def bind(self, frame):
if not self.ui.get_widget('/MenuBar/ViewMenu/ShowBonds'
).get_active():
self.bonds = np.empty((0, 5), int)
return
from ase.atoms import Atoms
from ase.calculators.neighborlist import NeighborList
nl = NeighborList(self.images.r * 1.5, skin=0, self_interaction=False)
nl.update(Atoms(positions=self.images.P[frame],
cell=(self.images.repeat[:, np.newaxis] *
self.images.A[frame]),
pbc=self.images.pbc))
nb = nl.nneighbors + nl.npbcneighbors
self.bonds = np.empty((nb, 5), int)
if nb == 0:
return
n1 = 0
for a in range(self.images.natoms):
indices, offsets = nl.get_neighbors(a)
n2 = n1 + len(indices)
self.bonds[n1:n2, 0] = a
self.bonds[n1:n2, 1] = indices
self.bonds[n1:n2, 2:] = offsets
n1 = n2
i = self.bonds[:n2, 2:].any(1)
self.bonds[n2:, 0] = self.bonds[i, 1]
self.bonds[n2:, 1] = self.bonds[i, 0]
self.bonds[n2:, 2:] = -self.bonds[i, 2:]
def get_fingerprints(atoms):
elements =['O','Ru']
Gs = make_symmetry_functions(elements)
fp = np.zeros([2, len(Gs['O'])])
cutoff ={'name': 'Cosine', 'kwargs': {'Rc': 6.5}}
cutoff_globle = 6.5
_nl = NeighborList(cutoffs=([cutoff_globle / 2.] *
len(atoms)),
self_interaction=False,
bothways=True,
skin=0.)
_nl.update(atoms)
amp_obj = FingerprintCalculator(neighborlist=_nl, Gs=Gs, cutoff=cutoff,fortran=False)
amp_obj.initialize(fortran=False,atoms=atoms)
n=0
fingerprint = []
for index in range(12,14):
symbol = atoms[index].symbol
neighborindices, neighboroffsets = _nl.get_neighbors(index)
neighborsymbols = [atoms[_].symbol for _ in neighborindices]
neighborpositions = [atoms.positions[neighbor] + np.dot(offset, atoms.cell)
for (neighbor, offset) in zip(neighborindices,
neighboroffsets)]
indexfp = amp_obj.get_fingerprint(
index, symbol, neighborsymbols, neighborpositions)
fp[n] = indexfp[1]
n = n+1
return fp
def find_tip_coordination(a, bondlength=2.6, bulk_nn=4):
"""
Find position of tip in crack cluster from coordination
"""
nl = NeighborList([bondlength / 2.0] * len(a),
skin=0.0,
self_interaction=False,
bothways=True)
nl.update(a)
nn = np.array([len(nl.get_neighbors(i)[0]) for i in range(len(a))])
a.set_array('n_neighb', nn)
g = a.get_array('groups')
y = a.positions[:, 1]
above = (nn < bulk_nn) & (g != 0) & (y > a.cell[1, 1] / 2.0)
below = (nn < bulk_nn) & (g != 0) & (y < a.cell[1, 1] / 2.0)
a.set_array('above', above)
a.set_array('below', below)
bond1 = np.asscalar(above.nonzero()[0][a.positions[above, 0].argmax()])
bond2 = np.asscalar(below.nonzero()[0][a.positions[below, 0].argmax()])
# These need to be ints, otherwise they are no JSON serializable.
a.info['bond1'] = bond1
a.info['bond2'] = bond2
return bond1, bond2
def get_bondpairs(atoms, radius=1.1):
"""Get all pairs of bonding atoms
Return all pairs of atoms which are closer than radius times the
sum of their respective covalent radii. The pairs are returned as
tuples::
(a, b, (i1, i2, i3))
so that atoms a bonds to atom b displaced by the vector::
_ _ _
i c + i c + i c ,
1 1 2 2 3 3
where c1, c2 and c3 are the unit cell vectors and i1, i2, i3 are
integers."""
from ase.data import covalent_radii
from ase.calculators.neighborlist import NeighborList
cutoffs = radius * covalent_radii[atoms.numbers]
nl = NeighborList(cutoffs=cutoffs, self_interaction=False)
nl.update(atoms)
bondpairs = []
for a in range(len(atoms)):
indices, offsets = nl.get_neighbors(a)
bondpairs.extend([(a, a2, offset)
for a2, offset in zip(indices, offsets)])
return bondpairs
def get_bondpairs(atoms, radius=1.1):
"""Get all pairs of bonding atoms
Return all pairs of atoms which are closer than radius times the
sum of their respective covalent radii. The pairs are returned as
tuples::
(a, b, (i1, i2, i3))
so that atoms a bonds to atom b displaced by the vector::
_ _ _
i c + i c + i c ,
1 1 2 2 3 3
where c1, c2 and c3 are the unit cell vectors and i1, i2, i3 are
integers."""
from ase.data import covalent_radii
from ase.calculators.neighborlist import NeighborList
cutoffs = radius * covalent_radii[atoms.numbers]
nl = NeighborList(cutoffs=cutoffs, self_interaction=False)
nl.update(atoms)
bondpairs = []
for a in range(len(atoms)):
indices, offsets = nl.get_neighbors(a)
bondpairs.extend([(a, a2, offset)
for a2, offset in zip(indices, offsets)])
return bondpairs
def calculate_image_center(atoms, watchindex, pdirs):
"""Calculates the center of the image in the pdir basis coordinates."""
# The first moment of the image around the center atom is calculated.
atoms = atoms.copy()
from ase.calculators.neighborlist import NeighborList
_nl = NeighborList(cutoffs=([6.5 / 2.] * len(atoms)),
self_interaction=False,
bothways=True,
skin=0.)
_nl.update(atoms)
position = atoms.positions[watchindex]
# Step 1: Calculating neighbors of atom.
n_indices, n_offsets = _nl.get_neighbors(watchindex)
Rs = [atoms.positions[n_index] +
np.dot(n_offset, atoms.get_cell()) - position
for n_index, n_offset in zip(n_indices, n_offsets)]
xtilde = 0.
ytilde = 0.
ztilde = 0.
for rs in Rs:
xtilde += rs[0] * np.dot([1, 0, 0], pdirs[0])
xtilde += rs[1] * np.dot([0, 1, 0], pdirs[0])
xtilde += rs[2] * np.dot([0, 0, 1], pdirs[0])
ytilde += rs[0] * np.dot([1, 0, 0], pdirs[1])
ytilde += rs[1] * np.dot([0, 1, 0], pdirs[1])
ytilde += rs[2] * np.dot([0, 0, 1], pdirs[1])
ztilde += rs[0] * np.dot([1, 0, 0], pdirs[2])
ztilde += rs[1] * np.dot([0, 1, 0], pdirs[2])
ztilde += rs[2] * np.dot([0, 0, 1], pdirs[2])
return xtilde, ytilde, ztilde
def __init__(self, filename):
atoms = ase.io.read(filename, format='vasp')
cell = atoms.get_cell()
symb = atoms.get_atomic_numbers()
cutoffs = np.ones((len(atoms))) * 1.35 # radius around each atom (half the max bondlength)
nl = NeighborList(cutoffs, 0., self_interaction = False, bothways = False)
nl.update(atoms)
std_len = 2.35805097505
# Loop over atoms
bond_no = 0
bonds = np.zeros((nl.nneighbors,4))
for atom1idx, (indices, offsets, atom1pos) in enumerate(zip(nl.neighbors, nl.displacements, nl.positions)):
# Loop over bonds
for atom2idx, offset in zip(indices, offsets):
#if symb[atom1idx] == symb[atom2idx] == 'Si':
atom2pos = nl.positions[atom2idx] + np.dot(offset, cell)
#print "pos[%i] = %.2f %.2f %.2f" % (atom1idx, atom1pos[0],atom1pos[1],atom1pos[2])
#print "pos[%i] = %.2f %.2f %.2f" % (atom2idx, atom2pos[0],atom2pos[1],atom2pos[2])
bond = atom2pos - atom1pos
bond_center = atom1pos + bond/2.
bond_z = bond_center[2]
bondlength = np.sqrt(np.dot(bond,bond))
bonds[bond_no] = [bond_z, bondlength, symb[atom1idx], symb[atom2idx]]
bond_no += 1
self.bonds = bonds
print bonds
def find_tip_coordination(a, bondlength=2.6, bulk_nn=4):
"""
Find position of tip in crack cluster from coordination
"""
nl = NeighborList([bondlength/2.0]*len(a),
skin=0.0,
self_interaction=False,
bothways=True)
nl.update(a)
nn = np.array([len(nl.get_neighbors(i)[0]) for i in range(len(a))])
a.set_array('n_neighb', nn)
g = a.get_array('groups')
y = a.positions[:, 1]
above = (nn < bulk_nn) & (g != 0) & (y > a.cell[1,1]/2.0)
below = (nn < bulk_nn) & (g != 0) & (y < a.cell[1,1]/2.0)
a.set_array('above', above)
a.set_array('below', below)
bond1 = np.asscalar(above.nonzero()[0][a.positions[above, 0].argmax()])
bond2 = np.asscalar(below.nonzero()[0][a.positions[below, 0].argmax()])
# These need to be ints, otherwise they are no JSON serializable.
a.info['bond1'] = bond1
a.info['bond2'] = bond2
return bond1, bond2
def update(self, atoms):
# check all the elements are available in the potential
self.Nelements = len(self.elements)
elements = np.unique(atoms.get_chemical_symbols())
unavailable = np.logical_not(
np.array([item in self.elements for item in elements]))
if np.any(unavailable):
raise RuntimeError('These elements are not in the potential: %s' %
elements[unavailable])
# cutoffs need to be a vector for NeighborList
cutoffs = self.cutoff * np.ones(len(atoms))
# convert the elements to an index of the position
# in the eam format
self.index = np.array(
[self.elements.index(el) for el in atoms.get_chemical_symbols()])
self.pbc = atoms.get_pbc()
# since we need the contribution of all neighbors to the
# local electron density we cannot just calculate and use
# one way neighbors
self.neighbors = NeighborList(cutoffs,
skin=self.parameters.skin,
self_interaction=False,
bothways=True)
self.neighbors.update(atoms)
def bind(self, frame):
if not self.ui.get_widget('/MenuBar/ViewMenu/ShowBonds').get_active():
self.bonds = np.empty((0, 5), int)
return
from ase.atoms import Atoms
from ase.calculators.neighborlist import NeighborList
nl = NeighborList(self.images.r * 1.5, skin=0, self_interaction=False)
nl.update(
Atoms(positions=self.images.P[frame],
cell=(self.images.repeat[:, np.newaxis] *
self.images.A[frame]),
pbc=self.images.pbc))
nb = nl.nneighbors + nl.npbcneighbors
self.bonds = np.empty((nb, 5), int)
if nb == 0:
return
n1 = 0
for a in range(self.images.natoms):
indices, offsets = nl.get_neighbors(a)
n2 = n1 + len(indices)
self.bonds[n1:n2, 0] = a
self.bonds[n1:n2, 1] = indices
self.bonds[n1:n2, 2:] = offsets
n1 = n2
i = self.bonds[:n2, 2:].any(1)
self.bonds[n2:, 0] = self.bonds[i, 1]
self.bonds[n2:, 1] = self.bonds[i, 0]
self.bonds[n2:, 2:] = -self.bonds[i, 2:]
def __init__(self, filename):
atoms = ase.io.read(filename, format='vasp')
cell = atoms.get_cell()
symb = atoms.get_atomic_numbers()
cutoffs = np.ones(
(len(atoms)
)) * 1.35 # radius around each atom (half the max bondlength)
nl = NeighborList(cutoffs, 0., self_interaction=False, bothways=False)
nl.update(atoms)
std_len = 2.35805097505
# Loop over atoms
bond_no = 0
bonds = np.zeros((nl.nneighbors, 4))
for atom1idx, (indices, offsets, atom1pos) in enumerate(
zip(nl.neighbors, nl.displacements, nl.positions)):
# Loop over bonds
for atom2idx, offset in zip(indices, offsets):
#if symb[atom1idx] == symb[atom2idx] == 'Si':
atom2pos = nl.positions[atom2idx] + np.dot(offset, cell)
#print "pos[%i] = %.2f %.2f %.2f" % (atom1idx, atom1pos[0],atom1pos[1],atom1pos[2])
#print "pos[%i] = %.2f %.2f %.2f" % (atom2idx, atom2pos[0],atom2pos[1],atom2pos[2])
bond = atom2pos - atom1pos
bond_center = atom1pos + bond / 2.
bond_z = bond_center[2]
bondlength = np.sqrt(np.dot(bond, bond))
bonds[bond_no] = [
bond_z, bondlength, symb[atom1idx], symb[atom2idx]
]
bond_no += 1
self.bonds = bonds
print bonds
def calculate(self, image, key):
cutoff = self.globals.cutoff
n = NeighborList(cutoffs=[cutoff / 2.] * len(image),
self_interaction=False,
bothways=True,
skin=0.)
n.update(image)
return [n.get_neighbors(index) for index in xrange(len(image))]
def update_neighbor_list(self, atoms):
cut = 0.5 * max(self.data['cutoffs'].values())
self.nl = NeighborList([cut] * len(atoms),
skin=0,
bothways=True,
self_interaction=False)
self.nl.update(atoms)
self.atoms = atoms
def update(self, atoms):
if (self.neighbors is None) or (len(self.neighbors.cutoffs) !=
len(atoms)):
cutoffs = self.cutoff * np.ones(len(atoms))
self.neighbors = NeighborList(cutoffs,
self_interaction=False,
bothways=True)
self.neighbors.update(atoms)
def initialize(self, atoms):
self.par = {}
self.rc = 0.0
self.numbers = atoms.get_atomic_numbers()
maxseq = 0.0
seen = {}
for Z in self.numbers:
if Z not in seen:
seen[Z] = True
ss = parameters[chemical_symbols[Z]][1] * Bohr
if maxseq < ss:
maxseq = ss
rc = self.rc = beta * maxseq * 0.5 * (sqrt(3) + sqrt(4))
rr = rc * 2 * sqrt(4) / (sqrt(3) + sqrt(4))
self.acut = np.log(9999.0) / (rr - rc)
for Z in self.numbers:
if Z not in self.par:
p = parameters[chemical_symbols[Z]]
s0 = p[1] * Bohr
eta2 = p[3] / Bohr
kappa = p[4] / Bohr
x = eta2 * beta * s0
gamma1 = 0.0
gamma2 = 0.0
for i, n in enumerate([12, 6, 24]):
r = s0 * beta * sqrt(i + 1)
x = n / (12 * (1.0 + exp(self.acut * (r - rc))))
gamma1 += x * exp(-eta2 * (r - beta * s0))
gamma2 += x * exp(-kappa / beta * (r - beta * s0))
self.par[Z] = {'E0': p[0],
's0': s0,
'V0': p[2],
'eta2': eta2,
'kappa': kappa,
'lambda': p[5] / Bohr,
'n0': p[6] / Bohr**3,
'rc': rc,
'gamma1': gamma1,
'gamma2': gamma2}
#if rc + 0.5 > self.rc:
# self.rc = rc + 0.5
self.ksi = {}
for s1, p1 in self.par.items():
self.ksi[s1] = {}
for s2, p2 in self.par.items():
#self.ksi[s1][s2] = (p2['n0'] / p1['n0'] *
# exp(eta1 * (p1['s0'] - p2['s0'])))
self.ksi[s1][s2] = p2['n0'] / p1['n0']
self.forces = np.empty((len(atoms), 3))
self.sigma1 = np.empty(len(atoms))
self.deds = np.empty(len(atoms))
self.nl = NeighborList([0.5 * self.rc + 0.25] * len(atoms),
self_interaction=False)
def calculate(self,
atoms=None,
properties=['energy'],
system_changes=all_changes):
Calculator.calculate(self, atoms, properties, system_changes)
natoms = len(self.atoms)
sigma = self.parameters.sigma
epsilon = self.parameters.epsilon
rc = self.parameters.rc
if rc is None:
rc = 3 * sigma
if 'numbers' in system_changes:
self.nl = NeighborList([rc / 2] * natoms, self_interaction=False)
self.nl.update(self.atoms)
positions = self.atoms.positions
cell = self.atoms.cell
e0 = 4 * epsilon * ((sigma / rc)**12 - (sigma / rc)**6)
energy = 0.0
forces = np.zeros((natoms, 3))
stress = np.zeros((3, 3))
for a1 in range(natoms):
neighbors, offsets = self.nl.get_neighbors(a1)
cells = np.dot(offsets, cell)
d = positions[neighbors] + cells - positions[a1]
r2 = (d**2).sum(1)
c6 = (sigma**2 / r2)**3
c6[r2 > rc**2] = 0.0
energy -= e0 * (c6 != 0.0).sum()
c12 = c6**2
energy += 4 * epsilon * (c12 - c6).sum()
f = (24 * epsilon * (2 * c12 - c6) / r2)[:, np.newaxis] * d
#print d
#print r2**.5
#print offsets
#print f
#print neighbors
forces[a1] -= f.sum(axis=0)
for a2, f2 in zip(neighbors, f):
forces[a2] += f2
stress += np.dot(f.T, d)
#stress = np.dot(stress, cell)
stress += stress.T.copy()
stress *= -0.5 / self.atoms.get_volume()
self.results['energy'] = energy
self.results['forces'] = forces
self.results['stress'] = stress.flat[[0, 4, 8, 5, 2, 1]]
def vacancy_energy(bulk, remove_index=0):
Nat = bulk.get_number_of_atoms()
vac = bulk.copy()
vac.set_calculator(bulk.get_calculator())
nl = NeighborList([a0*sqrt(3.0)/4*0.6]*len(bulk), self_interaction=False, bothways=True)
nl.update(bulk)
indices, offsets = nl.get_neighbors(remove_index)
offset_factor=0.13
for i, offset in zip(indices, offsets):
ri = vac.positions[remove_index] - (vac.positions[i] + dot(offset, vac.get_cell()))
vac.positions[i] += offset_factor*ri
offset_factor += 0.01
del vac[remove_index] # remove an atom to introduce a vacancy
# perturb positions
vac.rattle(0.1)
##
try:
model.calculator.set(local_gap_error='local_gap_error')
vac.get_potential_energy()
unrelaxed_local_gap_error_max = amax(model.calculator.results['local_gap_error'])
unrelaxed_local_gap_error_sum = sum(model.calculator.results['local_gap_error'])
except:
unrelaxed_local_gap_error_max = None
unrelaxed_local_gap_error_sum = None
if isinstance(model, Potential):
model.calculator.set(local_gap_error='')
# relax atom positions, holding cell fixed
vac = relax_atoms(vac, tol=fmax, traj_file="model-"+model.name+"-test-vacancy-energy.opt.xyz")
vac.write("model-"+model.name+"test-vacancy-energy-relaxed.xyz")
##
try:
model.calculator.set(local_gap_error='local_gap_error')
vac.get_potential_energy()
relaxed_local_gap_error_max = amax(model.calculator.results['local_gap_error'])
relaxed_local_gap_error_sum = sum(model.calculator.results['local_gap_error'])
except:
relaxed_local_gap_error_max = None
relaxed_local_gap_error_sum = None
if isinstance(model, Potential):
model.calculator.set(local_gap_error='')
##
# compute vacancy formation energy as difference of bulk and vac energies
print 'bulk cell energy', bulk_energy
print 'vacancy cell energy', vac.get_potential_energy()
e_form = vac.get_potential_energy() - bulk_energy*vac.get_number_of_atoms()/bulk.get_number_of_atoms()
print 'vacancy formation energy', e_form
return (e_form, unrelaxed_local_gap_error_max, unrelaxed_local_gap_error_sum, relaxed_local_gap_error_max, relaxed_local_gap_error_sum)
def buildNeighborList(self):
atoms = self.atoms
nl = NeighborList([0.8 for atom in atoms],
self_interaction=False, bothways=True)
nl.update(atoms)
self.nl = nl
neigh = []
for i in range(self.natom):
neigh.append(self.sort_nei(i))
# print neigh[i]
self.neigh = neigh
def buildNeighborList(self):
atoms = self.atoms
nl = NeighborList([0.8 for atom in atoms],
self_interaction=False,
bothways=True)
nl.update(atoms)
self.nl = nl
neigh = []
for i in range(self.natom):
neigh.append(self.sort_nei(i))
# print neigh[i]
self.neigh = neigh
def testNeighborlist(self):
atoms=read('range',format='lammps')
atoms. set_pbc((1, 1, 1))
nl = NeighborList([0.8 for atom in atoms],self_interaction=False,bothways=True)
nl.update(atoms)
ang=[]
for i in xrange(3):
indices, offsets = nl. get_neighbors(i)
angs=[]
for j, offset in zip(indices, offsets):
pos= atoms. positions[j] + dot(offset, atoms. get_cell())-atoms.positions[i]
ang1=atan2(pos[1],pos[0])+pi
angs.append((j,ang1))
newangs=sorted(angs,key=lambda d:d[1])
print newangs
def update(self, atoms):
# check all the elements are available in the potential
elements = np.unique(atoms.get_chemical_symbols())
unavailable = np.logical_not(
np.array([item in self.elements for item in elements]))
if np.any(unavailable):
raise RuntimeError('These elements are not in the potential: %s' %
elements[unavailable])
# check if anything has changed to require re-calculation
if (self.positions is None or
len(self.positions) != len(atoms.get_positions()) or
(self.positions != atoms.get_positions()).any() or
(self.cell != atoms.get_cell()).any() or
(self.pbc != atoms.get_pbc()).any()):
# cutoffs need to be a vector for NeighborList
cutoffs = self.cutoff * np.ones(len(atoms))
# convert the elements to an index of the position
# in the eam format
self.index = np.array([atoms.calc.elements.index(el)
for el in atoms.get_chemical_symbols()])
self.pbc = atoms.get_pbc()
# since we need the contribution of all neighbors to the
# local electron density we cannot just calculate and use
# one way neighbors
self.neighbors = NeighborList(cutoffs, skin=self.skin,
self_interaction=False,
bothways=True)
self.neighbors.update(atoms)
self.calculate(atoms)
def find_connected(self, index, dmax=None, scale=1.5):
"""Find the atoms connected to self[index] and return them.
