Usage of Dataset class, the CO molecule as example

In this tutorial, the basics of the Dataset class are briefly reviewed in a convergence study of the CO molecule, before presenting an example of application where the polarizability tensor \(\alpha\) is computed. It is advised to have done the tutorial on the methane molecule before in order to be familiar with the fundamentals of Dataset calculations.

from BigDFT import Datasets as D
from BigDFT import Calculators as C
from BigDFT import Inputfiles as I
import numpy as np
import matplotlib.pyplot as plt

Convergence of the ground state of the CO molecule

In this example, the convergence analysis of the Ground State (GS) energy of the CO molecule is performed with respect to the size of the simulation domain.

First, we instantiate both the calculator and the Dataset objects.

calc = C.SystemCalculator(omp=2,mpi_run='mpirun -np 4',skip=True,verbose=False)
study = D.Dataset(label='CO',run_dir='conv-CO',posinp='CO_posinp.xyz',molecule_shape='linear')

The object study is characterized by its label ‘CO_GS’ and contains the path run_dir in which all the calculations of the dataset will be performed. The variable molecule_shape has been introduced to show how further information can be passed to the dataset instances. For reminder, global options can be extracted as follows

print(study.global_options())

{'label': 'CO', 'run_dir': 'conv-CO', 'posinp': 'CO_posinp.xyz', 'molecule_shape': 'linear'}

Next, the input file is created while essential computational parameters are provided.

# Define the default parameters of the input file
inp = I.Inputfile()
inp.set_hgrid(0.37)
inp.set_scf_convergence(gnrm=1.0e-5)

The convergence analysis will be performed on the values of rmult.

We prepare the study for the convergence analysis by appending the run associated to the values of rmult. Each run is characterized by an id and contains the InputFile object as input as well as the runner used to perform the calculation. If the same id is provided more than once, the function gives a Value Error.

rmult = [5.0,6.0,7.0,8.0]

for r in rmult:
    inp.set_rmult(coarse=r,fine=9.0)
    study.append_run(id={'rmult':r},runner=calc,input=inp)

The following member of the Dataset class shows how to refer to the various calculation of study.

print(study.calculators)
print(study.ids)

[{'calc': <BigDFT.Calculators.SystemCalculator object at 0x7fab00f522d0>, 'runs': [0, 1, 2, 3]}]
[{'rmult': 5.0}, {'rmult': 6.0}, {'rmult': 7.0}, {'rmult': 8.0}]

A particular instance is accessed by

print(study.ids[2])
print(study.runs[2])

{'rmult': 7.0}
{'label': 'CO', 'run_dir': 'conv-CO', 'posinp': 'CO_posinp.xyz', 'molecule_shape': 'linear', 'input': {'dft': {'hgrids': 0.37, 'gnrm_cv': 1e-05, 'rmult': [7.0, 9.0]}, 'lin_general': {'rpnrm_cv': 'default'}, 'mix': {'rpnrm_cv': 'default'}}}

study.names contains a list of strings with the ids of the run. May be useful for labelling.

study.names

['rmult__5.0', 'rmult__6.0', 'rmult__7.0', 'rmult__8.0']

The appended simulation can be executed with the run method. The skip=True in the runner instance guarantees that computation already performed are not executed again.

study.run()

