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howto:converging_cutoff [2017/06/20 14:29] – 130.237.185.202howto:converging_cutoff [2024/05/29 15:46] (current) – oschuett
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-====== How to Converge the CUTOFF and REL_CUTOFF ====== +This page has been moved to: https://manual.cp2k.org/trunk/methods/dft/cutoff.html
- +
-===== Introduction ===== +
-''QUICKSTEP'', as with nearly all ab initio Density Functional Theory +
-simulation packages, requires the use of a real-space (RS) +
-integration grid to represent certain functions, such as the +
-electron density and the product Gaussian functions. ''QUICKSTEP'' +
-uses a multi-grid system for mapping the product Gaussians onto the +
-RS grid(s), so that wide and smooth Gaussian functions are mapped +
-onto a coarser grid than narrow and sharp Gaussians. The electron +
-density is always mapped onto the finest grid. +
- +
-Choosing a fine enough integration grid for a calculation is crucial +
-in obtaining meaningful and accurate results. In this tutorial, we +
-will show the reader how to systematically find the correct settings +
-for obtaining a sufficiently fine integration grid for his/her +
-calculation. +
- +
-This tutorial assumes the reader already has some knowledge of how +
-to perform a simple energy calculation using ''QUICKSTEP'' (this can +
-be found in tutorial: [[static_calculation|Calculating Energy and Forces using Quickstep]]). +
- +
-A completed example from an earlier calculation can be obtained from +
-the file {{:converging_grid.tgz|converging_grid.tgz}} that comes with this tutorial. The +
-calculations were carried out using CP2K version 2.4. +
- +
- +
-==== ''QUICKSTEP'' Multi-Grid ==== +
-Before we go through the input file, it is worthwhile to explain +
-how the multi-grid is constructed in ''QUICKSTEP'', and how the +
-Gaussians are mapped onto the different grid levels. Hopefully this +
-will offer the reader a clear picture of how the key control +
-parameters affect the grids, and thus the overall accuracy of a +
-calculation. +
- +
-All multi-grid related settings for a calculation is controlled via +
-keywords in [[inp>FORCE_EVAL/DFT/MGRID|MULTIGRID]] subsection of [[inp>FORCE_EVAL/DFT|DFT]] subsection in +
-[[inp>FORCE_EVAL|FORCE_EVAL]]. The number of levels for the multi-grid is defined by +
-[[inp>FORCE_EVAL/DFT/MGRID#NGRIDS|NGRIDS]], and by default this is set to 4. The keyword [[inp>FORCE_EVAL/DFT/MGRID#CUTOFF|CUTOFF]] +
-defines the planewave cutoff (default unit is in Ry) for the +
-//finest// level of the multi-grid.  The higher the planewave cutoff, +
-the finer the grid. The corresponding planewave cutoffs for the +
-subsequent grid levels (from finer to coarser) are defined by the +
-formula: +
-\begin{equation*} +
-  E^i_{\mathrm{cut}} = \frac{E_{\mathrm{cut}}^1} +
-                            {\alpha^{(i-1)}} +
-\end{equation*} +
-where \(\alpha\) has a default value of 3.0, and since ''CP2K'' +
-versions 2.0, can be configured by the keyword +
-[[inp>FORCE_EVAL/DFT/MGRID#PROGRESSION_FACTOR|PROGRESSION_FACTOR]]. Therefore, the higher the value of [[inp>FORCE_EVAL/DFT/MGRID#CUTOFF|CUTOFF]] +
-the finer grid for all multi-grid levels. +
- +
-Having constructed the multi-grid, ''QUICKSTEP'' then needs to map +
-the Gaussians onto the grids. The keyword [[inp>FORCE_EVAL/DFT/MGRID#REL_CUTOFF|REL_CUTOFF]] controls +
