Converging the cutoff for a more difficult problem

This exercise is similar to the previous one, but uses a setup and system more typical of CP2K usage. We will use a system of 32 H₂O water molecules within a periodic box. Here is the input template:

input_template.inp

&GLOBAL
  PRINT_LEVEL MEDIUM
  PROJECT cuttoff-test
  RUN_TYPE ENERGY_FORCE
&END GLOBAL
 
 
&FORCE_EVAL
  METHOD Quickstep
  &DFT
    BASIS_SET_FILE_NAME BASIS_MOLOPT
    POTENTIAL_FILE_NAME GTH_POTENTIALS
    WFN_RESTART_FILE_NAME ../cuttoff-test-RESTART.wfn
    CHARGE 0
    MULTIPLICITY 1
    &MGRID
      NGRIDS 4
      CUTOFF LT_cutoff
      REL_CUTOFF LT_rel_cutoff
    &END
    &QS
      EPS_DEFAULT 1.0E-12
      METHOD GPW
    &END
 
    &SCF
      SCF_GUESS RESTART
      EPS_SCF 5.e-7
      MAX_SCF 15
      &OT
        PRECONDITIONER FULL_ALL
        MINIMIZER DIIS
      &END OT
      &OUTER_SCF
        EPS_SCF 5.0E-7
        MAX_SCF 1
      &END OUTER_SCF
    &END SCF
 
    &XC
      &XC_FUNCTIONAL PBE
      &END XC_FUNCTIONAL
      &XC_GRID
        ! defaults
        XC_SMOOTH_RHO NONE
        XC_DERIV PW
      &END XC_GRID
    &END XC
 
  &END DFT
  &SUBSYS
    &CELL
      ABC 9.8528 9.8528 9.8528
      PERIODIC XYZ
    &END CELL
 
    &KIND H
      BASIS_SET DZVP-MOLOPT-SR-GTH-q1
      POTENTIAL GTH-PBE-q1
    &END
 
    &KIND O
      BASIS_SET DZVP-MOLOPT-SR-GTH-q6
      POTENTIAL GTH-PBE-q6
    &END KIND
 
    &TOPOLOGY
      COORDINATE XYZ
      COORD_FILE_NAME ../structure.xyz
      CONNECTIVITY OFF
    &END TOPOLOGY
  &END SUBSYS
 
  &PRINT
    &FORCES
    &END
  &END
&END FORCE_EVAL

Compared to the Si example, this is a larger system, we are using the OT optimizer in a good setup for a small to medium insulating system:

    &SCF
      SCF_GUESS RESTART
      EPS_SCF 5.e-7
      MAX_SCF 15
      &OT
        PRECONDITIONER FULL_ALL
        MINIMIZER DIIS
      &END OT
      &OUTER_SCF
        EPS_SCF 5.0E-7
        MAX_SCF 1
      &END OUTER_SCF
    &END SCF

and we are also saving the forces on the atoms

  &PRINT
    &FORCES
    &END
  &END

We save the forces as for many purposes (MD) converging the forces reasonably is more important than the total energy of the system.

The runcutoff file is a shell script as before to generate the different input files:

#!/bin/bash

cutoffs="100 200 300 400 500 600 700 800 900 1000 1100 1200"

template_file=input_template.inp
input_file=input.inp

rel_cutoff=60

for ii in $cutoffs ; do
    work_dir=cutoff_${ii}Ry
    if [ ! -d $work_dir ] ; then
        mkdir $work_dir
    else
        rm -r $work_dir/*
    fi
    sed -e "s/LT_rel_cutoff/${rel_cutoff}/g" \
        -e "s/LT_cutoff/${ii}/g" \
    $template_file > $work_dir/$input_file
done

When you run the shell script you should get a series of directories, cutoff_${cutoff}Ry. Run the input files in each directory (you may want to setup a script to do this).

At the end you should have a set of output files that contain the total energy of the system and the forces on each atom.

What is converged?

Compare the convergence of forces to the default convergence criteria for geometry optimization.

What sets the required cutoff? It is the basis set (which is dictated by the pseudopotentials). You will need to be able to represent the Gaussian with largest exponent well on the realspace grids. Oxygen, being very electronegative (on the right of the period table with many protons) has very contracted 2s states. You can see in the output

       Normalised Cartesian orbitals:

                        Set   Shell   Orbital            Exponent    Coefficient

                          1       1    2s               10.389228       0.396646
                                                         3.849621       0.208811
                                                         1.388401      -0.301641
                                                         0.496955      -0.274061
                                                         0.162492      -0.033677

That there is a Gaussian with an exponent of 10.4 Bohr^-2. If we compare to the basis set for Silicon

 Si DZVP-MOLOPT-GTH DZVP-MOLOPT-GTH-q4
 1
 2 0 2 6 2 2 1
      2.693604434572  0.015333179500 -0.073325401200 -0.005800105400  0.023996406700  0.043919650100
      1.359613855428 -0.283798205000  0.484815594600 -0.059172026000  0.055459199900  0.134639409600
      0.513245176029 -0.228939692700 -0.276015880000  0.121487149900 -0.269559268100  0.517732111300
      0.326563011394  0.728834000900 -0.228394679700  0.423382421100 -0.259506329000  0.282311245100
      0.139986977410  0.446205299300 -0.018311553000  0.474592116300  0.310318217600  0.281350794600
      0.068212286977  0.122025292800  0.365245476200  0.250129397700  0.647414251100  0.139066843800

we see that the largest exponent is only 2.7 Bohr^-2, so can be represented on a much coarser grid.

The convergence is largely dominated by the calculation of the gradient terms in a GGA functional (compare a simulation with LDA to the PBE used here). The evaluation of these terms on the grids are demanding, and very dependent on the functional.

    &XC
      &XC_FUNCTIONAL PBE
      &END XC_FUNCTIONAL
      &XC_GRID
        ! defaults
        XC_SMOOTH_RHO NONE
        XC_DERIV PW
      &END XC_GRID
    &END XC

For BLYP functional some smoothing needs to be applied. The smoothing may also converge forces more rapidly than the default settings, but at the expense of modifying the functional slightly.

    &XC
      &XC_FUNCTIONAL PBE
      &END XC_FUNCTIONAL
      &XC_GRID
        XC_SMOOTH_RHO NN50
        XC_DERIV NN50_SMOOTH
      &END
    &END XC

&XC_FUNCTIONAL PADE # or BLYP
&END XC_FUNCTIONAL

    &KIND O
      BASIS_SET DZVP-MOLOPT-SR-GTH-q6
      POTENTIAL GTH-PADE-q6
    &END KIND