If dmax is not None:
Atoms are defined to be connected if they are nearer than dmax
to each other.
If dmax is None:
Atoms are defined to be connected if they are nearer than the
sum of their covalent radii * scale to each other.
"""
# set neighbor lists
neighborlist = []
if dmax is None:
# define neighbors according to covalent radii
radii = scale * covalent_radii[self.get_atomic_numbers()]
for atom in self:
positions = self.positions - atom.position
distances = np.sqrt(np.sum(positions**2, axis=1))
radius = scale * covalent_radii[atom.get_atomic_number()]
neighborlist.append(np.where(distances < radii + radius)[0])
else:
# define neighbors according to distance
nl = NeighborList([0.5 * dmax] * len(self), skin=0)
nl.update(self)
for i, atom in enumerate(self):
neighborlist.append(list(nl.get_neighbors(i)[0]))
connected = list(neighborlist[index])
isolated = False
while not isolated:
isolated = True
for i in connected:
for j in neighborlist[i]:
if j in connected:
pass
else:
connected.append(j)
isolated = False
atoms = Cluster()
for i in connected:
atoms.append(self[i])
return atoms
def relax(self, individual):
"""Relaxes the individual using a hard-sphere cutoff method.
Args:
individual (Individual): the individual to relax
"""
rank = gparameters.mpi.rank
print("Relaxing individual {} on rank {} with hard-sphere cutoff method".format(individual.id, rank))
radii = [2.0 for atom in individual]
nl = NeighborList(radii, bothways=True, self_interaction=False)
nl.update(individual)
ntries = 0
modified = True
while modified and ntries < 100:
modified = False
for atom in individual:
indices, offsets = nl.get_neighbors(atom.index)
for neigh in indices:
if individual.get_distance(atom.index, neigh) < self.cutoff:
individual.set_distance(atom.index, neigh, self.cutoff, fix=0.5)
modified = True
nl.update(individual)
individual.wrap()
ntries += 1
if ntries == 100:
print("WARNING! Iterated through the hard-sphere cutoff relaxation 100 times and it still did not converge!")
def testNeighborlist(self):
atoms = read('range', format='lammps')
atoms.set_pbc((1, 1, 1))
nl = NeighborList([0.8 for atom in atoms],
self_interaction=False,
bothways=True)
nl.update(atoms)
ang = []
for i in xrange(3):
indices, offsets = nl.get_neighbors(i)
angs = []
for j, offset in zip(indices, offsets):
pos = atoms.positions[j] + dot(
offset, atoms.get_cell()) - atoms.positions[i]
ang1 = atan2(pos[1], pos[0]) + pi
angs.append((j, ang1))
newangs = sorted(angs, key=lambda d: d[1])
print newangs
def calculate(self, atoms=None,
properties=['energy'],
system_changes=all_changes):
Calculator.calculate(self, atoms, properties, system_changes)
natoms = len(self.atoms)
sigma = self.parameters.sigma
epsilon = self.parameters.epsilon
rc = self.parameters.rc
if rc is None:
rc = 3 * sigma
if 'numbers' in system_changes:
self.nl = NeighborList([rc / 2] * natoms, self_interaction=False)
self.nl.update(self.atoms)
positions = self.atoms.positions
cell = self.atoms.cell
e0 = 4 * epsilon * ((sigma / rc)**12 - (sigma / rc)**6)
energy = 0.0
forces = np.zeros((natoms, 3))
stress = np.zeros((3, 3))
for a1 in range(natoms):
neighbors, offsets = self.nl.get_neighbors(a1)
cells = np.dot(offsets, cell)
d = positions[neighbors] + cells - positions[a1]
r2 = (d**2).sum(1)
c6 = (sigma**2 / r2)**3
c6[r2 > rc**2] = 0.0
energy -= e0 * (c6 != 0.0).sum()
c12 = c6**2
energy += 4 * epsilon * (c12 - c6).sum()
f = (24 * epsilon * (2 * c12 - c6) / r2)[:, np.newaxis] * d
#print d
#print r2**.5
#print offsets
#print f
#print neighbors
forces[a1] -= f.sum(axis=0)
for a2, f2 in zip(neighbors, f):
forces[a2] += f2
stress += np.dot(f.T, d)
#stress = np.dot(stress, cell)
stress += stress.T.copy()
stress *= -0.5 / self.atoms.get_volume()
self.results['energy'] = energy
self.results['forces'] = forces
self.results['stress'] = stress.flat[[0, 4, 8, 5, 2, 1]]
class NeighborPairs:
"""Class for looping over pairs of atoms using a neighbor list."""
def __init__(self, cutoff_a, cell_cv, pbc_c, self_interaction):
self.neighbors = NeighborList(cutoff_a, skin=0, sorted=True,
self_interaction=self_interaction)
self.atoms = Atoms('X%d' % len(cutoff_a), cell=cell_cv, pbc=pbc_c)
# Warning: never use self.atoms.get_scaled_positions() for
# anything. Those positions suffer from roundoff errors!
def set_positions(self, spos_ac):
self.spos_ac = spos_ac
self.atoms.set_scaled_positions(spos_ac)
self.neighbors.update(self.atoms)
def iter(self):
cell_cv = self.atoms.cell
for a1, spos1_c in enumerate(self.spos_ac):
a2_a, offsets = self.neighbors.get_neighbors(a1)
for a2, offset in zip(a2_a, offsets):
spos2_c = self.spos_ac[a2] + offset
R_c = np.dot(spos2_c - spos1_c, cell_cv)
yield a1, a2, R_c, offset
def initialize(self, atoms):
self.par = {}
self.rc = 0.0
self.numbers = atoms.get_atomic_numbers()
maxseq = max(par[1] for par in parameters.values()) * Bohr
rc = self.rc = beta * maxseq * 0.5 * (sqrt(3) + sqrt(4))
rr = rc * 2 * sqrt(4) / (sqrt(3) + sqrt(4))
self.acut = np.log(9999.0) / (rr - rc)
for Z in self.numbers:
if Z not in self.par:
p = parameters[chemical_symbols[Z]]
s0 = p[1] * Bohr
eta2 = p[3] / Bohr
kappa = p[4] / Bohr
x = eta2 * beta * s0
gamma1 = 0.0
gamma2 = 0.0
for i, n in enumerate([12, 6, 24]):
r = s0 * beta * sqrt(i + 1)
x = n / (12 * (1.0 + exp(self.acut * (r - rc))))
gamma1 += x * exp(-eta2 * (r - beta * s0))
gamma2 += x * exp(-kappa / beta * (r - beta * s0))
self.par[Z] = {'E0': p[0],
's0': s0,
'V0': p[2],
'eta2': eta2,
'kappa': kappa,
'lambda': p[5] / Bohr,
'n0': p[6] / Bohr**3,
'rc': rc,
'gamma1': gamma1,
'gamma2': gamma2}
#if rc + 0.5 > self.rc:
# self.rc = rc + 0.5
self.ksi = {}
for s1, p1 in self.par.items():
self.ksi[s1] = {}
for s2, p2 in self.par.items():
#self.ksi[s1][s2] = (p2['n0'] / p1['n0'] *
# exp(eta1 * (p1['s0'] - p2['s0'])))
self.ksi[s1][s2] = p2['n0'] / p1['n0']
self.forces = np.empty((len(atoms), 3))
self.sigma1 = np.empty(len(atoms))
self.deds = np.empty(len(atoms))
self.nl = NeighborList([0.5 * self.rc + 0.25] * len(atoms),
self_interaction=False)
class NeighborPairs:
"""Class for looping over pairs of atoms using a neighbor list."""
def __init__(self, cutoff_a, cell_cv, pbc_c, self_interaction):
self.neighbors = NeighborList(cutoff_a,
skin=0,
sorted=True,
self_interaction=self_interaction)
self.atoms = Atoms('X%d' % len(cutoff_a), cell=cell_cv, pbc=pbc_c)
# Warning: never use self.atoms.get_scaled_positions() for
# anything. Those positions suffer from roundoff errors!
def set_positions(self, spos_ac):
self.spos_ac = spos_ac
self.atoms.set_scaled_positions(spos_ac)
self.neighbors.update(self.atoms)
def iter(self):
cell_cv = self.atoms.cell
for a1, spos1_c in enumerate(self.spos_ac):
a2_a, offsets = self.neighbors.get_neighbors(a1)
for a2, offset in zip(a2_a, offsets):
spos2_c = self.spos_ac[a2] + offset
R_c = np.dot(spos2_c - spos1_c, cell_cv)
yield a1, a2, R_c, offset
def check_min_dist(totalsol, type='Defect', nat=None, min_len=0.7, STR=''):
if type == 'Defect' or type == 'Crystal' or type == 'Surface':
if nat == None:
nat = len(totalsol)
cutoffs = [2.0 for one in totalsol]
nl = NeighborList(cutoffs, bothways=True, self_interaction=False)
nl.update(totalsol)
for one in totalsol[0:nat]:
nbatoms = Atoms()
nbatoms.append(one)
indices, offsets = nl.get_neighbors(one.index)
for index, d in zip(indices, offsets):
index = int(index)
sym = totalsol[index].symbol
pos = totalsol[index].position + numpy.dot(
d, totalsol.get_cell())
at = Atom(symbol=sym, position=pos)
nbatoms.append(at)
while True:
dflag = False
for i in range(1, len(nbatoms)):
d = nbatoms.get_distance(0, i)
if d < min_len:
nbatoms.set_distance(0, i, min_len + .01, fix=0.5)
STR += '--- WARNING: Atoms too close (<0.7A) - Implement Move ---\n'
dflag = True
if dflag == False:
break
for i in range(len(indices)):
totalsol[indices[i]].position = nbatoms[i + 1].position
totalsol[one.index].position = nbatoms[0].position
nl.update(totalsol)
elif type == 'Cluster':
for i in range(len(totalsol)):
for j in range(len(totalsol)):
if i != j:
d = totalsol.get_distance(i, j)
if d < min_len:
totalsol.set_distance(i, j, min_len, fix=0.5)
STR += '--- WARNING: Atoms too close (<0.7A) - Implement Move ---\n'
else:
print 'WARNING: In Check_Min_Dist in EvalEnergy: Structure Type not recognized'
return totalsol, STR
def find_connected(self, index, dmax=None, scale=1.5):
"""Find the atoms connected to self[index] and return them.
If dmax is not None:
Atoms are defined to be connected if they are nearer than dmax
to each other.
If dmax is None:
Atoms are defined to be connected if they are nearer than the
sum of their covalent radii * scale to each other.
"""
if index < 0:
index = len(self) + index
# set neighbor lists
if dmax is None:
# define neighbors according to covalent radii
radii = scale * covalent_radii[self.get_atomic_numbers()]
else:
# define neighbors according to distance
radii = [0.5 * dmax] * len(self)
nl = NeighborList(radii, skin=0, self_interaction=False, bothways=True)
nl.update(self)
connected = [index] + list(nl.get_neighbors(index)[0])
isolated = False
while not isolated:
isolated = True
for i in connected:
for j in nl.get_neighbors(i)[0]:
if j in connected:
pass
else:
connected.append(j)
isolated = False
atoms = Cluster()
for i in connected:
atoms.append(self[i])
return atoms
def check_min_dist(totalsol, type='Defect', nat=None, min_len=0.7, STR=''):
if type=='Defect' or type=='Crystal' or type=='Surface':
if nat==None:
nat=len(totalsol)
cutoffs=[2.0 for one in totalsol]
nl=NeighborList(cutoffs,bothways=True,self_interaction=False)
nl.update(totalsol)
for one in totalsol[0:nat]:
nbatoms=Atoms()
nbatoms.append(one)
indices, offsets=nl.get_neighbors(one.index)
for index, d in zip(indices,offsets):
index = int(index)
sym=totalsol[index].symbol
pos=totalsol[index].position + numpy.dot(d,totalsol.get_cell())
at=Atom(symbol=sym,position=pos)
nbatoms.append(at)
while True:
dflag=False
for i in range(1,len(nbatoms)):
d=nbatoms.get_distance(0,i)
if d < min_len:
nbatoms.set_distance(0,i,min_len+.01,fix=0.5)
STR+='--- WARNING: Atoms too close (<0.7A) - Implement Move ---\n'
dflag=True
if dflag==False:
break
for i in range(len(indices)):
totalsol[indices[i]].position=nbatoms[i+1].position
totalsol[one.index].position=nbatoms[0].position
nl.update(totalsol)
elif type=='Cluster':
for i in range(len(totalsol)):
for j in range(len(totalsol)):
if i != j:
d=totalsol.get_distance(i,j)
if d < min_len:
totalsol.set_distance(i,j,min_len,fix=0.5)
STR+='--- WARNING: Atoms too close (<0.7A) - Implement Move ---\n'
else:
print 'WARNING: In Check_Min_Dist in EvalEnergy: Structure Type not recognized'
return totalsol, STR
def lattice_alteration_nn(indiv, Optimizer):
"""Move function to perform random move along random axis for nearest neighbor distance to random atoms
Inputs:
indiv = Individual class object to be altered
Optimizer = Optimizer class object with needed parameters
Outputs:
indiv = Altered Individual class object
"""
if 'MU' in Optimizer.debug:
debug = True
else:
debug = False
if Optimizer.structure == 'Defect':
if Optimizer.isolate_mutation:
indc, indb, vacant, swaps, stro = find_defects(
indiv[0], Optimizer.solidbulk, 0)
ind = indc.copy()
ind.extend(indb)
else:
ind = indiv[0].copy()
indc = indiv[0].copy()
else:
ind = indiv[0].copy()
indc = indiv[0].copy()
if len(indc) != 0:
ctoff1 = [1.0 for one in ind]
nl = NeighborList(ctoff1, bothways=True, self_interaction=False)
nl.update(ind)
try:
natomsmove = random.randint(1, len(indc) / 2)
except ValueError:
natomsmove = 1
passn = 0
for count in range(natomsmove):
try:
indexmv = random.choice([i for i in range(len(indc))])
indices, offsets = nl.get_neighbors(indexmv)
nns = Atoms()
nns.append(ind[indexmv])
for index, d in zip(indices, offsets):
index = int(index)
pos = ind[index].position + numpy.dot(d, ind.get_cell())
nns.append(Atom(symbol=ind[index].symbol, position=pos))
dist = [nns.get_distance(0, i) for i in range(1, len(nns))]
r = sum(dist) / len(dist)
dir = random.choice([[1, 0, 0], [-1, 0, 0], [0, 1, 0],
[0, -1, 0], [0, 0, 1], [0, 0, -1]])
ind[indexmv].position += [i * r for i in dir]
except:
passn += 1
indiv[0] = ind.copy()
else:
natomsmove = 0
passn = 0
Optimizer.output.write(
'Lattice Alteration NN Mutation performed on individual\n')
Optimizer.output.write('Index = ' + repr(indiv.index) + '\n')
natomsmove -= passn
Optimizer.output.write('Number of atoms moved = ' + repr(natomsmove) +
'\n')
Optimizer.output.write(repr(indiv[0]) + '\n')
muttype = 'LANN' + repr(natomsmove)
if indiv.energy == 0:
indiv.history_index = indiv.history_index + 'm' + muttype
else:
indiv.history_index = repr(indiv.index) + 'm' + muttype
return indiv
def find_defects(solid, bulko, rcutoff, atomlistcheck = False, trackvacs = False, trackswaps = False, debug = False, dcheck = 0.6):
"""Function to find interstitials, vacancies, and substitutional atoms (swaps) in a defected structure.
Identifies species by comparison to perfect structure.
Inputs:
solid = ASE atoms class for defected structure
bulko = ASE atoms class for perfect structure
rcutoff = float value of distance to surrounding atoms to include
atomlistcheck = False/list of atom types and concentrations according to atomlist format
trackvacs = True/False whether or not to identify vacancies in defect
trackswaps = True/False whether or not to identify substitutional defects
debug = False/file object to write debug structures"""
# Combine perfect and defect structures together
b = bulko.copy()
b.extend(solid)
b.set_pbc(True)
# Debug: Write solid and bulko to file
if debug:
print len(bulko)
write_xyz(debug, b, 'Find Ints: Solid and Bulko')
# Identify nearest neighbor atoms for each atom in perfect structure
ntot = len(bulko)
ctoff1 = [1.2 for one in b]
nl = NeighborList(ctoff1, bothways = True, self_interaction = False)
nl.update(b)
slist = []
blist = []
wlist = []
# Loop over each atom in perfect structure
for one in range(ntot):
indices, offsets = nl.get_neighbors(one)
for index, d in zip(indices, offsets):
index = int(index)
if index >= ntot:
pos = b[index].position + numpy.dot(d, bulko.get_cell())
natm1 = Atom(position = pos)
dist, dx, dy, dz = calc_dist(b[one], natm1)
if dist <= dcheck:
# Assume atoms closer than 0.6 Angstroms to be equivalent
slist.append(index-ntot)
blist.append(one)
if b[one].symbol == b[index].symbol:
wlist.append(index-ntot)
# Identify those atoms corresponding to interstitials, vacancies, and substitutions
oslist = [atm.index for atm in solid if atm.index not in slist]
vlist = [atm.index for atm in bulko if atm.index not in blist]
swlist = [atm.index for atm in solid if atm.index not in wlist and atm.index not in oslist]
# Create Atoms objects for each identified defect
ntot = len(solid)
cluster = Atoms()
for one in oslist:
cluster.append(solid[one])
vacant = Atoms()
if trackvacs == True:
for one in vlist:
vacant.append(Atom(symbol = bulko[one].symbol, position = bulko[one].position))
solid.append(Atom(symbol = 'X', position = bulko[one].position))
oslist.append(len(solid)-1)
stro = 'Cluster Identified with length = {0}\nIdentified {1} vacancies\n'.format(len(cluster), len(vlist))
swaps = Atoms()
if trackswaps == True:
for one in swlist:
swaps.append(solid[one])
oslist.append(one)
stro = 'Cluster Identified with length = {0}\nIdentified {1} swaps\n'.format(len(cluster), len(swlist))
else:
stro = 'Cluster Identified with length = {0}\n'.format(len(cluster))
# Debug: write cluster to file
if debug:
b = cluster.copy()
write_xyz(debug, b, 'Find Ints: Cluster')
debug.flush()
print('Found cluster size = ', len(b))
# Identify atoms surrounding the identified defects in the defected structure
box = Atoms()
bulki = Atoms()
if rcutoff != 0:
if rcutoff > 2.0:
cutoffs = [rcutoff for one in solid]
else:
cutoffs = [2.0 for one in solid]
solid.set_pbc(True)
nl = NeighborList(cutoffs, bothways = True, self_interaction = False)
nl.update(solid)
nbatmsd = []
repinds = []
for one in oslist:
if one not in repinds:
if one < ntot:
nbatmsd.append((0, one))
repinds.append(one)
for one in oslist:
indices, offsets = nl.get_neighbors(one)
for index, d in zip(indices, offsets):
index = int(index)
if index not in repinds and index < ntot:
opos = copy.copy(solid[index].position)
solid[index].position = solid[index].position + numpy.dot(d, solid.get_cell())
dist = solid.get_distance(one, index)
solid[index].position = opos
if dist <= rcutoff:
nbatmsd.append((dist, index))
repinds.append(index)
else:
nbatmsd = []
repinds = []
for one in oslist:
if one not in repinds:
if one < ntot:
nbatmsd.append((0, one))
repinds.append(one)
nbatmsd = sorted(nbatmsd, key = lambda one:one[0], reverse = True)
indices = []
natomsbox = 0
# Select only atoms closest to defects that satisfy concentrations specified by atomlist given in atomlistcheck
if atomlistcheck:
for sym, c, m, u in atomlistcheck:
i = 0
nbsym = [one for one in nbatmsd if solid[one[1]].symbol == sym]
if len(nbsym) > c:
while i < c:
a = nbsym.pop()
box.append(solid[a[1]])
indices.append(a[1])
i += 1
else:
for a in nbsym:
box.append(solid[a[1]])
indices.append(a[1])
i += 1
if len(box)-natomsbox < c:
try:
while True:
for n in range(len(nbatmsd)-1, -1, -1):
inds, offsets = nl.get_neighbors(nbatmsd[n][1])
for one, d in zip(inds, offsets):
if len(box)-natomsbox < c:
if one not in indices and one < ntot and solid[one].symbol == sym:
opos = copy.copy(solid[one].position)
solid[one].position = solid[one].position + numpy.dot(d, solid.get_cell())
dist = solid.get_distance(nbatmsd[n][1], one)
solid[one].position = opos
if dist <= rcutoff*5.0:
box.append(solid[one])
indices.append(one)
else:
raise StopIteration()
for one, d in zip(inds, offsets):
if len(box)-natomsbox < c:
if one not in indices and one < ntot and solid[one].symbol == sym:
opos = copy.copy(solid[one].position)
solid[one].position = solid[one].position + numpy.dot(d, solid.get_cell())
dist = solid.get_distance(nbatmsd[n][1], one)
solid[one].position = opos
box.append(solid[one])
indices.append(one)
else:
raise StopIteration()
except StopIteration:
pass
natomsbox = len(box)
# Double check for sanity
for sym, c, m, u in atomlistcheck:
symsbox = [one for one in box if one.symbol == sym]
if len(symsbox) != c:
stro += 'WARNING!!!! : FAILURE IN FIND_DEFECTS TO MATCH PROVIDED ATOMLIST. DEBUG!!!!\n'
# If atomlistcheck is False then use all the atoms in the given cutoff distance
else:
for a in nbatmsd:
box.append(solid[a[1]])
indices.append(a[1])
# Add remaining atoms in defect to defected bulk atoms object
for one in range(len(solid)):
if one not in indices and one < ntot:
bulki.append(solid[one])
# Check for accidental vacancy admissions
#checklist = [atm for atm in box if atm.symbol == 'X']
#checklist.extend([atm for atm in bulki if atm.symbol == 'X'])
# Set up new individual
indiv = box.copy()
bulki.set_cell(bulko.get_cell())
indiv.set_cell(bulko.get_cell())
bulki.set_pbc(True)
indiv.set_pbc(True)
stro += 'Atomlist check = {0}\n'.format(atomlistcheck)
stro += 'Bulko = {0}\n'.format(bulko)
stro += 'New individual ({0} atoms) : {1}\n'.format(len(indiv), indiv)
stro += 'New bulki ({0} atoms) : {1}\n'.format(len(bulki), bulki)
# Debug: write new indiv to file
if debug:
b = indiv.copy()
write_xyz(debug, b, 'Find Ints: New Individual')
# Debug: write new bulki to file
b = bulki.copy()
write_xyz(debug, b, 'Find Ints: New Bulki')
debug.flush()
print(len(bulko))
return indiv, bulki, vacant, swaps, stro
def update_neighbor_list(self, atoms):
cut = 0.5 * max(self.data['cutoffs'].values())
self.nl = NeighborList([cut] * len(atoms), skin=0, bothways=True)
self.nl.update(atoms)
self.atoms = atoms
class ANNCalculator(Calculator):
def __init__(self, potentials, **kwargs):
Calculator.__init__(self, **kwargs)
self.ann = ANNPotentials(potentials)
self.cutoff = self.ann.Rc_max
self.cutoff2 = self.cutoff**2
self.neighbors = None
self.implemented_properties = {
'energy': self.calculate_energy,
'forces': self.calculate_energy_and_forces,
}
self.results = {}
def __del__(self):
try:
del self.ann
except (AttributeError, NameError):
pass
def release(self):
del self.ann
def update(self, atoms):
if (self.neighbors is None) or (len(self.neighbors.cutoffs) !=
len(atoms)):
cutoffs = self.cutoff * np.ones(len(atoms))
self.neighbors = NeighborList(cutoffs,
self_interaction=False,
bothways=True)
self.neighbors.update(atoms)
def calculate(self,
atoms=None,
properties=['energy'],
system_changes=all_changes):
# Calculator essentially does: self.atoms = atoms
Calculator.calculate(self, atoms, properties, system_changes)
has_results = [p in self.results for p in properties]
if (len(system_changes) > 0) or (not np.all(has_results)):
self.update(self.atoms)
if ('energy' in properties) and ('forces' in properties):