-which product Gaussians are mapped onto which level of the +
-multi-grid.  ''CP2K'' tries to map each Gaussian onto a grid such +
-that the number of grid points covered by the Gaussian---no matter +
-how wide or narrow---are roughly the same. [[inp>FORCE_EVAL/DFT/MGRID#REL_CUTOFF|REL_CUTOFF]] defines the +
-planewave cutoff of a reference grid covered by a Gaussian with +
-unit standard deviation (\(e^{\vert\vec{r}\vert^2}\)). A Gaussian +
-is mapped onto the coarsest level of the multi-grid, on which the +
-function will cover number of grid points greater than or equal to +
-the number of grid points \(e^{\lvert\vec{r}\rvert^2}\) will cover on +
-a reference grid defined by [[inp>FORCE_EVAL/DFT/MGRID#REL_CUTOFF|REL_CUTOFF]]. +
- +
-Therefore, the two most important keywords effecting the +
-integration grid and the accuracy of a calculation are [[inp>FORCE_EVAL/DFT/MGRID#CUTOFF|CUTOFF]] and +
-[[inp>FORCE_EVAL/DFT/MGRID#REL_CUTOFF|REL_CUTFF]]. If [[inp>FORCE_EVAL/DFT/MGRID#CUTOFF|CUTOFF]] is too low, then all grids will be coarse +
-and the calculation may become inaccurate; and if ''REL_CUTOFF'' is +
-too low, then even if you have a high [[inp>FORCE_EVAL/DFT/MGRID#CUTOFF|CUTOFF]], all Gaussians will +
-be mapped onto the coarsest level of the multi-grid, and thus the +
-effective integration grid for the calculation may still be too +
-coarse. +
- +
- +
-===== Example: Bulk Si with 8 atoms in a cubic cell ===== +
-We demonstrate the process using an example based on Bulk Si with 8 +
-atoms in a face centred cubic unit cell. +
- +
- +
-==== Template Input File ==== +
-To systematically find the best [[inp>FORCE_EVAL/DFT/MGRID#CUTOFF|CUTOFF]] and [[inp>FORCE_EVAL/DFT/MGRID#REL_CUTOFF|REL_CUTOFF]] values +
-which are sufficient for a given accuracy (say, \(10^{-6}\) Ry in total +
-energy), we need to perform a series of single point energy +
-calculations. It is much easier to use a set of scripts that can +
-automate this process. +
- +
-To do this, we first write a template input file: ''template.inp'', +
-as shown below: +
- +
-<code cp2k> +
-&GLOBAL +
-  PROJECT Si_bulk8 +
-  RUN_TYPE ENERGY +
-  PRINT_LEVEL MEDIUM +
-&END GLOBAL +
-&FORCE_EVAL +
-  METHOD Quickstep +
-  &DFT +
-    BASIS_SET_FILE_NAME  BASIS_SET +
-    POTENTIAL_FILE_NAME  GTH_POTENTIALS +
-    &MGRID +
-      NGRIDS 4 +
-      CUTOFF LT_cutoff +
-      REL_CUTOFF LT_rel_cutoff +
-    &END MGRID +
-    &QS +
-      EPS_DEFAULT 1.0E-10 +
-    &END QS +
-    &SCF +
-      SCF_GUESS ATOMIC +
-      EPS_SCF 1.0E-6 +
-      MAX_SCF 1 +
-      ADDED_MOS 10 +
-      CHOLESKY INVERSE +
-      &SMEAR ON +
-        METHOD FERMI_DIRAC +
-        ELECTRONIC_TEMPERATURE [K] 300 +
-      &END SMEAR +
-      &DIAGONALIZATION +
-        ALGORITHM STANDARD +
-      &END DIAGONALIZATION +
-      &MIXING +
-        METHOD BROYDEN_MIXING +
-        ALPHA 0.4 +
-        BETA 0.5 +
-        NBROYDEN 8 +
-      &END MIXING +
-    &END SCF +
-    &XC +
-      &XC_FUNCTIONAL PADE +
-      &END XC_FUNCTIONAL +
-    &END XC +
-  &END DFT +
-  &SUBSYS +
-    &KIND Si +
-      ELEMENT   Si +
-      BASIS_SET SZV-GTH-PADE +
-      POTENTIAL GTH-PADE-q4 +
-    &END KIND +
-    &CELL +
-      SYMMETRY CUBIC +
-      A     5.430697500    0.000000000    0.000000000 +
-      B     0.000000000    5.430697500    0.000000000 +
-      C     0.000000000    0.000000000    5.430697500 +
