howto:converging_cutoff
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- | ====== Introduction ====== | + | This page has been moved to: https:// |
- | + | ||
- | '' | + | |
- | 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. '' | + | |
- | 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 '' | + | |
- | 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 {{: | + | |
- | calculations were carried out using CP2K SVN trunk revision 13180. | + | |
- | + | ||
- | ===== '' | + | |
- | + | ||
- | Before we go through the input file, it is worth while to explain | + | |
- | how the multi-grid is constructed in '' | + | |
- | Gaussians are mapped onto the different grid levels. Hopefully this | + | |
- | will offer the reader with 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 [[http:// | + | |
- | [[http:// | + | |
- | [[http:// | + | |
- | defines the planewave cutoff (default unit is in Ry) for the | + | |
- | //finest// level of the multi-grid. | + | |
- | 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 '' | + | |
- | versions 3.0, can be configured by the keyword | + | |
- | [[http:// | + | |
- | the finer grid for all multi-grid levels. | + | |
- | + | ||
- | Having constructed the multi-grid, '' | + | |
- | the Gaussians onto the grids. The keyword [[http:// | + | |
- | which product Gaussians are mapped onto which level of the | + | |
- | multi-grid. | + | |
- | that the number of grid points covered by the Gaussian---no matter | + | |
- | how wide or narrow---are roughly the same. [[http:// | + | |
- | 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 [[http:// | + | |
- | + | ||
- | Therefore, the two most important keywords effecting the | + | |
- | integration grid and the accuracy of a calculation are [[http:// | + | |
- | [[http:// | + | |
- | and the calculation may become inaccurate; and if '' | + | |
- | too low, then even if you have a high [[http:// | + | |
- | 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 [[http:// | + | |
- | 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: '' | + | |
- | as shown below: | + | |
- | + | ||
- | <code cp2k> | + | |
- | & | + | |
- | PROJECT Si_bulk8 | + | |
- | RUN_TYPE ENERGY | + | |
- | PRINT_LEVEL MEDIUM | + | |
- | &END GLOBAL | + | |
- | & | + | |
- | METHOD Quickstep | + | |
- | &DFT | + | |
- | BASIS_SET_FILE_NAME | + | |
- | POTENTIAL_FILE_NAME | + | |
- | & | + | |
- | 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 | + | |
- | & | + | |
- | ALGORITHM STANDARD | + | |
- | &END DIAGONALIZATION | + | |
- | & | + | |
- | METHOD BROYDEN_MIXING | + | |
- | ALPHA 0.4 | + | |
- | BETA 0.5 | + | |
- | NBROYDEN 8 | + | |
- | &END MIXING | + | |
- | &END SCF | + | |
- | &XC | + | |
- | & | + | |
- | &END XC_FUNCTIONAL | + | |
- | &END XC | + | |
- | &END DFT | + | |
- | & | + | |
- | &KIND Si | + | |
- | ELEMENT | + | |
- | BASIS_SET SZV-GTH-PADE | + | |
- | POTENTIAL GTH-PADE-q4 | + | |
- | &END KIND | + | |
- | &CELL | + | |
- | SYMMETRY CUBIC | + | |
- | A | + | |
- | B | + | |
- | C | + | |
- | &END CELL | + | |
- | & | + | |
- | Si 0.000000000 | + | |
- | Si 0.000000000 | + | |
- | Si 2.715348700 | + | |
- | Si 2.715348700 | + | |
- | Si 4.073023100 | + | |
- | Si 1.357674400 | + | |
- | Si 1.357674400 | + | |
- | Si 4.073023100 | + | |
- | &END COORD | + | |
- | &END SUBSYS | + | |
- | & | + | |
- | & | + | |
- | &END TOTAL_NUMBERS | + | |
- | &END PRINT | + | |
- | &END FORCE_EVAL | + | |
- | </ | + | |
- | + | ||
- | 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 '' | + | |
- | understanding most parts the above input. | + | |
- | + | ||
- | Some noticeable settings are: | + | |
- | <code cp2k> | + | |
- | & | + | |
- | PROJECT Si_bulk8 | + | |
- | RUN_TYPE ENERGY | + | |
- | PRINT_LEVEL MEDIUM | + | |
- | &END GLOBAL | + | |
- | </ | + | |
- | The keyword [[http:// | + | |
- | 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, | + | |
- | cheaper each run is the better. We set [[http:// | + | |
- | 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 [[http:// | + | |
- | + | ||
- | The most important part in the template input is: | + | |
- | <code cp2k> | + | |
- | & | + | |