# Forces evaluation requires energy. No need to compute
# energy twice.
del properties[properties.index('energy')]
for p in properties:
if p in self.implemented_properties:
self.implemented_properties[p](self.atoms)
else:
raise NotImplementedError(
"Property not implemented: {}".format(p))
def calculate_energy(self, atoms):
energy = 0.0
atom_types = atoms.get_chemical_symbols()
for i in range(len(atoms)):
indices, offsets = self.neighbors.get_neighbors(i)
type_i = atom_types[i]
coords_i = atoms.positions[i]
coords_j = np.empty((len(indices), 3), dtype=np.double)
types_j = []
inb = 0
for j, offset in zip(indices, offsets):
coo = (atoms.positions[j] + np.dot(offset, atoms.get_cell()))
d2 = np.sum((coo - coords_i)**2)
if d2 <= self.cutoff2:
coords_j[inb] = coo
types_j.append(atom_types[j])
inb += 1
energy += self.ann.atomic_energy(coords_i, type_i, coords_j[:inb],
types_j)
self.results['energy'] = energy
def calculate_energy_and_forces(self, atoms):
energy = 0.0
atom_types = atoms.get_chemical_symbols()
forces = np.zeros((len(atoms), 3), dtype=np.double)
for i in range(len(atoms)):
indices, offsets = self.neighbors.get_neighbors(i)
type_i = atom_types[i]
index_i = i + 1
index_j = np.empty(indices.size, dtype=np.intc)
coords_i = atoms.positions[i]
coords_j = np.empty((indices.size, 3), dtype=np.double)
types_j = []
inb = 0
for j, offset in zip(indices, offsets):
coo = (atoms.positions[j] + np.dot(offset, atoms.get_cell()))
d2 = np.sum((coo - coords_i)**2)
if d2 <= self.cutoff2:
coords_j[inb] = coo
index_j[inb] = j + 1
types_j.append(atom_types[j])
inb += 1
energy += self.ann.atomic_energy_and_forces(
coords_i, type_i, index_i, coords_j[:inb], types_j,
index_j[:inb], forces)
self.results['energy'] = energy
self.results['forces'] = forces
d = 0.0
for a in range(len(atoms)):
i, offsets = nl.get_neighbors(a)
for j in i:
c[j] += 1
c[a] += len(i)
d += (((R[i] + np.dot(offsets, cell) - R[a])**2).sum(1)**0.5).sum()
return d, c
for sorted in [False, True]:
for p1 in range(2):
for p2 in range(2):
for p3 in range(2):
print p1, p2, p3
atoms.set_pbc((p1, p2, p3))
nl = NeighborList(atoms.numbers * 0.2 + 0.5,
skin=0.0, sorted=sorted)
nl.update(atoms)
d, c = count(nl, atoms)
atoms2 = atoms.repeat((p1 + 1, p2 + 1, p3 + 1))
nl2 = NeighborList(atoms2.numbers * 0.2 + 0.5,
skin=0.0, sorted=sorted)
nl2.update(atoms2)
d2, c2 = count(nl2, atoms2)
c2.shape = (-1, 10)
dd = d * (p1 + 1) * (p2 + 1) * (p3 + 1) - d2
print dd
print c2 - c
assert abs(dd) < 1e-10
assert not (c2 - c).any()
h2 = Atoms('H2', positions=[(0, 0, 0), (0, 0, 1)])
def find_defects(solid,
bulko,
rcutoff,
atomlistcheck=False,
trackvacs=False,
trackswaps=False,
debug=False,
dcheck=0.6):
"""Function to find interstitials, vacancies, and substitutional atoms (swaps) in a defected structure.
Identifies species by comparison to perfect structure.
Inputs:
solid = ASE atoms class for defected structure
bulko = ASE atoms class for perfect structure
rcutoff = float value of distance to surrounding atoms to include
atomlistcheck = False/list of atom types and concentrations according to atomlist format
trackvacs = True/False whether or not to identify vacancies in defect
trackswaps = True/False whether or not to identify substitutional defects
debug = False/file object to write debug structures"""
# Combine perfect and defect structures together
b = bulko.copy()
b.extend(solid)
b.set_pbc(True)
#Debug: Write solid and bulko to file
if debug:
print len(bulko)
write_xyz(debug, b, 'Find Ints: Solid and Bulko')
# Identify nearest neighbor atoms for each atom in perfect structure
ntot = len(bulko)
ctoff1 = [1.2 for one in b]
nl = NeighborList(ctoff1, bothways=True, self_interaction=False)
nl.update(b)
slist = []
blist = []
wlist = []
#Loop over each atom in perfect structure
for one in range(ntot):
indices, offsets = nl.get_neighbors(one)
for index, d in zip(indices, offsets):
index = int(index)
if index >= ntot:
pos = b[index].position + numpy.dot(d, bulko.get_cell())
natm1 = Atom(position=pos)
dist, dx, dy, dz = calc_dist(b[one], natm1)
if dist <= dcheck:
#Assume atoms closer than 0.6 Angstroms to be equivalent
slist.append(index - ntot)
blist.append(one)
if b[one].symbol == b[index].symbol:
wlist.append(index - ntot)
#Identify those atoms corresponding to interstitials, vacancies, and substitutions
oslist = [atm.index for atm in solid if atm.index not in slist]
vlist = [atm.index for atm in bulko if atm.index not in blist]
swlist = [
atm.index for atm in solid
if atm.index not in wlist and atm.index not in oslist
]
# Create Atoms objects for each identified defect
ntot = len(solid)
cluster = Atoms()
for one in oslist:
cluster.append(solid[one])
vacant = Atoms()
if trackvacs == True:
for one in vlist:
vacant.append(
Atom(symbol=bulko[one].symbol, position=bulko[one].position))
solid.append(Atom(symbol='X', position=bulko[one].position))
oslist.append(len(solid) - 1)
stro = 'Cluster Identified with length = {0}\nIdentified {1} vacancies\n'.format(
len(cluster), len(vlist))
swaps = Atoms()
if trackswaps == True:
for one in swlist:
swaps.append(solid[one])
oslist.append(one)
stro = 'Cluster Identified with length = {0}\nIdentified {1} swaps\n'.format(
len(cluster), len(swlist))
else:
stro = 'Cluster Identified with length = {0}\n'.format(len(cluster))
#Debug: write cluster to file
if debug:
b = cluster.copy()
write_xyz(debug, b, 'Find Ints: Cluster')
debug.flush()
print 'Found cluster size = ', len(b)
# Identify atoms surrounding the identified defects in the defected structure
box = Atoms()
bulki = Atoms()
if rcutoff != 0:
if rcutoff > 2.0:
cutoffs = [rcutoff for one in solid]
else:
cutoffs = [2.0 for one in solid]
solid.set_pbc(True)
nl = NeighborList(cutoffs, bothways=True, self_interaction=False)
nl.update(solid)
nbatmsd = []
repinds = []
for one in oslist:
if one not in repinds:
if one < ntot:
nbatmsd.append((0, one))
repinds.append(one)
for one in oslist:
indices, offsets = nl.get_neighbors(one)
for index, d in zip(indices, offsets):
index = int(index)
if index not in repinds and index < ntot:
opos = copy.copy(solid[index].position)
solid[index].position = solid[index].position + numpy.dot(
d, solid.get_cell())
dist = solid.get_distance(one, index)
solid[index].position = opos
if dist <= rcutoff:
nbatmsd.append((dist, index))
repinds.append(index)
else:
nbatmsd = []
repinds = []
for one in oslist:
if one not in repinds:
if one < ntot:
nbatmsd.append((0, one))
repinds.append(one)
nbatmsd = sorted(nbatmsd, key=lambda one: one[0], reverse=True)
indices = []
natomsbox = 0
# Select only atoms closest to defects that satisfy concentrations specified by atomlist given in atomlistcheck
if atomlistcheck:
for sym, c, m, u in atomlistcheck:
i = 0
nbsym = [one for one in nbatmsd if solid[one[1]].symbol == sym]
if len(nbsym) > c:
while i < c:
a = nbsym.pop()
box.append(solid[a[1]])
indices.append(a[1])
i += 1
else:
for a in nbsym:
box.append(solid[a[1]])
indices.append(a[1])
i += 1
if len(box) - natomsbox < c:
try:
while True:
for n in range(len(nbatmsd) - 1, -1, -1):
inds, offsets = nl.get_neighbors(nbatmsd[n][1])
for one, d in zip(inds, offsets):
if len(box) - natomsbox < c:
if one not in indices and one < ntot and solid[
one].symbol == sym:
opos = copy.copy(
solid[one].position)
solid[one].position = solid[
one].position + numpy.dot(
d, solid.get_cell())
dist = solid.get_distance(
nbatmsd[n][1], one)
solid[one].position = opos
if dist <= rcutoff * 5.0:
box.append(solid[one])
indices.append(one)
else:
raise StopIteration()
for one, d in zip(inds, offsets):
if len(box) - natomsbox < c:
if one not in indices and one < ntot and solid[
one].symbol == sym:
opos = copy.copy(
solid[one].position)
solid[one].position = solid[
one].position + numpy.dot(
d, solid.get_cell())
dist = solid.get_distance(
nbatmsd[n][1], one)
solid[one].position = opos
box.append(solid[one])
indices.append(one)
else:
raise StopIteration()
except StopIteration:
pass
natomsbox = len(box)
#Double check for sanity
for sym, c, m, u in atomlistcheck:
symsbox = [one for one in box if one.symbol == sym]
if len(symsbox) != c:
stro += 'WARNING!!!! : FAILURE IN FIND_DEFECTS TO MATCH PROVIDED ATOMLIST. DEBUG!!!!\n'
# If atomlistcheck is False then use all the atoms in the given cutoff distance
else:
for a in nbatmsd:
box.append(solid[a[1]])
indices.append(a[1])
# Add remaining atoms in defect to defected bulk atoms object
for one in range(len(solid)):
if one not in indices and one < ntot:
bulki.append(solid[one])
#Check for accidental vacancy admissions
#checklist=[atm for atm in box if atm.symbol=='X']
#checklist.extend([atm for atm in bulki if atm.symbol=='X'])
#Set up new individual
indiv = box.copy()
bulki.set_cell(bulko.get_cell())
indiv.set_cell(bulko.get_cell())
bulki.set_pbc(True)
indiv.set_pbc(True)
stro += 'Atomlist check = {0}\n'.format(atomlistcheck)
stro += 'Bulko = {0}\n'.format(bulko)
stro += 'New individual ({0} atoms) : {1}\n'.format(len(indiv), indiv)
stro += 'New bulki ({0} atoms) : {1}\n'.format(len(bulki), bulki)
#Debug: write new indiv to file
if debug:
b = indiv.copy()
write_xyz(debug, b, 'Find Ints: New Individual')
#Debug: write new bulki to file
b = bulki.copy()
write_xyz(debug, b, 'Find Ints: New Bulki')
debug.flush()
print len(bulko)
return indiv, bulki, vacant, swaps, stro
class OPLSff:
def __init__(self, fileobj=None, warnings=0):
self.warnings = warnings
self.data = {}
if fileobj is not None:
self.read(fileobj)
def read(self, fileobj, comments='#'):
if isinstance(fileobj, str):
fileobj = open(fileobj)
def read_block(name, symlen, nvalues):
"""Read a data block.
name: name of the block to store in self.data
symlen: length of the symbol
nvalues: number of values expected
"""
if name not in self.data:
self.data[name] = {}
data = self.data[name]
def add_line():
line = fileobj.readline().strip()
if not len(line): # end of the block
return False
line = line.split('#')[0] # get rid of comments
if len(line) > symlen:
symbol = line[:symlen]
words = line[symlen:].split()
if len(words) >= nvalues:
if nvalues == 1:
data[symbol] = float(words[0])
else:
data[symbol] = [
float(word) for word in words[:nvalues]
]
return True
while add_line():
pass
read_block('one', 2, 3)
read_block('bonds', 5, 2)
read_block('angles', 8, 2)
read_block('dihedrals', 11, 4)
read_block('cutoffs', 5, 1)
self.bonds = BondData(self.data['bonds'])
self.angles = AnglesData(self.data['angles'])
self.dihedrals = DihedralsData(self.data['dihedrals'])
self.cutoffs = CutoffList(self.data['cutoffs'])
def write_lammps(self, atoms, prefix='lammps'):
"""Write input for a LAMMPS calculation."""
self.prefix = prefix
btypes, atypes, dtypes = self.write_lammps_atoms(atoms)
self.write_lammps_definitions(atoms, btypes, atypes, dtypes)
self.write_lammps_in()
def write_lammps_in(self):
# XXX change this
# XXX some input file for syntax checks
# XXX change this
fileobj = self.prefix + '_in'
if isinstance(fileobj, str):
fileobj = open(fileobj, 'w')
fileobj.write("""
# (written by ASE)
clear
variable dump_file string "dump_traj"
variable data_file string "dump_data"
units metal
boundary p p f
atom_style full
""")
fileobj.write('read_data ' + self.prefix + '_atoms\n')
fileobj.write('include ' + self.prefix + '_opls\n')
fileobj.write("""
### run
fix fix_nve all nve
dump dump_all all custom 1 trj_lammps id type x y z vx vy vz fx fy fz
thermo_style custom step temp press cpu pxx pyy pzz pxy pxz pyz ke pe etotal vol lx ly lz atoms
thermo_modify flush yes
thermo 1
run 0
print "__end_of_ase_invoked_calculation__"
log /dev/stdout
""")
fileobj.close()
def write_lammps_atoms(self, atoms):
"""Write atoms infor for LAMMPS"""
fileobj = self.prefix + '_atoms'
if isinstance(fileobj, str):
fileobj = open(fileobj, 'w')
# header
fileobj.write(fileobj.name + ' (by ' + str(self.__class__) + ')\n\n')
fileobj.write(str(len(atoms)) + ' atoms\n')
fileobj.write(str(len(atoms.types)) + ' atom types\n')
btypes, blist = self.get_bonds(atoms)
if len(blist):
fileobj.write(str(len(blist)) + ' bonds\n')
fileobj.write(str(len(btypes)) + ' bond types\n')
atypes, alist = self.get_angles()
if len(alist):
fileobj.write(str(len(alist)) + ' angles\n')
fileobj.write(str(len(atypes)) + ' angle types\n')
dtypes, dlist = self.get_dihedrals(alist, atypes)
if len(dlist):
fileobj.write(str(len(dlist)) + ' dihedrals\n')
fileobj.write(str(len(dtypes)) + ' dihedral types\n')
# cell
p = prism(atoms.get_cell())
xhi, yhi, zhi, xy, xz, yz = p.get_lammps_prism_str()
fileobj.write('\n0.0 %s xlo xhi\n' % xhi)
fileobj.write('0.0 %s ylo yhi\n' % yhi)
fileobj.write('0.0 %s zlo zhi\n' % zhi)
# atoms
fileobj.write('\nAtoms\n\n')
tag = atoms.get_tags()
for i, r in enumerate(map(p.pos_to_lammps_str, atoms.get_positions())):
q = 0 # charge will be overwritten
fileobj.write('%6d %3d %3d %s %s %s %s' %
((i + 1, 1, tag[i] + 1, q) + tuple(r)))
fileobj.write(' # ' + atoms.types[tag[i]] + '\n')
# velocities
velocities = atoms.get_velocities()
if velocities is not None:
fileobj.write('\nVelocities\n\n')
for i, v in enumerate(velocities):
fileobj.write('%6d %g %g %g\n' % (i + 1, v[0], v[1], v[2]))
# masses
fileobj.write('\nMasses\n\n')
for i, typ in enumerate(atoms.types):
cs = atoms.split_symbol(typ)[0]
fileobj.write(
'%6d %g # %s -> %s\n' %
(i + 1, atomic_masses[chemical_symbols.index(cs)], typ, cs))
# bonds
if len(blist):
fileobj.write('\nBonds\n\n')
for ib, bvals in enumerate(blist):
fileobj.write(
'%8d %6d %6d %6d ' %
(ib + 1, bvals[0] + 1, bvals[1] + 1, bvals[2] + 1))
fileobj.write('# ' + btypes[bvals[0]] + '\n')
# angles
if len(alist):
fileobj.write('\nAngles\n\n')
for ia, avals in enumerate(alist):
fileobj.write('%8d %6d %6d %6d %6d ' %
(ia + 1, avals[0] + 1, avals[1] + 1,
avals[2] + 1, avals[3] + 1))
fileobj.write('# ' + atypes[avals[0]] + '\n')
# dihedrals
if len(dlist):
fileobj.write('\nDihedrals\n\n')
for i, dvals in enumerate(dlist):
fileobj.write('%8d %6d %6d %6d %6d %6d ' %
(i + 1, dvals[0] + 1, dvals[1] + 1, dvals[2] + 1,
dvals[3] + 1, dvals[4] + 1))
fileobj.write('# ' + dtypes[dvals[0]] + '\n')
return btypes, atypes, dtypes
def update_neighbor_list(self, atoms):
cut = 0.5 * max(self.data['cutoffs'].values())
self.nl = NeighborList([cut] * len(atoms),
skin=0,
bothways=True,
self_interaction=False)
self.nl.update(atoms)
self.atoms = atoms
def get_bonds(self, atoms):
"""Find bonds and return them and their types"""
cutoffs = CutoffList(self.data['cutoffs'])
self.update_neighbor_list(atoms)
types = atoms.get_types()
tags = atoms.get_tags()
cell = atoms.get_cell()
positions = atoms.get_positions()
bond_list = []
bond_types = []
for i, atom in enumerate(atoms):
iname = types[tags[i]]
indices, offsets = self.nl.get_neighbors(i)
for j, offset in zip(indices, offsets):
if j <= i:
continue # do not double count
jname = types[tags[j]]
cut = cutoffs.value(iname, jname)
if cut is None:
if self.warnings > 1:
print('Warning: cutoff %s-%s not found' %
(iname, jname))
continue # don't have it
dist = np.linalg.norm(atom.position - atoms[j].position -
np.dot(offset, cell))
if dist > cut:
continue # too far away
name, val = self.bonds.name_value(iname, jname)
if name is None:
if self.warnings:
print('Warning: potential %s-%s not found' %
(iname, jname))
continue # don't have it
if name not in bond_types:
bond_types.append(name)
bond_list.append([bond_types.index(name), i, j])
return bond_types, bond_list
def get_angles(self, atoms=None):
cutoffs = CutoffList(self.data['cutoffs'])
if atoms is not None:
self.update_neighbor_list(atoms)
else:
atoms = self.atoms
types = atoms.get_types()
tags = atoms.get_tags()
cell = atoms.get_cell()
positions = atoms.get_positions()
ang_list = []
ang_types = []
# center atom *-i-*
for i, atom in enumerate(atoms):
iname = types[tags[i]]
indicesi, offsetsi = self.nl.get_neighbors(i)
# search for first neighbor j-i-*
for j, offsetj in zip(indicesi, offsetsi):
jname = types[tags[j]]
cut = cutoffs.value(iname, jname)
if cut is None:
continue # don't have it
dist = np.linalg.norm(atom.position - atoms[j].position -
np.dot(offsetj, cell))
if dist > cut:
continue # too far away
# search for second neighbor j-i-k
for k, offsetk in zip(indicesi, offsetsi):
if k <= j:
continue # avoid double count
kname = types[tags[k]]
cut = cutoffs.value(iname, kname)
if cut is None:
continue # don't have it
dist = np.linalg.norm(atom.position -
np.dot(offsetk, cell) -
atoms[k].position)
if dist > cut:
continue # too far away
name, val = self.angles.name_value(jname, iname, kname)
if name is None:
continue # don't have it
if name not in ang_types:
ang_types.append(name)
ang_list.append([ang_types.index(name), j, i, k])
return ang_types, ang_list
def get_dihedrals(self, ang_types, ang_list):
'Dihedrals derived from angles.'