-    &END CELL +
-    &COORD +
-      Si    0.000000000    0.000000000    0.000000000 +
-      Si    0.000000000    2.715348700    2.715348700 +
-      Si    2.715348700    2.715348700    0.000000000 +
-      Si    2.715348700    0.000000000    2.715348700 +
-      Si    4.073023100    1.357674400    4.073023100 +
-      Si    1.357674400    1.357674400    1.357674400 +
-      Si    1.357674400    4.073023100    4.073023100 +
-      Si    4.073023100    4.073023100    1.357674400 +
-    &END COORD +
-  &END SUBSYS +
-  &PRINT +
-    &TOTAL_NUMBERS  ON +
-    &END TOTAL_NUMBERS +
-  &END PRINT +
-&END FORCE_EVAL +
-</code> +
- +
-We go through this input file quickly. Readers who have gone +
-through the [[static_calculation|tutorial on how to perform a simple static energy and +
-force calculation]] using ''QUICKSTEP'' should have no trouble in +
-understanding most parts the above input. +
- +
-Some noticeable settings are: +
-<code cp2k> +
-&GLOBAL +
-  PROJECT Si_bulk8 +
-  RUN_TYPE ENERGY +
-  PRINT_LEVEL MEDIUM +
-&END GLOBAL +
-</code> +
-The keyword [[inp>GLOBAL#RUN_TYPE|RUN_TYPE]] is set to ''ENERGY'', this tells ''CP2K'' to only +
-calculate the energies of the system, forces will not be +
-calculated. Since we are only interested in the convergence of the +
-integration grid, just looking at the total energy usually suffices; +
-and since we will be performing a series of computations, the +
-cheaper each run is the better. We set [[inp>GLOBAL#PRINT_LEVEL|PRINT_LEVEL]] to ''MEDIUM'', so +
-that the information about how many Gaussian functions are mapped +
-onto which grid are printed. We need this information to analyse the +
-suitability of the chosen [[inp>FORCE_EVAL/DFT/MGRID#REL_CUTOFF|REL_CUTOFF]] value. +
- +
-The most important part in the template input is: +
-<code cp2k> +
-&MGRID +
-  NGRIDS 4 +
-  CUTOFF LT_cutoff +
-  REL_CUTOFF LT_rel_cutoff +
-&END MGRID +
-</code> +
-The symbols ''LT_cutoff'' and ''LT_rel_cutoff'' are //markers//, which +
-the automated scripts will search for and replace with the relevant +
-values. The default units for both [[inp>FORCE_EVAL/DFT/MGRID#CUTOFF|CUTOFF]] and [[inp>FORCE_EVAL/DFT/MGRID#REL_CUTOFF|REL_CUTOFF]] are +
-Ry. +
- +
-In ''SCF'' subsection, we have set +
-<code cp2k> +
-MAX_SCF 1 +
-</code> +
-So that no self-consistent loops will be performed. This is okay for +
-checking the integration grid, because irrespective of +
-self-consistency, grid settings with fine enough meshes should give +
-consistent energies. +
- +
- +
-==== Converging ''CUTOFF'' ==== +
-We start by setting [[inp>FORCE_EVAL/DFT/MGRID#REL_CUTOFF|REL_CUTOFF]] to a relatively high number, and +
-systematically vary [[inp>FORCE_EVAL/DFT/MGRID#CUTOFF|CUTOFF]]. Setting [[inp>FORCE_EVAL/DFT/MGRID#REL_CUTOFF|REL_CUTOFF]] to 60 Ry is +
-usually sufficient for most calculations, and in any case this will +
-be checked later when we vary [[inp>FORCE_EVAL/DFT/MGRID#REL_CUTOFF|REL_CUTOFF]]. +
- +
- +
-=== Generating Inputs === +
-We want to perform a series of calculations, with [[inp>FORCE_EVAL/DFT/MGRID#CUTOFF|CUTOFF]] ranging +
-from 50 Ry to 500 Ry in steps of 50 Ry. From experience, the +
-desired [[inp>FORCE_EVAL/DFT/MGRID#CUTOFF|CUTOFF]] for an accuracy of \(10^{-6}\) Ry for the total +
-energy should be well within this range. To do this, we first need +
-to make sure the basis and pseudopotential parameter files +
