CatKit

Table of Contents

1 Graph-atoms (Gratoms) object

The Gratoms object is a child class of the ASE Atoms object class. Effectively, this means that it has all the same functionality as an Atoms object with some additional features as well.

1.1 Graph information

The Gratoms object primary function is to conveniently store and manage graph information. 

from catkit import Gratoms
from catkit.build import molecule
import numpy as np

atoms0 = molecule('C4H10')[0]

print(type(atoms0))
print('\nAtomic numbers')
numbers = atoms0.numbers

print('#+attr_latex: :mode math :environment matrix')
print('|' + '|'.join(numbers.astype(str)))

print('\nConnectivity matrix:'.format())
matrix = atoms0.connectivity
table_matrix = np.array(matrix, dtype=str)

print('#+attr_latex: :mode math :environment matrix')
for row in table_matrix:
    print('|' + '|'.join(row.astype(str)))

atoms1 = atoms0.copy()
del atoms1[0]

print('\nAtomic numbers')
numbers = atoms1.numbers

print('#+attr_latex: :mode math :environment matrix')
print('|' + '|'.join(numbers.astype(str)))

print('\nConnectivity matrix:'.format())
matrix = atoms1.connectivity
table_matrix = np.array(matrix, dtype=str)

print('#+attr_latex: :mode math :environment matrix')
for row in table_matrix:
    print('|' + '|'.join(row.astype(str)))

print('\nAre isomorphs: {}'.format(atoms0.is_isomorph(atoms1)))

<class 'catkit.gratoms.Gratoms'>

Atomic numbers

6 6 6 6 1 1 1 1 1 1 1 1 1 1

Connectivity matrix:

0 1 1 1 1 0 0 0 0 0 0 0 0 0
1 0 0 0 0 1 1 1 0 0 0 0 0 0
1 0 0 0 0 0 0 0 1 1 1 0 0 0
1 0 0 0 0 0 0 0 0 0 0 1 1 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0

Atomic numbers

6 6 6 1 1 1 1 1 1 1 1 1 1

Connectivity matrix:

0 0 0 0 1 1 1 0 0 0 0 0 0
0 0 0 0 0 0 0 1 1 1 0 0 0
0 0 0 0 0 0 0 0 0 0 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0

Are isomorphs: False

2 PawPrint

The fingerprint generator is designed to be a general purpose utility for returning manipulated parameters from a list of possible operations. The possible operations which are currently implemented cat be found in ./pawprint/operations.py.

The complete list of seeding parameters which can be called from is available from the data dictionary produced from Mendeleev. 

import json

with open('../../catkit/data/properties.json', 'r') as f:
    data = json.load(f)

