# CP2K Open Source Molecular Dynamics

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exercises:2014_ethz_mmm:nacl_free_energy

# Free Energy Profile of NaCl Dissociation

• You'll have to run many similar simulations. Try to automatize as much as possible.
• The first two task can be run directly on the login node, i.e. without using bsub.
• The third task should be run on 4 cores with bsub -n 4.

## 1. Task: Potential energy curve (gas phase)

Plot the gas phase dissociation profile of NaCl of the potential energy. For this you have to run the input file NaCl_gasphase.inp at a range of Na-Cl distances.

## 2. Task: Free energy curve at 1K (gas phase)

Plot the gas phase dissociation profile of NaCl of the free energy at 1K.

For this you have to run constrained MD simulations at 1K for a range of Na-Cl distances. You have to add the MOTION-section provided below to the NaCl_gasphase.inp and change the RUN_TYPE.

Each constrained MD will produce a .LagrangeMultLog-files, which look like this:

Shake  Lagrangian Multipliers:            -0.054769270
Rattle Lagrangian Multipliers:            -0.020937479
Shake  Lagrangian Multipliers:            -0.020937479
Rattle Lagrangian Multipliers:            -0.020937479
...

From these files you can calculate the average Lagrange multiplier of the Shake-algorithm like this:

grep Shake NACL-XXX.LagrangeMultLog | awk '{c++ ; s=s+$4}END{print s/c}' The average Lagrange multiplier is the average force$F(x)$required to constrain the atoms at the distance$x$. From these forces the free energy difference can be obtained via integration: \begin{equation} \Delta A = -\int_a^b F(x)\, dx \end{equation} A dissociation profile can be obtained by choosing the closest distance$d_{min}\$ as lower integration-bound: \begin{equation} A(d) = -\int_{d_{min}}^d F(x)\, dx \end{equation}

Make sure that you get the units right. The Largange multipliers are written in atomic units (Hartree/bohr), while the distances are in Angstrom.

Compare the free-energy dissociation curve at 1K with the potential energy curve. What do you expect? What do you observe?

## 3. Task: Free energy curve of NaCl in water at 350K

Take the solvated system from the first exercise and add the constraint for a distance of 2.9 Å. Then run 100.000 MD steps MD at 350K. From the MD output calculate the average Largange multiplier. As a check for convergence you can divide the trajectory into two parts and calculate the average for each part separately. Once you are convinced of the result you can use it to complete the table given below. From the complete table calculate the free energy dissociation profile via numerical integration.

## Required Files

### Input file for NaCl in gasphase

NaCl_gasphase.inp
&FORCE_EVAL
METHOD FIST
&MM
&FORCEFIELD
&SPLINE
EPS_SPLINE 1.0E-8
EMAX_SPLINE 300000.0
&END
&CHARGE
ATOM Na
CHARGE 1.0
&END CHARGE
&CHARGE
ATOM Cl
CHARGE -1.0
&END CHARGE
&NONBONDED
&LENNARD-JONES
atoms Na Cl
EPSILON [kcalmol]  .0838
SIGMA   [angstrom] 3.63
RCUT    [angstrom] 11.4
&END LENNARD-JONES
&LENNARD-JONES
atoms Na Na
EPSILON [kcalmol]  0.0469
SIGMA   [angstrom] 2.7275
RCUT    [angstrom] 11.4
&END LENNARD-JONES
&LENNARD-JONES
atoms Cl Cl
EPSILON [kcalmol]  0.150
SIGMA   [angstrom] 4.54
RCUT    [angstrom] 11.4
&END LENNARD-JONES
&END NONBONDED
&END FORCEFIELD
&POISSON
&EWALD
EWALD_TYPE spme
ALPHA .3
GMAX 12
O_SPLINE 6
&END EWALD
&END POISSON
&END MM
&SUBSYS
&CELL
ABC 12.4138 12.4138 12.4138
&END CELL
&COORD
Na    0.0    0.0 0.0 NAP
Cl    MYDIST 0.0 0.0 CLM
&END COORD
&COLVAR
&DISTANCE
ATOMS 1 2
&END DISTANCE
&PRINT
&END
&END COLVAR
&TOPOLOGY
CONNECTIVITY GENERATE
&GENERATE
BONDLENGTH_MAX 7
&END
&END
&END SUBSYS
&END FORCE_EVAL

&GLOBAL
PROJECT NACL-MYDIST
RUN_TYPE ENERGY
&END GLOBAL

### Motion section for constrained MD

motion.inp
&MOTION
&CONSTRAINT
&COLLECTIVE
COLVAR 1
INTERMOLECULAR
TARGET [angstrom] MYDIST
&END COLLECTIVE
&LAGRANGE_MULTIPLIERS
COMMON_ITERATION_LEVELS 1
&END
&END CONSTRAINT
&MD
ENSEMBLE NVT
TIMESTEP 0.5
STEPS    100
TEMPERATURE 1
&THERMOSTAT
&NOSE
LENGTH 3
YOSHIDA 3
TIMECON 1000
MTS 2
&END NOSE
&END
&PRINT
&ENERGY OFF
&END ENERGY
&PROGRAM_RUN_INFO OFF
&END PROGRAM_RUN_INFO
&END PRINT
&END MD
&PRINT
&TRAJECTORY OFF
&END
&VELOCITIES OFF
&END VELOCITIES
&FORCES OFF
&END FORCES
&RESTART_HISTORY OFF
&END RESTART_HISTORY
&RESTART OFF
&END RESTART
&END PRINT
&END MOTION

### Average Largange multiplier for NaCl in water at 350K (incomplete)

# dist     avg. Shake Lagrange multiplier
2.5         0.0896372
2.6         0.0469698
2.7         0.0231717
2.8         0.0100625
2.9                          <--- Take missing value from your trajectory
3.0        -0.000996937
3.1        -0.00271078
3.2        -0.00335324
3.3        -0.00348111
3.4        -0.00303697
3.5        -0.00259636
3.6        -0.00201541
3.7        -0.00119027
3.8        -0.000408723
3.9        -8.19056e-05
4.0         0.000972204
4.1         0.00136578
4.2         0.0016246
4.3         0.00212447
4.4         0.00199128
4.5         0.00183284
4.6         0.00188221
4.7         0.00166909
4.8         0.00137179
4.9         0.00114308
5.0         0.000671159
5.1         0.000780625
5.2         0.000556307
5.3         0.000397211
5.4         0.000237853
5.5         0.000119549
5.6        -0.000220194
5.7        -0.000332539
5.8        -0.000674227
5.9        -0.00075852
6.0        -0.00043128
exercises/2014_ethz_mmm/nacl_free_energy.txt · Last modified: 2020/08/21 10:15 (external edit)

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