cutoffs = CutoffList(self.data['cutoffs'])
atoms = self.atoms
types = atoms.get_types()
tags = atoms.get_tags()
cell = atoms.get_cell()
dih_list = []
dih_types = []
def append(name, i, j, k, l):
if name not in dih_types:
dih_types.append(name)
index = dih_types.index(name)
if (([index, i, j, k, l] not in dih_list)
and ([index, l, k, j, i] not in dih_list)):
dih_list.append([index, i, j, k, l])
for angle in ang_types:
l, i, j, k = angle
iname = types[tags[i]]
jname = types[tags[j]]
kname = types[tags[k]]
# search for l-i-j-k
indicesi, offsetsi = self.nl.get_neighbors(i)
for l, offsetl in zip(indicesi, offsetsi):
if l == j:
continue # avoid double count
lname = types[tags[l]]
cut = cutoffs.value(iname, lname)
if cut is None:
continue # don't have it
dist = np.linalg.norm(atoms[i].position - atoms[l].position -
np.dot(offsetl, cell))
if dist > cut:
continue # too far away
name, val = self.dihedrals.name_value(lname, iname, jname,
kname)
if name is None:
continue # don't have it
append(name, l, i, j, k)
# search for i-j-k-l
indicesk, offsetsk = self.nl.get_neighbors(k)
for l, offsetl in zip(indicesk, offsetsk):
if l == j:
continue # avoid double count
lname = types[tags[l]]
cut = cutoffs.value(kname, lname)
if cut is None:
continue # don't have it
dist = np.linalg.norm(atoms[k].position - atoms[l].position -
np.dot(offsetl, cell))
if dist > cut:
continue # too far away
name, val = self.dihedrals.name_value(iname, jname, kname,
lname)
if name is None:
continue # don't have it
append(name, i, j, k, l)
return dih_types, dih_list
def write_lammps_definitions(self, atoms, btypes, atypes, dtypes):
"""Write force field definitions for LAMMPS."""
fileobj = self.prefix + '_opls'
if isinstance(fileobj, str):
fileobj = open(fileobj, 'w')
fileobj.write('# OPLS potential\n')
fileobj.write('# write_lammps' +
str(time.asctime(time.localtime(time.time()))))
# bonds
if len(btypes):
fileobj.write('\n# bonds\n')
fileobj.write('bond_style harmonic\n')
for ib, btype in enumerate(btypes):
fileobj.write('bond_coeff %6d' % (ib + 1))
for value in self.bonds.nvh[btype]:
fileobj.write(' ' + str(value))
fileobj.write(' # ' + btype + '\n')
# angles
if len(atypes):
fileobj.write('\n# angles\n')
fileobj.write('angle_style harmonic\n')
for ia, atype in enumerate(atypes):
fileobj.write('angle_coeff %6d' % (ia + 1))
for value in self.angles.nvh[atype]:
fileobj.write(' ' + str(value))
fileobj.write(' # ' + atype + '\n')
# dihedrals
if len(dtypes):
fileobj.write('\n# dihedrals\n')
fileobj.write('dihedral_style opls\n')
for i, dtype in enumerate(dtypes):
fileobj.write('dihedral_coeff %6d' % (i + 1))
for value in self.dihedrals.nvh[dtype]:
fileobj.write(' ' + str(value))
fileobj.write(' # ' + dtype + '\n')
# Lennard Jones settings
fileobj.write('\n# L-J parameters\n')
fileobj.write('pair_style lj/cut/coul/long 10.0 7.4' +
' # consider changing these parameters\n')
fileobj.write('special_bonds lj/coul 0.0 0.0 0.5\n')
data = self.data['one']
for ia, atype in enumerate(atoms.types):
if len(atype) < 2:
atype = atype + ' '
fileobj.write('pair_coeff ' + str(ia + 1) + ' ' + str(ia + 1))
for value in data[atype][:2]:
fileobj.write(' ' + str(value))
fileobj.write(' # ' + atype + '\n')
fileobj.write('pair_modify shift yes mix geometric\n')
# Coulomb
fileobj.write("""
# Coulomb
kspace_style pppm 1e-5
kspace_modify slab 3.0
""")
# Charges
fileobj.write('\n# charges\n')
for ia, atype in enumerate(atoms.types):
if len(atype) < 2:
atype = atype + ' '
fileobj.write('set type ' + str(ia + 1))
fileobj.write(' charge ' + str(data[atype][2]))
fileobj.write(' # ' + atype + '\n')
def newclus(ind1, ind2, Optimizer):
"""Select a box in the cluster configuration"""
if 'CX' in Optimizer.debug:
debug = True
else:
debug = False
Optimizer.output.write('Box Cluster Cx between individual {} and individual {}'.format(repr(ind1.index), repr(ind2.index)))
# Perserve starting conditions of individual
solid1 = ind1[0].copy()
solid2 = ind2[0].copy()
cello1 = ind1[0].get_cell()
cello2 = ind2[0].get_cell()
cell1 = numpy.maximum.reduce(solid1.get_positions())
cell1m = numpy.minimum.reduce(solid1.get_positions())
cell2 = numpy.maximum.reduce(solid2.get_positions())
cell2m = numpy.minimum.reduce(solid2.get_positions())
cell = numpy.minimum(cell1, cell2)
pbc1 = solid1.get_pbc()
pbc2 = solid2.get_pbc()
# Get starting concentrations and number of atoms
nat1 = len(solid1)
nat2 = len(solid2)
# Pick a origin point for box in the cell
pt1 = random.choice(solid1)
pt1f = [(pt1.position[i]-cell1m[i])/cell1[i] for i in range(3)]
pt2 = [pt1f[i]*cell2[i]+cell2m[i] for i in range(3)]
solid2.append(Atom(position=pt2))
pt2 = solid2[len(solid2)-1]
# Find max neighborsize of circle cut
r = random.uniform(0, min(nat1, nat2)/5.0)
if debug:
print('DEBUG CX: Point one = {}'.format(pt1.position))
print('DEBUG CX: Point two = {}'.format(pt2.position))
# Find atoms within sphere of neighborsize r for both individuals
# Make sure that crossover is only selection of atoms not all
while True:
ctoff = [r for on in solid1]
nl = NeighborList(ctoff, bothways=True, self_interaction=False)
nl.update(solid1)
indices1, offsets = nl.get_neighbors(pt1.index)
if len(indices1) == 0:
r = r*1.2
elif len(indices1) < nat1*.75:
break
else:
r = r*0.8
if debug:
print('Neighborsize of box = {}'.format(repr(r)))
print('Position in solid1 = {}'.format(repr(pt1.position)))
print('Position in solid2 = {}'.format(repr(pt2.position)))
group1 = Atoms(cell=solid1.get_cell(), pbc=solid1.get_pbc())
group1.append(pt1)
indices1a = [pt1.index]
for index, d in zip(indices1, offsets):
if index not in indices1a:
index = int(index)
pos = solid1[index].position + numpy.dot(d, solid1.get_cell())
group1.append(Atom(symbol=solid1[index].symbol, position=pos))
indices1a.append(index)
indices1 = indices1a
ctoff = [r for on in solid2]
nl = NeighborList(ctoff, bothways=True, self_interaction=False)
nl.update(solid2)
indices2, offsets = nl.get_neighbors(pt2.index)
group2 = Atoms(cell=solid2.get_cell(), pbc=solid2.get_pbc())
indices2a = []
for index, d in zip(indices2, offsets):
if index not in indices2a:
index = int(index)
pos = solid2[index].position + numpy.dot(d, solid2.get_cell())
group2.append(Atom(symbol=solid2[index].symbol, position=pos))
indices2a.append(index)
indices2 = indices2a
if len(indices2) == 0:
for one in group1:
while True:
sel = random.choice(solid2)
if sel.symbol == one.symbol:
if sel.index not in indices2:
group2.append(sel)
indices2.append(sel.index)
break
if Optimizer.forcing == 'Concentration':
symlist = list(set(group1.get_chemical_symbols()))
seplist = [[atm for atm in group2 if atm.symbol == sym] for sym in symlist]
group2n = Atoms(cell=group2.get_cell(), pbc=group2.get_pbc())
indices2n = []
dellist = []
for one in group1:
sym1 = one.symbol
listpos = [i for i, s in enumerate(symlist) if s == sym1][0]
if len(seplist[listpos]) > 0:
pos = random.choice(range(len(seplist[listpos])))
group2n.append(seplist[listpos][pos])
indices2n.append(indices2[seplist[listpos][pos].index])
del seplist[listpos][pos]
else:
dellist.append(one.index)
if len(dellist) != 0:
dellist.sort(reverse=True)
for one in dellist:
del group1[one]
del indices1[one]
indices2n.append(pt2.index)
indices2 = indices2n
group2 = group2n.copy()
else:
dellist = []
while len(group2) < len(group1)-len(dellist):
# Too many atoms in group 1
dellist.append(random.choice(group1).index)
if len(dellist) != 0:
dellist.sort(reverse=True)
for one in dellist:
del group1[one]
del indices1[one]
dellist = []
while len(group1) < len(group2)-len(dellist):
# Too many atoms in group 2
dellist.append(random.choice(group2).index)
if len(dellist) != 0:
dellist.sort(reverse=True)
for one in dellist:
del group2[one]
del indices2[one]
other2 = Atoms(cell=solid2.get_cell(), pbc=solid2.get_pbc())
for one in solid2:
if one.index not in indices2:
other2.append(one)
other1 = Atoms(cell=solid1.get_cell(), pbc=solid1.get_pbc())
for one in solid1:
if one.index not in indices1:
other1.append(one)
# Exchange atoms in sphere and build new solids
nsolid1 = other1.copy()
nsolid1.extend(group2.copy())
nsolid2 = other2.copy()
nsolid2.extend(group1.copy())
# DEBUG: Write crossover to file
if debug:
write_xyz(Optimizer.debugfile, nsolid1, 'CX(randalloybx):nsolid1')
write_xyz(Optimizer.debugfile, nsolid2, 'CX(randalloybx):nsolid2')
# DEBUG: Check structure of atoms exchanged
for sym, c, m, u in Optimizer.atomlist:
if Optimizer.structure == 'Defect':
nc = len([atm for atm in nsolid1 if atm.symbol == sym])
nc += len([atm for atm in ind1.bulki if atm.symbol == sym])
oc = len([atm for atm in solid1 if atm.symbol == sym])
oc += len([atm for atm in ind1.bulki if atm.symbol == sym])
else:
nc = len([atm for atm in nsolid1 if atm.symbol == sym])
oc = len([atm for atm in solid1 if atm.symbol == sym])
Optimizer.output.write('CX(clustbx):New solid1 contains '+repr(nc)+' '+repr(sym)+' atoms\n')
if debug:
print('DEBUG CX: New solid1 contains {} {} atoms'.format(repr(nc), repr(sym)))
if oc != nc:
# pdb.set_trace()
print('CX: Issue in maintaining atom concentration\n Dropping new individual')
Optimizer.output.write('CX: Issue in maintaining atom concentration\n Dropping new individual 1\n')
nsolid1 = solid1
for sym, c, m, u in Optimizer.atomlist:
if Optimizer.structure == 'Defect':
nc = len([atm for atm in nsolid2 if atm.symbol == sym])
nc += len([atm for atm in ind2.bulki if atm.symbol == sym])
oc = len([atm for atm in solid2 if atm.symbol == sym])
oc += len([atm for atm in ind2.bulki if atm.symbol == sym])
else:
nc = len([atm for atm in nsolid2 if atm.symbol == sym])
oc = len([atm for atm in solid2 if atm.symbol == sym])
Optimizer.output.write('CX(clustbx):New solid2 contains '+repr(nc)+' '+repr(sym)+' atoms\n')
if debug:
print('DEBUG CX: New solid2 contains {} and {} atoms'.format(repr(nc), repr(sym)))
if oc != nc:
#pdb.set_trace()
print('CX: Issue in maintaining atom concentration\n Dropping new individual')
Optimizer.output.write('CX: Issue in maintaining atom concentration\n Dropping new individual 2\n')
solid2.pop()
nsolid2 = solid2
if Optimizer.forcing != 'Concentration':
for i in range(len(Optimizer.atomlist)):
atms1 = [inds for inds in nsolid1 if inds.symbol == Optimizer.atomlist[i][0]]
atms2 = [inds for inds in nsolid2 if inds.symbol == Optimizer.atomlist[i][0]]
if len(atms1) == 0:
if len(atms2) == 0:
nsolid1[random.randint(0, len(indi1)-1)].symbol == Optimizer.atomlist[i][0]
nsolid2[random.randint(0, len(indi2)-1)].symbol == Optimizer.atomlist[i][0]
else:
nsolid1.append(atms2[random.randint(0, len(atms2)-1)])
nsolid1.pop(random.randint(0, len(nsolid1)-2))
else:
if len(atms2) == 0:
nsolid2.append(atms1[random.randint(0, len(atms1)-1)])
nsolid2.pop(random.randint(0, len(nsolid2)-2))
nsolid1.set_cell(cello1)
nsolid2.set_cell(cello2)
nsolid1.set_pbc(pbc1)
nsolid2.set_pbc(pbc2)
ind1[0] = nsolid1.copy()
ind2[0] = nsolid2.copy()
return ind1, ind2
def eval_energy(input):
"""Function to evaluate energy of an individual
Inputs:
input = [Optimizer class object with parameters, Individual class structure to be evaluated]
Outputs:
energy, bul, individ, signal
energy = energy of Individual evaluated
bul = bulk structure of Individual if simulation structure is Defect
individ = Individual class structure evaluated
signal = string of information about evaluation
"""
if input[0] == None:
energy = 0
bul = 0
individ = 0
rank = MPI.COMM_WORLD.Get_rank()
signal = 'Evaluated none individual on ' + repr(rank) + '\n'
else:
[Optimizer, individ] = input
if Optimizer.calc_method == 'MAST':
energy = individ.energy
bul = individ.energy
signal = 'Recieved MAST structure\n'
else:
if Optimizer.parallel: rank = MPI.COMM_WORLD.Get_rank()
if not Optimizer.genealogy:
STR = '----Individual ' + str(
individ.index) + ' Optimization----\n'
else:
STR = '----Individual ' + str(
individ.history_index) + ' Optimization----\n'
indiv = individ[0]
if 'EE' in Optimizer.debug:
debug = True
else:
debug = False
if debug:
write_xyz(Optimizer.debugfile, indiv, 'Recieved by eval_energy')
Optimizer.debugfile.flush()
if Optimizer.structure == 'Defect':
indi = indiv.copy()
if Optimizer.alloy == True:
bulk = individ.bulki
else:
bulk = individ.bulko
nat = indi.get_number_of_atoms()
csize = bulk.get_cell()
totalsol = Atoms(cell=csize, pbc=True)
totalsol.extend(indi)
totalsol.extend(bulk)
for sym, c, m, u in Optimizer.atomlist:
nc = len([atm for atm in totalsol if atm.symbol == sym])
STR += 'Defect configuration contains ' + repr(
nc) + ' ' + repr(sym) + ' atoms\n'
elif Optimizer.structure == 'Surface':
totalsol = Atoms()
totalsol.extend(indiv)
nat = indiv.get_number_of_atoms()
totalsol.extend(individ.bulki)
for sym, c, m, u in Optimizer.atomlist:
nc = len([atm for atm in totalsol if atm.symbol == sym])
STR += 'Surface-Bulk configuration contains ' + repr(
nc) + ' ' + repr(sym) + ' atoms\n'
cell = numpy.maximum.reduce(indiv.get_cell())
totalsol.set_cell([cell[0], cell[1], 500])
totalsol.set_pbc([True, True, False])
if Optimizer.constrain_position:
ts = totalsol.copy()
indc, indb, vacant, swap, stro = find_defects(
ts, Optimizer.solidbulk, 0)
sbulk = Optimizer.solidbulk.copy()
bcom = sbulk.get_center_of_mass()
#totalsol.translate(-bulkcom)
#indc.translate(-bulkcom)
#totalsol.append(Atom(position=[0,0,0]))
# for one in indc:
# index = [atm.index for atm in totalsol if atm.position[0]==one.position[0] and atm.position[1]==one.position[1] and atm.position[2]==one.position[2]][0]
# if totalsol.get_distance(-1,index) > Optimizer.sf:
# r = random.random()
# totalsol.set_distance(-1,index,Optimizer.sf*r,fix=0)
# totalsol.pop()
# totalsol.translate(bulkcom)
com = indc.get_center_of_mass()
dist = (sum((bcom[i] - com[i])**2 for i in range(3)))**0.5
if dist > Optimizer.sf:
STR += 'Shifting structure to within region\n'
r = random.random() * Optimizer.sf
comv = numpy.linalg.norm(com)
ncom = [one * r / comv for one in com]
trans = [ncom[i] - com[i] for i in range(3)]
indices = []
for one in indc:
id = [
atm.index for atm in totalsol
if atm.position[0] == one.position[0]
and atm.position[1] == one.position[1]
and atm.position[2] == one.position[2]
][0]
totalsol[id].position += trans
# Check for atoms that are too close
min_len = 0.7
#pdb.set_trace()
if not Optimizer.fixed_region:
if Optimizer.structure == 'Defect' or Optimizer.structure == 'Surface':
cutoffs = [2.0 for one in totalsol]
nl = NeighborList(cutoffs,
bothways=True,
self_interaction=False)
nl.update(totalsol)
for one in totalsol[0:nat]:
nbatoms = Atoms()
nbatoms.append(one)
indices, offsets = nl.get_neighbors(one.index)
for index, d in zip(indices, offsets):
index = int(index)
sym = totalsol[index].symbol
pos = totalsol[index].position + numpy.dot(
d, totalsol.get_cell())
at = Atom(symbol=sym, position=pos)
nbatoms.append(at)
while True:
dflag = False
for i in range(1, len(nbatoms)):
d = nbatoms.get_distance(0, i)
if d < min_len:
nbatoms.set_distance(0,
i,
min_len + .01,
fix=0.5)
STR += '--- WARNING: Atoms too close (<0.7A) - Implement Move ---\n'
dflag = True
if dflag == False:
break
for i in range(len(indices)):
totalsol[indices[i]].position = nbatoms[i + 1].position
totalsol[one.index].position = nbatoms[0].position
nl.update(totalsol)
if debug:
write_xyz(Optimizer.debugfile, totalsol,
'After minlength check')
Optimizer.debugfile.flush()
else:
for i in range(len(indiv)):
for j in range(len(indiv)):
if i != j:
d = indiv.get_distance(i, j)
if d < min_len:
indiv.set_distance(i, j, min_len, fix=0.5)
STR += '--- WARNING: Atoms too close (<0.7A) - Implement Move ---\n'
if debug:
write_xyz(Optimizer.debugfile, indiv,
'After minlength check')
Optimizer.debugfile.flush()
# Set calculator to use to get forces/energies
if Optimizer.parallel:
calc = setup_calculator(Optimizer)
if Optimizer.fixed_region:
pms = copy.deepcopy(calc.parameters)
try:
pms['mass'][
len(pms['mass']) - 1] += '\ngroup RO id >= ' + repr(
nat) + '\nfix freeze RO setforce 0.0 0.0 0.0\n'
except KeyError:
pms['pair_coeff'][0] += '\ngroup RO id >= ' + repr(
nat) + '\nfix freeze RO setforce 0.0 0.0 0.0\n'
calc = LAMMPS(parameters=pms,
files=calc.files,
keep_tmp_files=calc.keep_tmp_files,
tmp_dir=calc.tmp_dir)
lmin = copy.copy(Optimizer.lammps_min)
Optimizer.lammps_min = None
Optimizer.static_calc = setup_calculator(Optimizer)
Optimizer.lammps_min = lmin
else:
calc = Optimizer.calc
if Optimizer.structure == 'Defect' or Optimizer.structure == 'Surface':
totalsol.set_calculator(calc)
totalsol.set_pbc(True)
else:
indiv.set_calculator(calc)
indiv.set_pbc(
True) #Current bug in ASE optimizer-Lammps prevents pbc=false
if Optimizer.structure == 'Cluster':
indiv.set_cell([500, 500, 500])
indiv.translate([250, 250, 250])
cwd = os.getcwd()
# Perform Energy Minimization
if not Optimizer.parallel:
Optimizer.output.flush()
if Optimizer.ase_min == True:
try:
if Optimizer.structure == 'Defect' or Optimizer.structure == 'Surface':
dyn = BFGS(totalsol)
else:
dyn = BFGS(indiv)
dyn.run(fmax=Optimizer.ase_min_fmax,
steps=Optimizer.ase_min_maxsteps)
except OverflowError:
STR += '--- Error: Infinite Energy Calculated - Implement Random ---\n'
box = Atoms()
indiv = gen_pop_box(Optimizer.natoms, Optimizer.atomlist,
Optimizer.size)
indiv.set_calculator(calc)
dyn = BFGS(indiv)
dyn.run(fmax=fmax, steps=steps)
except numpy.linalg.linalg.LinAlgError:
STR += '--- Error: Singular Matrix - Implement Random ---\n'
indiv = gen_pop_box(Optimizer.natoms, Optimizer.atomlist,
Optimizer.size)
indiv.set_calculator(calc)
dyn = BFGS(indiv)
dyn.run(fmax=fmax, steps=steps)
# Get Energy of Minimized Structure
if Optimizer.structure == 'Defect' or Optimizer.structure == 'Surface':
en = totalsol.get_potential_energy()
#force=numpy.maximum.reduce(abs(totalsol.get_forces()))
if Optimizer.fitness_scheme == 'enthalpyfit':
pressure = totalsol.get_isotropic_pressure(
totalsol.get_stress())
cell_max = numpy.maximum.reduce(totalsol.get_positions())
cell_min = numpy.minimum.reduce(totalsol.get_positions())
cell = cell_max - cell_min
volume = cell[0] * cell[1] * cell[2]
else:
pressure = 0
volume = 0
na = totalsol.get_number_of_atoms()
ena = en / na
energy = en
individ[0] = totalsol[0:nat]
bul = totalsol[(nat):len(totalsol)]
STR += 'Number of positions = ' + repr(
len(bul) + len(individ[0])) + '\n'
individ[0].set_cell(csize)
indiv = individ[0]
else:
en = indiv.get_potential_energy()
if Optimizer.fitness_scheme == 'enthalpyfit':