print('|Keys| First 10 values')
print('|-')
for k, v in data.items():
    print('|{}|{}'.format(k, ', '.join([str(round(_, 3)) for _ in v[1:11]])))
Keys First 10 values
atomic_number 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
atomic_radius 0.79, nan, 1.55, 1.12, 0.98, 0.91, 0.92, nan, nan, nan
atomic_radius_rahm 1.54, 1.34, 2.2, 2.19, 2.05, 1.9, 1.79, 1.71, 1.63, 1.56
atomic_volume 14.1, 31.8, 13.1, 5.0, 4.6, 5.3, 17.3, 14.0, 17.1, 16.8
atomic_weight 1.008, 4.003, 6.94, 9.012, 10.81, 12.011, 14.007, 15.999, 18.998, 20.18
boiling_point 20.28, 4.216, 1118.15, 3243.0, 3931.0, 5100.0, 77.4, 90.19, 85.01, 27.1
c6 6.499, 1.42, 1392.0, 227.0, 99.5, 46.6, 24.2, 15.6, 9.52, 6.2
c6_gb 6.51, 1.47, 1410.0, 214.0, 99.2, 47.9, 25.7, 16.7, 10.2, 6.91
covalent_radius_bragg nan, nan, 1.5, 1.15, nan, 0.77, 0.65, 0.65, 0.67, nan
covalent_radius_cordero 0.31, 0.28, 1.28, 0.96, 0.84, 0.73, 0.71, 0.66, 0.57, 0.58
covalent_radius_pyykko 0.32, 0.46, 1.33, 1.02, 0.85, 0.75, 0.71, 0.63, 0.64, 0.67
covalent_radius_pyykko_double nan, nan, 1.24, 0.9, 0.78, 0.67, 0.6, 0.57, 0.59, 0.96
covalent_radius_pyykko_triple nan, nan, nan, 0.85, 0.73, 0.6, 0.54, 0.53, 0.53, nan
covalent_radius_slater 0.25, nan, 1.45, 1.05, 0.85, 0.7, 0.65, 0.6, 0.5, nan
dband_center_bulk nan, nan, nan, nan, nan, nan, nan, nan, nan, nan
dband_center_slab 1.0, nan, nan, nan, nan, 1.0, 1.0, 1.0, 1.0, nan
dband_kurtosis_bulk nan, nan, nan, nan, nan, nan, nan, nan, nan, nan
dband_kurtosis_slab 1.0, nan, nan, nan, nan, 1.0, 1.0, 1.0, 1.0, nan
dband_skewness_bulk nan, nan, nan, nan, nan, nan, nan, nan, nan, nan
dband_skewness_slab 1.0, nan, nan, nan, nan, 1.0, 1.0, 1.0, 1.0, nan
dband_width_bulk nan, nan, nan, nan, nan, nan, nan, nan, nan, nan
dband_width_slab 1.0, nan, nan, nan, nan, 1.0, 1.0, 1.0, 1.0, nan
density 0.071, 0.147, 0.534, 1.848, 2.34, 2.25, 0.808, 1.149, 1.108, 1.204
dipole_polarizability 4.507, 1.384, 164.0, 37.71, 20.53, 20.53, 7.6, 5.24, 3.7, 2.67
electron_affinity 0.754, -19.7, 0.618, -2.4, 0.28, 1.262, -1.4, 1.461, 3.401, nan
en_allen 13.61, 24.59, 5.392, 9.323, 12.13, 15.05, 18.13, 21.36, 24.8, 28.31
en_ghosh 0.264, 0.443, 0.105, 0.145, 0.185, 0.225, 0.265, 0.305, 0.344, 0.384
en_pauling 2.2, nan, 0.98, 1.57, 2.04, 2.55, 3.04, 3.44, 3.98, nan
evaporation_heat 0.904, 0.08, 148.0, 309.0, 504.5, nan, nan, nan, 6.54, 1.74
fusion_heat 0.117, nan, 2.89, 12.21, 23.6, nan, nan, nan, 0.51, nan
gas_basicity nan, 148.5, nan, nan, nan, nan, 318.7, 459.6, 315.1, 174.4
group_id 1, 18, 1, 2, 13, 14, 15, 16, 17, 18
heat_of_formation 217.998, nan, 159.3, 324.0, 565.0, 716.87, 472.44, 249.229, 79.335, nan
lattice_constant 3.75, 3.57, 3.49, 2.29, 8.73, 3.57, 4.039, 6.83, nan, 4.43
melting_point 14.01, 0.95, 553.69, 1551.0, 2573.0, 3820.0, 63.29, 54.8, 53.53, 48.0
metallic_radius nan, nan, 1.23, 0.89, 0.8, nan, nan, nan, nan, nan
metallic_radius_c12 0.78, 1.22, 1.55, 1.12, 0.98, 0.86, 0.53, nan, nan, nan
period 1, 1, 2, 2, 2, 2, 2, 2, 2, 2
proton_affinity nan, 177.8, nan, nan, nan, nan, 342.2, 485.2, 340.1, 198.8
specific_heat nan, 5.188, 3.489, 1.824, 1.025, 0.711, nan, nan, nan, 1.029
thermal_conductivity 0.181, 0.152, 84.8, 201.0, 27.4, 1.59, 0.026, 0.027, 0.028, nan
vdw_radius 1.1, 1.4, 1.82, 1.53, 1.92, 1.7, 1.55, 1.52, 1.47, 1.54
vdw_radius_alvarez 1.2, 1.43, 2.12, 1.98, 1.91, 1.77, 1.66, 1.5, 1.46, 1.58
vdw_radius_batsanov nan, nan, 2.2, 1.9, 1.8, 1.7, 1.6, 1.55, 1.5, nan
vdw_radius_bondi 1.2, 1.4, 1.81, nan, nan, 1.7, 1.55, 1.52, 1.47, 1.54
vdw_radius_dreiding 3.195, nan, nan, nan, 4.02, 3.898, 3.662, 3.405, 3.472, nan
vdw_radius_mm3 1.62, 1.53, 2.55, 2.23, 2.15, 2.04, 1.93, 1.82, 1.71, 1.6
vdw_radius_rt 1.1, nan, nan, nan, nan, 1.77, 1.64, 1.58, 1.46, 1.81
vdw_radius_truhlar nan, nan, nan, 1.53, 1.92, nan, nan, nan, nan, nan
vdw_radius_uff 2.886, 2.362, 2.451, 2.745, 4.083, 3.851, 3.66, 3.5, 3.364, 3.243

A list of atoms objects can also be passed to any of the generators.This will increase the dimensionality of the numpy array returned by 1 for each atoms object in the supplied list of images. Fingerprints produced in this way are returned in the same order as the list of objects provided.

