Practical procedure using CASM
- Create prim.json file -> this file contains structural information about the primitive cell (we usually use exp cell) and initialize project:
casm init
Data structure:
Basis:
Coordinate -> coordiante for each site
occupant_dof -> [Na,Va] "Va" for vacancy
…
Coordinate_mode -> cartesian or fractional
Description
Lattice_vectors
Title
An example: (built from a NaSiCON structure, only a few sites are included as an example)
{
"basis" : [
{
"coordinate" : [ 0.500000, 0.500000, 0.500000],
"occupant_dof" : ["Na","Va"]
},
{
"coordinate" : [ 0.000000, 0.000000, 0.000000],
"occupant_dof" : ["Na","Va"]
},
{
"coordinate" : [ 0.889670, 0.610330, 0.250000],
"occupant_dof" : ["Na","Va"]
},
{
"coordinate" : [ 0.610330, 0.250000, 0.889670],
"occupant_dof" : ["Na","Va"]
},
{
"coordinate" : [ 0.250000, 0.889670, 0.610330],
"occupant_dof" : ["Na","Va"]
},
{
"coordinate" : [ 0.389670, 0.750000, 0.110330],
"occupant_dof" : ["Na","Va"]
},
{
"coordinate" : [ 0.750000, 0.110330, 0.389670],
"occupant_dof" : ["Na","Va"]
},
{
"coordinate" : [ 0.110330, 0.389670, 0.750000],
"occupant_dof" : ["Na","Va"]
},
{
"coordinate" : [ 0.352810, 0.352810, 0.352810],
"occupant_dof" : ["Zr"]
}
],
"coordinate_mode" : "Fractional",
"description" : "Si-based NASICON ",
"lattice_vectors" : [
[4.593150 ,2.651856 , 7.393667],
[-4.593150, 2.651856 , 7.393667],
[-0.000000, -5.303713, 7.393667]
],
"title" : "NASICON_prim"
}
- Create composition axes This is to define the composition that used for phase diagram 2 coupled axes are used for 2D cases, see "useful emails" for reason why we need this 2 coupled axes .casm/composition_axes.json
{
"current_axes" : "coupled",
"custom_axes" : {
"coupled" : {
"a" : [
[ 2.000000000000 ],
[ 6.000000000000 ],
[ 4.000000000000 ],
[ 0.000000000000 ],
[ 6.000000000000 ],
[ 24.000000000000 ]
],
"b" : [
[ 2.000000000000 ],
[ 6.000000000000 ],
[ 4.000000000000 ],
[ 0.000000000000 ],
[ -6.000000000000 ],
[ 24.000000000000 ]
],
"components" : [ "Na", "Va", "Zr", "Si", "P", "O" ],
"independent_compositions" : 2,
"origin" : [
[ 8.000000000000 ],
[ 0.000000000000 ],
[ 4.000000000000 ],
[ 6.000000000000 ],
[ 0.000000000000 ],
[ 24.000000000000 ]
]
}
}
}
Composition = Origin + (End-Origin)x (End = a or b here) Then compute composition axes
casm composition -c
- Import calculated DFT results
Use
vasp.relax.reportto generate properties.calc.json in each directories Generate a file list containing all the path to POSCARreports_path_primitive.txtImport results into.casm/config_list.jsonif you want to update new results, make sure you exclude old paths inreports_path_primitive.txtotherwise it will have duplications in database
casm import --batch reports_path.txt --ideal --data --min-energy
- Choose chemical reference (per species = per atom)
'[
{"Na": 8.0, "Zr": 4.0, "Si": 6.0, "P": 0.0, "O": 24.0, "energy_per_species": -7.39616323214285714285},
{"Na": 2.0, "Zr": 4.0, "Si": 0.0, "P": 6.0, "O": 24.0, "energy_per_species": -7.93335068250000000000},
{"Na": 8.0, "Zr": 0.0, "Si": 6.0, "P": 0.0, "O": 24.0, "energy_per_species": 0.00000000000000000000}
]'
Pass the piece above directly to the command!!
casm ref --set '[{"Na": 8.0, "Zr": 4.0, "Si": 6.0, "P": 0.0, "O": 24.0, "energy_per_species": -7.39616323214285714285}, {"Na": 2.0, "Zr": 4.0, "Si": 0.0, "P": 6.0, "O": 24.0, "energy_per_species": -7.93335068250000000000}, {"Na": 1.0, "energy_per_species": -1.308547}, {"Zr": 1.0, "energy_per_species": -8.547687}]'
The chemical reference can be updated later
casm update
Here I used the lowest energy structure should be used
casm ref --set '[{"Na": 8.0, "Zr": 4.0, "Si": 6.0, "P": 0.0, "O": 24.0, "energy_per_species": -11.732566428571428}, {"Na": 2.0, "Zr": 4.0, "Si": 0.0, "P": 6.0, "O": 24.0, "energy_per_species": -12.525085}, {"Na": 1.0, "energy_per_species": -4.2040927}, {"Zr": 1.0, "energy_per_species": -30.6929575}]'
- Create basis function (it's better to use chebychev basis function) basis_sets/bset.default/bspecs.json Occupation can be changed to other properties like spin etc.. Orbit_branch_specs: set the size of cluster for generating basis function, usually decrease with the increment of order
{
"basis_functions" : {
"site_basis_functions" : "occupation"
},
"orbit_branch_specs" : {
"2" : {"max_length" : 10.0000},
"3" : {"max_length" : 6.00000},
"4" : {"max_length" : 5.00000}
}
}
Then compile to get basis function -> it might take 30 mins!
