class molecular_crystal:
"""
Class for storing and generating molecular crystals based on symmetry
constraints. Based on the crystal.random_crystal class for atomic crystals.
Given a spacegroup, list of molecule objects, molecular stoichiometry, and
a volume factor, generates a molecular crystal consistent with the given
constraints.
Args:
group: the spacegroup number (1-230), or a
`pyxtal.symmetry.Group <pyxtal.symmetry.Group.html>`_ object
molecules: a list of pymatgen.core.structure.Molecule objects for
each type of molecule. Alternatively, you may supply a file path,
or the name of molecules from the built_in
`database <pyxtal.database.collection.html>`_
numMols: A list of the number of each type of molecule within the
primitive cell (NOT the conventioal cell)
volume_factor: A volume factor used to generate a larger or smaller
unit cell. Increasing this gives extra space between molecules
allow_inversion: Whether or not to allow chiral molecules to be
inverted. If True, the final crystal may contain mirror images of
the original molecule. Unless the chemical properties of the mirror
image are known, it is highly recommended to keep this value False
orientations: Once a crystal with the same spacegroup and molecular
stoichiometry has been generated, you may pass its
valid_orientations attribute here to avoid repeating the
calculation, but this is not required
lattice (optional): the `pyxtal.lattice.Lattice <pyxtal.lattice.Lattice.html>`_
object to define the unit cell
tm (optional): the `pyxtal.tolerance.Tol_matrix <pyxtal.tolerance.tolerance.html>`_
object to define the distances
sites (optional): pre-assigned wyckoff sites (e.g., `[["4a"], ["2b"]]`)
seed (optional): the cif file from user
diag (optional): if use the nonstandart setting (P21/n, Pn, C2/n)?
"""
def __init__(
self,
group,
molecules,
numMols,
volume_factor=1.1,
select_high=True,
allow_inversion=True,
orientations=None,
lattice=None,
tm=Tol_matrix(prototype="molecular"),
sites=None,
seed=None,
diag=False,
relax_h=False,
):
self.dim = 3 # The number of periodic dimensions (1,2,3)
self.PBC = [1, 1, 1]
self.diag = diag
if type(group) != Group:
group = Group(group, self.dim)
self.sg = group.number
self.selec_high = select_high
self.seed = seed
self.relax_h = relax_h
self.init_common(
molecules,
numMols,
volume_factor,
select_high,
allow_inversion,
orientations,
group,
lattice,
tm,
sites,
)
def init_common(
self,
molecules,
numMols,
volume_factor,
select_high,
allow_inversion,
orientations,
group,
lattice,
tm,
sites,
):
# init functionality which is shared by 3D, 2D, and 1D crystals
self.valid = False
self.numattempts = 0 # number of attempts to generate the crystal.
if type(group) == Group:
self.group = group
"""A pyxtal.symmetry.Group object storing information about the space/layer
/Rod/point group, and its Wyckoff positions."""
else:
self.group = Group(group, dim=self.dim)
self.number = self.group.number
"""
The international group number of the crystal:
1-230 for 3D space groups
1-80 for 2D layer groups
1-75 for 1D Rod groups
1-32 for crystallographic point groups
None otherwise
"""
self.Msgs()
self.factor = volume_factor # volume factor for the unit cell.
numMols = np.array(numMols) # must convert it to np.array
self.numMols0 = numMols # in the PRIMITIVE cell
self.numMols = self.numMols0 * cellsize(
self.group) # in the CONVENTIONAL cell
# boolean numbers
self.allow_inversion = allow_inversion
self.select_high = select_high
# Set the tolerance matrix
# The Tol_matrix object for checking inter-atomic distances within the structure.
if type(tm) == Tol_matrix:
self.tol_matrix = tm
else:
try:
self.tol_matrix = Tol_matrix(prototype=tm)
# TODO remove bare except
except:
msg = "Error: tm must either be a Tol_matrix object +\n"
msg += "or a prototype string for initializing one."
printx(msg, priority=1)
return
self.molecules = [] # A pyxtal_molecule objects,
for mol in molecules:
self.molecules.append(pyxtal_molecule(mol, self.tol_matrix))
self.sites = {}
for i, mol in enumerate(self.molecules):
if sites is not None and sites[i] is not None:
self.check_consistency(sites[i], self.numMols[i])
self.sites[i] = sites[i]
else:
self.sites[i] = None
# if seeds, directly parse the structure from cif
# At the moment, we only support one specie
if self.seed is not None:
seed = structure_from_ext(self.seed,
self.molecules[0].mol,
relax_h=self.relax_h)
if seed.match():
self.mol_sites = [seed.make_mol_site()]
self.group = Group(seed.wyc.number)
self.lattice = seed.lattice
self.molecules = [pyxtal_molecule(seed.molecule)]
self.diag = seed.diag
self.valid = True # Need to add a check function
else:
raise ValueError("Cannot extract the structure from cif")
# The valid orientations for each molecule and Wyckoff position.
# May be copied when generating a new molecular_crystal to save a
# small amount of time
if orientations is None:
self.get_orientations()
else:
self.valid_orientations = orientations
if self.seed is None:
if lattice is not None:
