Computation of the Lennard Jones curve for two Ar atoms

In this exercise you will compute the Lennard-Jones energy curve for a system of two Ar atoms.
In Part I you find the instructions for computing the energy of two Ar atoms at a distance $r=3.00 Å$.
In Part II you find the instructions for getting the energy profile as a function of $r$.
Additonal parameters for Ne are provided at the end of Part II.

Part I: Single Point (Energy) calculation

In this section a commented CP2K input example for a single point calculation is provided. Comments are added and signaled with '!'.

1. Step

Save the following input to a file named energy.inp

energy.inp

&GLOBAL                  ! section to select the kind of calculation
   RUN_TYPE ENERGY       ! select type of calculation. In this case: ENERGY (=Single point calculation)
&END GLOBAL
&FORCE_EVAL              ! section with parameters and system description
  METHOD FIST            ! Molecular Mechanics method
  &MM                    ! specification of MM parameters 
    &FORCEFIELD          ! parameters needed to describe the potential 
    &SPLINE
    EMAX_SPLINE 10000    ! numeric parameter to ensure calculation stability. Should not be changed
    &END
        &NONBONDED       ! parameters for the non bonded interactions
          &LENNARD-JONES ! Lennard-Jones parameters
          atoms Ar Ar
          EPSILON    [K_e] 119.8
          SIGMA [angstrom]   3.401
          RCUT  [angstrom]  25.0
        &END LENNARD-JONES
      &END NONBONDED
      &CHARGE
        ATOM Ar
        CHARGE 0.0
      &END CHARGE
    &END FORCEFIELD
    &POISSON              ! solver for non periodic calculations
     PERIODIC NONE
      &EWALD
        EWALD_TYPE none
      &END EWALD
    &END POISSON
  &END MM
  &SUBSYS                 ! system description 
    &CELL
     ABC [angstrom] 10 10 10  
     PERIODIC NONE
    &END CELL
    &COORD                
      UNIT angstrom
      Ar  0 0 0
      Ar  3 0 0
    &END COORD
   &END SUBSYS
&END FORCE_EVAL

2. Step

Run CP2K with the following arguments:

$ cp2k.popt -i energy.inp -o energy.out

3. Step

Afterwards the file energy.out will look like this:

 **** **** ******  **  PROGRAM STARTED AT                2014-01-20 11:32:08.142
 ***** ** ***  *** **   PROGRAM STARTED ON                   some_server.ethz.ch
 **    ****   ******    PROGRAM STARTED BY                                   you
 ***** **    ** ** **   PROGRAM PROCESS ID                                 24183
 **** **  *******  **  PROGRAM STARTED IN                     /home/you/XERCISES

...
  ENERGY| Total FORCE_EVAL ( FIST ) energy (a.u.):           0.003617048870059
...

  **** **** ******  **  PROGRAM ENDED AT                 2014-01-20 12:24:18.154
 ***** ** ***  *** **   PROGRAM RAN ON                       some_server.ethz.ch
 **    ****   ******    PROGRAM RAN BY                                       you
 ***** **    ** ** **   PROGRAM PROCESS ID                                 24993
  **** **  *******  **  PROGRAM STOPPED IN                   /home/you/EXERCISES

If you get the closing Banner you know that cp2k worked. The following line tells you the result:

ENERGY| Total FORCE_EVAL ( FIST ) energy (a.u.):              0.003617048870059

This is the energy (in Hartree) for a system of 2 Ar atoms at distance $ r=3.00 Å$

Note, that in the input-file EPSILON is given in units of Kelvin, whereas in the output the energy is printed in Hartree, which is the unit of energy in the system of atomic units (a.u.). To convert from Kelvin to Hartree you have to multiply with the Boltzmann constant $ k_\text{b} = 3.1668154 \cdot 10^{-6} \frac{E_\text{H}}{\text{K}} $ .

Part II: Computation of the LJ energy curve

In this section a few scripts to get the LJ energy profiles are presented.

1. Step

In order to get a good profile, a set of energy values as a function of the interatomic distance is needed. You can use the energy.inp input file and change the Ar coordinates in order to get different starting distances.

The output file will be rewritten every time you run a calculation, unless you change its name.

To do so:

$ mv energy.out energy_dist3A.out

If you run multiple calculations, it is always good to keep track of what you have done by producing an input and an output for every distance you are planning to run.

For doing so:

$ cp energy.inp energy_dist2A.inp

then edit the input file with the new coordinates (e.g. 2 Å). you can now run CP2K and produce the output file:

$ cp2k.popt -i energy_dist2A.inp -o energy_dist2A.out

2. Step

When you have tested a few distances, you can produce a table looking like:

Input file	Distance (Å)	Energy (Eh)
energy_dist1A.inp	1	…
energy_dist2A.inp	2	…
energy_dist3A.inp	3	…
…	…	…

This is the Lennard Jones energy curve for two Ar atoms. By using any plotting program you can now get a representation of the energy profile.

3. Step

Here are reported the LJ parameters for Ne atoms. Those are to replace the Ar parameters in the input file, along with your Ne coordinates that have to replace the Ar coordinates. A new LJ curve for Ne atoms can be now generated.

         &NONBONDED   
          &LENNARD-JONES ! Lennard-Jones Ne parameters
           atoms Ne Ne 
           EPSILON    [K_e] 36.8 
           SIGMA [angstrom]  2.8
           RCUT  [angstrom] 25.0
          &END LENNARD-JONES
         &END NONBONDED
         &CHARGE
          ATOM Ne
          CHARGE 0.0
         &END CHARGE