-''BASIS_SET'' and ''GTH_POTENTIALS'' are in the working directory +
-together with ''template.inp'', then one can write a bash script, +
-such as the file ''cutoff_inputs.sh'' shown below: +
-<code bash> +
-#!/bin/bash +
- +
-cutoffs="50 100 150 200 250 300 350 400 450 500" +
- +
-basis_file=BASIS_SET +
-potential_file=GTH_POTENTIALS +
-template_file=template.inp +
-input_file=Si_bulk8.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 +
-    cp $basis_file $work_dir +
-    cp $potential_file $work_dir +
-done +
-</code> +
- +
-The user should remember to set the permission of the new script +
-file to be executable: +
-<code> +
-chmod u+x ./cutoff_inputs.sh +
-</code> +
- +
-Entering the command line +
-<code> +
-./cutoff_inputs.sh +
-</code> +
-generates directories ''cutoff_50Ry'', ''cutoff_100Ry'', ..., +
-each containing ''BASIS_SET'', ''GTH_POTENTIALS'' and an input file +
-''Si_bulk8.inp'', which is exactly the same as ''template.inp'', except +
-that [[inp>FORCE_EVAL/DFT/MGRID#REL_CUTOFF|REL_CUTOFF]] is set to 60, and [[inp>FORCE_EVAL/DFT/MGRID#CUTOFF|CUTOFF]] is set to the respective +
-values in the range between 50 Ry and 500 Ry. +
- +
- +
-=== Running Calculations === +
-With the input files generated and checked, the next step is to +
-run them. A bash script such as ''cutoff_run.sh'' shown below does +
-the job: +
- +
-<code bash> +
-#!/bin/bash +
- +
-cutoffs="50 100 150 200 250 300 350 400 450 500" +
- +
-cp2k_bin=cp2k.popt +
-input_file=Si_bulk8.inp +
-output_file=Si_bulk8.out +
-no_proc_per_calc=2 +
-no_proc_to_use=16 +
- +
-counter=1 +
-max_parallel_calcs=$(expr $no_proc_to_use / $no_proc_per_calc) +
-for ii in $cutoffs ; do +
-    work_dir=cutoff_${ii}Ry +
-    cd $work_dir +
-    if [ -f $output_file ] ; then +
-        rm $output_file +
-    fi +
-    mpirun -np $no_proc_per_calc $cp2k_bin -o $output_file $input_file & +
-    cd .. +
-    mod_test=$(echo "$counter % $max_parallel_calcs" | bc) +
-    if [ $mod_test -eq 0 ] ; then +
-        wait +
-    fi +
-    counter=$(expr $counter + 1) +
-done +
-wait +
-</code> +
- +
-The above script is slightly complex, because it allows several +
-jobs to run in parallel. Setting the variable ''cp2k_bin'' defines +
-the path to the ''CP2K'' binary. In this case, the parallel version +
-''cp2k.popt'' is found in the system ''PATH''. ''no_proc_per_calc'' sets +
-the number of MPI processes to be used in parallel for each +
-job. ''no_proc_to_use'' sets the total number of processors to be +
-used for running all of the jobs. In the above example, the jobs +
-are run on a 24 core local workstation, a total of 16 cores are +
-used for performing the [[inp>FORCE_EVAL/DFT/MGRID#CUTOFF|CUTOFF]] convergence test calculations, +
-and 2 cores are used for each calculation. This means up to 8 jobs +
-will run in parallel, until the jobs are exhausted from the list +
-given in ''cutoffs''. +
- +
-The reader can write their own script where they see fit, and if +
-he/she just want the jobs to run in serial, then there is no need +
-for this complexity. +
- +
-Again +
-<code> +
-chmod u+x ./cutoff_run.sh +
-</code> +
-followed by +
-<code> +
-./cutoff_run.sh & +
-</code> +
-runs the calculations in the background. This calculation only +
-took a couple of minutes to complete on our local workstation. +
- +
- +
-=== Analysing Results === +
