrated? Hwne does equlibration occur?
5.
Obtain RDFs using vmd
6.
cd to the ANALYZE subdir, edit the *.in files, and do the analysis (use the bash script)
7.
How do your results (structures in the form of the RDFs—plot against Soper experimental RDFs; internal
energy/enthalpy) compare to the literature, see for example: http://pubs.acs.org/doi/abs/10.1021/jp110481m
8.
The SPC/E potential you have used is from Berendsen et al., see: https://en.wikipedia.org/wiki/Water_model
and https://dx.doi.org/10.1021%2Fj100308a038
Do you expect the results you obtained?
If you have time, you can use the end point of your (hopefully fully equilibrated) NVT trajectory to do an NVE run. That can
be analyzed in a similar way but also to obtain dynamical quantities like diffusion coefficient, IR spectra, etc. Speak with me
and I will help you out. Note that the SPC/E water molecule is rigid. We can do a run using TIP3P-F flexible water to get a
view of the internal IR vibrations.
15
CP2K example 2: Water with DFT
@SET BASE_NAME run
@SET ID 01
&GLOBAL
PROJECT ${BASE_NAME}-${ID}
RUN_TYPE MD
&END GLOBAL
&MOTION
&MD
ENSEMBLE NVT
STEPS 20 ! Now you are calculating dft on the fly, it will be much slower
TIMESTEP 0.5
TEMPERATURE 300.0
&THERMOSTAT
TYPE NOSE
REGION MASSIVE
&NOSE
LENGTH 3
YOSHIDA 3
TIMECON [wavenumber_t] 2300
MTS 2
&END NOSE
&END THERMOSTAT
&PRINT ON
&ENERGY
&EACH
MD 1
&END EACH
FILENAME =${BASE_NAME}-${ID}.ener
&END ENERGY
&END PRINT
&END MD
16
&PRINT
&TRAJECTORY ON
&EACH
MD 1
&END EACH
FILENAME =${BASE_NAME}-${ID}.xyz
FORMAT XYZ
&END TRAJECTORY
&VELOCITIES ON
&EACH
MD 1
&END EACH
FILENAME =${BASE_NAME}-${ID}_vel.xyz
FORMAT XYZ
&END VELOCITIES
&FORCES ON
&EACH
MD 1
&END EACH
FILENAME =${BASE_NAME}-${ID}_force.xyz
FORMAT XYZ
&END FORCES
&RESTART ON
&EACH
MD 1
&END EACH
FILENAME =${BASE_NAME}-${ID}.restart
&END RESTART
&END PRINT
&END MOTION
CP2K example 2: Water with DFT (note how sections in blue differ from classical potential example)
&FORCE_EVAL
METHOD QS
&DFT
POTENTIAL_FILE_NAME ./GTH_POTENTIALS
BASIS_SET_FILE_NAME ./GTH_BASIS_SETS
! WFN_RESTART_FILE_NAME ./run-01-RESTART.wfn
&MGRID
CUTOFF 280
&END MGRID
&SCF
MAX_SCF 20
EPS_SCF 1.0E-7
SCF_GUESS RESTART
&OUTER_SCF
EPS_SCF 1.0E-7
MAX_SCF 20
&END
&OT T
MINIMIZER DIIS
N_DIIS 7
&END OT
&PRINT
&RESTART ON
&END RESTART
&RESTART_HISTORY OFF
&END RESTART_HISTORY
&END PRINT
&END SCF
&QS
EPS_DEFAULT 1.0E-12
MAP_CONSISTENT
EXTRAPOLATION ASPC
EXTRAPOLATION_ORDER 3
&END QS
&XC
&XC_GRID
XC_SMOOTH_RHO NN10
XC_DERIV SPLINE2_SMOOTH
&END XC_GRID
&XC_FUNCTIONAL BLYP
&END XC_FUNCTIONAL
&vdW_POTENTIAL
DISPERSION_FUNCTIONAL PAIR_POTENTIAL
&PAIR_POTENTIAL
TYPE DFTD2
REFERENCE_FUNCTIONAL BLYP
R_CUTOFF 40.0
&END PAIR_POTENTIAL
&END vdW_POTENTIAL
&END XC
&END DFT
&SUBSYS
&CELL
ABC 12.4138 12.4138 12.4138
&END CELL
&COORD
O 1.2025696987709971E+01 1.2412376840360351E+00
H 1.1959096889663195E+01 1.3409373770618183E+00
H 1.1593234139420252E+01 2.0327876480659519E+00
…
O 1.2024298671712041E+01 9.9218625553065536E+00
H 1.2053386790559529E+01 9.6994663967598260E+00
H 1.1277449073604592E+01 9.4150658994176109E+00
&END COORD
&KIND O
BASIS_SET TZV2P-GTH
POTENTIAL GTH-BLYP-q6
&END KIND
&KIND H
BASIS_SET TZV2P-GTH
POTENTIAL GTH-BLYP-q1
&END KIND
&END SUBSYS
&END FORCE_EVAL
!&EXT_RESTART
! RESTART_FILE_NAME ./run-01.restart
!&END EXT_RESTART
17
1.1100847567157336E+01
1.0106406672798471E+01
1.1421274324532323E+01
9.2400384614568534E+00
1.0223617621157310E+01
8.9496605424081750E+00
Running and analyzing example 2
1. cd $WRKDIR/liq_blypd2_tzv2p_short (this is the input we just went over = Exercise5 for the class)
2. sbatch runit.bash
1.