 <BigDFT> Run already performed, found final file: forces_rmult__5.0.xyz
 <BigDFT> Run already performed, found final file: forces_rmult__5.0.xyz
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 13.240 MB
 Walltime since initialization:  00:00:00.002416237
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 13.172 MB
 Walltime since initialization:  00:00:00.002035260
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
 <BigDFT> Run already performed, found final file: forces_rmult__5.0.xyz
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 12.984 MB
 Walltime since initialization:  00:00:00.002722207
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
 <BigDFT> Run already performed, found final file: forces_rmult__5.0.xyz
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 13.168 MB
 Walltime since initialization:  00:00:00.001309965
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
 <BigDFT> Run already performed, found final file: forces_rmult__6.0.xyz
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 12.948 MB
 Walltime since initialization:  00:00:00.001916676
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
 <BigDFT> Run already performed, found final file: forces_rmult__6.0.xyz
 <BigDFT> Run already performed, found final file: forces_rmult__6.0.xyz
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 13.044 MB
 Walltime since initialization:  00:00:00.003671661
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 12.996 MB
 Walltime since initialization:  00:00:00.003537731
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
 <BigDFT> Run already performed, found final file: forces_rmult__6.0.xyz
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 12.852 MB
 Walltime since initialization:  00:00:00.002670475
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
 <BigDFT> Run already performed, found final file: forces_rmult__7.0.xyz
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 12.964 MB
 Walltime since initialization:  00:00:00.003039964
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
 <BigDFT> Run already performed, found final file: forces_rmult__7.0.xyz
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 12.920 MB
 Walltime since initialization:  00:00:00.002309739
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
 <BigDFT> Run already performed, found final file: forces_rmult__7.0.xyz
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 12.944 MB
 Walltime since initialization:  00:00:00.002341033
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
 <BigDFT> Run already performed, found final file: forces_rmult__7.0.xyz
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 13.036 MB
 Walltime since initialization:  00:00:00.001929867
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
 <BigDFT> Run already performed, found final file: forces_rmult__8.0.xyz
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 13.040 MB
 Walltime since initialization:  00:00:00.002977071
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
 <BigDFT> Run already performed, found final file: forces_rmult__8.0.xyz
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 13.096 MB
 Walltime since initialization:  00:00:00.003468013
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
 <BigDFT> Run already performed, found final file: forces_rmult__8.0.xyz
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 13.164 MB
 Walltime since initialization:  00:00:00.002740734
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
 <BigDFT> Run already performed, found final file: forces_rmult__8.0.xyz
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 13.064 MB
 Walltime since initialization:  00:00:00.002684471
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1

{0: <BigDFT.Logfiles.Logfile at 0x7fab096d15d0>,
 1: <BigDFT.Logfiles.Logfile at 0x7fab00f01e10>,
 2: <BigDFT.Logfiles.Logfile at 0x7fab0946c290>,
 3: <BigDFT.Logfiles.Logfile at 0x7fab00ec2fd0>}

Analyzing the dataset output

The class member study.results contains a dictionary with the logfiles of the computations performed by the run method, returned in the order of which the append_run was performed.

results = study.results

Several operation can be performed on the results by using the methods of the Logfile class.

For example, the total energy w.r.t. the domain size is obtained as

for ci in study.calculators[0]['runs']:
    print(study.ids[ci]['rmult'],results[ci].energy,study.names[ci])
    plt.scatter(study.ids[ci]['rmult'],results[ci].energy,label=study.names[ci])
plt.legend()
plt.title('Energy',size=12)
plt.ylim(-21.661,-21.662)
plt.show()

5.0 -21.661153985020135 rmult__5.0
6.0 -21.66134584205134 rmult__6.0
7.0 -21.6613579335895 rmult__7.0
8.0 -21.661359464443258 rmult__8.0

Other useful quantities can be extract using the methods of the Logfile class, for instance

print(results[0].dipole)
print(results[0].evals[0][0])
print(results[0].log['dft']['rmult'])
print(results[0].log['Electric Dipole Moment (AU)'])

[-0.0002296574, -0.0002296574, 0.09288163]
[-1.07897861 -0.5212773  -0.44461433 -0.44461428 -0.33423529]
[5.0, 9.0]
{'P vector': [-0.0002296574, -0.0002296574, 0.09288163], 'norm(P)': 0.0928822004}

dos = results[0].get_dos(label=study.names[0])
dos.append_from_bandarray(results[2].evals,label=study.names[2])
dos.plot(sigma=0.2)

<AxesSubplot:xlabel='Energy [eV]', ylabel='DoS'>

Alternatively, results associated to specific id and/or attribute can be extracted as follows:

study.fetch_results()

[<BigDFT.Logfiles.Logfile at 0x7fab096d15d0>,
 <BigDFT.Logfiles.Logfile at 0x7fab00f01e10>,
 <BigDFT.Logfiles.Logfile at 0x7fab0946c290>,
 <BigDFT.Logfiles.Logfile at 0x7fab00ec2fd0>]

