#!/usr/bin/env python
# Copyright 2020-2023 The PySCF Developers. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
#
# Authors: Xing Zhang <zhangxing.nju@gmail.com>
#
import numpy as np
from pyscf import __config__
from pyscf import lib
from pyscf.gto import mole
from functools import reduce
SYMPREC = getattr(__config__, 'pbc_symm_space_group_symprec', 1e-6) #this has the unit of length
[docs]
def search_point_group_ops(cell, tol=SYMPREC):
a = cell.lattice_vectors()
G = np.dot(a, a.T)
pbc_axis = np.array([1,1,1], dtype=bool)
if cell.dimension < 3:
pbc_axis[cell.dimension:] = False
a_norm = np.sqrt(np.diag(G))
a_angle = np.arccos(G / np.outer(a_norm, a_norm))
tol2 = tol**2
rotations = []
for op in lib.cartesian_prod([[1,0,-1],]*9):
W = np.asarray(op, dtype=np.int32).reshape(3,3)
G_tilde = reduce(np.dot, (W.T, G, W))
#check change of metric
a_tilde_norm = np.sqrt(np.diag(G_tilde))
length_error = np.abs(a_norm - a_tilde_norm)
if (length_error > tol).any():
continue
tmp = (a_norm + a_tilde_norm)
a_tilde_angle = np.arccos(G_tilde / np.outer(a_tilde_norm, a_tilde_norm))
angle_error = np.sin(a_angle - a_tilde_angle) **2 * np.outer(tmp,tmp) / 4
if (angle_error > tol2).any():
continue
#check if rotation inverts non-periodic axes
if not (W[np.diag(~pbc_axis)] == 1).all():
continue
#check if rotation swaps periodic and non-periodic axes
pbc_axis2 = np.logical_and.outer(pbc_axis, pbc_axis)
if W[~(pbc_axis2 | np.eye(3, dtype=bool))].any():
continue
rotations.append(W)
rotations = np.asarray(rotations)
return rotations
[docs]
def search_space_group_ops(cell, rotations=None, tol=SYMPREC):
'''
Search for the allowed space group operations for a specific cell.
Notes:
The current implementation treats the cell with the spins on all
atoms flipped as the same as the original cell. If this is not desired,
then one can use different names for the two sets of atoms and set their
magnetic moment to 0.
'''
if rotations is None: rotations = search_point_group_ops(cell, tol=tol)
a = cell.lattice_vectors()
coords = cell.get_scaled_positions()
atmgrp = mole.atom_types(cell._atom, magmom=cell.magmom)
atmgrp_spin_inv = {} #spin up and down inverted
has_spin = False
for atm in atmgrp.keys():
if atm[-2:] == '_u':
has_spin = True
atmgrp_spin_inv[atm] = atmgrp[atm[:-2]+'_d']
elif atm[-2:] == '_d':
has_spin = True
atmgrp_spin_inv[atm] = atmgrp[atm[:-2]+'_u']
else:
atmgrp_spin_inv[atm] = atmgrp[atm]
def test_trans(R, t, spin_inverse=False):
for atm, idx in atmgrp.items():
x = coords[idx]
xt = np.dot(x, R.T) + t
if not spin_inverse:
x_xt = np.concatenate((x,xt))
else:
x_xt = np.concatenate((coords[atmgrp_spin_inv[atm]],xt))
x_xt = np.mod(x_xt, 1)
x_xt = np.round(x_xt, -np.log10(tol).astype(int))
x_xt = np.mod(x_xt, 1)
sorted_idx = np.lexsort(x_xt.T)
x_xt = x_xt[sorted_idx]
diff = np.dot(x_xt[::2] - x_xt[1::2], a)
if (np.abs(diff) > tol).any():
return False
return True
grp_len = [len(v) for v in atmgrp.values()]
atm = [k for k in atmgrp.keys() if len(atmgrp[k]) == min(grp_len)][0]
x = coords[atmgrp[atm]]
x_spin_inv = None
if atm[-2:] in ['_u', '_d']:
x_spin_inv = coords[atmgrp_spin_inv[atm]]
from pyscf.pbc.symm.space_group import SPGElement
ops = []
for rot in rotations:
w = x - np.dot(x[0], rot.T)
if x_spin_inv is not None:
w_spin_inv = x_spin_inv - np.dot(x[0], rot.T)
w = np.vstack((w, w_spin_inv))
w = np.mod(w, 1)
w = np.round(w, -np.log10(tol).astype(int))
w = np.mod(w, 1)
w = np.unique(w, axis=0)
for trans in w:
if test_trans(rot, trans):
ops.append(SPGElement(rot, trans))
elif has_spin:
if test_trans(rot, trans, True):
ops.append(SPGElement(rot, trans))
return ops
[docs]
def get_crystal_class(cell, ops=None, tol=SYMPREC):
if ops is None: ops = search_space_group_ops(cell, tol=tol)
rotations = []
for op in ops:
rotations.append(op.rot)
rotations = np.unique(np.asarray(rotations), axis=0)
maps = {-6 : 0,
-4 : 1,
-3 : 2,
-2 : 3,
-1 : 4,
1 : 5,
2 : 6,
3 : 7,
4 : 8,
6 : 9}
table = [0,] * 10
for rot in rotations:
trace = np.trace(rot)
det = np.linalg.det(rot)
if trace == 3:
assert(det == 1)
table[maps[1]] += 1
elif trace == -3:
assert(det == -1)
table[maps[-1]] += 1
elif trace == 2:
assert(det == 1)
table[maps[6]] += 1
elif trace == -2:
assert(det == -1)
table[maps[-6]] += 1
elif trace == 0:
if det == 1:
table[maps[3]] += 1
elif det == -1:
table[maps[-3]] += 1
elif trace == 1:
if det == 1:
table[maps[4]] += 1
elif det == -1:
table[maps[-2]] += 1
elif trace == -1:
if det == 1:
table[maps[2]] += 1
elif det == -1:
table[maps[-4]] += 1
else:
raise ValueError("Input rotation matrix is wrong: %s" % rot)
from pyscf.pbc.symm.tables import CrystalClass, LaueClass
laue_class = None
crystal_class = None
for k, v in CrystalClass.items():
count = 0
for i in range(10):
if table[i] == v[i]: count += 1
if count == 10:
crystal_class = k
break
for k, v in LaueClass.items():
if crystal_class in v:
laue_class = k
break
if crystal_class is None or laue_class is None:
raise RuntimeError("Unable to determine crystal class.")
return crystal_class, laue_class
if __name__ == "__main__":
from pyscf.pbc import gto
cell = gto.Cell()
cell.atom = """
Cu 1.000000 1.00000 0.0000
O 0.000000 1.00000 0.0000
O 1.000000 2.00000 0.0000
Cu 1.000000 3.00000 0.0000
O 1.000000 4.00000 0.0000
O 2.000000 3.00000 0.0000
Cu 3.000000 3.00000 0.0000
O 4.000000 3.00000 0.0000
O 3.000000 2.00000 0.0000
Cu 3.000000 1.00000 0.0000
O 3.000000 0.00000 0.0000
O 2.000000 1.00000 0.0000
"""
cell.a = [[4.0, 0., 0.], [0., 4.0, 0.], [0., 0., 16.0]]
cell.dimension = 2
cell.magmom = [1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, -1]
cell.build()
ops = search_space_group_ops(cell)
for op in ops: print(op)
point_group = get_crystal_class(cell, ops=ops)[0]
print(point_group)