- | NGRIDS 4 | + | |
- | CUTOFF LT_cutoff | + | |
- | REL_CUTOFF LT_rel_cutoff | + | |
- | &END MGRID | + | |
- | </ | + | |
- | The symbols '' | + | |
- | the automated scripts will search for and replace with the relevant | + | |
- | values. The default units for both [[http:// | + | |
- | Ry. | + | |
- | + | ||
- | In '' | + | |
- | <code cp2k> | + | |
- | MAX_SCF 1 | + | |
- | </ | + | |
- | So that no self-consistent loops will be performed. This is okay for | + | |
- | checking the integration grid, because irrespective of | + | |
- | self-consistency, | + | |
- | consistent energies. | + | |
- | ===== Converging '' | + | |
- | + | ||
- | We start by setting [[http:// | + | |
- | systematically vary [[http:// | + | |
- | usually sufficient for most calculations, | + | |
- | be checked later when we vary [[http:// | + | |
- | + | ||
- | ==== Generating Inputs ==== | + | |
- | + | ||
- | We want to perform a series of calculations, | + | |
- | from 50 Ry to 500 Ry in steps of 50 Ry. From experience, the | + | |
- | desired [[http:// | + | |
- | energy should be well within this range. To do this, we first need | + | |
- | to make sure the basis and pseudopotential parameter files | + | |
- | '' | + | |
- | together with '' | + | |
- | such as the file '' | + | |
- | <code bash> | + | |
- | # | + | |
- | + | ||
- | cutoffs=" | + | |
- | + | ||
- | 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 " | + | |
- | -e " | + | |
- | $template_file > $work_dir/ | + | |
- | cp $basis_file $work_dir | + | |
- | cp $potential_file $work_dir | + | |
- | done | + | |
- | </ | + | |
- | + | ||
- | The user should remember to set the permission of the new script | + | |
- | file to be executable: | + | |
- | < | + | |
- | chmod u+x ./ | + | |
- | </ | + | |
- | + | ||
- | Entering the command line | + | |
- | < | + | |
- | ./ | + | |
- | </ | + | |
- | generates directories '' | + | |
- | each containing '' | + | |
- | '' | + | |
- | that [[http:// | + | |
- | values in the range between 50 Ry and 500 Ry. | + | |
- | ==== Running Calculations ==== | + | |
- | + | ||
- | With the input files generated and checked, the next step is to | + | |
- | run them. A bash script such as '' | + | |
- | the job: | + | |
- | + | ||
- | <code bash> | + | |
- | # | + | |
- | + | ||
- | cutoffs=" | + | |
- | + | ||
- | cp2k_bin=cp2k.popt | + | |
- | input_file=Si_bulk8.inp | + | |
- | output_file=Si_bulk8.out | + | |
- | no_proc_per_calc=2 | + | |
- | no_proc_to_use=16 | + | |
- | + | ||
- | counter=1 | + | |
- | max_parallel_calcs=$(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 " | + | |
- | if [ $mod_test -eq 0 ] ; then | + | |
- | wait | + | |
- | fi | + | |
- | counter=$(expr $counter + 1) | + | |
- | done | + | |
- | wait | + | |
- | </ | + | |
- | + | ||
- | The above script is slightly complex, because it allows several | + | |
- | jobs to run in parallel. Setting the variable '' | + | |
- | the path to the '' | + | |
- | '' | + | |
- | the number of MPI processes to be used in parallel for each | + | |
- | job. '' | + | |
- | used for running all of the jobs. In the above example, the jobs | + | |
- | are run on a 24 core local workstation, | + | |
- | used for performing the [[http:// | + | |
- | 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 '' | + | |
- | + | ||
- | 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 | + | |
- | < | + | |
- | chmod u+x ./ | + | |
- | </ | + | |
- | followed by | + | |
- | < | + | |
- | ./ | + | |
- | </ | + | |
- | 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 '' | + | |
- | directories. | + | |
- | + | ||
- | The total energy can be found in the section of the output shown | + | |
- | below (in this example from '' | + | |
- | + | ||
- | < | + | |
- | SCF WAVEFUNCTION OPTIMIZATION | + | |
- | + | ||
- | | + | |
- | | + | |
- | + | ||
- | | + | |
- | | + | |
- | Core density on regular grids: | + | |
- | Total charge density on r-space grids: | + | |
- | Total charge density g-space grids: | + | |
- | + | ||
- | 1 NoMix/Diag. 0.40E+00 | + | |
- | 1 NoMix/Diag. 0.40E+00 | + | |
- | + | ||
- | *** SCF run NOT converged *** | + | |
- | + | ||