# Use the provided lattice
self.lattice = lattice
self.volume = lattice.volume
# Make sure the custom lattice PBC axes are correct.
if lattice.PBC != self.PBC:
self.lattice.PBC = self.PBC
printx("\n Warning: converting custom lattice PBC to " +
str(self.PBC))
else:
# Determine the unique axis
if self.dim == 2:
if self.number in range(3, 8):
unique_axis = "c"
else:
unique_axis = "a"
elif self.dim == 1:
if self.number in range(3, 8):
unique_axis = "a"
else:
unique_axis = "c"
else:
unique_axis = "c"
# Generate a Lattice instance
self.volume = self.estimate_volume()
# The Lattice object used to generate lattice matrices
if self.dim == 3 or self.dim == 0:
self.lattice = Lattice(
self.group.lattice_type,
self.volume,
PBC=self.PBC,
unique_axis=unique_axis,
)
elif self.dim == 2:
self.lattice = Lattice(
self.group.lattice_type,
self.volume,
PBC=self.PBC,
unique_axis=unique_axis,
thickness=self.thickness,
)
elif self.dim == 1:
self.lattice = Lattice(
self.group.lattice_type,
self.volume,
PBC=self.PBC,
unique_axis=unique_axis,
area=self.area,
)
self.generate_crystal()
def check_consistency(self, site, numMol):
num = 0
for s in site:
num += int(s[:-1])
if numMol == num:
return True
else:
msg = "\nThe requested number of molecules is inconsistent: " + str(
site)
msg += "\nfrom numMols: {:d}".format(numMol)
msg += "\nfrom Wyckoff list: {:d}".format(num)
raise ValueError(msg)
def estimate_volume(self):
"""
Given the molecular stoichiometry, estimate the volume needed for a unit cell.
Returns:
the estimated volume (in cubic Angstroms) needed for the unit cell
"""
volume = 0
for numMol, mol in zip(self.numMols, self.molecules):
volume += numMol * mol.volume
return abs(self.factor * volume)
def check_short_distances(self, r=1.0, exclude_H=True):
"""
A function to check short distance pairs
Mainly used for debug, powered by pymatgen
Args:
r: the given cutoff distances
exclude_H: whether or not ignore the H atoms
Returns:
a list of pairs within the cutoff
"""
pairs = []
pmg_struc = self.to_pymatgen()
if exclude_H:
pmg_struc.remove_species('H')
res = pmg_struc.get_all_neighbors(r)
for i, neighs in enumerate(res):
for n in neighs:
pairs.append(
[pmg_struc.sites[i].specie, n.specie, n.nn_distance])
return pairs
def Msgs(self):
self.Msg1 = (
"Error: the stoichiometry is incompatible with the wyckoff sites choice"
)
self.Msg2 = "Error: failed in the cycle of generating structures"
self.Msg3 = "Warning: failed in the cycle of adding species"
self.Msg4 = "Warning: failed in the cycle of choosing wyckoff sites"
self.Msg5 = "Finishing: added the specie"
self.Msg6 = "Finishing: added the whole structure"
self.Msg7 = "Error: invalid paramaters for initialization"
def get_orientations(self):
"""
Calculates the valid orientations for each Molecule and Wyckoff
position. Returns a list with 4 indices:
- index 1: the molecular prototype's index within self.molecules
- index 2: the Wyckoff position's 1st index (based on multiplicity)
- index 3: the WP's 2nd index (within the group of equal multiplicity)
- index 4: the index of the valid orientation for the molecule/WP pair
For example, self.valid_orientations[i][j][k] would be a list of valid
orientations for self.molecules[i], in the Wyckoff position
self.group.wyckoffs_organized[j][k]
"""
self.valid_orientations = []
for pyxtal_mol in self.molecules:
self.valid_orientations.append([])
wp_index = -1
for i, x in enumerate(self.group.wyckoffs_organized):
self.valid_orientations[-1].append([])
for j, wp in enumerate(x):
wp_index += 1
allowed = orientation_in_wyckoff_position(
pyxtal_mol.mol,
wp,
already_oriented=True,
allow_inversion=self.allow_inversion,
)
if allowed is not False:
self.valid_orientations[-1][-1].append(allowed)
else:
self.valid_orientations[-1][-1].append([])
def check_compatible(self, group, numMols, valid_orientations):
"""
Checks if the number of molecules is compatible with the Wyckoff
positions. Considers the number of degrees of freedom for each Wyckoff
position, and makes sure at least one valid combination of WP's exists.
"""
# Store whether or not at least one degree of freedom exists
has_freedom = False
# Store the wp's already used that don't have any freedom
used_indices = []
# Loop over species
for i_mol, numIon in enumerate(numMols):
# Get lists of multiplicity, maxn and freedom
l_mult0 = []
l_maxn0 = []
l_free0 = []
indices0 = []
for i_wp, wp in enumerate(group):
# Check that at least one valid orientation exists
j, k = jk_from_i(i_wp, group.wyckoffs_organized)
if len(valid_orientations[i_mol][j][k]) > 0:
indices0.append(i_wp)
l_mult0.append(len(wp))
l_maxn0.append(numIon // len(wp))
if np.allclose(wp[0].rotation_matrix, np.zeros([3, 3])):
l_free0.append(False)
else:
l_free0.append(True)
# Remove redundant multiplicities:
l_mult = []
l_maxn = []
l_free = []
indices = []
for mult, maxn, free, i_wp in zip(l_mult0, l_maxn0, l_free0,
indices0):
if free is True:
if mult not in l_mult:
l_mult.append(mult)
l_maxn.append(maxn)
l_free.append(True)
indices.append(i_wp)
elif free is False and i_wp not in used_indices:
l_mult.append(mult)
l_maxn.append(1)
l_free.append(False)
indices.append(i_wp)
# Loop over possible combinations
# Create pointer variable to move through lists
p = 0
# Store the number of each WP, used across possible WP combinations
n0 = [0] * len(l_mult)
n = deepcopy(n0)
for i, mult in enumerate(l_mult):
if l_maxn[i] != 0:
p = i
n[i] = l_maxn[i]
break
p2 = p
if n == n0:
print("n == n0", n, n0)
return False
while True:
num = np.dot(n, l_mult)
dobackwards = False
# The combination works: move to next species
if num == numIon:
# Check if at least one degree of freedom exists
for val, free, i_wp in zip(n, l_free, indices):
if val > 0:
if free is True:
has_freedom = True
elif free is False:
indices.append(i_wp)
break
# All combinations failed: return False
if n == n0 and p >= len(l_mult) - 1:
#print("All combinations failed: return False")
return False
# Too few atoms
if num < numIon:
# Forwards routine
# Move p to the right and max out
if p < len(l_mult) - 1:
p += 1
n[p] = min((numIon - num) // l_mult[p], l_maxn[p])
else:
# p is already at last position: trigger backwards routine
dobackwards = True
# Too many atoms
if num > numIon or dobackwards is True:
# Backwards routine
# Set n[p] to 0, move p backwards to non-zero, and decrease by 1
n[p] = 0
while p > 0 and p > p2:
p -= 1
if n[p] != 0:
n[p] -= 1
if n[p] == 0 and p == p2:
p2 = p + 1
break
# All species passed: return True
if has_freedom is True:
return True
# All species passed, but no degrees of freedom: return 0
elif has_freedom is False:
return 0
def to_file(self, filename=None, fmt="cif", permission='w', **kwargs):
"""
Creates a file with the given filename and file type to store the structure.
