====== Geometry optimization of NaCl clusters ======

Use this short script to drive CP2K

<code>
#!/bin/bash
#

for ii in 2 4 6 8 10 12
do
   sed -e "s/MY_SUPERCELL/${ii}/g" template.inp > input_${ii}.inp
   cp2k.popt input_${ii}.inp > NaCl_supercell_${ii}.out
done
</code>

where the template input is this geometry optimization using the classical forcefield FIST module of CP2K.

<code>
@SET NREP MY_SUPERCELL
@SET OPTIMIZER LBFGS # BFGS

&FORCE_EVAL
  METHOD Fist
  &MM
    &FORCEFIELD
      &CHARGE
        ATOM Na
        CHARGE +1.000
      &END CHARGE
      &CHARGE
        ATOM Cl
        CHARGE -1.000
      &END CHARGE
      &NONBONDED
        &BMHFT
          map_atoms NA NA
          atoms NA NA
          RCUT 10.0
        &END BMHFT
        &BMHFT
          map_atoms NA CL
          atoms NA CL
          RCUT 10.0
        &END BMHFT
        &BMHFT
          map_atoms CL CL
          atoms CL CL
          RCUT 10.0
        &END BMHFT
      &END NONBONDED
    &END FORCEFIELD
    &POISSON
      &EWALD
        EWALD_TYPE spme
        ALPHA .35
        GMAX 12*${NREP}
        O_SPLINE 6
      &END EWALD
    &END POISSON
  &END MM
  &SUBSYS
    &CELL
      #ABC 5.620 5.620 5.620
      ABC 2*5.620 2*5.620 2*5.620
      MULTIPLE_UNIT_CELL ${NREP} ${NREP} ${NREP}
    &END CELL
    &TOPOLOGY
      COORD_FILE_NAME NaCl.pdb
      COORDINATE PDB
      CONN_FILE_FORMAT OFF
      MULTIPLE_UNIT_CELL ${NREP} ${NREP} ${NREP}
    &END TOPOLOGY
  &END SUBSYS
&END FORCE_EVAL

&GLOBAL
  PROJECT NaCl
  RUN_TYPE GEO_OPT
&END GLOBAL

&MOTION
  &GEO_OPT
    OPTIMIZER ${OPTIMIZER}
  &END
&END MOTION

</code>

The script runs very quickly when the LBFGS optimizer is used. But see what happens if we switch to the BFGS optimizer instead (change the OPTIMIZER variable in the cp2k input file - you might want to reduce the size of the supercells in the driver script - NREP varying from 1 to 6 perhaps). Look at the timings that cp2k prints at the end of a run and see if you can see the culprit. Also look for warnings in your outputs (this is a good habit to get into).

How does the conjugate gradients optimizer compare to LBFGS in efficiency for this system?
====== Cell optimization of NaCl ======

For studying many properties of solid materials it is important that the lattice parameters used in a simulation are close to equilibrium for the model chemistry (Hamiltonian) used. Otherwise, large stresses can be present that complicate comparison to experiment. Successful cell optimization requires that the energy changes smoothly with cell volume - and for this the energy cutoff is the most important parameter. The input file template below can be used with driver script to examine how the energy volume curve of NaCl changes with the PW cutoff.

<code>
@SET SCALE_FACTOR MY_SCALING
@SET NREP 1
@SET OPTIMIZER BFGS # LBFGS
@SET CUTOFF MY_CUTOFF
@SET SAFTEY_CUTOFF 1.1

&FORCE_EVAL
  METHOD QS
  &DFT
    BASIS_SET_FILE_NAME BASIS_MOLOPT
    POTENTIAL_FILE_NAME GTH_POTENTIALS
    &MGRID
      CUTOFF ${CUTOFF}
      REL_CUTOFF 60
    &END MGRID
    &QS
      EPS_DEFAULT 1.0E-12
    &END QS
    &SCF
      SCF_GUESS RESTART
      &OT ON
        MINIMIZER DIIS
      &END OT
    &END SCF
    &XC
      &XC_FUNCTIONAL Pade
      &END XC_FUNCTIONAL
    &END XC
  &END DFT
  &SUBSYS
    &CELL
      ABC 5.620*${SCALE_FACTOR} 5.620*${SCALE_FACTOR} 5.620*${SCALE_FACTOR}
      MULTIPLE_UNIT_CELL ${NREP} ${NREP} ${NREP}
      #&CELL_REF
      #  ABC 5.620*${SAFETY_FACTOR} 5.620*${SAFETY_FACTOR} 5.620*${SAFETY_FACTOR}
      #  MULTIPLE_UNIT_CELL ${NREP} ${NREP} ${NREP}
      #&END
    &END CELL
    &COORD
scaled
Na 0.000   0.000   0.000
Cl 0.500   0.500   0.500
Na 0.000   0.500   0.500
Cl 0.500   0.000   0.000
Na 0.500   0.000   0.500
Cl 0.000   0.500   0.000
Na 0.500   0.500   0.000
Cl 0.000   0.000   0.500
    &END
    &TOPOLOGY
      MULTIPLE_UNIT_CELL ${NREP} ${NREP} ${NREP}
    &END TOPOLOGY
    &KIND Na
      BASIS_SET DZVP-MOLOPT-SR-GTH
      POTENTIAL GTH-PADE-q9
    &END KIND
    &KIND Cl
      BASIS_SET DZVP-MOLOPT-SR-GTH
      POTENTIAL GTH-PADE-q7
    &END KIND
  &END SUBSYS
&END FORCE_EVAL

&GLOBAL
  PROJECT NaCl
  RUN_TYPE ENERGY
&END GLOBAL

&MOTION
  &GEO_OPT
    OPTIMIZER ${OPTIMIZER}
  &END
  &CELL_OPT
    KEEP_SYMMETRY
  &END
&END MOTION
</code>
 The driver script could be something like

<code>
#!/bin/bash
#

CUTOFF="280"

for ii in 0.800 0.825 0.850 0.875 0.900 0.925 0.950 0.975 1.000 1.025 1.050 1.075 1.100
do
   #this assumes that the input template is in NaCl_QS.inp
   sed -e "s/MY_SCALING/${ii}/g" NaCl_QS.inp > temp.inp
   sed -e "s/MY_CUTOFF/${CUTOFF}/g" temp.inp > input_${ii}.inp
   
   #this line should changed to point to your cp2k executable
   mpirun -np 2 cp2k.popt input_${ii}.inp > NaCl_${CUTOFF}_${ii}.out
done

</code>

You can extract energies from the outputs with a command like
<code>
grep 'ENERGY|' *out | awk '{print $10}' > NaCl_energy_volume.dat
</code>

and you can plot the results in your favourite graphing software.

What is happening here? Try changing the PW cutoff (defined in the driver script) and using the CELL_REF variable.

Copy the input template to a new file and change the RUN_TYPE to CELL_OPT. You'll also need to ask the code to calculate the stress tensor (in FORCE_EVAL section) ANALYTICALLY! Also define the CUTOFF and SCALING_FACTOR. Start the cell optimization from small cells (SCALING_FACTOR 0.85) or large cells (SCALING_FACTOR 1.10) - do you get the same results? 

If you have access a machine with several cores (16 or so ideally) check whether increasing the supercell size (NREP variable) affects the results.