2.1 Non-local fingerprint generation

Currently, the fingerprint generator has operations for producing convolutions over all atoms in a provided list of atoms objects. There is only a single type of convolution which performs this type of operation currently:

  1. periodic_convolution Calculates the square of each atoms parameter in the unit cell.
  2. bonding_convolution Calculates a convolution over indexed bonded atoms.

These functions can take additional keyword arguments as well, these are provided in the form of a dictionary as demonstrated in the following example. 

from catkit.pawprint import Fingerprinter
from catkit.build import surface
from ase.build import bulk
import numpy as np

bulk = bulk('Pd', cubic=True)
bulk[3].symbol = 'Pt'

slab = surface('Al', size=(2, 2, 3), a=3.8, vacuum=10)

images = [bulk, slab]

parameters = [
    'atomic_number',
    'atomic_radius',
    'atomic_volume',
]

operations = [
    'periodic_convolution',
    ['periodic_convolution', {'d': 1}]
]

fp = Fingerprinter(images)
fingerprints = fp.get_fp(parameters, operations)

print('#+attr_latex: :mode math :environment matrix')
for fp in np.array(fingerprints):
    fp_table = np.round(fp, 3)
    print('|' + '|'.join(fp_table.astype(str)))
12432.0 7.563 320.44 136896.0 90.749 3844.8
2028.0 24.539 1200.0 20280.0 245.388 12000.0

2.2 Local fingerprint generation

Localized fingerprints can also be generated. This is demonstrated for a catalytic structure of Palladium with a single Carbon adsorbate. 

from catkit.pawprint import Fingerprinter
from ase.build import fcc111
from ase.build import add_adsorbate
import numpy as np

atoms = fcc111('Pd', size=(2, 2, 3), vacuum=10.0)
add_adsorbate(atoms, 'C', 1, 'fcc')

# -1 is the tag convention to identify bonded atoms
tags = atoms.get_tags()
tags[-1] = -1
atoms.set_tags(tags)

parameters = [
    'atomic_number',
    'atomic_radius',
    'boiling_point',
    'covalent_radius_cordero',
    'evaporation_heat',
    'fusion_heat',
    'group_id',
    'period',
]

operations = [
    'bonding_convolution'
]

fp = Fingerprinter(atoms)
fingerprints = fp.get_fp(parameters, operations)

print('#+attr_latex: :mode math :environment matrix')
fp_table = np.round(fingerprints[0], 3)
print('|' + '|'.join(fp_table.astype(str)))
276.0 1.247 17406300.0 1.015 nan nan 140.0 10.0

The generators purpose is not to restrict which fingerprints can be generated, however, if no seed parameter is available for a particular chemical species, then an Numpy NaN value will be returned.

2.3 Writing personalized operations

Currently, the default structure of and operation is as follows: 

def periodic_convolution(
        atoms,
        atoms_parameters,
        connectivity):

Where the atoms, atoms_properties, and connectivity properties are required. This is because these properties are passed to all operation functions currently implemented so that they do not need to be generated multiple times. This way change in future versions if it seems that these are better suited as global variables (This may makes the code overly difficult to follow).

Here is an example of a simple operation which supplies the adsorbate connectivity. 

from catkit.pawprint import Fingerprinter
from ase.build import fcc111
from ase.build import add_adsorbate
import numpy as np

atoms = fcc111('Pd', size=(2, 2, 3), vacuum=10.0)
add_adsorbate(atoms, 'C', 1, 'fcc')

# -1 is the tag convention to identify bonded atoms
tags = atoms.get_tags()
tags[-1] = -1
atoms.set_tags(tags)

parameters = [
    'atomic_number',
    'dband_center_slab',
    'dband_width_slab',
    'dband_skewness_slab',
    'dband_kurtosis_slab'
]

def example_operation(
        atoms,
        atoms_parameters,
        connectivity):
    # This is a CatKit convention
    bond_index = np.where(atoms.get_tags() == -1)[0]

    return np.sum(connectivity[bond_index], axis=1)

operations = [
    'bonding_convolution',
    example_operation
]

fp = Fingerprinter(atoms)
fingerprints = fp.get_fp(parameters, operations)
fp_table = np.round(fingerprints[0], 3)

print('#+attr_latex: :mode math :environment matrix')
print('|' + '|'.join(fp_table.astype(str)))
276.0 -1.57 6.517 -81.368 3651.487 3.0

Author: Jacob Boes

Created: 2018-06-01 Fri 05:25

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