-After all of the calculations have finished, all the information +
-about total energies and distribution of Gaussians on the +
-multi-grid are written in the ''Si_bulk8.out'' files in each job +
-directories. +
- +
-The total energy can be found in the section of the output shown +
-below (in this example from ''cutoff_100Ry/Si_bulk8.out''): +
- +
-<code> +
-SCF WAVEFUNCTION OPTIMIZATION +
- +
- Step     Update method      Time    Convergence         Total energy    Change +
- ------------------------------------------------------------------------------ +
- +
- Trace(PS):                                   32.0000000000 +
- Electronic density on regular grids:        -31.9999999980        0.0000000020 +
- Core density on regular grids:               31.9999999944       -0.0000000056 +
- Total charge density on r-space grids:       -0.0000000036 +
- Total charge density g-space grids:          -0.0000000036 +
- +
-    1 NoMix/Diag. 0.40E+00    0.4     1.10090760       -32.3804557631 -3.24E+01 +
-    1 NoMix/Diag. 0.40E+00    0.4     1.10090760       -32.3804557631 -3.24E+01 +
- +
- *** SCF run NOT converged *** +
- +
- +
- Electronic density on regular grids:        -31.9999999980        0.0000000020 +
- Core density on regular grids:               31.9999999944       -0.0000000056 +
- Total charge density on r-space grids:       -0.0000000036 +
- Total charge density g-space grids:          -0.0000000036 +
- +
- Overlap energy of the core charge distribution:               0.00000000005320 +
- Self energy of the core charge distribution:                -82.06393942512820 +
- Core Hamiltonian energy:                                     16.92855916540793 +
- Hartree energy:                                              42.17635056223367 +
- Exchange-correlation energy:                                 -9.42142606564066 +
- Electronic entropic energy:                                   0.00000000000000 +
- Fermi energy:                                                 0.00000000000000 +
- +
- Total energy:                                               -32.38045576307407 +
-</code> +
- +
-Regexp search +
-<code> +
-"^[ \t]*Total energy:" +
-</code> +
-will find the relevant line. +
- +
-Similarly, information on distribution of Gaussians on the +
-multi-grid can be found in the section: +
-<code> +
-------------------------------------------------------------------------------- +
-----                             MULTIGRID INFO                            ---- +
-------------------------------------------------------------------------------- +
-count for grid        1:           2720          cutoff [a.u.]           50.00 +
-count for grid        2:           5000          cutoff [a.u.]           16.67 +
-count for grid        3:           2760          cutoff [a.u.]            5.56 +
-count for grid        4:             16          cutoff [a.u.]            1.85 +
-total gridlevel count  :          10496 +
-</code> +
-which tells us that for [[inp>FORCE_EVAL/DFT/MGRID#CUTOFF|CUTOFF]] of 100 Ry and [[inp>FORCE_EVAL/DFT/MGRID#REL_CUTOFF|REL_CUTOFF]] of 60 +
-Ry, 2720 product Gaussians has been distributed to grid level 1, +
-the finest level, 5000 for level 2, 2760 for level 3 and 16 for +
-level 4, the coarsest. The planewave cutoff for each multi-grid +
-level can be read from the right-hand-side columns. Here ''[a.u.]'' +
-means the Hartree energy unit, 1 Ha = 2 Ry. +