pressure = indiv.get_isotropic_pressure(indiv.get_stress())
cell_max = numpy.maximum.reduce(indiv.get_positions())
cell_min = numpy.minimum.reduce(indiv.get_positions())
cell = cell_max - cell_min
volume = cell[0] * cell[1] * cell[2]
else:
pressure = 0
volume = 0
na = indiv.get_number_of_atoms()
ena = en / na
energy = ena
individ[0] = indiv
bul = 0
else:
if Optimizer.structure == 'Defect' or Optimizer.structure == 'Surface':
if Optimizer.calc_method == 'VASP':
en = totalsol.get_potential_energy()
calcb = Vasp(restart=True)
totalsol = calcb.get_atoms()
stress = calcb.read_stress()
else:
try:
totcop = totalsol.copy()
if debug:
write_xyz(Optimizer.debugfile, totcop,
'Individual sent to lammps')
OUT = totalsol.calc.calculate(totalsol)
totalsol = OUT['atoms']
totalsol.set_pbc(True)
if Optimizer.fixed_region:
if debug:
print 'Energy of fixed region calc = ', OUT[
'thermo'][-1]['pe']
totalsol.set_calculator(Optimizer.static_calc)
OUT = totalsol.calc.calculate(totalsol)
totalsol = OUT['atoms']
totalsol.set_pbc(True)
if debug:
print 'Energy of static calc = ', OUT[
'thermo'][-1]['pe']
en = OUT['thermo'][-1]['pe']
stress = numpy.array([
OUT['thermo'][-1][i]
for i in ('pxx', 'pyy', 'pzz', 'pyz', 'pxz', 'pxy')
]) * (-1e-4 * GPa)
#force=numpy.maximum.reduce(abs(totalsol.get_forces()))
if debug:
write_xyz(Optimizer.debugfile, totalsol,
'After Lammps Minimization')
Optimizer.debugfile.flush()
except Exception, e:
os.chdir(cwd)
STR += 'WARNING: Exception during energy eval:\n' + repr(
e) + '\n'
f = open('problem-structures.xyz', 'a')
write_xyz(f,
totcop,
data='Starting structure hindex=' +
individ.history_index)
write_xyz(f, totalsol, data='Lammps Min structure')
en = 10
stress = 0
f.close()
if Optimizer.fitness_scheme == 'enthalpyfit':
pressure = totalsol.get_isotropic_pressure(stress)
cell_max = numpy.maximum.reduce(totalsol.get_positions())
cell_min = numpy.minimum.reduce(totalsol.get_positions())
cell = cell_max - cell_min
volume = cell[0] * cell[1] * cell[2]
else:
pressure = totalsol.get_isotropic_pressure(stress)
volume = 0
na = totalsol.get_number_of_atoms()
ena = en / na
energy = en
if Optimizer.structure == 'Defect':
if Optimizer.fixed_region == True or Optimizer.finddefects == False:
individ[0] = totalsol[0:nat]
bul = totalsol[(nat):len(totalsol)]
individ[0].set_cell(csize)
else:
if 'FI' in Optimizer.debug:
outt = find_defects(
totalsol,
Optimizer.solidbulk,
Optimizer.sf,
atomlistcheck=Optimizer.atomlist,
trackvacs=Optimizer.trackvacs,
trackswaps=Optimizer.trackswaps,
debug=Optimizer.debugfile)
else:
outt = find_defects(
totalsol,
Optimizer.solidbulk,
Optimizer.sf,
atomlistcheck=Optimizer.atomlist,
trackvacs=Optimizer.trackvacs,
trackswaps=Optimizer.trackswaps,
debug=False)
individ[0] = outt[0]
bul = outt[1]
individ.vacancies = outt[2]
individ.swaps = outt[3]
STR += outt[4]
indiv = individ[0]
else:
top, bul = find_top_layer(totalsol, Optimizer.surftopthick)
indiv = top.copy()
individ[0] = top.copy()
else:
class EAM(Calculator):
r"""
EAM Interface Documentation
Introduction
============
The Embedded Atom Method (EAM) [1]_ is a classical potential which is
good for modelling metals, particularly fcc materials. Because it is
an equiaxial potential the EAM does not model directional bonds
well. However, the Angular Dependent Potential (ADP) [2]_ which is an
extended version of EAM is able to model directional bonds and is also
included in the EAM calculator.
Generally all that is required to use this calculator is to supply a
potential file or as a set of functions that describe the potential.
The files containing the potentials for this calculator are not
included but many suitable potentials can be downloaded from The
Interatomic Potentials Repository Project at
http://www.ctcms.nist.gov/potentials/
Theory
======
A single element EAM potential is defined by three functions: the
embedded energy, electron density and the pair potential. A two
element alloy contains the individual three functions for each element
plus cross pair interactions. The ADP potential has two additional
sets of data to define the dipole and quadrupole directional terms for
each alloy and their cross interactions.
The total energy `E_{\rm tot}` of an arbitrary arrangement of atoms is
given by the EAM potential as
.. math::
E_{\rm tot} = \sum_i F(\bar\rho_i) + \frac{1}{2}\sum_{i\ne j} \phi(r_{ij})
and
.. math::
\bar\rho_i = \sum_j \rho(r_{ij})
where `F` is an embedding function, namely the energy to embed an atom `i` in
the combined electron density `\bar\rho_i` which is contributed from
each of its neighbouring atoms `j` by an amount `\rho(r_{ij})`,
`\phi(r_{ij})` is the pair potential function representing the energy
in bond `ij` which is due to the short-range electro-static
interaction between atoms, and `r_{ij}` is the distance between an
atom and its neighbour for that bond.
The ADP potential is defined as
.. math::
E_{\rm tot} = \sum_i F(\bar\rho_i) + \frac{1}{2}\sum_{i\ne j} \phi(r_{ij})
+ {1\over 2} \sum_{i,\alpha} (\mu_i^\alpha)^2
+ {1\over 2} \sum_{i,\alpha,\beta} (\lambda_i^{\alpha\beta})^2
- {1 \over 6} \sum_i \nu_i^2
where `\mu_i^\alpha` is the dipole vector, `\lambda_i^{\alpha\beta}`
is the quadrupole tensor and `\nu_i` is the trace of
`\lambda_i^{\alpha\beta}`.
Running the Calculator
======================
EAM calculates the cohesive atom energy and forces. Internally the
potential functions are defined by splines which may be directly
supplied or created by reading the spline points from a data file from
which a spline function is created. The LAMMPS compatible ``.alloy``
and ``.adp`` formats are supported. The LAMMPS ``.eam`` format is
slightly different from the ``.alloy`` format and is currently not
supported.
For example::
from ase.calculators.eam import EAM
mishin = EAM(potential='Al99.eam.alloy')
mishin.write_potential('new.eam.alloy')
mishin.plot()
slab.set_calculator(mishin)
slab.get_potential_energy()
slab.get_forces()
The breakdown of energy contribution from the indvidual components are
stored in the calculator instance ``.results['energy_components']``
Arguments
=========
========================= ====================================================
Keyword Description
========================= ====================================================
``potential`` file of potential in ``.alloy`` or ``.adp`` format
(This is generally all you need to supply)
``elements[N]`` array of N element abbreviations
``embedded_energy[N]`` arrays of embedded energy functions
``electron_density[N]`` arrays of electron density functions
``phi[N,N]`` arrays of pair potential functions
``d_embedded_energy[N]`` arrays of derivative embedded energy functions
``d_electron_density[N]`` arrays of derivative electron density functions
``d_phi[N,N]`` arrays of derivative pair potentials functions
``d[N,N], q[N,N]`` ADP dipole and quadrupole function
``d_d[N,N], d_q[N,N]`` ADP dipole and quadrupole derivative functions
``skin`` skin distance passed to NeighborList(). If no atom
has moved more than the skin-distance since the last
call to the ``update()`` method then the neighbor
list can be reused. Defaults to 1.0.
``form`` the form of the potential ``alloy`` or ``adp``. This
will be determined from the file suffix or must be
set if using equations
========================= ====================================================
Additional parameters for writing potential files
=================================================
The following parameters are only required for writing a potential in
``.alloy`` or ``.adp`` format file.
========================= ====================================================
Keyword Description
========================= ====================================================
``header`` Three line text header. Default is standard message.
``Z[N]`` Array of atomic number of each element
``mass[N]`` Atomic mass of each element
``a[N]`` Array of lattice parameters for each element
``lattice[N]`` Lattice type
``nrho`` No. of rho samples along embedded energy curve
``drho`` Increment for sampling density
``nr`` No. of radial points along density and pair
potential curves
``dr`` Increment for sampling radius
========================= ====================================================
Special features
================
``.plot()``
Plots the individual functions. This may be called from multiple EAM
potentials to compare the shape of the individual curves. This
function requires the installation of the Matplotlib libraries.
Notes/Issues
=============
* Although currently not fast, this calculator can be good for trying
small calculations or for creating new potentials by matching baseline
data such as from DFT results. The format for these potentials is
compatible with LAMMPS_ and so can be used either directly by LAMMPS or
with the ASE LAMMPS calculator interface.
* Supported formats are the LAMMPS_ ``.alloy`` and ``.adp``. The
``.eam`` format is currently not supported. The form of the
potential will be determined from the file suffix.
* Any supplied values will override values read from the file.
* The derivative functions, if supplied, are only used to calculate
forces.
* There is a bug in early versions of scipy that will cause eam.py to
crash when trying to evaluate splines of a potential with one
neighbor such as caused by evaluating a dimer.
.. _LAMMPS: http://lammps.sandia.gov/
.. [1] M.S. Daw and M.I. Baskes, Phys. Rev. Letters 50 (1983)
1285.
.. [2] Y. Mishin, M.J. Mehl, and D.A. Papaconstantopoulos,
Acta Materialia 53 2005 4029--4041.
End EAM Interface Documentation
"""
implemented_properties = ['energy', 'forces']
default_parameters = dict(
skin=1.0,
potential=None,
header="""EAM/ADP potential file\nGenerated from eam.py\nblank\n""")
def __init__(self,
restart=None,
ignore_bad_restart_file=False,
label=os.curdir,
atoms=None,
**kwargs):
if 'potential' in kwargs:
self.read_potential(kwargs['potential'])
Calculator.__init__(self, restart, ignore_bad_restart_file, label,
atoms, **kwargs)
valid_args = (
'potential',
'elements',
'header',
'drho',
'dr',
'cutoff',
'atomic_number',
'mass',
'a',
'lattice',
'embedded_energy',
'electron_density',
'phi',
# derivatives
'd_embedded_energy',
'd_electron_density',
'd_phi',
'd',
'q',
'd_d',
'd_q', # adp terms
'skin',
'form',
'Z',
'nr',
'nrho',
'mass')
# set any additional keyword arguments
for arg, val in self.parameters.iteritems():
if arg in valid_args:
setattr(self, arg, val)
else:
raise RuntimeError('unknown keyword arg "%s" : not in %s' %
(arg, valid_args))
def set_form(self, fileobj):
"""set the form variable based on the file name suffix"""
extension = os.path.splitext(fileobj)[1]
if extension == '.eam':
self.form = 'eam'
raise NotImplementedError
elif extension == '.alloy':
self.form = 'alloy'
elif extension == '.adp':
self.form = 'adp'
else:
raise RuntimeError('unknown file extension type: %s' % extension)
def read_potential(self, fileobj):
"""Reads a LAMMPS EAM file in alloy or adp format
and creates the interpolation functions from the data
"""
if isinstance(fileobj, str):
f = open(fileobj)
self.set_form(fileobj)
else:
f = fileobj
lines = f.readlines()
self.header = lines[:3]
i = 3
# make the data one long line so as not to care how its formatted
data = []
for line in lines[i:]:
data.extend(line.split())
self.Nelements = int(data[0])
d = 1
self.elements = data[d:(d + self.Nelements)]
d += self.Nelements
self.nrho = int(data[d])
self.drho = float(data[d + 1])
self.nr = int(data[d + 2])
self.dr = float(data[d + 3])
self.cutoff = float(data[d + 4])
self.embedded_data = np.zeros([self.Nelements, self.nrho])
self.density_data = np.zeros([self.Nelements, self.nr])
self.Z = np.zeros([self.Nelements], dtype=int)
self.mass = np.zeros([self.Nelements])
self.a = np.zeros([self.Nelements])
self.lattice = []
d += 5
# reads in the part of the eam file for each element
for elem in range(self.Nelements):
self.Z[elem] = int(data[d])
self.mass[elem] = float(data[d + 1])
self.a[elem] = float(data[d + 2])
self.lattice.append(data[d + 3])
d += 4
self.embedded_data[elem] = np.float_(data[d:(d + self.nrho)])
d += self.nrho
self.density_data[elem] = np.float_(data[d:(d + self.nr)])
d += self.nr
# reads in the r*phi data for each interaction between elements
self.rphi_data = np.zeros([self.Nelements, self.Nelements, self.nr])
for i in range(self.Nelements):
for j in range(i + 1):
self.rphi_data[j, i] = np.float_(data[d:(d + self.nr)])
d += self.nr
self.r = np.arange(0, self.nr) * self.dr
self.rho = np.arange(0, self.nrho) * self.drho
self.set_splines()
if (self.form == 'adp'):
self.read_adp_data(data, d)
self.set_adp_splines()
def set_splines(self):
# this section turns the file data into three functions (and
# derivative functions) that define the potential
self.embedded_energy = np.empty(self.Nelements, object)
self.electron_density = np.empty(self.Nelements, object)
self.d_embedded_energy = np.empty(self.Nelements, object)
self.d_electron_density = np.empty(self.Nelements, object)
for i in range(self.Nelements):
self.embedded_energy[i] = spline(self.rho,
self.embedded_data[i],
k=3)
self.electron_density[i] = spline(self.r,
self.density_data[i],
k=3)
self.d_embedded_energy[i] = self.deriv(self.embedded_energy[i])
self.d_electron_density[i] = self.deriv(self.electron_density[i])
self.phi = np.empty([self.Nelements, self.Nelements], object)
self.d_phi = np.empty([self.Nelements, self.Nelements], object)
# ignore the first point of the phi data because it is forced
# to go through zero due to the r*phi format in alloy and adp
for i in range(self.Nelements):
for j in range(i, self.Nelements):
if self.form == 'eam': # not stored as rphi
# should we ignore the first point for eam ?
raise RuntimeError('.eam format not yet supported')
self.phi[i, j] = spline(self.r[1:],
self.rphi_data[i, j][1:],
k=3)
else:
self.phi[i,
j] = spline(self.r[1:],
self.rphi_data[i, j][1:] / self.r[1:],
k=3)
self.d_phi[i, j] = self.deriv(self.phi[i, j])
if j != i:
self.phi[j, i] = self.phi[i, j]
self.d_phi[j, i] = self.d_phi[i, j]
def set_adp_splines(self):
self.d = np.empty([self.Nelements, self.Nelements], object)
self.d_d = np.empty([self.Nelements, self.Nelements], object)
self.q = np.empty([self.Nelements, self.Nelements], object)
self.d_q = np.empty([self.Nelements, self.Nelements], object)
for i in range(self.Nelements):
for j in range(i, self.Nelements):
self.d[i, j] = spline(self.r[1:], self.d_data[i, j][1:], k=3)
self.d_d[i, j] = self.deriv(self.d[i, j])
self.q[i, j] = spline(self.r[1:], self.q_data[i, j][1:], k=3)
self.d_q[i, j] = self.deriv(self.q[i, j])
# make symmetrical
if j != i:
self.d[j, i] = self.d[i, j]
self.d_d[j, i] = self.d_d[i, j]
self.q[j, i] = self.q[i, j]
self.d_q[j, i] = self.d_q[i, j]
def read_adp_data(self, data, d):
"""read in the extra adp data from the potential file"""
self.d_data = np.zeros([self.Nelements, self.Nelements, self.nr])
# should be non symetrical combinations of 2
for i in range(self.Nelements):
for j in range(i + 1):
self.d_data[j, i] = data[d:d + self.nr]
d += self.nr
self.q_data = np.zeros([self.Nelements, self.Nelements, self.nr])
# should be non symetrical combinations of 2
for i in range(self.Nelements):
for j in range(i + 1):
self.q_data[j, i] = data[d:d + self.nr]
d += self.nr
def write_potential(self, filename, nc=1, numformat='%.8e'):
"""Writes out the potential in the format given by the form
variable to 'filename' with a data format that is nc columns
wide. Note: array lengths need to be an exact multiple of nc
"""
f = open(filename, 'w')
assert self.nr % nc == 0
assert self.nrho % nc == 0
for line in self.header:
f.write(line)
f.write('%d ' % self.Nelements)
for i in range(self.Nelements):
f.write('%s ' % str(self.elements[i]))
f.write('\n')
f.write('%d %f %d %f %f \n' %
(self.nrho, self.drho, self.nr, self.dr, self.cutoff))
# start of each section for each element
# rs = np.linspace(0, self.nr * self.dr, self.nr)
# rhos = np.linspace(0, self.nrho * self.drho, self.nrho)
rs = np.arange(0, self.nr) * self.dr
rhos = np.arange(0, self.nrho) * self.drho
for i in range(self.Nelements):
f.write('%d %f %f %s\n' %
(self.Z[i], self.mass[i], self.a[i], str(self.lattice[i])))
np.savetxt(f,
self.embedded_energy[i](rhos).reshape(
self.nrho / nc, nc),
fmt=nc * [numformat])
np.savetxt(f,
self.electron_density[i](rs).reshape(self.nr / nc, nc),
fmt=nc * [numformat])
# write out the pair potentials in Lammps DYNAMO setfl format
# as r*phi for alloy format
for i in range(self.Nelements):
for j in range(i, self.Nelements):
np.savetxt(f,
(rs * self.phi[i, j](rs)).reshape(self.nr / nc, nc),
fmt=nc * [numformat])
if self.form == 'adp':
# these are the u(r) or dipole values
for i in range(self.Nelements):
for j in range(i + 1):
np.savetxt(f, self.d_data[i, j])
# these are the w(r) or quadrupole values
for i in range(self.Nelements):
for j in range(i + 1):
np.savetxt(f, self.q_data[i, j])
f.close()
def update(self, atoms):
# check all the elements are available in the potential
self.Nelements = len(self.elements)
elements = np.unique(atoms.get_chemical_symbols())
unavailable = np.logical_not(
np.array([item in self.elements for item in elements]))
if np.any(unavailable):
raise RuntimeError('These elements are not in the potential: %s' %
elements[unavailable])
# cutoffs need to be a vector for NeighborList
cutoffs = self.cutoff * np.ones(len(atoms))
# convert the elements to an index of the position
# in the eam format
self.index = np.array(
[self.elements.index(el) for el in atoms.get_chemical_symbols()])
self.pbc = atoms.get_pbc()
# since we need the contribution of all neighbors to the
# local electron density we cannot just calculate and use
# one way neighbors
self.neighbors = NeighborList(cutoffs,
skin=self.parameters.skin,
self_interaction=False,
bothways=True)
self.neighbors.update(atoms)
def calculate(self,
atoms=None,
properties=['energy'],
system_changes=all_changes):
"""EAM Calculator
atoms: Atoms object
Contains positions, unit-cell, ...
properties: list of str
List of what needs to be calculated. Can be any combination
of 'energy', 'forces'
system_changes: list of str
List of what has changed since last calculation. Can be
any combination of these five: 'positions', 'numbers', 'cell',
'pbc', 'initial_charges' and 'initial_magmoms'.
