# Code:gmxliquid

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In this tutorial, I'm assuming you already have the gromacs commands (grompp, mdrun, etc.) loaded. I'm also assuming you have gromacs 5, which made significant changes to the way command-line tools are used.

You'll also need the starting files here. Or, on circe, just run

cp -R /shares/mri_workshop/Liquids .
cd Liquids


# Create an input system

First, we do some size calculations in the python prompt.

>>> # Compute number of EtOH molecules
>>> # 8 nm^3 = 8e-21 cc
>>> # 0.4 % By vol.
>>> # rho_EtOH = 0.78924 g / cc
>>> # FW = 46 g/mol
>>>
>>> 8e-21*0.4*0.78924/46.0*6.022e23
33


Next, we need to generate an 8 nm$^3$ box with 33 EtOH molecules

gmx insert-molecules -box 2 2 2 -ci etoh.pdb -o box.pdb -nmol 33
nano topol.top # check for line "ETH  33" (no changes required)


If the topology file and forcefields are 'there', we can create a test simulation using just these molecules. We'll do this just to check that grompp works

gmx grompp -c box.pdb -f equ.mdp -o equ.tpr


If this completes without errors, we know that we could simulate the ETH molecules we have now. That would give a high-density gas, rather than the liquid we want. Next, the complete water+EtOH mixture can be made by filling the voids with water. We'll use TIP4P here.

gmx solvate -cs tip4p -cp box.pdb -o sys.pdb


Since this last command added waters, you have to update the topology file, adding "SOL 130" (or your number of waters)

nano topol.top


# run minimization

Molecular structures can be touchy, since contacting atoms causes large forces and 'blows up' a system. The risk of this can be reduced by minimizing the energy of initial starting systems.

First, we have to create a file describing how gromacs should do the minimization.

gmx grompp -p topol.top -f min.mdp -c sys.pdb -o min


A lot of backup files (starting with '#') accumulate, and we remove them like so:

rm -f \#* mdout.mdp


Now we're ready to run minimization. Since the system is small, minimization is cheap and fast - so we do it on the head node. For larger systems, this command would be put in a job-script.

gmx mdrun -deffnm min


The latest gromacs has a bug of some sort or can't work with OPLS-AA for EtOH, since I get a segfault here. Hopefully this will be fixed soon. Otherwise, you can manually delete the EtOH from sys.pdb and topol.top and then re-run the grompp and mdrun steps.

Now we're ready to take the minimized structure and run dynamics. This first round is called equilibration, since we intend to let the system settle into a thermal equilibrium state.

gmx grompp -c min.gro -f equ.mdp -o equ.tpr


To run this one, we'll use the cluster by writing down the command in a script file. That script gets sent to the cluster. No changes to equ.sh should be required.

nano equ.sh
sbatch equ.sh
squeue -u whoami


As the job is running you can read through the log file.

less equ.log
tail -f equ.log
# enter Ctl-C to stop tailing


Note that the energy is output at every time-step. Why is the total energy changing with time? What about the total volume?

# run dynamics

Running dynamics uses the same procedure as before, but now we need to worry about how much and which output to produce.

nano run.mdp # no changes required
gmx grompp -c equ.gro -f run.mdp -o run.tpr


Check and start the job (no changes required).

nano run.sh
sbatch run.sh
squeue -u whoami


Read through run.log

less run.log
tail -f run.log
# enter Ctl-C to stop tailing


Notice that the total energy remains relatively constant now, but the individual energies are still very noisy. What does this say about the shape of the molecules?

# analyze dynamic data

Let's first check what happened during equilibration. Since the volume was allowed to change, we should be able to plot it vs. time:

gmx energy -f equ.edr -o equ.en.xvg
# Select: Potential Kinetic-En. Total-Energy Volume

• At what time does the potential energy stabilize?
• What is the density?
• answer: (33*46 + 18*133)/Avogadro / 7.0333834916722191e-21 = 0.9236 g/mL
• These two quantities inform on the heat and volume change of mixing.
• Pure H2O (TIP4P): rho = 1.001, H ~ 11.6 kcal/mol, D = 3.9e-5 cm^2/s, eps = 52
• Pure H2O (expt): rho = 0.9971, H = 10.5 kcal/mol, D = 2.3e-5 cm^2/s, eps = 78.4
• Gas-phase TIP4P energy = 0 (no self interactions in the model)
• Gas-phase OPLSAA-EtOH energy = 25 kJ/mol ($\pm$1)
• (J. Chem. Phys. 123, 234505, 2005)
• Pure EtOH: rho = 0.7873, H = 10.0 kcal/mol, D = 1.0e-5 cm^2/s, eps(expt) = 23
• (J. Phys. Chem. B 1997, 101, 78-86, J. Phys. Chem. B, 2014, 118 (34), 10156-66)

Gnuplot can make this plot with

plot 'equ.en.xvg' u 1:2 w l, 'equ.en.xvg' u 1:5 axis x1y2 w l


The radial distribution function is a classical measure of the structuring of liquid water. The one we calculate here shows the density of molecules within spherical shells around the central molecule.

gmx rdf -rdf mol_com -ng 2 -s run -f run.trr -o run.w-rdf.xvg
# select Water as "reference group", select "Water", then "ETH"
# re-run for ETH-ETH rdf
gmx rdf -rdf mol_com -ng 1 -s run -f run.trr -o run.e-rdf.xvg


gnuplot can plot these together with:

plot 'run.w-rdf.xvg' u 1:2 w l, 'run.w-rdf.xvg' u 1:3 w l, 'run.e-rdf.xvg' u 1:2 w l


Notice how waters stack much more closely together than EtOH? How is this related to their liquid densities?