- | + | ||
- | | + | |
- | Core density on regular grids: | + | |
- | Total charge density on r-space grids: | + | |
- | Total charge density g-space grids: | + | |
- | + | ||
- | | + | |
- | Self energy of the core charge distribution: | + | |
- | Core Hamiltonian energy: | + | |
- | | + | |
- | | + | |
- | | + | |
- | Fermi energy: | + | |
- | + | ||
- | Total energy: | + | |
- | </ | + | |
- | + | ||
- | Regexp search | + | |
- | < | + | |
- | "^[ \t]*Total energy:" | + | |
- | </ | + | |
- | will find the relevant line. | + | |
- | + | ||
- | Similarly, information on distribution of Gaussians on the | + | |
- | multi-grid can be found in the section: | + | |
- | < | + | |
- | ------------------------------------------------------------------------------- | + | |
- | ---- | + | |
- | ------------------------------------------------------------------------------- | + | |
- | count for grid 1: | + | |
- | count for grid 2: | + | |
- | count for grid 3: | + | |
- | count for grid 4: | + | |
- | total gridlevel count : 10496 | + | |
- | </ | + | |
- | which tells us that for [[http:// | + | |
- | Ry, 2720 product Gaussians | + | |
- | 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 '' | + | |
- | 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. | + | |
- | done, again, by using a simple script. '' | + | |
- | below is such an example: | + | |
- | + | ||
- | <code sh> | + | |
- | # | + | |
- | + | ||
- | cutoffs=" | + | |
- | + | ||
- | input_file=Si_bulk8.inp | + | |
- | output_file=Si_bulk8.out | + | |
- | plot_file=cutoff_data.ssv | + | |
- | + | ||
- | rel_cutoff=60 | + | |
- | + | ||
- | echo "# Grid cutoff vs total energy" | + | |
- | echo "# Date: $(date)" | + | |
- | echo "# PWD: $PWD" >> $plot_file | + | |
- | echo "# REL_CUTOFF = $rel_cutoff" | + | |
- | echo -n "# Cutoff (Ry) | Total Energy (Ha)" >> $plot_file | + | |
- | grid_header=true | + | |
- | for ii in $cutoffs ; do | + | |
- | work_dir=cutoff_${ii}Ry | + | |
- | total_energy=$(grep -e '^[ \t]*Total energy' | + | |
- | ngrids=$(grep -e '^[ \t]*QS| Number of grid levels:' | + | |
- | awk ' | + | |
- | if $grid_header ; then | + | |
- | for ((igrid=1; igrid <= $ngrids; igrid++)) ; do | + | |
- | printf " | NG on grid %d" $igrid >> $plot_file | + | |
- | done | + | |
- | printf " | + | |
- | grid_header=false | + | |
- | fi | + | |
- | printf " | + | |
- | for ((igrid=1; igrid <= $ngrids; igrid++)) ; do | + | |
- | grid=$(grep -e '^[ \t]*count for grid' $work_dir/ | + | |
- | awk -v igrid=$igrid '(NR == igrid){print $5}' | + | |
- | printf " | + | |
- | done | + | |
- | printf " | + | |
- | done | + | |
- | </ | + | |
- | + | ||
- | Type | + | |
- | < | + | |
- | chmod u+x ./ | + | |
- | </ | + | |
- | and then run it using | + | |
- | < | + | |
- | ./ | + | |
- | </ | + | |
- | will produce a file named '' | + | |
- | < | + | |
- | # Grid cutoff vs total energy | + | |
- | # Date: Mon Jan 20 21:20:34 GMT 2014 | + | |
- | # PWD: / | + | |
- | # REL_CUTOFF = 60 | + | |
- | # Cutoff (Ry) | Total Energy (Ha) | NG on grid 1 | NG on grid 2 | NG on grid 3 | NG on grid 4 | + | |
- | | + | |
- | 100.00 | + | |
- | 150.00 | + | |
- | 200.00 | + | |
- | 250.00 | + | |
- | 300.00 | + | |
- | 350.00 | + | |
- | 400.00 | + | |
- | 450.00 | + | |
- | 500.00 | + | |
- | </ | + | |
- | + | ||
- | The data shows that given the [[http:// | + | |
- | [[http:// | + | |
- | less than \(10^{-8}\) Ha. The reader may also notice that as [[http:// | + | |
- | increases, the number of Gaussians being assigned to the finest | + | |
- | grids decreases. Therefore, simply increasing [[http:// | + | |
- | increasing [[http:// | + | |
- | in energy, as more and more Gaussians get pushed to coarser grid | + | |
- | levels, negating the increase in [[http:// | + | |
- | + | ||
- | In this example, the test results point to 250 Ry as a good choice | + | |
- | for [[http:// | + | |
- | distribution of Gaussian functions on the grids are reasonable: it | + | |
- | is the lowest | + | |
- | but at the same time with the majority of the Gaussians on the | + | |
- | coarser grids. | + | |
- | ===== Converging '' | + | |
- | + | ||