"""
Calculator.calculate(self, atoms, properties, system_changes)
# we shouldn't really recalc if charges or magmos change
if len(system_changes) > 0: # something wrong with this way
self.update(self.atoms)
self.calculate_energy(self.atoms)
if 'forces' in properties:
self.calculate_forces(self.atoms)
# check we have all the properties requested
for property in properties:
if property not in self.results:
if property is 'energy':
self.calculate_energy(self.atoms)
if property is 'forces':
self.calculate_forces(self.atoms)
# we need to remember the previous state of parameters
# if 'potential' in parameter_changes and potential != None:
# self.read_potential(potential)
def calculate_energy(self, atoms):
"""Calculate the energy
the energy is made up of the ionic or pair interaction and
the embedding energy of each atom into the electron cloud
generated by its neighbors
"""
pair_energy = 0.0
embedding_energy = 0.0
mu_energy = 0.0
lam_energy = 0.0
trace_energy = 0.0
self.total_density = np.zeros(len(atoms))
if (self.form == 'adp'):
self.mu = np.zeros([len(atoms), 3])
self.lam = np.zeros([len(atoms), 3, 3])
for i in range(len(atoms)): # this is the atom to be embedded
neighbors, offsets = self.neighbors.get_neighbors(i)
offset = np.dot(offsets, atoms.get_cell())
rvec = (atoms.positions[neighbors] + offset - atoms.positions[i])
## calculate the distance to the nearest neighbors
r = np.sqrt(np.sum(np.square(rvec), axis=1)) # fast
# r = np.apply_along_axis(np.linalg.norm, 1, rvec) # sloow
nearest = np.arange(len(r))[r <= self.cutoff]
for j_index in range(self.Nelements):
use = self.index[neighbors[nearest]] == j_index
if not use.any():
continue
pair_energy += np.sum(self.phi[self.index[i], j_index](
r[nearest][use])) / 2.
density = np.sum(self.electron_density[j_index](
r[nearest][use]))
self.total_density[i] += density
if self.form == 'adp':
self.mu[i] += self.adp_dipole(
r[nearest][use], rvec[nearest][use],
self.d[self.index[i], j_index])
self.lam[i] += self.adp_quadrupole(
r[nearest][use], rvec[nearest][use],
self.q[self.index[i], j_index])
# add in the electron embedding energy
embedding_energy += self.embedded_energy[self.index[i]](
self.total_density[i])
components = dict(pair=pair_energy, embedding=embedding_energy)
if self.form == 'adp':
mu_energy += np.sum(self.mu**2) / 2.
lam_energy += np.sum(self.lam**2) / 2.
for i in range(len(atoms)): # this is the atom to be embedded
trace_energy -= np.sum(self.lam[i].trace()**2) / 6.
adp_result = dict(adp_mu=mu_energy,
adp_lam=lam_energy,
adp_trace=trace_energy)
components.update(adp_result)
self.positions = atoms.positions.copy()
self.cell = atoms.get_cell().copy()
energy = 0.0
for i in components.keys():
energy += components[i]
self.energy_free = energy
self.energy_zero = energy
self.results['energy_components'] = components
self.results['energy'] = energy
def calculate_forces(self, atoms):
# calculate the forces based on derivatives of the three EAM functions
self.update(atoms)
self.results['forces'] = np.zeros((len(atoms), 3))
for i in range(len(atoms)): # this is the atom to be embedded
neighbors, offsets = self.neighbors.get_neighbors(i)
offset = np.dot(offsets, atoms.get_cell())
# create a vector of relative positions of neighbors
rvec = atoms.positions[neighbors] + offset - atoms.positions[i]
r = np.sqrt(np.sum(np.square(rvec), axis=1))
nearest = np.arange(len(r))[r < self.cutoff]
d_embedded_energy_i = self.d_embedded_energy[self.index[i]](
self.total_density[i])
urvec = rvec.copy() # unit directional vector
for j in np.arange(len(neighbors)):
urvec[j] = urvec[j] / r[j]
for j_index in range(self.Nelements):
use = self.index[neighbors[nearest]] == j_index
if not use.any():
continue
rnuse = r[nearest][use]
density_j = self.total_density[neighbors[nearest][use]]
scale = (self.d_phi[self.index[i], j_index](rnuse) +
(d_embedded_energy_i *
self.d_electron_density[j_index](rnuse)) +
(self.d_embedded_energy[j_index](density_j) *
self.d_electron_density[self.index[i]](rnuse)))
self.results['forces'][i] += np.dot(scale, urvec[nearest][use])
if (self.form == 'adp'):
adp_forces = self.angular_forces(
self.mu[i], self.mu[neighbors[nearest][use]],
self.lam[i], self.lam[neighbors[nearest][use]], rnuse,
rvec[nearest][use], self.index[i], j_index)
self.results['forces'][i] += adp_forces
def angular_forces(self, mu_i, mu, lam_i, lam, r, rvec, form1, form2):
# calculate the extra components for the adp forces
# rvec are the relative positions to atom i
psi = np.zeros(mu.shape)
for gamma in range(3):
term1 = (mu_i[gamma] - mu[:, gamma]) * self.d[form1][form2](r)
term2 = np.sum(
(mu_i - mu) * self.d_d[form1][form2](r)[:, np.newaxis] *
(rvec * rvec[:, gamma][:, np.newaxis] / r[:, np.newaxis]),
axis=1)
term3 = 2 * np.sum((lam_i[:, gamma] + lam[:, :, gamma]) * rvec *
self.q[form1][form2](r)[:, np.newaxis],
axis=1)
term4 = 0.0
for alpha in range(3):
for beta in range(3):
rs = rvec[:, alpha] * rvec[:, beta] * rvec[:, gamma]
term4 += ((lam_i[alpha, beta] + lam[:, alpha, beta]) *
self.d_q[form1][form2](r) * rs) / r
term5 = ((lam_i.trace() + lam.trace(axis1=1, axis2=2)) *
(self.d_q[form1][form2](r) * r + 2 * self.q[form1][form2]
(r)) * rvec[:, gamma]) / 3.
# the minus for term5 is a correction on the adp
# formulation given in the 2005 Mishin Paper and is posted
# on the NIST website with the AlH potential
psi[:, gamma] = term1 + term2 + term3 + term4 - term5
return np.sum(psi, axis=0)
def adp_dipole(self, r, rvec, d):
# calculate the dipole contribution
mu = np.sum((rvec * d(r)[:, np.newaxis]), axis=0)
return mu # sign to agree with lammps
def adp_quadrupole(self, r, rvec, q):
# slow way of calculating the quadrupole contribution
r = np.sqrt(np.sum(rvec**2, axis=1))
lam = np.zeros([rvec.shape[0], 3, 3])
qr = q(r)
for alpha in range(3):
for beta in range(3):
lam[:, alpha, beta] += qr * rvec[:, alpha] * rvec[:, beta]
return np.sum(lam, axis=0)
def deriv(self, spline):
"""Wrapper for extracting the derivative from a spline"""
def d_spline(aspline):
return spline(aspline, 1)
return d_spline
def plot(self, name=''):
"""Plot the individual curves"""
try:
import matplotlib.pyplot as plt
except ImportError:
raise NotAvailable('This needs matplotlib module.')
if self.form == 'eam' or self.form == 'alloy':
nrow = 2
elif self.form == 'adp':
nrow = 3
else:
raise RuntimeError('Unknown form of potential: %s' % self.form)
if hasattr(self, 'r'):
r = self.r
else:
r = np.linspace(0, self.cutoff, 50)
if hasattr(self, 'rho'):
rho = self.rho
else:
rho = np.linspace(0, 10.0, 50)
plt.subplot(nrow, 2, 1)
self.elem_subplot(rho, self.embedded_energy, r'$\rho$',
r'Embedding Energy $F(\bar\rho)$', name, plt)
plt.subplot(nrow, 2, 2)
self.elem_subplot(r, self.electron_density, r'$r$',
r'Electron Density $\rho(r)$', name, plt)
plt.subplot(nrow, 2, 3)
self.multielem_subplot(r, self.phi, r'$r$',
r'Pair Potential $\phi(r)$', name, plt)
plt.ylim(-1.0, 1.0) # need reasonable values
if self.form == 'adp':
plt.subplot(nrow, 2, 5)
self.multielem_subplot(r, self.d, r'$r$', r'Dipole Energy', name,
plt)
plt.subplot(nrow, 2, 6)
self.multielem_subplot(r, self.q, r'$r$', r'Quadrupole Energy',
name, plt)
plt.plot()
def elem_subplot(self, curvex, curvey, xlabel, ylabel, name, plt):
plt.xlabel(xlabel)
plt.ylabel(ylabel)
for i in np.arange(self.Nelements):
label = name + ' ' + self.elements[i]
plt.plot(curvex, curvey[i](curvex), label=label)
plt.legend()
def multielem_subplot(self, curvex, curvey, xlabel, ylabel, name, plt):
plt.xlabel(xlabel)
plt.ylabel(ylabel)
for i in np.arange(self.Nelements):
for j in np.arange(i + 1):
label = name + ' ' + self.elements[i] + '-' + self.elements[j]
plt.plot(curvex, curvey[i, j](curvex), label=label)
plt.legend()
class EMT:
disabled = False # Set to True to disable (asap does this).
def __init__(self, fakestress=False):
self.energy = None
self.name = 'EMT'
self.version = '1.0'
# fakestress is needed to fake some stress value for the testsuite
# in order to test the filter functionality.
self.fakestress = fakestress
if self.disabled:
print >> sys.stderr, """
ase.EMT has been disabled by Asap. Most likely, you
intended to use Asap's EMT calculator, but accidentally
imported ase's EMT calculator after Asap's. This could
happen if your script contains the lines
from asap3 import *
from ase.calculators.emt import EMT
Swap the two lines to solve the problem.
(or 'from ase import *' in older versions of ASE.) Swap
the two lines to solve the problem.
In the UNLIKELY event that you actually wanted to use
ase.calculators.emt.EMT although asap3 is loaded into memory,
please reactivate it with the command
ase.calculators.emt.EMT.disabled = False
"""
raise RuntimeError('ase.EMT has been disabled. ' +
'See message printed above.')
def get_name(self):
return self.name
def get_version(self):
return self.version
def get_spin_polarized(self):
return False
def initialize(self, atoms):
self.par = {}
self.rc = 0.0
self.numbers = atoms.get_atomic_numbers()
maxseq = max(par[1] for par in parameters.values()) * Bohr
rc = self.rc = beta * maxseq * 0.5 * (sqrt(3) + sqrt(4))
rr = rc * 2 * sqrt(4) / (sqrt(3) + sqrt(4))
self.acut = np.log(9999.0) / (rr - rc)
for Z in self.numbers:
if Z not in self.par:
p = parameters[chemical_symbols[Z]]
s0 = p[1] * Bohr
eta2 = p[3] / Bohr
kappa = p[4] / Bohr
x = eta2 * beta * s0
gamma1 = 0.0
gamma2 = 0.0
for i, n in enumerate([12, 6, 24]):
r = s0 * beta * sqrt(i + 1)
x = n / (12 * (1.0 + exp(self.acut * (r - rc))))
gamma1 += x * exp(-eta2 * (r - beta * s0))
gamma2 += x * exp(-kappa / beta * (r - beta * s0))
self.par[Z] = {'E0': p[0],
's0': s0,
'V0': p[2],
'eta2': eta2,
'kappa': kappa,
'lambda': p[5] / Bohr,
'n0': p[6] / Bohr**3,
'rc': rc,
'gamma1': gamma1,
'gamma2': gamma2}
#if rc + 0.5 > self.rc:
# self.rc = rc + 0.5
self.ksi = {}
for s1, p1 in self.par.items():
self.ksi[s1] = {}
for s2, p2 in self.par.items():
#self.ksi[s1][s2] = (p2['n0'] / p1['n0'] *
# exp(eta1 * (p1['s0'] - p2['s0'])))
self.ksi[s1][s2] = p2['n0'] / p1['n0']
self.forces = np.empty((len(atoms), 3))
self.sigma1 = np.empty(len(atoms))
self.deds = np.empty(len(atoms))
self.nl = NeighborList([0.5 * self.rc + 0.25] * len(atoms),
self_interaction=False)
def update(self, atoms):
if (self.energy is None or
len(self.numbers) != len(atoms) or
(self.numbers != atoms.get_atomic_numbers()).any()):
self.initialize(atoms)
self.calculate(atoms)
elif ((self.positions != atoms.get_positions()).any() or
(self.pbc != atoms.get_pbc()).any() or
(self.cell != atoms.get_cell()).any()):
self.calculate(atoms)
def calculation_required(self, atoms, quantities):
if len(quantities) == 0:
return False
return (self.energy is None or
len(self.numbers) != len(atoms) or
(self.numbers != atoms.get_atomic_numbers()).any() or
(self.positions != atoms.get_positions()).any() or
(self.pbc != atoms.get_pbc()).any() or
(self.cell != atoms.get_cell()).any())
def get_number_of_iterations(self):
return 0
def get_potential_energy(self, atoms):
self.update(atoms)
return self.energy
def get_numeric_forces(self, atoms):
self.update(atoms)
p = atoms.positions
p0 = p.copy()
forces = np.empty_like(p)
eps = 0.0001
for a in range(len(p)):
for c in range(3):
p[a, c] += eps
self.calculate(atoms)
de = self.energy
p[a, c] -= 2 * eps
self.calculate(atoms)
de -= self.energy
p[a, c] += eps
forces[a, c] = -de / (2 * eps)
p[:] = p0
return forces
def get_forces(self, atoms):
self.update(atoms)
return self.forces.copy()
def get_stress(self, atoms):
if self.fakestress:
return np.zeros((6))
else:
raise NotImplementedError
def calculate(self, atoms):
self.positions = atoms.get_positions().copy()
self.cell = atoms.get_cell().copy()
self.pbc = atoms.get_pbc().copy()
self.nl.update(atoms)
self.energy = 0.0
self.sigma1[:] = 0.0
self.forces[:] = 0.0
natoms = len(atoms)
for a1 in range(natoms):
Z1 = self.numbers[a1]
p1 = self.par[Z1]
ksi = self.ksi[Z1]
neighbors, offsets = self.nl.get_neighbors(a1)
offsets = np.dot(offsets, atoms.cell)
for a2, offset in zip(neighbors, offsets):
d = self.positions[a2] + offset - self.positions[a1]
r = sqrt(np.dot(d, d))
if r < self.rc + 0.5:
Z2 = self.numbers[a2]
p2 = self.par[Z2]
self.interact1(a1, a2, d, r, p1, p2, ksi[Z2])
for a in range(natoms):
Z = self.numbers[a]
p = self.par[Z]
try:
ds = -log(self.sigma1[a] / 12) / (beta * p['eta2'])
except (OverflowError, ValueError):
self.deds[a] = 0.0
self.energy -= p['E0']
continue
x = p['lambda'] * ds
y = exp(-x)
z = 6 * p['V0'] * exp(-p['kappa'] * ds)
self.deds[a] = ((x * y * p['E0'] * p['lambda'] + p['kappa'] * z) /
(self.sigma1[a] * beta * p['eta2']))
e = p['E0'] * ((1 + x) * y - 1) + z
self.energy += p['E0'] * ((1 + x) * y - 1) + z
for a1 in range(natoms):
Z1 = self.numbers[a1]
p1 = self.par[Z1]
ksi = self.ksi[Z1]
neighbors, offsets = self.nl.get_neighbors(a1)
offsets = np.dot(offsets, atoms.cell)
for a2, offset in zip(neighbors, offsets):
d = self.positions[a2] + offset - self.positions[a1]
r = sqrt(np.dot(d, d))
if r < self.rc + 0.5:
Z2 = self.numbers[a2]
p2 = self.par[Z2]
self.interact2(a1, a2, d, r, p1, p2, ksi[Z2])
def interact1(self, a1, a2, d, r, p1, p2, ksi):
x = exp(self.acut * (r - self.rc))
theta = 1.0 / (1.0 + x)
y1 = (0.5 * p1['V0'] * exp(-p2['kappa'] * (r / beta - p2['s0'])) *
ksi / p1['gamma2'] * theta)
y2 = (0.5 * p2['V0'] * exp(-p1['kappa'] * (r / beta - p1['s0'])) /
ksi / p2['gamma2'] * theta)
self.energy -= y1 + y2
f = ((y1 * p2['kappa'] + y2 * p1['kappa']) / beta +
(y1 + y2) * self.acut * theta * x) * d / r
self.forces[a1] += f
self.forces[a2] -= f
self.sigma1[a1] += (exp(-p2['eta2'] * (r - beta * p2['s0'])) *
ksi * theta / p1['gamma1'])
self.sigma1[a2] += (exp(-p1['eta2'] * (r - beta * p1['s0'])) /
ksi * theta / p2['gamma1'])
def interact2(self, a1, a2, d, r, p1, p2, ksi):
x = exp(self.acut * (r - self.rc))
theta = 1.0 / (1.0 + x)
y1 = (exp(-p2['eta2'] * (r - beta * p2['s0'])) *
ksi / p1['gamma1'] * theta * self.deds[a1])
y2 = (exp(-p1['eta2'] * (r - beta * p1['s0'])) /
ksi / p2['gamma1'] * theta * self.deds[a2])
f = ((y1 * p2['eta2'] + y2 * p1['eta2']) +
(y1 + y2) * self.acut * theta * x) * d / r
self.forces[a1] -= f
self.forces[a2] += f
def set_atoms(self,*args,**kwargs):
'empty function for compatibility with other calculators and tests'
pass
class EMT:
disabled = False # Set to True to disable (asap does this).
def __init__(self):
self.energy = None
if self.disabled:
print >> sys.stderr, """
ase.EMT has been disabled by Asap. Most likely, you
intended to use Asap's EMT calculator, but accidentally
imported ase's EMT calculator after Asap's. This could
happen if your script contains the lines
from asap3 import *
from ase.calculators.emt import EMT
Swap the two lines to solve the problem.
(or 'from ase import *' in older versions of ASE.) Swap
the two lines to solve the problem.