By default, creates cif files for crystals and xyz files for clusters.
By default, the filename is based on the stoichiometry.
Args:
filename: the file path
fmt: the file type (`cif`, `xyz`, etc.)
permission: `w` or `a+`
sym_num: `w` or `a+`
Returns:
Nothing. Creates a file at the specified path
"""
if self.valid:
if fmt == "cif":
if self.dim == 3:
return write_cif(self, filename, "from_pyxtal", permission,
**kwargs)
else:
pmg_struc = self.to_pymatgen()
pmg_struc.sort()
return pmg_struc.to(fmt=fmt, filename=filename)
else:
pmg_struc = self.to_pymatgen()
pmg_struc.sort()
return pmg_struc.to(fmt=fmt, filename=filename)
else:
printx("Cannot create file: structure did not generate.",
priority=1)
def copy(self):
"""
simply copy the structure
"""
return deepcopy(self)
def optimize_lattice(self):
"""
optimize the lattice if the cell has a bad inclination angles
"""
for i in range(5):
lattice, trans, opt = self.lattice.optimize()
if opt:
for site in self.mol_sites:
pos_absolute = np.dot(site.position, self.lattice.matrix)
pos_frac = pos_absolute.dot(lattice.inv_matrix)
site.position = pos_frac - np.floor(pos_frac)
site.lattice = lattice
# for P21/c, Pc, C2/c, check if opt the inclination angle
if self.group.number in [7, 14, 15]:
for j, op in enumerate(site.wp.ops):
vec = op.translation_vector.dot(trans)
vec -= np.floor(vec)
op1 = op.from_rotation_and_translation(
op.rotation_matrix, vec)
site.wp.ops[j] = op1
#to do needs to update diag if necessary
_, perm = Wyckoff_position.from_symops(site.wp.ops,
self.group.number)
if not isinstance(perm, list):
self.diag = True
else:
self.diag = False
self.lattice = lattice
else:
break
def _get_coords_and_species(self, absolute=False, unitcell=True):
"""
extract the coordinates and species information
Args:
abosulte: if True, return the cartesian coords otherwise fractional
Returns:
total_coords: N*3 numpy array
species: N-length list, e.g. ["C", "C", ...]
"""
species = []
total_coords = None
for site in self.mol_sites:
coords, site_species = site.get_coords_and_species(
absolute, unitcell=unitcell)
species.extend(site_species)
if total_coords is None:
total_coords = coords
else:
total_coords = np.append(total_coords, coords, axis=0)
return total_coords, species
def to_ase(self, resort=True):
"""
export to ase Atoms object
"""
from ase import Atoms
if self.valid:
lattice = self.lattice.copy()
coords, species = self._get_coords_and_species(True)
latt, coords = lattice.add_vacuum(coords, frac=False, PBC=self.PBC)
atoms = Atoms(species, positions=coords, cell=latt, pbc=self.PBC)
if resort:
permutation = np.argsort(atoms.numbers)
atoms = atoms[permutation]
return atoms
else:
printx("No valid structure can be converted to ase.", priority=1)
def to_pymatgen(self):
"""
export to Pymatgen structure object
"""
from pymatgen.core.structure import Structure
if self.valid:
lattice = self.lattice.copy()
coords, species = self._get_coords_and_species()
# Add space above and below a 2D or 1D crystals
latt, coords = lattice.add_vacuum(coords, PBC=self.PBC)
return Structure(latt, species, coords)
else:
printx("No valid structure can be converted to pymatgen.",
priority=1)
def __str__(self):
s = "------Random Molecular Crystal------"
s += "\nDimension: " + str(self.dim)
if self.group.number in [7, 14, 15] and self.diag:
symbol = self.group.alias
else:
symbol = self.group.symbol
s += "\nGroup: " + symbol
s += "\nVolume factor: " + str(self.factor)
s += "\n" + str(self.lattice)
if self.valid:
s += "\nWyckoff sites:"
for wyc in self.mol_sites:
s += "\n\t{}".format(wyc)
else:
s += "\nStructure not generated."
return s
def __repr__(self):
return str(self)
def show(self, **kwargs):
"""
display the crystal structure
"""
from pyxtal.viz import display_molecular
return display_molecular(self, **kwargs)
def _check_lattice_vs_shape(self, factor=0.95):
"""
Make sure that the shape is compatible with the lattice vectors.