- | In the next step, we vary the value of [[http:// | + | |
- | [[http:// | + | |
- | + | ||
- | ==== Generating Inputs ==== | + | |
- | + | ||
- | For the energy convergence test with varying [[http:// | + | |
- | follow a similar procedure as that for [[http:// | + | |
- | template input file '' | + | |
- | '' | + | |
- | + | ||
- | <code sh> | + | |
- | # | + | |
- | + | ||
- | rel_cutoffs=" | + | |
- | + | ||
- | 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 " | + | |
- | -e " | + | |
- | $template_file > $work_dir/ | + | |
- | cp $basis_file $work_dir | + | |
- | cp $potential_file $work_dir | + | |
- | done | + | |
- | </ | + | |
- | + | ||
- | Setting the permission for the script to " | + | |
- | it produces directories '' | + | |
- | each containing files '' | + | |
- | '' | + | |
- | [[http:// | + | |
- | 100 respectively. | + | |
- | ==== Running Calculations ==== | + | |
- | + | ||
- | Again to run the calculations, | + | |
- | '' | + | |
- | + | ||
- | <code sh> | + | |
- | # | + | |
- | + | ||
- | rel_cutoffs=" | + | |
- | + | ||
- | cp2k_bin=cp2k.popt | + | |
- | input_file=Si_bulk8.inp | + | |
- | output_file=Si_bulk8.out | + | |
- | no_proc_per_calc=2 | + | |
- | no_proc_to_use=16 | + | |
- | + | ||
- | counter=1 | + | |
- | max_parallel_calcs=$(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 " | + | |
- | if [ $mod_test -eq 0 ] ; then | + | |
- | wait | + | |
- | fi | + | |
- | counter=$(expr $counter + 1) | + | |
- | done | + | |
- | wait | + | |
- | </ | + | |
- | + | ||
- | 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: | + | |
- | < | + | |
- | ./ | + | |
- | </ | + | |
- | ==== 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 [[http:// | + | |
- | + | ||
- | To put all of the results from the [[http:// | + | |
- | one place, we can make some minor modifications to | + | |
- | '' | + | |
- | + | ||
- | <code sh> | + | |
- | # | + | |
- | + | ||
- | rel_cutoffs=" | + | |
- | + | ||
- | 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" | + | |
- | echo "# Date: $(date)" | + | |
- | echo "# PWD: $PWD" >> $plot_file | + | |
- | echo "# CUTOFF = ${cutoff}" | + | |
- | 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=$(grep -e '^[ \t]*Total energy' | + | |
- | ngrids=$(grep -e '^[ \t]*QS| Number of grid levels:' | + | |
- | awk ' | + | |
- | if $grid_header ; then | + | |
- | for ((igrid=1; igrid <= $ngrids; igrid++)) ; do | + | |
- | printf " | NG on grid %d" $igrid >> $plot_file | + | |
- | done | + | |
- | printf " | + | |
- | grid_header=false | + | |
- | fi | + | |
- | printf " | + | |
- | for ((igrid=1; igrid <= $ngrids; igrid++)) ; do | + | |
- | grid=$(grep -e '^[ \t]*count for grid' $work_dir/ | + | |
- | awk -v igrid=$igrid '(NR == igrid){print $5}' | + | |
- | printf " | + | |
- | done | + | |
- | printf " | + | |
- | done | + | |
- | </ | + | |
- | + | ||
- | Making the script executable, and running the script using | + | |
- | < | + | |
- | ./ | + | |
- | </ | + | |
- | produces the following results written in file | + | |
- | '' | + | |
- | + | ||
- | < | + | |
- | # Rel Grid cutoff vs total energy | + | |
- | # Date: Mon Jan 20 00:45:14 GMT 2014 | + | |
- | # PWD: / | + | |
- | # CUTOFF = 250 | + | |
- | # Rel Cutoff (Ry) | Total Energy (Ha) | NG on grid 1 | NG on grid 2 | NG on grid 3 | NG on grid 4 | + | |
- | | + | |
- | | + | |
- | | + | |
- | | + | |
- | | + | |
- | | + | |
- | | + | |
- | | + | |
- | | + | |
- | 100.00 | + | |
- | </ | + | |
- | + | ||
- | The results show that as one increases the value of [[http:// | + | |
- | more Gaussians get mapped onto the finer grids. The error in total | + | |
- | energy reduces to less than \(10^{-8}\) Ha when [[http:// | + | |
- | greater or equal to 60 Ry. The results thus indicate that 60 Ry is | + | |
- | indeed a suitable choice for the value of [[http:// | + | |
- | + | ||
- | So finally we conclude that the setting | + | |
- | <code cp2k> | + | |
- | & | + | |
- | CUTOFF 250 | + | |
- | REL_CUTOFF 60 | + | |
- | &END MGRID | + | |
- | </ | + | |
- | is sufficient for a calculation with the required accuracy. | + |
howto/converging_cutoff.txt · Last modified: 2024/05/29 15:46 by oschuett