- +
-It is much easier if we can gather all the information together +
-into one file, which allows us to plot the results.  This can be +
-done, again, by using a simple script. ''cutoff_analyse.sh'' shown +
-below is such an example: +
- +
-<code bash> +
-#!/bin/bash +
- +
-cutoffs="50 100 150 200 250 300 350 400 450 500" +
- +
-input_file=Si_bulk8.inp +
-output_file=Si_bulk8.out +
-plot_file=cutoff_data.ssv +
- +
-rel_cutoff=60 +
- +
-echo "# Grid cutoff vs total energy" > $plot_file +
-echo "# Date: $(date)" >> $plot_file +
-echo "# PWD: $PWD" >> $plot_file +
-echo "# REL_CUTOFF = $rel_cutoff" >> $plot_file +
-echo -n "# Cutoff (Ry) | Total Energy (Ha)" >> $plot_file +
-grid_header=true +
-for ii in $cutoffs ; do +
-    work_dir=cutoff_${ii}Ry +
-    total_energy=$(grep -e '^[ \t]*Total energy' $work_dir/$output_file | awk '{print $3}') +
-    ngrids=$(grep -e '^[ \t]*QS| Number of grid levels:' $work_dir/$output_file | \ +
-             awk '{print $6}') +
-    if $grid_header ; then +
-        for ((igrid=1; igrid <= ngrids; igrid++)) ; do +
-            printf " | NG on grid %d" $igrid >> $plot_file +
-        done +
-        printf "\n" >> $plot_file +
-        grid_header=false +
-    fi +
-    printf "%10.2f  %15.10f" $ii $total_energy >> $plot_file +
-    for ((igrid=1; igrid <= ngrids; igrid++)) ; do +
-        grid=$(grep -e '^[ \t]*count for grid' $work_dir/$output_file | \ +
-               awk -v igrid=$igrid '(NR == igrid){print $5}') +
-        printf "  %6d" $grid >> $plot_file +
-    done +
-    printf "\n" >> $plot_file +
-done +
-</code> +
- +
-Type +
-<code> +
-chmod u+x ./cutoff_analyse.sh +
-</code> +
-and then run it using +
-<code> +
-./cutoff_analyse.sh +
-</code> +
-will produce a file named ''cutoff_data.ssv'', which looks like: +
-<code> +
-# Grid cutoff vs total energy +
-# Date: Mon Jan 20 21:20:34 GMT 2014 +
-# PWD: /home/tong/tutorials/converging_grid/sample_output +
-# REL_CUTOFF = 60 +
-# Cutoff (Ry) | Total Energy (Ha) | NG on grid 1 | NG on grid 2 | NG on grid 3 | NG on grid 4 +
-     50.00   -32.3795329864    5048    5432      16       0 +
-    100.00   -32.3804557631    2720    5000    2760      16 +
-    150.00   -32.3804554850    2032    3016    5432      16 +
-    200.00   -32.3804554982    1880    2472    3384    2760 +
-    250.00   -32.3804554859     264    4088    3384    2760 +
-    300.00   -32.3804554843     264    2456    5000    2776 +
-    350.00   -32.3804554846      56    1976    5688    2776 +
-    400.00   -32.3804554851      56    1976    3016    5448 +
-    450.00   -32.3804554851       0    2032    3016    5448 +
-    500.00   -32.3804554850       0    2032    3016    5448 +
-</code> +
- +
-The data shows that given the [[inp>FORCE_EVAL/DFT/MGRID#REL_CUTOFF|REL_CUTOFF]] value of 60 Ry, setting +
-[[inp>FORCE_EVAL/DFT/MGRID#CUTOFF|CUTOFF]] to 250 Ry and above would give an error in total energy +
-less than \(10^{-8}\) Ha. The reader may also notice that as [[inp>FORCE_EVAL/DFT/MGRID#CUTOFF|CUTOFF]] +
-increases, the number of Gaussians being assigned to the finest +
-grids decreases. Therefore, simply increasing [[inp>FORCE_EVAL/DFT/MGRID#CUTOFF|CUTOFF]] without +
-increasing [[inp>FORCE_EVAL/DFT/MGRID#REL_CUTOFF|REL_CUTOFF]] may eventually lead to a slow convergence +
-in energy, as more and more Gaussians get pushed to coarser grid +