Experimental----
"""
#min_lat = min(self.lattice.get_para()[:3])
#for mol in self.molecules:
#
# if mol.has_stick_shape():
# if min_lat < factor*min([mol.box.width, mol.box.height, mol.box.length]):
# msg = "Warning: lattice-shape mismatch: "
# msg += "{:6.2f}".format(min_lat)
# msg += " {:6.2f}".format(min([mol.box.width, mol.box.height, mol.box.length]))
# print(msg)
# return False
return True
def generate_crystal(self):
"""
The main code to generate a random molecular crystal. If successful,
`self.valid` is True (False otherwise)
"""
# Check the minimum number of degrees of freedom within the Wyckoff positions
degrees = self.check_compatible(self.group, self.numMols,
self.valid_orientations)
if degrees is False:
self.valid = False
msg = "the space group is incompatible with the number of molecules"
#raise ValueError(msg)
return
else:
if degrees == 0:
self.lattice_attempts = 20
self.coord_attempts = 3
self.ori_attempts = 1
else:
self.lattice_attempts = 40
self.coord_attempts = 30
self.ori_attempts = 5
if not self.lattice.allow_volume_reset:
self.lattice_attempts = 1
for cycle1 in range(self.lattice_attempts):
self.cycle1 = cycle1
# 1, Generate a lattice
if self.lattice.allow_volume_reset:
self.volume = self.estimate_volume()
self.lattice.volume = self.volume
self.lattice.reset_matrix()
if self._check_lattice_vs_shape():
for cycle2 in range(self.coord_attempts):
self.cycle2 = cycle2
output = self._generate_coords()
if output:
self.mol_sites = output
break
if self.valid:
return
printx("Couldn't generate crystal after max attempts.", priority=1)
return
def _generate_coords(self):
"""
generate coordinates for random crystal
"""
mol_sites_total = []
# Add molecules
for i, numMol in enumerate(self.numMols):
pyxtal_mol = self.molecules[i]
valid_ori = self.valid_orientations[i]
output = self._generate_mol_wyckoffs(i, numMol, pyxtal_mol,
valid_ori, mol_sites_total)
if output is not None:
mol_sites_total.extend(output)
else:
# correct multiplicity not achieved exit and start over
return None
self.valid = True
return mol_sites_total
def _generate_mol_wyckoffs(self, id, numMol, pyxtal_mol, valid_ori,
mol_wyks):
"""
generates a set of wyckoff positions to accomodate a given number
of molecules
Args:
numMol: Number of ions to accomodate
pyxtal_mol: Type of species being placed on wyckoff site
mol_wyks: current wyckoff sites
Returns:
if sucess, wyckoff_sites_tmp: list of wyckoff sites for valid sites
otherwise, None
"""
numMol_added = 0
mol_sites_tmp = []
# Now we start to add the specie to the wyckoff position
sites_list = deepcopy(self.sites[id]) # the list of Wyckoff site
if sites_list is not None:
self.wyckoff_attempts = max(len(sites_list) * 2, 10)
else:
# the minimum numattempts is to put all atoms to the general WPs
min_wyckoffs = int(numMol /
len(self.group.wyckoffs_organized[0][0]))
self.wyckoff_attempts = max(2 * min_wyckoffs, 10)
for cycle in range(self.wyckoff_attempts):
# Choose a random WP for given multiplicity: 2a, 2b, 2c
if sites_list is not None:
site = sites_list[0]
else: # Selecting the merging
site = None
# NOTE: The molecular version return wyckoff indices, not ops
diff = numMol - numMol_added
wp = choose_wyckoff_molecular(self.group, diff, site, valid_ori,
self.select_high, self.dim)
if wp is not False:
# Generate a list of coords from the wyckoff position
mult = wp.multiplicity # remember the original multiplicity
pt = self.lattice.generate_point()
# merge coordinates if the atoms are close
mtol = pyxtal_mol.radius * 0.5
pt, wp, oris = WP_merge(pt, self.lattice.matrix, wp, mtol,
valid_ori)
if wp is not False:
if site is not None and mult != wp.multiplicity:
continue
if self.dim == 2 and self.thickness is not None and self.thickness < 0.1:
pt[-1] = 0.5
ms0 = self._generate_orientation(pyxtal_mol, pt, oris, wp)
if ms0 is not None:
# Check current WP against existing WP's
passed_wp_check = True
for ms1 in mol_sites_tmp + mol_wyks:
if not check_mol_sites(
ms0, ms1, tm=self.tol_matrix):
passed_wp_check = False
if passed_wp_check:
if sites_list is not None:
sites_list.pop(0)
mol_sites_tmp.append(ms0)
numMol_added += len(ms0.wp)
# We have enough molecules of the current type
if numMol_added == numMol:
return mol_sites_tmp
return None
def _check_ori_dist(self, ori):
#mat, lengths = self.lattice.get_lengths()
#for mol in self.molecules:
# if mol.has_stick_shape():
# axis = mol.axes.T[0].dot(ori.r.as_matrix().T) #get coords
# mol_length = max([mol.box.length, mol.box.width, mol.box.height])
# for vec, dist in zip(mat, lengths):
# #print(vec, mol_length, dist, mol_length/dist, angle(axis, vec, False))
# if mol_length/dist < 1.6 and abs(angle(axis, vec, False)-90)>80:
# #print("=============> bad ori", axis)
# return True
#return False
return True
def _generate_orientation(self, pyxtal_mol, pt, oris, wp):
# Use a Wyckoff_site object for the current site
self.numattempts += 1
#ensure that the orientation is good
count = 0
while count < 100:
ori = random.choice(oris).copy()
ori.change_orientation(flip=True)
if self._check_ori_dist(ori):
#print("===good orientation", count, self._check_ori_dist(ori))
break
count += 1
#print(count, self.molecules[0].axes.T[0].dot(ori.r.as_matrix().T))
#print(ori.r.as_matrix())
ms0 = mol_site(pyxtal_mol, pt, ori, wp, self.lattice, self.diag)
# Check distances within the WP
if ms0.check_distances():
return ms0
else:
# Maximize the smallest distance for the general
# positions if needed
if len(pyxtal_mol.mol) > 1 and ori.degrees > 0:
# bisection method
def fun_dist(angle, ori, mo, pt):
ori0 = ori.copy()
ori.change_orientation(angle)
ms0 = mol_site(
mo,
pt,
ori,
wp,
self.lattice,
self.diag,
)
d = ms0.compute_distances()
return d
angle_lo = ori.angle
angle_hi = angle_lo + np.pi
fun_lo = fun_dist(angle_lo, ori, pyxtal_mol, pt)
fun_hi = fun_dist(angle_hi, ori, pyxtal_mol, pt)
fun = fun_hi
for it in range(self.ori_attempts):
self.numattempts += 1
if (fun > 0.8) & (ms0.check_distances()):
return ms0
angle = (angle_lo + angle_hi) / 2
fun = fun_dist(angle, ori, pyxtal_mol, pt)
#print('Bisection: ', it, fun)
if fun_lo > fun_hi:
angle_hi, fun_hi = angle, fun
else:
angle_lo, fun_lo = angle, fun
return None
class random_crystal:
"""
Class for storing and generating atomic crystals based on symmetry
constraints. Given a spacegroup, list of atomic symbols, the stoichiometry,
and a volume factor, generates a random crystal consistent with the
spacegroup's symmetry.
