Free Energy Profile of NaCl Dissociation

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

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