If an attribute and/or an id is provided, fetch_results extracts only the wanted results, for instance

print(study.fetch_results(attribute='energy'))
print(study.fetch_results({'rmult': 8.0},attribute='energy'))

[-21.661153985020135, -21.66134584205134, -21.6613579335895, -21.661359464443258]
[-21.661359464443258]

Post processing analysis

It is also possible to define a post-processing function that is passed to the Dataset instance. This function is called after the run and the output of study.run and contains the output of the post-processing function. We show some examples.

1. Extraction of the ground state dipole

def get_dipole(dataset):
    dipole = dataset.fetch_results(attribute='dipole')
    return dipole

study.set_postprocessing_function(get_dipole)

dipole_GS = study.run();

 <BigDFT> Run already performed, found final file: forces_rmult__5.0.xyz
 <BigDFT> Run already performed, found final file: forces_rmult__5.0.xyz
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 13.188 MB
 Walltime since initialization:  00:00:00.002320176
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 13.116 MB
 Walltime since initialization:  00:00:00.001857607
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
 <BigDFT> Run already performed, found final file: forces_rmult__5.0.xyz
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 12.880 MB
 Walltime since initialization:  00:00:00.002457699
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
 <BigDFT> Run already performed, found final file: forces_rmult__5.0.xyz
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 12.920 MB
 Walltime since initialization:  00:00:00.001436096
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
 <BigDFT> Run already performed, found final file: forces_rmult__6.0.xyz
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 13.136 MB
 Walltime since initialization:  00:00:00.001975332
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
 <BigDFT> Run already performed, found final file: forces_rmult__6.0.xyz
 <BigDFT> Run already performed, found final file: forces_rmult__6.0.xyz
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 13.192 MB
 Walltime since initialization:  00:00:00.002590704
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 13.024 MB
 Walltime since initialization:  00:00:00.004530220
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
 <BigDFT> Run already performed, found final file: forces_rmult__6.0.xyz
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 12.972 MB
 Walltime since initialization:  00:00:00.001923389
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
 <BigDFT> Run already performed, found final file: forces_rmult__7.0.xyz
 <BigDFT> Run already performed, found final file: forces_rmult__7.0.xyz
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 12.976 MB
 Walltime since initialization:  00:00:00.003120294
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 12.968 MB
 Walltime since initialization:  00:00:00.003271214
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
 <BigDFT> Run already performed, found final file: forces_rmult__7.0.xyz
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 13.192 MB
 Walltime since initialization:  00:00:00.003475566
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
 <BigDFT> Run already performed, found final file: forces_rmult__7.0.xyz
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 13.140 MB
 Walltime since initialization:  00:00:00.001982148
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
 <BigDFT> Run already performed, found final file: forces_rmult__8.0.xyz
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 13.068 MB
 Walltime since initialization:  00:00:00.003002721
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
 <BigDFT> Run already performed, found final file: forces_rmult__8.0.xyz
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 12.948 MB
 Walltime since initialization:  00:00:00.002069531
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
 <BigDFT> Run already performed, found final file: forces_rmult__8.0.xyz
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 13.040 MB
 Walltime since initialization:  00:00:00.002824836
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
 <BigDFT> Run already performed, found final file: forces_rmult__8.0.xyz
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 12.864 MB
 Walltime since initialization:  00:00:00.002868074
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1

dipole_GS

[[-0.0002296574, -0.0002296574, 0.09288163],
 [-3.391146e-05, -3.391146e-05, 0.09150228],
 [-2.716707e-06, -2.716707e-06, 0.09138863],
 [-1.027985e-05, -1.027985e-05, 0.09137423]]

2. Extraction of the box size

def get_size(dataset): # how to do def get_size(study,unit)
    sizes = []
    results = dataset.fetch_results()
    for calc,res in enumerate(results):
        sizes.append(res.log['Sizes of the simulation domain']['AU'])
    return sizes

study.set_postprocessing_function(get_size)

boxsize = study.run();