But first: edit if needed the input and script; module load vmd; vmd geometry.xyz or vmd –e liq.vmd to see the starting
geometry
3. While the run is happening, continue the readings or ask questions
4. Examine the output:
1.
Use gnuplot on the *.ener file to check energy conservation (plot column 2 versus 4, then column 2 versus 5 and 6)
2.
Use vmd to view the trajectory: module load vmd; vmd run-01.xyz or use the vmd script (may need to edit)
3.
We only did an extremely short run. Why? Compare timings in the *.ener file to the classical case. How many processor
cores are we using now? How much more costly is Born-Oppenheimer MD with DFT compared to that with a classical
potential 2-body Lennard-Jones plus charges potential?
5. Since this is so costly, you only ran 20 steps to get a feel for DFT-MD. Now you will analyze a precomputed long trajectory:
6. cd $WRKDIR/liq_blypd2_tzv2p (this is the identical input but this run went longer)
7. Examine the files as before. Use gnuplot, vmd, etc. You can cd to ANALYZE sub-dir and do analysis.
8. Finally, compare the results of the classical simulation with the DFT one and also with experiment.
You can use gnuplot to plot RDFs obtained from SPC/E and BLYP-D2 and the experimental ones
(Soper files). How do the plots look? What about enthalpy? Put some results together to show
the whole class.
18
Running and analyzing example 3 (formic acid at air-water interface)
19
1.
cd $WRKDIR/water_slab_with_formic_acid_blypd2_dzvp_nve300_short . How does the input file compare to
the one for DFT liquid water? (Hint: use the linux sdiff command: ’sdiff –aw 192 file file2 |less’). What does the
system look like (use: ’vmd geometry.xyz’)? What is the purpose of the vacuum? The constraints?
2.
Run it: sbatch runit.bash
3.
While the run is happening, continue the readings or ask questions
4.
Examine the output
1.
Use gnuplot on the *.ener file to check energy conservation (plot column 2 versus 4, then column 2 versus 5 and 6)
2.
Use vmd to view the trajectory
3.
The formic acid starts to fall. How can we monitor its height above the water surface? (hint ’use grep C position_file > C’,
then use gnuplot) . (Ask me for a gnuplot file to make a good plot.)
4.
We only did an extremely short run. Why?
5.
Since this is so costly, you only ran 50 steps to get a feel for this problem. Now you will analyze a pre-computed
longer trajectory:
6.
cd $WRKDIR/water_slab_with_formic_acid_blypd2_dzvp_nve300 (this is the identical input but this run went
longer, to 10 ps)
7.
Examine the files as before. Use gnuplot, vmd (use the scripts and try to understand them), etc. You can cd to
ANALYZE sub-dir and do analysis (first do: ’ssh taito-gpu’, vmd will run faster on gpus). Note that the analyze.x
code called now is slightly different. (You may need to compile it.) Also, vmd is used for calculating RDFs.
8.
Is there any chemistry happening? If yes, what are the mechanisms and time scales? (Formic acid is a weak acid
so the deprotonation was not expected. Out of 50 trajectories, I only saw two deprotonate.) Make some nice
vmd snaphots of the Grotthus steps and present to the class. Compare to this Lee et al. paper.