casm bset -u
- Prepare fitting ECI Create a folder e.g. fit_1 Select candidates for fitting and save to "train"
casm select --set is_calculated -o train
Create casm-learn input file fit.json using lasso algorithm Candidate list file: "filename" (train here) should exist in this folder
{
"estimator": {
"method": "Lasso",
"kwargs": {
"alpha": 0.0001,
"max_iter": 1000000.0
}
},
"feature_selection": {
"method": "SelectFromModel",
"kwargs": null
},
"problem_specs": {
"data": {
"y": "formation_energy",
"X": "corr",
"kwargs": null,
"type": "selection",
"filename": "train"
},
"cv": {
"penalty": 0.0,
"method": "LeaveOneOut"
}
},
"n_halloffame": 25
}
- Fit ECI
casm-learn -s fit.json
Problem specs file will be generated "fit_specs.pkl" storing the training data, weights, and cross-validation train/test sets and "fit_halloffame.pkl" storing the selected candidates Then adjust fit.json and repeat fitting until the fitting is satisfied (use least feature to reproduce most results). See "casm-learn --settings-format"
casm-learn --settings-format
Generation: eci.json and use it for monte carlo
casm-learn -s fit.json --select 0
- Plot convex hull Query energies from database:
casm query -k 'comp(a)' 'formation_energy' 'clex(formation_energy)' 'hull_dist(ALL,atom_frac)' 'clex_hull_dist(ALL,atom_frac)' -c train -o data.dat
Query hull from database
casm query -k 'comp(a)' 'formation_energy' 'clex(formation_energy)' 'on_hull(ALL,comp)' 'on_clex_hull(ALL,comp)' 'comp_n(Na)' -c train -o hull.dat
- You'll see that the difference between cluster expansion (clex) convex hull is far away from DFT convex hull. To fix this , firstly, fix the correlation (cluster expansion coefficient, see useful emails Point term) and fit the weight. Then use:
filename=$1
./clean.sh
rm ${filename%.*}_*
casm-learn -s $filename
casm-learn -s $filename --checkhull
casm-learn -s $filename --select 0
casm-learn -s $filename --hall --indiv 0 --format json > ${filename%.*}-eci.json
#casm query -k 'comp(a)' 'formation_energy' 'clex(formation_energy)' 'hull_dist(ALL,atom_frac)' 'clex_hull_dist(ALL,atom_frac)' -c ALL -o data.dat
#casm query -k 'comp(a)' 'formation_energy' 'clex(formation_energy)' 'on_hull(ALL,comp)' 'on_clex_hull(ALL,comp)' 'comp_n(Na)' -c ALL -o hull.dat
casm query -k 'comp(a)' 'formation_energy' 'clex(formation_energy)' 'hull_dist(ALL,atom_frac)' 'clex_hull_dist(ALL,atom_frac)' -c train -o data.dat
casm query -k 'comp(a)' 'formation_energy' 'clex(formation_energy)' 'on_hull(ALL,comp)' 'on_clex_hull(ALL,comp)' 'comp_n(Na)' -c train -o hull.dat
python plot_convex_refactor.py
mv Convex_hull.pdf ${filename%.*}.pdf
mv hull.dat ${filename%.*}_hull.dat
mv data.dat ${filename%.*}_fit.dat
echo ${filename%.*}
open ${filename%.*}.pdf
- To do fitting. Tuning the weight of train file until the error (CV) become small. In addition, the ECI should follow the general trend: pair is dominant then triplet, quadruplet etc. First of all, use following command to query corr to train_weight.dat
casm query -k "formation_energy corr" -c train -o casm_learn_input
Next, add a column called "weight" and put all the point term Then, using following fit.json to do fitting
{
"estimator": {
"method": "Lasso",
"kwargs": {
"alpha": 0.0001,
"max_iter": 1000000.0
}
},
"feature_selection": {
"method": "SelectFromModel",
"kwargs": null
},
"problem_specs": {
"data": {
"y": "formation_energy",
"X": "corr",
"kwargs": null,
"type": "selection",
"filename": "train"
},
"cv": {
"penalty": 0.0,
"method": "LeaveOneOut"
},
"weight":{
"method":"wCustom"
}
},
"n_halloffame": 25
}