import numpy as np
from ase import Atoms
from ase.cluster.util import get_element_info
[docs]def Icosahedron(symbol, noshells, latticeconstant=None):
"""
Returns a cluster with the icosahedra symmetry.
Parameters
----------
symbol : str or int
The chemical symbol (or atomic number) of the element.
noshells : int
The number of shells (>= 1).
latticeconstant : float, optional
The lattice constant. If not given, then it is extracted from
`ase.data`.
"""
symbol, atomic_number, latticeconstant = get_element_info(
symbol, latticeconstant)
# Interpret noshells
if noshells < 1:
raise ValueError(
"The number of shells must be equal to or greater than one.")
t = 0.5 + np.sqrt(5) / 2.0
verticies = np.array([[t, 0., 1.],
[t, 0., -1.],
[-t, 0., 1.],
[-t, 0., -1.],
[1., t, 0.],
[-1., t, 0.],
[1., -t, 0.],
[-1., -t, 0.],
[0., 1., t],
[0., -1., t],
[0., 1., -t],
[0., -1., -t]])
positions = []
tags = []
positions.append(np.zeros(3))
tags.append(1)
for n in range(1, noshells):
# Construct square edges (6)
for k in range(0, 12, 2):
v1 = verticies[k]
v2 = verticies[k + 1]
for i in range(n + 1):
pos = i * v1 + (n - i) * v2
positions.append(pos)
tags.append(n + 1)
# Construct triangle planes (12)
if n > 1:
map = {0: (8, 9), 1: (10, 11),
2: (8, 9), 3: (10, 11),
4: (0, 1), 5: (2, 3),
6: (0, 1), 7: (2, 3),
8: (4, 5), 9: (6, 7),
10: (4, 5), 11: (6, 7)}
for k in range(12):
v0 = n * verticies[k]
v1 = (verticies[map[k][0]] - verticies[k])
v2 = (verticies[map[k][1]] - verticies[k])
for i in range(n):
for j in range(n - i):
if i == 0 and j == 0:
continue
pos = v0 + i * v1 + j * v2
positions.append(pos)
tags.append(n + 1)
# Fill missing triangle planes (8)
if n > 2:
map = {0: (9, 6, 8, 4,),
1: (11, 6, 10, 4),
2: (9, 7, 8, 5,),
3: (11, 7, 10, 5)}
for k in range(4):
v0 = n * verticies[k]
v1 = (verticies[map[k][0]] - verticies[k])
v2 = (verticies[map[k][1]] - verticies[k])
v3 = (verticies[map[k][2]] - verticies[k])
v4 = (verticies[map[k][3]] - verticies[k])
for i in range(1, n):
for j in range(1, n - i):
pos = v0 + i * v1 + j * v2
positions.append(pos)
tags.append(n + 1)
pos = v0 + i * v3 + j * v4
positions.append(pos)
tags.append(n + 1)
# Scale the positions
scaling_factor = latticeconstant / np.sqrt(2 * (1 + t**2))
positions = np.array(positions) * scaling_factor
symbols = [atomic_number] * len(positions)
atoms = Atoms(symbols=symbols, positions=positions, tags=tags)
atoms.center(about=(0, 0, 0))
atoms.cell[:] = 0
return atoms