Args:
group: the spacegroup number (1-230), or a
`pyxtal.symmetry.Group <pyxtal.symmetry.Group.html>`_ object
species: a list of atomic symbols for each ion type, e.g., `["Ti", "O"]`
numIons: a list of the number of each type of atom within the
primitive cell (NOT the conventional cell), e.g., `[4, 2]`
factor (optional): volume factor used to generate the crystal
sites (optional): pre-assigned wyckoff sites (e.g., `[["4a"], ["2b"]]`)
lattice (optional): the `pyxtal.lattice.Lattice <pyxtal.lattice.Lattice.html>`_
object to define the unit cell
tm (optional): the `pyxtal.tolerance.Tol_matrix <pyxtal.tolerance.Tol_matrix.html>`_
object to define the distances
seed (optional): the cif/POSCAR file from user
"""
def __init__(
self,
group=None,
species=None,
numIons=None,
factor=1.1,
lattice=None,
sites=None,
tm=Tol_matrix(prototype="atomic"),
seed=None,
):
self.dim = 3 #periodic dimensions of the crystal
self.PBC = [1, 1, 1] #The periodic boundary axes of the crystal
if seed is None:
if type(group) != Group:
group = Group(group, self.dim)
self.sg = group.number #The international spacegroup number
self.seed = None
self.init_common(species, numIons, factor, group, lattice, sites,
tm)
else:
self.seed = seed
self.from_seed()
def from_seed(self):
"""
Load the seed structure from Pymatgen/ASE/POSCAR/CIFs
Internally they will be handled by Pymatgen
"""
self.valid = True
from ase import Atoms
from pymatgen import Structure
if isinstance(self.seed, Atoms): #ASE atoms
from pymatgen.io.ase import AseAtomsAdaptor
pmg_struc = AseAtomsAdaptor.get_structure(self.seed)
self.from_pymatgen(pmg_struc)
elif isinstance(self.seed, Structure): #Pymatgen
self.from_pymatgen(self.seed)
elif isinstance(self.seed, str):
pmg_struc = Structure.from_file(self.seed)
self.from_pymatgen(pmg_struc)
formula = ""
for i, s in zip(self.numIons, self.species):
formula += "{:s}{:d}".format(s, int(i))
self.formula = formula
self.factor = 1.0
self.number = self.group.number
self.source = 'Seed'
def from_pymatgen(self, structure):
"""
Load the seed structure from Pymatgen/ASE/POSCAR/CIFs
"""
from pymatgen.symmetry.analyzer import SpacegroupAnalyzer as sga
try:
# needs to do it twice in order to get the conventional cell
s = sga(structure)
structure = s.get_refined_structure()
s = sga(structure)
sym_struc = s.get_symmetrized_structure()
number = s.get_space_group_number()
except:
print("Failed to load the Pymatgen structure")
self.valid = False
if self.valid:
d = sym_struc.composition.as_dict()
species = [key for key in d.keys()]
numIons = []
for ele in species:
numIons.append(int(d[ele]))
self.numIons = numIons
self.species = species
self.group = Group(number)
atom_sites = []
for i, site in enumerate(sym_struc.equivalent_sites):
pos = site[0].frac_coords
wp = Wyckoff_position.from_group_and_index(
number, sym_struc.wyckoff_symbols[i])
specie = site[0].specie.number
atom_sites.append(atom_site(wp, pos, specie))
self.atom_sites = atom_sites
self.lattice = Lattice.from_matrix(sym_struc.lattice.matrix,
ltype=self.group.lattice_type)
def init_common(self, species, numIons, factor, group, lattice, sites, tm):
"""
Common init functionality for 0D-3D cases of random_crystal.
"""
self.source = 'Random'
self.valid = False
# Check that numIons are integers greater than 0
for num in numIons:
if int(num) != num or num < 1:
printx("Error: composition must be positive integers.",
priority=1)
return False
if type(group) == Group:
self.group = group
else:
self.group = Group(group, dim=self.dim)
self.number = self.group.number
"""
The international group number of the crystal:
1-230 for 3D space groups
1-80 for 2D layer groups
1-75 for 1D Rod groups
1-32 for crystallographic point groups
None otherwise
"""
# The number of attempts to generate the crystal
# number of atoms
# volume factor for the unit cell.
# The number of atom in the PRIMITIVE cell
# The number of each type of atom in the CONVENTIONAL cell.
# A list of atomic symbols for the types of atoms
# A list of warning messages
self.numattempts = 0
numIons = np.array(numIons)
self.factor = factor
self.numIons0 = numIons
self.numIons = self.numIons0 * cellsize(self.group)
formula = ""
for i, s in zip(self.numIons, species):
formula += "{:s}{:d}".format(s, int(i))
self.formula = formula
self.species = species
self.Msgs()
# Use the provided lattice
if lattice is not None:
self.lattice = lattice
self.volume = lattice.volume
# Make sure the custom lattice PBC axes are correct.
if lattice.PBC != self.PBC:
self.lattice.PBC = self.PBC
printx("\n Warning: converting custom lattice PBC to " +
str(self.PBC))
# Generate a Lattice instance based on a given volume estimation
elif lattice is None:
# Determine the unique axis
if self.dim == 2:
if self.number in range(3, 8):
unique_axis = "c"
else:
unique_axis = "a"
elif self.dim == 1:
if self.number in range(3, 8):
unique_axis = "a"
else:
unique_axis = "c"
else:
unique_axis = "c"
self.volume = self.estimate_volume()
if self.dim == 3 or self.dim == 0:
self.lattice = Lattice(
self.group.lattice_type,
self.volume,
PBC=self.PBC,
unique_axis=unique_axis,
)
elif self.dim == 2:
self.lattice = Lattice(
self.group.lattice_type,
self.volume,
PBC=self.PBC,
unique_axis=unique_axis,
# NOTE self.thickness is part of 2D class
thickness=self.thickness,
)
elif self.dim == 1:
self.lattice = Lattice(
self.group.lattice_type,
self.volume,
PBC=self.PBC,
unique_axis=unique_axis,
# NOTE self.area is part of 1D class
area=self.area,
)
# Set the tolerance matrix for checking inter-atomic distances
if type(tm) == Tol_matrix:
self.tol_matrix = tm
else:
try:
self.tol_matrix = Tol_matrix(prototype=tm)
# TODO Remove bare except
except:
printx(
("Error: tm must either be a Tol_matrix object or "
"a prototype string for initializing one."),
priority=1,
)
self.valid = False
return
self.sites = {}
for i, specie in enumerate(self.species):
if sites is not None and sites[i] is not None:
self.check_consistency(sites[i], self.numIons[i])
self.sites[specie] = sites[i]
else:
self.sites[specie] = None
# QZ: needs to check if it is compatible
self.generate_crystal()
def check_compatible(self, group, numIons):
"""
Checks if the number of atoms is compatible with the Wyckoff
positions. Considers the number of degrees of freedom for each Wyckoff
position, and makes sure at least one valid combination of WP's exists.
NOTE Comprhys: Is degrees of freedom used symnomously with multiplicity?
perhaps standardising to multiplicity would be clearer?
"""
# Store whether or not at least one degree of freedom exists
has_freedom = False
# Store the wp's already used that don't have any freedom
used_indices = []
# Loop over species
for numIon in numIons:
# Get lists of multiplicity, maxn and freedom
l_mult0 = []
l_maxn0 = []
l_free0 = []
indices0 = []
for i_wp, wp in enumerate(group):
indices0.append(i_wp)
l_mult0.append(len(wp))
l_maxn0.append(numIon // len(wp))
if np.allclose(wp[0].rotation_matrix, np.zeros([3, 3])):
l_free0.append(False)
else:
l_free0.append(True)
# Remove redundant multiplicities:
l_mult = []
l_maxn = []
l_free = []
indices = []
for mult, maxn, free, i_wp in zip(l_mult0, l_maxn0, l_free0,
indices0):
if free is True:
if mult not in l_mult:
l_mult.append(mult)
l_maxn.append(maxn)
l_free.append(True)
indices.append(i_wp)
elif free is False and i_wp not in used_indices:
l_mult.append(mult)
indices.append(i_wp)
if mult <= numIon:
l_maxn.append(1)
elif mult > numIon:
l_maxn.append(0)
l_free.append(False)
# Loop over possible combinations
p = 0 # Create pointer variable to move through lists
# Store the number of each WP, used across possible WP combinations
n0 = [0] * len(l_mult)
n = deepcopy(n0)
for i, mult in enumerate(l_mult):
if l_maxn[i] != 0:
p = i
n[i] = l_maxn[i]
break
p2 = p
if n == n0:
return False
while True:
num = np.dot(n, l_mult)
dobackwards = False
# The combination works: move to next species
if num == numIon:
# Check if at least one degree of freedom exists
for val, free, i_wp in zip(n, l_free, indices):
if val > 0:
if free is True:
has_freedom = True
elif free is False:
used_indices.append(i_wp)
break
# All combinations failed: return False
if n == n0 and p >= len(l_mult) - 1:
return False
# Too few atoms
if num < numIon:
# Forwards routine
# Move p to the right and max out
if p < len(l_mult) - 1:
p += 1
n[p] = min((numIon - num) // l_mult[p], l_maxn[p])
elif p == len(l_mult) - 1:
# p is already at last position: trigger backwards routine
dobackwards = True
# Too many atoms
if num > numIon or dobackwards is True:
# Backwards routine
# Set n[p] to 0, move p backwards to non-zero, and decrease by 1
n[p] = 0
while p > 0 and p > p2:
p -= 1
if n[p] != 0:
n[p] -= 1
if n[p] == 0 and p == p2:
p2 = p + 1
break
# All species passed: return True
if has_freedom is True:
return True
# All species passed, but no degrees of freedom: return 0
elif has_freedom is False:
return 0
def check_consistency(self, site, numIon):
num = 0
for s in site:
num += int(s[:-1])
if numIon == num:
return True
else:
msg = "\nThe requested number of atoms is inconsistent: " + str(
site)
msg += "\nfrom numIons: {:d}".format(numIon)
msg += "\nfrom Wyckoff list: {:d}".format(num)
raise ValueError(msg)
def check_short_distances(self, r=0.7, exclude_H=True):
"""
A function to check short distance pairs
Mainly used for debug, powered by pymatgen
Args:
r: the given cutoff distances
exclude_H: whether or not exclude the H atoms
Returns:
list of pairs within the cutoff
"""
if dim > 0:
pairs = []
pmg_struc = self.to_pymatgen()
if exclude_H:
pmg_struc.remove_species('H')
res = pmg_struc.get_all_neighbors(r)
for i, neighs in enumerate(res):
for n in neighs:
pairs.append(
[pmg_struc.sites[i].specie, n.specie, n.nn_distance])
else:
raise NotImplementedError("Does not support cluster for now")
return pairs
def Msgs(self):
"""
Define a set of error and warning message if generation fails.