In the UNLIKELY event that you actually wanted to use
ase.calculators.emt.EMT although asap3 is loaded into memory,
please reactivate it with the command
ase.calculators.emt.EMT.disabled = False
"""
raise RuntimeError('ase.EMT has been disabled. ' +
'See message printed above.')
def get_spin_polarized(self):
return False
def initialize(self, atoms):
self.par = {}
self.rc = 0.0
self.numbers = atoms.get_atomic_numbers()
maxseq = 0.0
seen = {}
for Z in self.numbers:
if Z not in seen:
seen[Z] = True
ss = parameters[chemical_symbols[Z]][1] * Bohr
if maxseq < ss:
maxseq = ss
rc = self.rc = beta * maxseq * 0.5 * (sqrt(3) + sqrt(4))
rr = rc * 2 * sqrt(4) / (sqrt(3) + sqrt(4))
self.acut = np.log(9999.0) / (rr - rc)
for Z in self.numbers:
if Z not in self.par:
p = parameters[chemical_symbols[Z]]
s0 = p[1] * Bohr
eta2 = p[3] / Bohr
kappa = p[4] / Bohr
x = eta2 * beta * s0
gamma1 = 0.0
gamma2 = 0.0
for i, n in enumerate([12, 6, 24]):
r = s0 * beta * sqrt(i + 1)
x = n / (12 * (1.0 + exp(self.acut * (r - rc))))
gamma1 += x * exp(-eta2 * (r - beta * s0))
gamma2 += x * exp(-kappa / beta * (r - beta * s0))
self.par[Z] = {'E0': p[0],
's0': s0,
'V0': p[2],
'eta2': eta2,
'kappa': kappa,
'lambda': p[5] / Bohr,
'n0': p[6] / Bohr**3,
'rc': rc,
'gamma1': gamma1,
'gamma2': gamma2}
#if rc + 0.5 > self.rc:
# self.rc = rc + 0.5
self.ksi = {}
for s1, p1 in self.par.items():
self.ksi[s1] = {}
for s2, p2 in self.par.items():
#self.ksi[s1][s2] = (p2['n0'] / p1['n0'] *
# exp(eta1 * (p1['s0'] - p2['s0'])))
self.ksi[s1][s2] = p2['n0'] / p1['n0']
self.forces = np.empty((len(atoms), 3))
self.sigma1 = np.empty(len(atoms))
self.deds = np.empty(len(atoms))
self.nl = NeighborList([0.5 * self.rc + 0.25] * len(atoms),
self_interaction=False)
def update(self, atoms):
if (self.energy is None or
len(self.numbers) != len(atoms) or
(self.numbers != atoms.get_atomic_numbers()).any()):
self.initialize(atoms)
self.calculate(atoms)
elif ((self.positions != atoms.get_positions()).any() or
(self.pbc != atoms.get_pbc()).any() or
(self.cell != atoms.get_cell()).any()):
self.calculate(atoms)
def calculation_required(self, atoms, quantities):
if len(quantities) == 0:
return False
return (self.energy is None or
len(self.numbers) != len(atoms) or
(self.numbers != atoms.get_atomic_numbers()).any() or
(self.positions != atoms.get_positions()).any() or
(self.pbc != atoms.get_pbc()).any() or
(self.cell != atoms.get_cell()).any())
def get_potential_energy(self, atoms):
self.update(atoms)
return self.energy
def get_numeric_forces(self, atoms):
self.update(atoms)
p = atoms.positions
p0 = p.copy()
forces = np.empty_like(p)
eps = 0.0001
for a in range(len(p)):
for c in range(3):
p[a, c] += eps
self.calculate(atoms)
de = self.energy
p[a, c] -= 2 * eps
self.calculate(atoms)
de -= self.energy
p[a, c] += eps
forces[a, c] = -de / (2 * eps)
p[:] = p0
return forces
def get_forces(self, atoms):
self.update(atoms)
return self.forces.copy()
def get_stress(self, atoms):
raise NotImplementedError
def calculate(self, atoms):
self.positions = atoms.get_positions().copy()
self.cell = atoms.get_cell().copy()
self.pbc = atoms.get_pbc().copy()
self.nl.update(atoms)
self.energy = 0.0
self.sigma1[:] = 0.0
self.forces[:] = 0.0
natoms = len(atoms)
for a1 in range(natoms):
Z1 = self.numbers[a1]
p1 = self.par[Z1]
ksi = self.ksi[Z1]
neighbors, offsets = self.nl.get_neighbors(a1)
offsets = np.dot(offsets, atoms.cell)
for a2, offset in zip(neighbors, offsets):
d = self.positions[a2] + offset - self.positions[a1]
r = sqrt(np.dot(d, d))
if r < self.rc + 0.5:
Z2 = self.numbers[a2]
p2 = self.par[Z2]
self.interact1(a1, a2, d, r, p1, p2, ksi[Z2])
for a in range(natoms):
Z = self.numbers[a]
p = self.par[Z]
try:
ds = -log(self.sigma1[a] / 12) / (beta * p['eta2'])
except (OverflowError, ValueError):
self.deds[a] = 0.0
self.energy -= p['E0']
continue
x = p['lambda'] * ds
y = exp(-x)
z = 6 * p['V0'] * exp(-p['kappa'] * ds)
self.deds[a] = ((x * y * p['E0'] * p['lambda'] + p['kappa'] * z) /
(self.sigma1[a] * beta * p['eta2']))
e = p['E0'] * ((1 + x) * y - 1) + z
self.energy += p['E0'] * ((1 + x) * y - 1) + z
for a1 in range(natoms):
Z1 = self.numbers[a1]
p1 = self.par[Z1]
ksi = self.ksi[Z1]
neighbors, offsets = self.nl.get_neighbors(a1)
offsets = np.dot(offsets, atoms.cell)
for a2, offset in zip(neighbors, offsets):
d = self.positions[a2] + offset - self.positions[a1]
r = sqrt(np.dot(d, d))
if r < self.rc + 0.5:
Z2 = self.numbers[a2]
p2 = self.par[Z2]
self.interact2(a1, a2, d, r, p1, p2, ksi[Z2])
def interact1(self, a1, a2, d, r, p1, p2, ksi):
x = exp(self.acut * (r - self.rc))
theta = 1.0 / (1.0 + x)
y1 = (0.5 * p1['V0'] * exp(-p2['kappa'] * (r / beta - p2['s0'])) *
ksi / p1['gamma2'] * theta)
y2 = (0.5 * p2['V0'] * exp(-p1['kappa'] * (r / beta - p1['s0'])) /
ksi / p2['gamma2'] * theta)
self.energy -= y1 + y2
f = ((y1 * p2['kappa'] + y2 * p1['kappa']) / beta +
(y1 + y2) * self.acut * theta * x) * d / r
self.forces[a1] += f
self.forces[a2] -= f
self.sigma1[a1] += (exp(-p2['eta2'] * (r - beta * p2['s0'])) *
ksi * theta / p1['gamma1'])
self.sigma1[a2] += (exp(-p1['eta2'] * (r - beta * p1['s0'])) /
ksi * theta / p2['gamma1'])
def interact2(self, a1, a2, d, r, p1, p2, ksi):
x = exp(self.acut * (r - self.rc))
theta = 1.0 / (1.0 + x)
y1 = (exp(-p2['eta2'] * (r - beta * p2['s0'])) *
ksi / p1['gamma1'] * theta * self.deds[a1])
y2 = (exp(-p1['eta2'] * (r - beta * p1['s0'])) /
ksi / p2['gamma1'] * theta * self.deds[a2])
f = ((y1 * p2['eta2'] + y2 * p1['eta2']) +
(y1 + y2) * self.acut * theta * x) * d / r
self.forces[a1] -= f
self.forces[a2] += f
def set_atoms(self,*args,**kwargs):
'empty function for compatibility with other calculators and tests'
pass
class OPLSff:
def __init__(self, fileobj=None, warnings=0):
self.warnings = warnings
self.data = {}
if fileobj is not None:
self.read(fileobj)
def read(self, fileobj, comments='#'):
if isinstance(fileobj, str):
fileobj = open(fileobj)
def read_block(name, symlen, nvalues):
"""Read a data block.
name: name of the block to store in self.data
symlen: length of the symbol
nvalues: number of values expected
"""
if name not in self.data:
self.data[name] = {}
data = self.data[name]
def add_line():
line = fileobj.readline().strip()
if not len(line): # end of the block
return False
line = line.split('#')[0] # get rid of comments
if len(line) > symlen:
symbol = line[:symlen]
words = line[symlen:].split()
if len(words) >= nvalues:
if nvalues == 1:
data[symbol] = float(words[0])
else:
data[symbol] = [float(word)
for word in words[:nvalues]]
return True
while add_line():
pass
read_block('one', 2, 3)
read_block('bonds', 5, 2)
read_block('angles', 8, 2)
read_block('dihedrals', 11, 4)
read_block('cutoffs', 5, 1)
self.bonds = BondData(self.data['bonds'])
self.angles = AnglesData(self.data['angles'])
self.dihedrals = DihedralsData(self.data['dihedrals'])
self.cutoffs = CutoffList(self.data['cutoffs'])
def write_lammps(self, atoms, prefix='lammps'):
"""Write input for a LAMMPS calculation."""
self.prefix = prefix
if hasattr(atoms, 'connectivities'):
connectivities = atoms.connectivities
else:
btypes, blist = self.get_bonds(atoms)
atypes, alist = self.get_angles()
dtypes, dlist = self.get_dihedrals(alist, atypes)
connectivities = {
'bonds': blist,
'bond types': btypes,
'angles': alist,
'angle types': atypes,
'dihedrals': dlist,
'dihedral types': dtypes,
}
self.write_lammps_definitions(atoms, btypes, atypes, dtypes)
self.write_lammps_in()
self.write_lammps_atoms(atoms, connectivities)
def write_lammps_in(self):
fileobj = self.prefix + '_in'
if isinstance(fileobj, str):
fileobj = open(fileobj, 'w')
fileobj.write("""# LAMMPS relaxation (written by ASE)
units metal
atom_style full
boundary p p p
#boundary p p f
""")
fileobj.write('read_data ' + self.prefix + '_atoms\n')
fileobj.write('include ' + self.prefix + '_opls\n')
fileobj.write("""
kspace_style pppm 1e-5
#kspace_modify slab 3.0
neighbor 1.0 bin
neigh_modify delay 0 every 1 check yes
thermo 1000
thermo_style custom step temp press cpu pxx pyy pzz pxy pxz pyz ke pe etotal vol lx ly lz atoms
dump 1 all xyz 1000 dump_relax.xyz
dump_modify 1 sort id
restart 100000 test_relax
min_style fire
minimize 1.0e-14 1.0e-5 100000 100000
""")
fileobj.close()
def write_lammps_atoms(self, atoms, connectivities):
"""Write atoms input for LAMMPS"""
fname = self.prefix + '_atoms'
fileobj = open(fname, 'w')
# header
fileobj.write(fileobj.name + ' (by ' + str(self.__class__) + ')\n\n')
fileobj.write(str(len(atoms)) + ' atoms\n')
fileobj.write(str(len(atoms.types)) + ' atom types\n')
blist = connectivities['bonds']
if len(blist):
btypes = connectivities['bond types']
fileobj.write(str(len(blist)) + ' bonds\n')
fileobj.write(str(len(btypes)) + ' bond types\n')
alist = connectivities['angles']
if len(alist):
atypes = connectivities['angle types']
fileobj.write(str(len(alist)) + ' angles\n')
fileobj.write(str(len(atypes)) + ' angle types\n')
dlist = connectivities['dihedrals']
if len(dlist):
dtypes = connectivities['dihedral types']
fileobj.write(str(len(dlist)) + ' dihedrals\n')
fileobj.write(str(len(dtypes)) + ' dihedral types\n')
# cell
p = prism(atoms.get_cell())
xhi, yhi, zhi, xy, xz, yz = p.get_lammps_prism_str()
fileobj.write('\n0.0 %s xlo xhi\n' % xhi)
fileobj.write('0.0 %s ylo yhi\n' % yhi)
fileobj.write('0.0 %s zlo zhi\n' % zhi)
# atoms
fileobj.write('\nAtoms\n\n')
tag = atoms.get_tags()
if atoms.has('molid'):
molid = atoms.get_array('molid')
else:
molid = [1] * len(atoms)
for i, r in enumerate(map(p.pos_to_lammps_str,
atoms.get_positions())):
q = self.data['one'][atoms.types[tag[i]]][2]
fileobj.write('%6d %3d %3d %s %s %s %s' % ((i + 1, molid[i],
tag[i] + 1,
q)
+ tuple(r)))
fileobj.write(' # ' + atoms.types[tag[i]] + '\n')
# velocities
velocities = atoms.get_velocities()
if velocities is not None:
fileobj.write('\nVelocities\n\n')
for i, v in enumerate(velocities):
fileobj.write('%6d %g %g %g\n' %
(i + 1, v[0], v[1], v[2]))
# masses
fileobj.write('\nMasses\n\n')
for i, typ in enumerate(atoms.types):
cs = atoms.split_symbol(typ)[0]
fileobj.write('%6d %g # %s -> %s\n' %
(i + 1,
atomic_masses[chemical_symbols.index(cs)],
typ, cs))
# bonds
if len(blist):
fileobj.write('\nBonds\n\n')
for ib, bvals in enumerate(blist):
fileobj.write('%8d %6d %6d %6d ' %
(ib + 1, bvals[0] + 1, bvals[1] + 1,
bvals[2] + 1))
try:
fileobj.write('# ' + btypes[bvals[0]])
except:
pass
fileobj.write('\n')
# angles
if len(alist):
fileobj.write('\nAngles\n\n')
for ia, avals in enumerate(alist):
fileobj.write('%8d %6d %6d %6d %6d ' %
(ia + 1, avals[0] + 1,
avals[1] + 1, avals[2] + 1, avals[3] + 1))
try:
fileobj.write('# ' + atypes[avals[0]])
except:
pass
fileobj.write('\n')
# dihedrals
if len(dlist):
fileobj.write('\nDihedrals\n\n')
for i, dvals in enumerate(dlist):
fileobj.write('%8d %6d %6d %6d %6d %6d ' %
(i + 1, dvals[0] + 1,
dvals[1] + 1, dvals[2] + 1,
dvals[3] + 1, dvals[4] + 1))
try:
fileobj.write('# ' + dtypes[dvals[0]])
except:
pass
fileobj.write('\n')
def update_neighbor_list(self, atoms):
cut = 0.5 * max(self.data['cutoffs'].values())
self.nl = NeighborList([cut] * len(atoms), skin=0,
bothways=True, self_interaction=False)
self.nl.update(atoms)
self.atoms = atoms
def get_bonds(self, atoms):
"""Find bonds and return them and their types"""
cutoffs = CutoffList(self.data['cutoffs'])
self.update_neighbor_list(atoms)
types = atoms.get_types()
tags = atoms.get_tags()
cell = atoms.get_cell()
bond_list = []
bond_types = []
for i, atom in enumerate(atoms):
iname = types[tags[i]]
indices, offsets = self.nl.get_neighbors(i)
for j, offset in zip(indices, offsets):
if j <= i:
continue # do not double count
jname = types[tags[j]]
cut = cutoffs.value(iname, jname)
if cut is None:
if self.warnings > 1:
print('Warning: cutoff %s-%s not found'
% (iname, jname))
continue # don't have it
dist = np.linalg.norm(atom.position - atoms[j].position
- np.dot(offset, cell))
if dist > cut:
continue # too far away
name, val = self.bonds.name_value(iname, jname)
if name is None:
if self.warnings:
print('Warning: potential %s-%s not found'
% (iname, jname))
continue # don't have it
if name not in bond_types:
bond_types.append(name)
bond_list.append([bond_types.index(name), i, j])
return bond_types, bond_list
def get_angles(self, atoms=None):
cutoffs = CutoffList(self.data['cutoffs'])
if atoms is not None:
self.update_neighbor_list(atoms)
else:
atoms = self.atoms
types = atoms.get_types()
tags = atoms.get_tags()
cell = atoms.get_cell()
ang_list = []
ang_types = []
# center atom *-i-*
for i, atom in enumerate(atoms):
iname = types[tags[i]]
indicesi, offsetsi = self.nl.get_neighbors(i)
# search for first neighbor j-i-*
for j, offsetj in zip(indicesi, offsetsi):
jname = types[tags[j]]
cut = cutoffs.value(iname, jname)
if cut is None:
continue # don't have it
dist = np.linalg.norm(atom.position - atoms[j].position
- np.dot(offsetj, cell))
if dist > cut:
continue # too far away
# search for second neighbor j-i-k
for k, offsetk in zip(indicesi, offsetsi):
if k <= j:
continue # avoid double count
kname = types[tags[k]]
cut = cutoffs.value(iname, kname)
if cut is None:
continue # don't have it
dist = np.linalg.norm(atom.position -
np.dot(offsetk, cell) -
atoms[k].position)
if dist > cut:
continue # too far away
name, val = self.angles.name_value(jname, iname,
kname)
if name is None:
if self.warnings > 1:
print('Warning: angles %s-%s-%s not found'
% (jname, iname, kname))
continue # don't have it
if name not in ang_types:
ang_types.append(name)
ang_list.append([ang_types.index(name), j, i, k])
return ang_types, ang_list
def get_dihedrals(self, ang_types, ang_list):
'Dihedrals derived from angles.'
cutoffs = CutoffList(self.data['cutoffs'])
atoms = self.atoms
types = atoms.get_types()
tags = atoms.get_tags()
cell = atoms.get_cell()
dih_list = []
dih_types = []
def append(name, i, j, k, l):
if name not in dih_types:
dih_types.append(name)
index = dih_types.index(name)
if (([index, i, j, k, l] not in dih_list) and
([index, l, k, j, i] not in dih_list)):
dih_list.append([index, i, j, k, l])
for angle in ang_types:
l, i, j, k = angle
iname = types[tags[i]]
jname = types[tags[j]]
kname = types[tags[k]]
# search for l-i-j-k
indicesi, offsetsi = self.nl.get_neighbors(i)
for l, offsetl in zip(indicesi, offsetsi):
if l == j:
continue # avoid double count
lname = types[tags[l]]
cut = cutoffs.value(iname, lname)
if cut is None:
continue # don't have it
dist = np.linalg.norm(atoms[i].position - atoms[l].position
- np.dot(offsetl, cell))
if dist > cut:
continue # too far away
name, val = self.dihedrals.name_value(lname, iname,
jname, kname)
if name is None:
continue # don't have it
append(name, l, i, j, k)
# search for i-j-k-l
indicesk, offsetsk = self.nl.get_neighbors(k)
for l, offsetl in zip(indicesk, offsetsk):
if l == j:
continue # avoid double count
lname = types[tags[l]]
cut = cutoffs.value(kname, lname)
if cut is None:
continue # don't have it
dist = np.linalg.norm(atoms[k].position - atoms[l].position
- np.dot(offsetl, cell))
if dist > cut:
continue # too far away
name, val = self.dihedrals.name_value(iname, jname,
kname, lname)
if name is None:
continue # don't have it
append(name, i, j, k, l)
return dih_types, dih_list
def write_lammps_definitions(self, atoms, btypes, atypes, dtypes):
"""Write force field definitions for LAMMPS."""
fileobj = self.prefix + '_opls'
if isinstance(fileobj, str):
fileobj = open(fileobj, 'w')
fileobj.write('# OPLS potential\n')
fileobj.write('# write_lammps' +
str(time.asctime(
time.localtime(time.time()))))
# bonds
if len(btypes):
fileobj.write('\n# bonds\n')
fileobj.write('bond_style harmonic\n')
for ib, btype in enumerate(btypes):
fileobj.write('bond_coeff %6d' % (ib + 1))
for value in self.bonds.nvh[btype]:
fileobj.write(' ' + str(value))
fileobj.write(' # ' + btype + '\n')
# angles
if len(atypes):
fileobj.write('\n# angles\n')
fileobj.write('angle_style harmonic\n')
for ia, atype in enumerate(atypes):
fileobj.write('angle_coeff %6d' % (ia + 1))
for value in self.angles.nvh[atype]:
fileobj.write(' ' + str(value))
fileobj.write(' # ' + atype + '\n')
# dihedrals
if len(dtypes):
fileobj.write('\n# dihedrals\n')
fileobj.write('dihedral_style opls\n')
for i, dtype in enumerate(dtypes):
fileobj.write('dihedral_coeff %6d' % (i + 1))
for value in self.dihedrals.nvh[dtype]:
fileobj.write(' ' + str(value))
fileobj.write(' # ' + dtype + '\n')
# Lennard Jones settings
fileobj.write('\n# L-J parameters\n')
fileobj.write('pair_style lj/cut/coul/long 10.0 7.4' +
' # consider changing these parameters\n')
fileobj.write('special_bonds lj/coul 0.0 0.0 0.5\n')
data = self.data['one']
for ia, atype in enumerate(atoms.types):
if len(atype) < 2:
atype = atype + ' '
fileobj.write('pair_coeff ' + str(ia + 1) + ' ' + str(ia + 1))
for value in data[atype][:2]:
fileobj.write(' ' + str(value))
fileobj.write(' # ' + atype + '\n')
fileobj.write('pair_modify shift yes mix geometric\n')
# Charges
fileobj.write('\n# charges\n')
for ia, atype in enumerate(atoms.types):
if len(atype) < 2:
atype = atype + ' '
fileobj.write('set type ' + str(ia + 1))
fileobj.write(' charge ' + str(data[atype][2]))
fileobj.write(' # ' + atype + '\n')
class OPLSff:
def __init__(self, fileobj=None, warnings=0):
self.warnings = warnings
self.data = {}
if fileobj is not None:
self.read(fileobj)
def read(self, fileobj, comments='#'):
if isinstance(fileobj, str):
fileobj = open(fileobj)
def read_block(name,
symlen, # length of the symbol
nvalues # of values expected
):
if name not in self.data:
self.data[name] = {}
data = self.data[name]
def add_line():
line = fileobj.readline()
if len(line) <= 1: # end of the block
return False
line = line.split('#')[0] # get rid of comments
if len(line) > symlen:
symbol = line[:symlen]
words = line[symlen:].split()
if len(words) >= nvalues:
if nvalues == 1:
data[symbol] = float(words[0])
else:
data[symbol] = [float(word)
for word in words[:nvalues]]
return True
while add_line():
pass
read_block('one', 2, 3)
read_block('bonds', 5, 2)
read_block('angles', 8, 2)
read_block('dihedrals', 11, 3)
read_block('cutoffs', 5, 1)
self.bonds = BondData(self.data['bonds'])
self.angles = AnglesData(self.data['angles'])
self.cutoffs = CutoffList(self.data['cutoffs'])
def write_lammps(self, atoms):
btypes, atypes = self.write_lammps_atoms(atoms)
self.write_lammps_definitions(atoms, btypes, atypes)
def write_lammps_atoms(self, atoms):
"""Write atoms infor for LAMMPS"""
fileobj = 'lammps_atoms'
if isinstance(fileobj, str):
fileobj = open(fileobj, 'w')
write_lammps_data(fileobj, atoms,
specorder=atoms.types,
speclist=(atoms.get_tags() + 1),
)
# masses
fileobj.write('\nMasses\n\n')
for i, typ in enumerate(atoms.types):
cs = atoms.split_symbol(typ)[0]
fileobj.write('%6d %g # %s -> %s\n' %
(i + 1,
atomic_masses[chemical_symbols.index(cs)],
typ, cs))
# bonds
btypes, blist = self.get_bonds(atoms)
fileobj.write('\n' + str(len(btypes)) + ' bond types\n')
fileobj.write(str(len(blist)) + ' bonds\n')
fileobj.write('\nBonds\n\n')
for ib, bvals in enumerate(blist):
fileobj.write('%8d %6d %6d %6d\n' %
(ib + 1, bvals[0] + 1, bvals[1] + 1, bvals[2] + 1))
# angles
atypes, alist = self.get_angles()
fileobj.write('\n' + str(len(atypes)) + ' angle types\n')
fileobj.write(str(len(alist)) + ' angles\n')
fileobj.write('\nAngles\n\n')
for ia, avals in enumerate(alist):
fileobj.write('%8d %6d %6d %6d %6d\n' %
(ia + 1, avals[0] + 1,
avals[1] + 1, avals[2] + 1, avals[3] + 1))
return btypes, atypes
def update_neighbor_list(self, atoms):
cut = 0.5 * max(self.data['cutoffs'].values())
self.nl = NeighborList([cut] * len(atoms), skin=0, bothways=True)
self.nl.update(atoms)
self.atoms = atoms
def get_bonds(self, atoms):
"""Find bonds and return them and their types"""
cutoffs = CutoffList(self.data['cutoffs'])
self.update_neighbor_list(atoms)
types = atoms.get_types()
tags = atoms.get_tags()
cell = atoms.get_cell()
positions = atoms.get_positions()
bond_list = []
bond_types = []
for i, atom in enumerate(atoms):
iname = types[tags[i]]
indices, offsets = self.nl.get_neighbors(i)
for j, offset in zip(indices, offsets):
if j <= i:
continue # do not double count
jname = types[tags[j]]
cut = cutoffs.value(iname, jname)
if cut is None:
if self.warnings > 1:
print ('Warning: cutoff %s-%s not found'
% (iname, jname))
continue # don't have it
dist = np.linalg.norm(atom.position - atoms[j].position
- np.dot(offset, cell))
if dist > cut:
continue # too far away
name, val = self.bonds.name_value(iname, jname)
if name is None:
if self.warnings:
print ('Warning: potential %s-%s not found'
% (iname, jname))
continue # don't have it
if name not in bond_types:
bond_types.append(name)
bond_list.append([bond_types.index(name), i, j])
return bond_types, bond_list
def get_angles(self, atoms=None):
cutoffs = CutoffList(self.data['cutoffs'])
if atoms is not None:
self.update_neighbor_list(atoms)
else:
atoms = self.atoms
types = atoms.get_types()
tags = atoms.get_tags()
cell = atoms.get_cell()
positions = atoms.get_positions()
ang_list = []
ang_types = []
for i, atom in enumerate(atoms):
iname = types[tags[i]]
indicesi, offsetsi = self.nl.get_neighbors(i)
for j, offsetj in zip(indicesi, offsetsi):
jname = types[tags[j]]
cut = cutoffs.value(iname, jname)
if cut is None:
continue # don't have it
dist = np.linalg.norm(atom.position - atoms[j].position
- np.dot(offsetj, cell))
if dist > cut:
continue # too far away
indicesj, offsetsj = self.nl.get_neighbors(j)
for k, offsetk in zip(indicesj, offsetsj):
if k <= i:
continue # avoid double count
kname = types[tags[k]]
cut = cutoffs.value(jname, kname)
if cut is None:
continue # don't have it
dist = np.linalg.norm(atoms[k].position +
np.dot(offsetk, cell) -
atoms[j].position)
if dist > cut:
continue # too far away
name, val = self.angles.name_value(iname, jname,
kname)
if name is None:
continue # don't have it
if name not in ang_types:
ang_types.append(name)
ang_list.append([ang_types.index(name), i, j, k])
return ang_types, ang_list
def write_lammps_definitions(self, atoms, btypes, atypes):
"""Write force field definitions for LAMMPS."""
