# Source code for ase.cluster.icosahedron

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(0, 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(0, 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