-levels, negating the increase in [[inp>FORCE_EVAL/DFT/MGRID#CUTOFF|CUTOFF]]. +
- +
-In this example, the test results point to 250 Ry as a good choice +
-for [[inp>FORCE_EVAL/DFT/MGRID#CUTOFF|CUTOFF]], as the total energy is converged, and the +
-distribution of Gaussian functions on the grids are reasonable: it +
-is the lowest cutoff energy where the finest grid level is used, +
-but at the same time with the majority of the Gaussians on the coarser grids. +
- +
- +
-==== Converging ''REL_CUTOFF'' ==== +
-In the next step, we vary the value of [[inp>FORCE_EVAL/DFT/MGRID#REL_CUTOFF|REL_CUTOFF]] while keeping +
-[[inp>FORCE_EVAL/DFT/MGRID#CUTOFF|CUTOFF]] fixed at 250 Ry. +
- +
- +
-=== Generating Inputs === +
-For the energy convergence test with varying [[inp>FORCE_EVAL/DFT/MGRID#REL_CUTOFF|REL_CUTOFF]], we +
-follow a similar procedure as that for [[inp>FORCE_EVAL/DFT/MGRID#CUTOFF|CUTOFF]]. Using the same +
-template input file ''template.inp'', we can write a script called +
-''rel_cutoff_inputs.sh'': +
- +
-<code bash> +
-#!/bin/bash +
- +
-rel_cutoffs="10 20 30 40 50 60 70 80 90 100" +
- +
-basis_file=BASIS_SET +
-potential_file=GTH_POTENTIALS +
-template_file=template.inp +
-input_file=Si_bulk8.inp +
- +
-cutoff=250 +
- +
-for ii in $rel_cutoffs ; do +
-    work_dir=rel_cutoff_${ii}Ry +
-    if [ ! -d $work_dir ] ; then +
-        mkdir $work_dir +
-    else +
-        rm -r $work_dir/* +
-    fi +
-    sed -e "s/LT_cutoff/${cutoff}/g" \ +
-        -e "s/LT_rel_cutoff/${ii}/g" \ +
-        $template_file > $work_dir/$input_file +
-    cp $basis_file $work_dir +
-    cp $potential_file $work_dir +
-done +
-</code> +
- +
-Setting the permission for the script to "executable", and running +
-it produces directories ''rel_cutoff_10Ry'', ''rel_cutoff_20Ry'', ..., +
-each containing files ''BASIS_SET'', ''GTH_POTENTIALS'' and an input +
-''Si_bulk8.inp'', which is identical to ''template.inp'', except that +
-[[inp>FORCE_EVAL/DFT/MGRID#CUTOFF|CUTOFF]] is set to 250, and [[inp>FORCE_EVAL/DFT/MGRID#REL_CUTOFF|REL_CUTOFF]] is set to 10, 20, ..., +
-100 respectively. +
- +
- +
-=== Running Calculations === +
-Again to run the calculations, we can use the script +
-''rel_cutoff_run.sh'', as shown below: +
- +
-<code bash> +
-#!/bin/bash +
- +
-rel_cutoffs="10 20 30 40 50 60 70 80 90 100" +
- +
-cp2k_bin=cp2k.popt +
-input_file=Si_bulk8.inp +
-output_file=Si_bulk8.out +
-no_proc_per_calc=2 +
-no_proc_to_use=16 +
- +
-counter=1 +
-max_parallel_calcs=$(expr $no_proc_to_use / $no_proc_per_calc) +
-for ii in $rel_cutoffs ; do +
-    work_dir=rel_cutoff_${ii}Ry +
-    cd $work_dir +
-    if [ -f $output_file ] ; then +
-        rm $output_file +
-    fi +
-    mpirun -np $no_proc_per_calc $cp2k_bin -o $output_file $input_file & +
-    cd .. +
-    mod_test=$(echo "$counter % $max_parallel_calcs" | bc) +
-    if [ $mod_test -eq 0 ] ; then +
-        wait +
-    fi +
-    counter=$(expr $counter + 1) +
-done +
-wait +
-</code> +
- +
-In the above example, again, we have used 16 cores in total, and +
-with each job using 2 MPI processes. To run the jobs, use: +
-<code> +
-./rel_cutoff_run.sh & +
-</code> +
- +
- +
-=== Analysing Results === +
-Total energies and distribution of Gaussian functions on the +
-multi-grid are obtained the same way from the results as that for +
-the [[inp>FORCE_EVAL/DFT/MGRID#CUTOFF|CUTOFF]] calculations. +
- +