The dielectric of a liquid measures its ability to be polarized by an applied field. High dielectric materials make good capacitors.

 gmx dipoles -f run.trr -s run.tpr -c dipcorr.xvg -corr total -P 1

Dipole moment (Debye)
---------------------
Average  =   2.2234  Std. Dev. =   0.1095  Error =   0.0001

The following averages for the complete trajectory have been calculated:

Total < M_x > = 7.79882 Debye
Total < M_y > = -1.11977 Debye
Total < M_z > = 9.49511 Debye

Total < M_x^2 > = 882.516 Debye^2
Total < M_y^2 > = 1239.78 Debye^2
Total < M_z^2 > = 925.457 Debye^2

Total < |M|^2 > = 3047.75 Debye^2
Total |< M >|^2 = 152.233 Debye^2

< |M|^2 > - |< M >|^2 = 2895.52 Debye^2

Finite system Kirkwood g factor G_k = 3.52836
Infinite system Kirkwood g factor g_k = 2.37948

Epsilon = 43.1739


Water and EtOH are constantly undergoing random collisions in solution. The net effect of this is diffusion of the two molecules. Einstein showed that this can be tracked by watching the mean squared displacement of the molecules over time. Since the distance traveled over a random walk with diffusion constant $D$ has a Gaussian distribution with variance $2D\Delta t$, where $\Delta t$ is the elapsed time, the mean squared displacement vs time should be a straight line with slope $2D$. Of course, over short times, this picture is only approximate, but it usually holds over longer times.

gmx msd -f run.trr -ngroup 2 -o run.msd.xvg

Fitting from 100 to 900 ps

D[     Water] 1.4336 (+/- 0.0850) 1e-5 cm^2/s
D[       ETH] 0.7312 (+/- 0.1279) 1e-5 cm^2/s


How do these compare with the literature values (above) for the pure liquids?

More detail on velocity correlation:

gmx velacc -mol -s run -f run.trr -o run.w-acf.xvg # Choose group 3 (Water)
gmx velacc -mol -s run -f run.trr -o run.e-acf.xvg # Choose group 2 (ETH)


you can compare these to some of the above references.

## Appendix

Here are cut and paste versions of the 3 most important files for running this tutorial.

TITLE     An empty 20 Ang. cube simulation box (box.pdb)
CRYST1   20.000   20.000   20.000  90.00  90.00  90.00 P 1           1
MODEL        1
ENDMDL


A topology using the opls-aa forcefield (topol.top).

#include "oplsaa.ff/forcefield.itp"
#include "oplsaa.ff/ethanol.itp"
#include "oplsaa.ff/tip4p.itp"

[ system ]
80 Proof Water

[ molecules ]
ETH             33


An ethanol molecule from the gromacs shares directory (etoh.pdb):

HETATM    1  C   ETH     1      -0.000  -0.000   0.000  0.00  0.00           C
HETATM    2  H   ETH     1      -0.785   0.244  -0.653  0.00  0.00           H
HETATM    3  H   ETH     1       0.322  -0.981  -0.190  0.00  0.00           H
HETATM    4  H   ETH     1      -0.335   0.073   0.993  0.00  0.00           H
HETATM    5  C   ETH     1       1.171   0.975  -0.220  0.00  0.00           C
HETATM    6  H   ETH     1       2.014   0.675   0.402  0.00  0.00           H
HETATM    7  H   ETH     1       1.468   0.957  -1.268  0.00  0.00           H
HETATM    8  OA  ETH     1       0.763   2.299   0.138  0.00  0.00           O
HETATM    9  HO  ETH     1       0.490   2.313   1.058  0.00  0.00           H


An mdp file for a short equilibration run (equ.mdp):

constraints              = none
continuation             = no
gen_vel                  = yes
gen_temp                 = 300
gen_seed                 = 9875945

integrator               = md

tinit                    = 0
dt                       = 0.001
nsteps                   = 100000 ; 100 ps
nstcomm                  = 500

nstlog                   = 5000
nstenergy                = 500
nstcalcenergy		 = 500
nstxout                  = 5000
nstvout                  = 5000
nstfout                  = 5000

comm-mode                = Linear

emtol                    = 100
emstep                   = 0.001

nstlist                  = 10
ns_type                  = grid
pbc                      = xyz
rlist                    = 0.9

coulombtype              = pme
rcoulomb                 = 0.9
vdw-type                 = Cut-Off
rvdw                     = 0.9

DispCorr                 = EnerPres
fourierspacing           = 0.1

pme_order                = 4
ewald_rtol               = 1e-5
ewald_geometry           = 3d
optimize_fft             = yes

Tcoupl                   = v-rescale
tc-grps                  = System
tau_t                    = 1.0
ref_t                    = 300

Pcoupl                   = Berendsen
; Pcoupl                   = Parrinello-Rahman
Pcoupltype               = isotropic
tau_p                    = 1.8
compressibility          = 4.5e-5
ref_p                    = 1.01325