Returns:
nothing
"""
self.Msg1 = (
"Error: the stoichiometry is incompatible with the wyckoff sites choice"
)
self.Msg2 = "Error: failed in the cycle of generating structures"
self.Msg3 = "Warning: failed in the cycle of adding species"
self.Msg4 = "Warning: failed in the cycle of choosing wyckoff sites"
self.Msg5 = "Finishing: added the specie"
self.Msg6 = "Finishing: added the whole structure"
self.Msg7 = "Error: invalid paramaters for initialization"
def estimate_volume(self):
"""
Estimates the volume of a unit cell based on the number and types of ions.
Assumes each atom takes up a sphere with radius equal to its covalent bond
radius.
Returns:
a float value for the estimated volume
"""
volume = 0
for numIon, specie in zip(self.numIons, self.species):
r = random.uniform(
Element(specie).covalent_radius,
Element(specie).vdw_radius)
volume += numIon * 4 / 3 * np.pi * r**3
return self.factor * volume
def to_file(self, filename=None, fmt=None, permission='w'):
"""
Creates a file with the given filename and file type to store the structure.
By default, creates cif files for crystals and xyz files for clusters.
For other formats, Pymatgen is used
Args:
filename: the file path
fmt: the file type (`cif`, `xyz`, etc.)
permission: `w` or `a+`
Returns:
Nothing. Creates a file at the specified path
"""
if self.valid:
if fmt is None:
if self.dim == 0:
fmt = 'xyz'
else:
fmt = 'cif'
if fmt == "cif":
if self.dim == 3:
from pyxtal.io import write_cif
return write_cif(self, filename, "from_pyxtal", permission)
else:
pmg_struc = self.to_pymatgen()
return pmg_struc.to(fmt=fmt, filename=filename)
else:
pmg_struc = self.to_pymatgen()
return pmg_struc.to(fmt=fmt, filename=filename)
else:
printx("Cannot create file: structure did not generate.",
priority=1)
def __str__(self):
s = "------Crystal from {:s}------".format(self.source)
s += "\nComposition: {}".format(self.formula)
s += "\nDimension: {}".format(self.dim)
s += "\nGroup: {} ({})".format(self.group.symbol, self.group.number)
s += "\nVolume factor: {}".format(self.factor)
s += "\n{}".format(self.lattice)
if self.valid:
s += "\nWyckoff sites:"
for wyc in self.atom_sites:
s += "\n\t{}".format(wyc)
else:
s += "\nStructure not generated."
return s
def __repr__(self):
return str(self)
def show(self, **kwargs):
"""
display the crystal structure
"""
from pyxtal.viz import display_atomic
return display_atomic(self, **kwargs)
def subgroup(self, H=None, eps=0.05, idx=None, once=False):
"""
generate a structure with lower symmetry
Args:
H: space group number (int)
eps: pertubation term (float)
idx: list
once: generate only one structure, otherwise output all
Returns:
a list of pyxtal structures with lower symmetries
"""
#randomly choose a subgroup from the available list
Hs = self.group.get_max_t_subgroup()['subgroup']
if idx is None:
idx = range(len(Hs))
else:
for id in idx:
if id >= len(Hs):
raise ValueError(
"The idx exceeds the number of possible splits")
if H is not None:
idx = [id for id in idx if Hs[idx] == H]
if len(idx) == 0:
raise ValueError("The space group H is incompatible with idx")
sites = [
str(site.wp.multiplicity) + site.wp.letter
for site in self.atom_sites
]
valid_splitters = []
bad_splitters = []
for id in idx:
splitter = wyckoff_split(G=self.group.number, wp1=sites, idx=id)
if splitter.valid_split:
valid_splitters.append(splitter)
else:
bad_splitters.append(splitter)
if len(valid_splitters) == 0:
# do one more step
new_strucs = []
for splitter in bad_splitters:
trail_struc = self.subgroup_by_splitter(splitter)
new_strucs.append(trail_struc.subgroup(once=True))
return new_strucs
else:
if once:
return self.subgroup_by_splitter(choice(valid_splitters),
eps=eps)
else:
new_strucs = []
for splitter in valid_splitters:
new_strucs.append(
self.subgroup_by_splitter(splitter, eps=eps))
return new_strucs
def subgroup_by_splitter(self, splitter, eps=0.05):
lat1 = np.dot(splitter.R[:3, :3].T, self.lattice.matrix)
multiples = np.linalg.det(splitter.R[:3, :3])
split_sites = []
for i, site in enumerate(self.atom_sites):
pos = site.position
for ops1, ops2 in zip(splitter.G2_orbits[i], splitter.H_orbits[i]):
pos0 = apply_ops(pos, ops1)[0]
pos0 -= np.floor(pos0)
pos0 += eps * (np.random.sample(3) - 0.5)
wp, _ = Wyckoff_position.from_symops(ops2,
group=splitter.H.number,
permutation=False)
split_sites.append(atom_site(wp, pos0, site.specie))
new_struc = deepcopy(self)
new_struc.group = splitter.H
lattice = Lattice.from_matrix(lat1, ltype=new_struc.group.lattice_type)
new_struc.lattice = lattice.mutate(degree=0.01, frozen=True)
new_struc.atom_sites = split_sites
new_struc.numIons = [
int(multiples * numIon) for numIon in self.numIons
]
new_struc.source = 'Wyckoff Split'
return new_struc
def generate_crystal(self):
"""
The main code to generate a random atomic crystal. If successful,
stores a pymatgen.core.structure object in self.struct and sets
self.valid to True. If unsuccessful, sets self.valid to False and
outputs an error message.