 <BigDFT> Run already performed, found final file: forces_rmult__5.0.xyz
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 13.096 MB
 Walltime since initialization:  00:00:00.001892042
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
 <BigDFT> Run already performed, found final file: forces_rmult__5.0.xyz
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 12.912 MB
 Walltime since initialization:  00:00:00.002937710
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
 <BigDFT> Run already performed, found final file: forces_rmult__5.0.xyz
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 13.148 MB
 Walltime since initialization:  00:00:00.002323018
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
 <BigDFT> Run already performed, found final file: forces_rmult__5.0.xyz
 Memory Consumption Report:
   Tot. No. of Allocations:  0
   Tot. No. of Deallocations:  0
   Remaining Memory (B):  0
   Memory occupation:
     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 13.040 MB
 Walltime since initialization:  00:00:00.002103268
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
 <BigDFT> Run already performed, found final file: forces_rmult__6.0.xyz
 <BigDFT> Run already performed, found final file: forces_rmult__6.0.xyz
 Memory Consumption Report:
 Memory Consumption Report:
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     Peak Value (MB):  0.000
     for the array: null
     in the routine: null
     Memory Peak of process: 13.132 MB
   Remaining Memory (B):  0
   Memory occupation:
 Walltime since initialization:  00:00:00.001781993
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 #( 1052 still in use)
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     in the routine: null
     Memory Peak of process: 13.124 MB
 Walltime since initialization:  00:00:00.001959716
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
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     in the routine: null
     Memory Peak of process: 13.020 MB
 Walltime since initialization:  00:00:00.002936658
 Max No. of dictionaries used:  1127 #( 1052 still in use)
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     in the routine: null
     Memory Peak of process: 12.848 MB
 Walltime since initialization:  00:00:00.001439685
 Max No. of dictionaries used:  1127 #( 1052 still in use)
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 Memory Consumption Report:
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     Memory Peak of process: 13.124 MB
 Walltime since initialization:  00:00:00.002528723
 Memory Consumption Report:
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     Peak Value (MB):  0.000
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     Memory Peak of process: 13.076 MB
 Walltime since initialization:  00:00:00.002172121
 Max No. of dictionaries used:  1127 #( 1052 still in use)
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     Memory Peak of process: 13.144 MB
 <BigDFT> Run already performed, found final file: forces_rmult__7.0.xyz
 Walltime since initialization:  00:00:00.002709484
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
 Memory Consumption Report:
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     Memory Peak of process: 13.096 MB
 Walltime since initialization:  00:00:00.003000579
 Max No. of dictionaries used:  1127 #( 1052 still in use)
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     Memory Peak of process: 13.024 MB
 Walltime since initialization:  00:00:00.001800861
 Max No. of dictionaries used:  1127 #( 1052 still in use)
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 <BigDFT> Run already performed, found final file: forces_rmult__8.0.xyz
 <BigDFT> Run already performed, found final file: forces_rmult__8.0.xyz
 Memory Consumption Report:
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     Memory Peak of process: 13.000 MB
 Walltime since initialization:  00:00:00.002194757
 Max No. of dictionaries used:  1127 #( 1052 still in use)
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     in the routine: null
     Memory Peak of process: 13.096 MB
 Walltime since initialization:  00:00:00.002099085
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
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 Memory Consumption Report:
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     Memory Peak of process: 13.228 MB
 Walltime since initialization:  00:00:00.001375382
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boxsize

[[15.54, 15.54, 15.91],
 [18.87, 18.87, 18.87],
 [21.83, 21.83, 21.83],
 [25.16, 25.16, 25.16]]

Computation of the statical polarizability tensor \(\alpha\)

We choose a single value of rmult, the lowest among the ones computed in the GS analysis for which a satisfactory convergence is obtained. The statical polarizability tensor of the CO molecule is then computed.

ind = 2
print('rmult value : ',study.ids[ind]['rmult'])

rmult value :  7.0

The input file is defined for the statical polarizability computation

inp.set_rmult(coarse=study.ids[ind]['rmult'],fine = 9.0)
print(inp)