-To put all of the results from the [[inp>FORCE_EVAL/DFT/MGRID#REL_CUTOFF|REL_CUTOFF]] calculations in +
-one place, we can make some minor modifications to +
-''cutoff_analyse.sh'' and save it as ''rel_cutoff_analyse.sh'': +
- +
-<code bash> +
- #!/bin/bash +
- +
-rel_cutoffs="10 20 30 40 50 60 70 80 90 100" +
- +
-input_file=Si_bulk8.inp +
-output_file=Si_bulk8.out +
-plot_file=rel_cutoff_data.ssv +
- +
-cutoff=250 +
- +
-echo "# Rel Grid cutoff vs total energy" > $plot_file +
-echo "# Date: $(date)" >> $plot_file +
-echo "# PWD: $PWD" >> $plot_file +
-echo "# CUTOFF = ${cutoff}" >> $plot_file +
-echo -n "# Rel Cutoff (Ry) | Total Energy (Ha)" >> $plot_file +
-grid_header=true +
-for ii in $rel_cutoffs ; do +
-    work_dir=rel_cutoff_${ii}Ry +
-    total_energy=$(grep -e '^[ \t]*Total energy' $work_dir/$output_file | awk '{print $3}') +
-    ngrids=$(grep -e '^[ \t]*QS| Number of grid levels:' $work_dir/$output_file | \ +
-             awk '{print $6}') +
-    if $grid_header ; then +
-        for ((igrid=1; igrid <= ngrids; igrid++)) ; do +
-            printf " | NG on grid %d" $igrid >> $plot_file +
-        done +
-        printf "\n" >> $plot_file +
-        grid_header=false +
-    fi +
-    printf "%10.2f  %15.10f" $ii $total_energy >> $plot_file +
-    for ((igrid=1; igrid <= ngrids; igrid++)) ; do +
-        grid=$(grep -e '^[ \t]*count for grid' $work_dir/$output_file | \ +
-               awk -v igrid=$igrid '(NR == igrid){print $5}') +
-        printf "  %6d" $grid >> $plot_file +
-    done +
-    printf "\n" >> $plot_file +
-done +
-</code> +
- +
-Making the script executable, and running the script using +
-<code> +
-./rel_cutoff_analyse.sh +
-</code> +
-produces the following results written in file +
-''rel_cutoff_data.ssv'': +
- +
-<code> +
-# Rel Grid cutoff vs total energy +
-# Date: Mon Jan 20 00:45:14 GMT 2014 +
-# PWD: /home/tong/tutorials/converging_grid/sample_output +
-# CUTOFF = 250 +
-# Rel Cutoff (Ry) | Total Energy (Ha) | NG on grid 1 | NG on grid 2 | NG on grid 3 | NG on grid 4 +
-     10.00   -32.3902980020       0       0    2032    8464 +
-     20.00   -32.3816384686       0     264    4088    6144 +
-     30.00   -32.3805115576       0    2032    3016    5448 +
-     40.00   -32.3805116025      56    1976    3016    5448 +
-     50.00   -32.3804555002     264    2456    5000    2776 +
-     60.00   -32.3804554859     264    4088    3384    2760 +
-     70.00   -32.3804554859    1880    2472    3384    2760 +
-     80.00   -32.3804554859    1880    2472    3384    2760 +
-     90.00   -32.3804554848    2032    3016    5432      16 +
-    100.00   -32.3804554848    2032    3016    5432      16 +
-</code> +
- +
-The results show that as one increases the value of [[inp>FORCE_EVAL/DFT/MGRID#REL_CUTOFF|REL_CUTOFF]], +
-more Gaussians get mapped onto the finer grids. The error in total +
-energy reduces to less than \(10^{-8}\) Ha when [[inp>FORCE_EVAL/DFT/MGRID#REL_CUTOFF|REL_CUTOFF]] is +
-greater or equal to 60 Ry. The results thus indicate that 60 Ry is +
-indeed a suitable choice for the value of [[inp>FORCE_EVAL/DFT/MGRID#REL_CUTOFF|REL_CUTOFF]]. +
- +
-So finally we conclude that the setting +
-<code cp2k> +
-&MGRID +
-  CUTOFF 250 +
-  REL_CUTOFF 60  +
-&END MGRID +
-</code> +
-is sufficient for a calculation with the required accuracy. +
howto/converging_cutoff.1497968992.txt.gz · Last modified: (external edit)