Optimization¶

import some modules¶

[1]:

from dftpy.ions import Ions
from dftpy.field import DirectField
from dftpy.grid import DirectGrid
from dftpy.functional import LocalPseudo, Functional, TotalFunctional
from dftpy.formats import io
from dftpy.math_utils import ecut2nr
from dftpy.time_data import TimeData
from dftpy.optimization import Optimization
from dftpy.mpi import sprint

pseudopotential file¶

[2]:

path_pp='../DATA/'
file1='Al_lda.oe01.recpot'
PP_list = {'Al': path_pp+file1}

build the ions or read from file¶

[3]:

from ase.build import bulk
atoms = bulk('Al', 'fcc', a=4.05, cubic=True)
ions = Ions.from_ase(atoms)
# ions = io.read(posfile)

make a grid¶

[4]:

nr = ecut2nr(ecut=35, lattice=ions.cell)
grid = DirectGrid(lattice=ions.cell, nr=nr)
sprint('The final grid size is ', nr)

The final grid size is  [20 20 20]

build local pseudo, and generate guess density¶

[5]:

PSEUDO = LocalPseudo(grid = grid, ions=ions, PP_list=PP_list)

rho_ini = DirectField(grid=grid)
rho_ini[:] = ions.get_ncharges()/ions.cell.volume

setting key: Al -> ../DATA/Al_lda.oe01.recpot

instance KEDF, XC and HARTREE functionals¶

[6]:

KE = Functional(type='KEDF',name='TFvW')
XC = Functional(type='XC',name='LDA')
HARTREE = Functional(type='HARTREE')

instance DFTpy evaluator¶

[7]:

evaluator = TotalFunctional(KE=KE, XC=XC, HARTREE=HARTREE, PSEUDO=PSEUDO)

instance and execute DFTpy density optimizer¶

[8]:

optimization_options = {'econv' : 1e-6*ions.nat}
opt = Optimization(EnergyEvaluator=evaluator, optimization_options = optimization_options,
        optimization_method = 'TN')

rho = opt.optimize_rho(guess_rho=rho_ini)

Step    Energy(a.u.)            dE              dP              Nd      Nls     Time(s)
0       -8.090977710718E+00     -8.090978E+00   7.877088E-01    1       1       1.902819E-02
1       -8.273226052119E+00     -1.822483E-01   7.033208E-02    2       1       3.294325E-02
2       -8.280858141000E+00     -7.632089E-03   4.803522E-03    7       1       5.704927E-02
3       -8.281101062862E+00     -2.429219E-04   3.640550E-04    5       1       7.545233E-02
4       -8.281135978745E+00     -3.491588E-05   3.590863E-05    6       1       9.528708E-02
5       -8.281138625688E+00     -2.646943E-06   2.500624E-06    5       1       1.117182E-01
6       -8.281138996216E+00     -3.705278E-07   4.567996E-08    8       1       1.352971E-01
#### Density Optimization Converged ####
Chemical potential (a.u.): 0.30115196532053357
Chemical potential (eV)  : 8.194762380333897

evaluate final energy¶

[9]:

energy = evaluator.Energy(rho=rho, ions=ions)
print('Energy (a.u.)', energy)

Energy (a.u.) -8.2811389962163

print the timing¶

[10]:

TimeData.output(lprint=True, sort='cost')

--------------------------------Time information--------------------------------
Label                       Cost(s)                 Number          Avg. Cost(s)
ewald.Energy_corr           0.0001                  1               0.0001
CBspline._calc_PME_Qarray   0.0016                  1               0.0016
ewald.Energy_rec_PME        0.0025                  1               0.0025
LocalPseudo.local_PP        0.0045                  1               0.0045
ewald.Energy_real_fast2     0.0054                  1               0.0054
TF                          0.0066                  41              0.0002
ewald.energy                0.0080                  41              0.0002
LDA                         0.0125                  41              0.0003
FFT                         0.0320                  84              0.0004
InvFFT                      0.0359                  83              0.0004
Hartree.compute             0.0364                  41              0.0009
vW                          0.0458                  41              0.0011
Optimize                    0.1377                  1               0.1377

[11]:

rho.write('rho.xsf', ions=ions)
rho.write('rho.cube', ions=ions)

Visualize with scikit-image and matplotlib¶

!pip install scikit-image matplotlib

[12]:

from dftpy.visualize import view

Visualize with VESTA¶

[15]:

view(ions=ions, data=rho, viewer='vesta')

save ./.dftpy.xsf in darwin platform