{'dft': {'hgrids': 0.37, 'gnrm_cv': 1e-05, 'rmult': [7.0, 9.0]}, 'lin_general': {'rpnrm_cv': 'default'}, 'mix': {'rpnrm_cv': 'default'}}

Next, let us define a dataset (called ef, i.e. electric field) for the computation of \(\alpha\) using an electric field intensity of \(1e^{-2} V/m\), which is assumed compatible with the linear response regime.

intensity = 1.e-2
ef = D.Dataset(label='alpha',run_dir='CO_alpha',posinp='CO_posinp.xyz',
               input=inp,d0=dipole_GS[ind],F=intensity)
for idir,coord in enumerate(['x','y','z']):
    efi = np.zeros(3)
    efi[idir] = intensity
    inp.apply_electric_field(efi.tolist())
    ef.append_run({'id':coord,'F':intensity},runner=calc,input=inp)

This yields the following elements in the dataset

ef.ids

[{'id': 'x', 'F': 0.01}, {'id': 'y', 'F': 0.01}, {'id': 'z', 'F': 0.01}]

Lastly, let us write a post-processing function on how to compute \(\alpha\)

def extract_alpha(ef):
    """
    alpha_ij isthe i-th component of the vector d-d0,
    computed with a field in the j-th direction,
    divided for the intensity of the field.
    """
    d0 = np.array(ef.get_global_option('d0'));
    F = ef.get_global_option('F');
    d = ef.fetch_results(attribute='dipole');
    alpha = np.mat(np.zeros(9)).reshape(3,3)
    for idir in range(3):
        alpha[idir] = (np.array(d[idir])-d0)/F
    return alpha

ef.set_postprocessing_function(extract_alpha)

alpha = ef.run();

 <BigDFT> Run already performed, found final file: forces_F__0.01,id__x.xyz
 Memory Consumption Report:
   Tot. No. of Allocations:  0
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     Memory Peak of process: 13.044 MB
 Walltime since initialization:  00:00:00.001600831
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     Memory Peak of process: 13.176 MB
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 Walltime since initialization:  00:00:00.001526451
 Max No. of dictionaries used:  1127 #( 1052 still in use)
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     Memory Peak of process: 13.196 MB
 Walltime since initialization:  00:00:00.002919425
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     Memory Peak of process: 13.212 MB
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     Memory Peak of process: 13.040 MB
 Walltime since initialization:  00:00:00.001618805
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     Memory Peak of process: 12.980 MB
 Walltime since initialization:  00:00:00.002415710
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     Memory Peak of process: 13.192 MB
 Walltime since initialization:  00:00:00.003128113
 Max No. of dictionaries used:  1127 #( 1052 still in use)
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   Tot. No. of Allocations:  0
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     Memory Peak of process: 12.980 MB
 Walltime since initialization:  00:00:00.001501875
 Max No. of dictionaries used:  1127 #( 1052 still in use)
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   Tot. No. of Allocations:  0
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     Memory Peak of process: 13.208 MB
 Walltime since initialization:  00:00:00.002225970
 Max No. of dictionaries used:  1127 #( 1052 still in use)
 Number of dictionary folders allocated:  1
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 Memory Consumption Report:
   Tot. No. of Allocations:  0
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     Memory Peak of process: 12.784 MB
 Walltime since initialization:  00:00:00.001519930
 Max No. of dictionaries used:  1127 #( 1052 still in use)
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     Memory Peak of process: 13.152 MB
 Walltime since initialization:  00:00:00.002236353
 Max No. of dictionaries used:  1127 #( 1052 still in use)
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     Memory Peak of process: 13.208 MB
 Walltime since initialization:  00:00:00.002061216
 Max No. of dictionaries used:  1127 #( 1052 still in use)
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The polarizability tensor is then

alpha

matrix([[ 1.26637417e+01, -2.31315400e-04,  4.23620000e-02],
        [-2.31315400e-04,  1.26637417e+01,  4.23620000e-02],
        [ 4.21875400e-04,  4.21875400e-04,  1.60751070e+01]])