"""
# Check the minimum number of degrees of freedom within the Wyckoff positions
self.numattempts = 1
degrees = self.check_compatible(self.group, self.numIons)
if degrees is False:
printx(self.Msg1, priority=1)
self.valid = False
return
if degrees == 0:
printx("Wyckoff positions have no degrees of freedom.", priority=2)
# NOTE why do these need to be changed from defaults?
self.lattice_attempts = 5
self.coord_attempts = 5
#self.wyckoff_attempts = 5
else:
self.lattice_attempts = 40
self.coord_attempts = 10
#self.wyckoff_attempts=10
# Calculate a minimum vector length for generating a lattice
# NOTE Comprhys: minvector never used?
# minvector = max(self.tol_matrix.get_tol(s, s) for s in self.species)
for cycle1 in range(self.lattice_attempts):
self.cycle1 = cycle1
# 1, Generate a lattice
if self.lattice.allow_volume_reset:
self.volume = self.estimate_volume()
self.lattice.volume = self.volume
self.lattice.reset_matrix()
try:
cell_matrix = self.lattice.get_matrix()
if cell_matrix is None:
continue
# TODO remove bare except
except:
continue
# Check that the correct volume was generated
if self.lattice.random:
if self.dim != 0 and abs(self.volume -
self.lattice.volume) > 1.0:
printx(
("Error, volume is not equal to the estimated value: "
"{} -> {} cell_para: {}").format(
self.volume, self.lattice.volume,
self.lattice.get_para),
priority=0,
)
self.valid = False
return
# to try to generate atomic coordinates
for cycle2 in range(self.coord_attempts):
self.cycle2 = cycle2
output = self._generate_coords(cell_matrix)
if output:
self.atom_sites = output
break
if self.valid:
return
return
def copy(self):
"""
simply copy the structure
"""
return deepcopy(self)
def _get_coords_and_species(self, absolute=False):
"""
extract the coordinates and species information
Args:
abosulte: if True, return the cartesian coords otherwise fractional
Returns:
total_coords (N*3 numpy array) and the list of species
"""
species = []
total_coords = None
for site in self.atom_sites:
species.extend([site.specie] * site.multiplicity)
if total_coords is None:
total_coords = site.coords
else:
total_coords = np.append(total_coords, site.coords, axis=0)
if absolute:
return total_coords.dot(self.lattice.matrix), species
else:
return total_coords, species
def to_ase(self):
"""
export to ase Atoms object
"""
from ase import Atoms
if self.valid:
if self.dim > 0:
lattice = self.lattice.copy()
coords, species = self._get_coords_and_species()
# Add space above and below a 2D or 1D crystals
latt, coords = lattice.add_vacuum(coords, PBC=self.PBC)
return Atoms(species,
scaled_positions=coords,
cell=latt,
pbc=self.PBC)
else:
coords, species = self._get_coords_and_species(True)
return Atoms(species, positions=coords)
else:
printx("No valid structure can be converted to ase.", priority=1)
def to_pymatgen(self):
"""
export to Pymatgen structure object
"""
from pymatgen.core.structure import Structure, Molecule
if self.valid:
if self.dim > 0:
lattice = self.lattice.copy()
coords, species = self._get_coords_and_species()
# Add space above and below a 2D or 1D crystals
latt, coords = lattice.add_vacuum(coords, PBC=self.PBC)
return Structure(latt, species, coords)
else:
# Clusters are handled as large molecules
coords, species = self._get_coords_and_species(True)
return Molecule(species, coords)
else:
printx("No valid structure can be converted to pymatgen.",
priority=1)
def _generate_coords(self, cell_matrix):
"""
generate coordinates for random crystal
"""
wyckoff_sites_list = []
# generate coordinates for each ion type in turn
for numIon, specie in zip(self.numIons, self.species):
output = self._generate_ion_wyckoffs(numIon, specie, cell_matrix,
wyckoff_sites_list)
if output is not None:
wyckoff_sites_list.extend(output)
else:
# correct multiplicity not achieved exit and start over
return None
# If numIon_added correct for all specie return structure
self.valid = True
return wyckoff_sites_list
def _generate_ion_wyckoffs(self, numIon, specie, cell_matrix, wyks):
"""
generates a set of wyckoff positions to accomodate a given number
of ions
Args:
numIon: Number of ions to accomodate
specie: Type of species being placed on wyckoff site
cell_matrix: Matrix of lattice vectors
wyks: current wyckoff sites
Returns:
Sucess:
wyckoff_sites_tmp: list of wyckoff sites for valid sites
Failue:
None
"""
numIon_added = 0
tol = self.tol_matrix.get_tol(specie, specie)
tol_matrix = self.tol_matrix
wyckoff_sites_tmp = []
# Now we start to add the specie to the wyckoff position
sites_list = deepcopy(self.sites[specie]) # the list of Wyckoff site
if sites_list is not None:
wyckoff_attempts = max(len(sites_list) * 2, 10)
else:
# the minimum numattempts is to put all atoms to the general WPs
min_wyckoffs = int(numIon /
len(self.group.wyckoffs_organized[0][0]))
wyckoff_attempts = max(2 * min_wyckoffs, 10)
cycle = 0
while cycle < wyckoff_attempts:
# Choose a random WP for given multiplicity: 2a, 2b
if sites_list is not None:
site = sites_list[0]
else: # Selecting the merging
site = None
wp = choose_wyckoff(self.group, numIon - numIon_added, site,
self.dim)
if wp is not False:
# Generate a list of coords from ops
mult = wp.multiplicity # remember the original multiplicity
pt = self.lattice.generate_point()
# Merge coordinates if the atoms are close
pt, wp, _ = WP_merge(pt, cell_matrix, wp, tol)
# For pure planar structure
if self.dim == 2 and self.thickness is not None and self.thickness < 0.1:
pt[-1] = 0.5
# If site the pre-assigned, do not accept merge
if wp is not False:
if site is not None and mult != wp.multiplicity:
cycle += 1
continue
# Use a Wyckoff_site object for the current site
new_site = atom_site(wp, pt, specie)
# Check current WP against existing WP's
passed_wp_check = True
for ws in wyckoff_sites_tmp + wyks:
if not check_atom_sites(new_site, ws, cell_matrix,
tol_matrix):
passed_wp_check = False
if passed_wp_check:
if sites_list is not None:
sites_list.pop(0)
wyckoff_sites_tmp.append(new_site)
numIon_added += new_site.multiplicity
# Check if enough atoms have been added
if numIon_added == numIon:
return wyckoff_sites_tmp
cycle += 1
self.numattempts += 1
return None