fileobj = 'lammps_opls'
if isinstance(fileobj, str):
fileobj = open(fileobj, 'w')
print >> fileobj, '# OPLS potential'
print >> fileobj, '# write_lammps', time.asctime(
time.localtime(time.time()))
# bonds
fileobj.write('\n# bonds\n')
fileobj.write('bond_style harmonic\n')
for ib, btype in enumerate(btypes):
fileobj.write('bond_coeff %6d' % (ib + 1))
for value in self.bonds.nvh[btype]:
fileobj.write(' ' + str(value))
fileobj.write(' # ' + btype + '\n')
# angles
fileobj.write('\n# angles\n')
fileobj.write('angle_style harmonic\n')
for ia, atype in enumerate(atypes):
fileobj.write('angle_coeff %6d' % (ia + 1))
for value in self.angles.nvh[atype]:
fileobj.write(' ' + str(value))
fileobj.write(' # ' + atype + '\n')
# Lennard Jones settings
fileobj.write('\n# L-J parameters\n')
fileobj.write('pair_style lj/cut/coul/long 10.0 7.4' +
' # consider changing these parameters\n')
fileobj.write('special_bonds lj/coul 0.0 0.0 0.5\n')
data = self.data['one']
for ia, atype in enumerate(atoms.types):
if len(atype) < 2:
atype = atype + ' '
fileobj.write('pair_coeff ' + str(ia + 1) + ' ' + str(ia + 1))
for value in data[atype][:2]:
fileobj.write(' ' + str(value))
fileobj.write(' # ' + atype + '\n')
fileobj.write('pair_modify shift yes mix geometric\n')
# Charges
fileobj.write('\n# charges\n')
for ia, atype in enumerate(atoms.types):
if len(atype) < 2:
atype = atype + ' '
fileobj.write('set type ' + str(ia + 1))
fileobj.write(' ' + str(data[atype][2]))
fileobj.write(' # ' + atype + '\n')
def lattice_alteration_nn(indiv, Optimizer):
"""Move function to perform random move along random axis for nearest neighbor distance to random atoms
Inputs:
indiv = Individual class object to be altered
Optimizer = Optimizer class object with needed parameters
Outputs:
indiv = Altered Individual class object
"""
if 'MU' in Optimizer.debug:
debug = True
else:
debug = False
if Optimizer.structure=='Defect':
if Optimizer.isolate_mutation:
indc,indb,vacant,swaps,stro = find_defects(indiv[0],Optimizer.solidbulk,0)
ind = indc.copy()
ind.extend(indb)
else:
ind=indiv[0].copy()
indc=indiv[0].copy()
else:
ind=indiv[0].copy()
indc=indiv[0].copy()
if len(indc) != 0:
ctoff1 = [1.0 for one in ind]
nl = NeighborList(ctoff1, bothways=True, self_interaction=False)
nl.update(ind)
try:
natomsmove=random.randint(1,len(indc)/2)
except ValueError:
natomsmove=1
passn=0
for count in range(natomsmove):
try:
indexmv = random.choice([i for i in range(len(indc))])
indices, offsets = nl.get_neighbors(indexmv)
nns = Atoms()
nns.append(ind[indexmv])
for index, d in zip(indices,offsets):
index = int(index)
pos = ind[index].position + numpy.dot(d,ind.get_cell())
nns.append(Atom(symbol=ind[index].symbol, position=pos))
dist = [nns.get_distance(0,i) for i in range(1, len(nns))]
r = sum(dist)/len(dist)
dir = random.choice([[1,0,0],[-1,0,0],[0,1,0],[0,-1,0],[0,0,1],[0,0,-1]])
ind[indexmv].position += [i*r for i in dir]
except:
passn+=1
indiv[0]=ind.copy()
else:
natomsmove=0
passn=0
Optimizer.output.write('Lattice Alteration NN Mutation performed on individual\n')
Optimizer.output.write('Index = '+repr(indiv.index)+'\n')
natomsmove-=passn
Optimizer.output.write('Number of atoms moved = '+repr(natomsmove)+'\n')
Optimizer.output.write(repr(indiv[0])+'\n')
muttype='LANN'+repr(natomsmove)
if indiv.energy==0:
indiv.history_index=indiv.history_index+'m'+muttype
else:
indiv.history_index=repr(indiv.index)+'m'+muttype
return indiv
def newoverlap(wfs, spos_ac):
assert wfs.ksl.block_comm.size == wfs.gd.comm.size * wfs.bd.comm.size
even_part = EvenPartitioning(wfs.gd.comm, #wfs.ksl.block_comm,
len(wfs.atom_partition.rank_a))
atom_partition = even_part.as_atom_partition()
tci = wfs.tci
gd = wfs.gd
kd = wfs.kd
nq = len(kd.ibzk_qc)
# New neighbor list because we want it "both ways", heh. Or do we?
neighbors = NeighborList(tci.cutoff_a, skin=0,
sorted=True, self_interaction=True, bothways=False)
atoms = Atoms('X%d' % len(tci.cutoff_a), cell=gd.cell_cv, pbc=gd.pbc_c)
atoms.set_scaled_positions(spos_ac)
neighbors.update(atoms)
# XXX
pcutoff_a = []
phicutoff_a = []
for setup in wfs.setups:
if setup.pt_j:
pcutoff = max([pt.get_cutoff() for pt in setup.pt_j])
else:
pcutoff = 0.0
if setup.phit_j:
phicutoff = max([phit.get_cutoff() for phit in setup.phit_j])
else:
phicutoff = 0.0
pcutoff_a.append(pcutoff)
phicutoff_a.append(phicutoff)
# Calculate the projector--basis function overlaps:
#
# a1 ~a1
# P = < p | Phi > ,
# i mu i mu
#
# i.e. projector is on a1 and basis function is on what we will call a2.
overlapcalc = TwoCenterIntegralCalculator(wfs.kd.ibzk_qc,
derivative=False)
P_aaqim = {} # keys: (a1, a2). Values: matrix blocks
dists_and_offsets = DistsAndOffsets(neighbors, spos_ac, gd.cell_cv)
#ng = 2**extra_parameters.get('log2ng', 10)
#transformer = FourierTransformer(rcmax, ng)
#tsoc = TwoSiteOverlapCalculator(transformer)
#msoc = ManySiteOverlapCalculator(tsoc, I_a, I_a)
msoc = wfs.tci.msoc
phit_Ij = [setup.phit_j for setup in tci.setups_I]
l_Ij = []
for phit_j in phit_Ij:
l_Ij.append([phit.get_angular_momentum_number()
for phit in phit_j])
pt_l_Ij = [setup.l_j for setup in tci.setups_I]
pt_Ij = [setup.pt_j for setup in tci.setups_I]
phit_Ijq = msoc.transform(phit_Ij)
pt_Ijq = msoc.transform(pt_Ij)
#self.Theta_expansions = msoc.calculate_expansions(l_Ij, phit_Ijq,
# l_Ij, phit_Ijq)
#self.T_expansions = msoc.calculate_kinetic_expansions(l_Ij, phit_Ijq)
P_expansions = msoc.calculate_expansions(pt_l_Ij, pt_Ijq,
l_Ij, phit_Ijq)
P_neighbors_a = {}
for a1 in atom_partition.my_indices:
for a2 in range(len(wfs.setups)):
R_ca_and_offset_a = dists_and_offsets.get(a1, a2)
if R_ca_and_offset_a is None: # No overlap between a1 and a2
continue
maxdistance = pcutoff_a[a1] + phicutoff_a[a2]
expansion = P_expansions.get(a1, a2)
P_qim = expansion.zeros((nq,), dtype=wfs.dtype)
disp = None
for R_c, offset in R_ca_and_offset_a:
r = np.linalg.norm(R_c)
if r > maxdistance:
continue
# Below lines are meant to make use of symmetry. Will not
# be relevant for P.
#remainder = (a1 + a2) % 2
#if a1 < a2 and not remainder:
# continue
# if a1 > a2 and remainder:
# continue
phases = overlapcalc.phaseclass(overlapcalc.ibzk_qc, offset)
disp = AtomicDisplacement(None, a1, a2, R_c, offset, phases)
disp.evaluate_overlap(expansion, P_qim)
if disp is not None: # there was at least one non-zero overlap
assert (a1, a2) not in P_aaqim
P_aaqim[(a1, a2)] = P_qim
P_neighbors_a.setdefault(a1, []).append(a2)
Pkeys = P_aaqim.keys()
Pkeys.sort()
def get_M1M2(a):
M1 = wfs.setups.M_a[a]
M2 = M1 + wfs.setups[a].nao
return M1, M2
oldstyle_P_aqMi = None
if 0:#wfs.world.size == 1:
oldstyle_P_aqMi = {}
for a, setup in enumerate(wfs.setups):
oldstyle_P_aqMi[a] = np.zeros((nq, wfs.setups.nao, setup.ni),
dtype=wfs.dtype)
print([(s.ni, s.nao) for s in wfs.setups])
for a1, a2 in Pkeys:
M1, M2 = get_M1M2(a2)
Pconj_qmi = P_aaqim[(a1, a2)].transpose(0, 2, 1).conjugate()
oldstyle_P_aqMi[a1][:, M1:M2, :] = Pconj_qmi
# XXX mind distribution
return P_neighbors_a, P_aaqim, oldstyle_P_aqMi
class EAM(Calculator):
r"""
EAM Interface Documentation
Introduction
============
The Embedded Atom Method (EAM) [1]_ is a classical potential which is
good for modelling metals, particularly fcc materials. Because it is
an equiaxial potential the EAM does not model directional bonds
well. However, the Angular Dependent Potential (ADP) [2]_ which is an
extended version of EAM is able to model directional bonds and is also
included in the EAM calculator.
Generally all that is required to use this calculator is to supply a
potential file or as a set of functions that describe the potential.
The files containing the potentials for this calculator are not
included but many suitable potentials can be downloaded from The
Interatomic Potentials Repository Project at
http://www.ctcms.nist.gov/potentials/
Theory
======
A single element EAM potential is defined by three functions: the
embedded energy, electron density and the pair potential. A two
element alloy contains the individual three functions for each element
plus cross pair interactions. The ADP potential has two additional
sets of data to define the dipole and quadrupole directional terms for
each alloy and their cross interactions.
The total energy `E_{\rm tot}` of an arbitrary arrangement of atoms is
given by the EAM potential as
.. math::
E_{\rm tot} = \sum_i F(\bar\rho_i) + \frac{1}{2}\sum_{i\ne j} \phi(r_{ij})
and
.. math::
\bar\rho_i = \sum_j \rho(r_{ij})
where `F` is an embedding function, namely the energy to embed an atom `i` in
the combined electron density `\bar\rho_i` which is contributed from
each of its neighbouring atoms `j` by an amount `\rho(r_{ij})`,
`\phi(r_{ij})` is the pair potential function representing the energy
in bond `ij` which is due to the short-range electro-static
interaction between atoms, and `r_{ij}` is the distance between an
atom and its neighbour for that bond.
The ADP potential is defined as
.. math::
E_{\rm tot} = \sum_i F(\bar\rho_i) + \frac{1}{2}\sum_{i\ne j} \phi(r_{ij})
+ {1\over 2} \sum_{i,\alpha} (\mu_i^\alpha)^2
+ {1\over 2} \sum_{i,\alpha,\beta} (\lambda_i^{\alpha\beta})^2
- {1 \over 6} \sum_i \nu_i^2
where `\mu_i^\alpha` is the dipole vector, `\lambda_i^{\alpha\beta}`
is the quadrupole tensor and `\nu_i` is the trace of
`\lambda_i^{\alpha\beta}`.
Running the Calculator
======================
EAM calculates the cohesive atom energy and forces. Internally the
potential functions are defined by splines which may be directly
supplied or created by reading the spline points from a data file from
which a spline function is created. The LAMMPS compatible ``.alloy``
and ``.adp`` formats are supported. The LAMMPS ``.eam`` format is
slightly different from the ``.alloy`` format and is currently not
supported.
For example::
from ase.calculators.eam import EAM
mishin = EAM(potential='Al99.eam.alloy')
mishin.write_potential('new.eam.alloy')
mishin.plot()
slab.set_calculator(mishin)
slab.get_potential_energy()
slab.get_forces()
The breakdown of energy contribution from the indvidual components are
stored in the calculator instance ``.results['energy_components']``
Arguments
=========
========================= ====================================================
Keyword Description
========================= ====================================================
``potential`` file of potential in ``.alloy`` or ``.adp`` format
(This is generally all you need to supply)
``elements[N]`` array of N element abbreviations
``embedded_energy[N]`` arrays of embedded energy functions
``electron_density[N]`` arrays of electron density functions
``phi[N,N]`` arrays of pair potential functions
``d_embedded_energy[N]`` arrays of derivative embedded energy functions
``d_electron_density[N]`` arrays of derivative electron density functions
``d_phi[N,N]`` arrays of derivative pair potentials functions
``d[N,N], q[N,N]`` ADP dipole and quadrupole function
``d_d[N,N], d_q[N,N]`` ADP dipole and quadrupole derivative functions
``skin`` skin distance passed to NeighborList(). If no atom
has moved more than the skin-distance since the last
call to the ``update()`` method then the neighbor
list can be reused. Defaults to 1.0.
``form`` the form of the potential ``alloy`` or ``adp``. This
will be determined from the file suffix or must be
set if using equations
========================= ====================================================
Additional parameters for writing potential files
=================================================
The following parameters are only required for writing a potential in
``.alloy`` or ``.adp`` format file.
========================= ====================================================
Keyword Description
========================= ====================================================
``header`` Three line text header. Default is standard message.
``Z[N]`` Array of atomic number of each element
``mass[N]`` Atomic mass of each element
``a[N]`` Array of lattice parameters for each element
``lattice[N]`` Lattice type
``nrho`` No. of rho samples along embedded energy curve
``drho`` Increment for sampling density
``nr`` No. of radial points along density and pair
potential curves
``dr`` Increment for sampling radius
========================= ====================================================
Special features
================
``.plot()``
Plots the individual functions. This may be called from multiple EAM
potentials to compare the shape of the individual curves. This
function requires the installation of the Matplotlib libraries.
Notes/Issues
=============
* Although currently not fast, this calculator can be good for trying
small calculations or for creating new potentials by matching baseline
data such as from DFT results. The format for these potentials is
compatible with LAMMPS_ and so can be used either directly by LAMMPS or
with the ASE LAMMPS calculator interface.
* Supported formats are the LAMMPS_ ``.alloy`` and ``.adp``. The
``.eam`` format is currently not supported. The form of the
potential will be determined from the file suffix.
* Any supplied values will override values read from the file.
* The derivative functions, if supplied, are only used to calculate
forces.
* There is a bug in early versions of scipy that will cause eam.py to
crash when trying to evaluate splines of a potential with one
neighbor such as caused by evaluating a dimer.
.. _LAMMPS: http://lammps.sandia.gov/
.. [1] M.S. Daw and M.I. Baskes, Phys. Rev. Letters 50 (1983)
1285.
.. [2] Y. Mishin, M.J. Mehl, and D.A. Papaconstantopoulos,
Acta Materialia 53 2005 4029--4041.
End EAM Interface Documentation
"""
implemented_properties = ["energy", "forces"]
default_parameters = dict(
skin=1.0, potential=None, header="""EAM/ADP potential file\nGenerated from eam.py\nblank\n"""
)
def __init__(self, restart=None, ignore_bad_restart_file=False, label=os.curdir, atoms=None, **kwargs):
if "potential" in kwargs:
self.read_potential(kwargs["potential"])
Calculator.__init__(self, restart, ignore_bad_restart_file, label, atoms, **kwargs)
valid_args = (
"potential",
"elements",
"header",
"drho",
"dr",
"cutoff",
"atomic_number",
"mass",
"a",
"lattice",
"embedded_energy",
"electron_density",
"phi",
# derivatives
"d_embedded_energy",
"d_electron_density",
"d_phi",
"d",
"q",
"d_d",
"d_q", # adp terms
"skin",
"form",
"Z",
"nr",
"nrho",
"mass",
)
# set any additional keyword arguments
for arg, val in self.parameters.iteritems():
if arg in valid_args:
setattr(self, arg, val)
else:
raise RuntimeError('unknown keyword arg "%s" : not in %s' % (arg, valid_args))
def set_form(self, fileobj):
"""set the form variable based on the file name suffix"""
extension = os.path.splitext(fileobj)[1]
if extension == ".eam":
self.form = "eam"
raise NotImplementedError
elif extension == ".alloy":
self.form = "alloy"
elif extension == ".adp":
self.form = "adp"
else:
raise RuntimeError("unknown file extension type: %s" % extension)
def read_potential(self, fileobj):
"""Reads a LAMMPS EAM file in alloy or adp format
and creates the interpolation functions from the data
"""
if isinstance(fileobj, str):
f = open(fileobj)
self.set_form(fileobj)
else:
f = fileobj
lines = f.readlines()
self.header = lines[:3]
i = 3
# make the data one long line so as not to care how its formatted
data = []
for line in lines[i:]:
data.extend(line.split())
self.Nelements = int(data[0])
d = 1
self.elements = data[d : (d + self.Nelements)]
d += self.Nelements
self.nrho = int(data[d])
self.drho = float(data[d + 1])
self.nr = int(data[d + 2])
self.dr = float(data[d + 3])
self.cutoff = float(data[d + 4])
self.embedded_data = np.zeros([self.Nelements, self.nrho])
self.density_data = np.zeros([self.Nelements, self.nr])
self.Z = np.zeros([self.Nelements], dtype=int)
self.mass = np.zeros([self.Nelements])
self.a = np.zeros([self.Nelements])
self.lattice = []
d += 5
# reads in the part of the eam file for each element
for elem in range(self.Nelements):
self.Z[elem] = int(data[d])
self.mass[elem] = float(data[d + 1])
self.a[elem] = float(data[d + 2])
self.lattice.append(data[d + 3])
d += 4
self.embedded_data[elem] = np.float_(data[d : (d + self.nrho)])
d += self.nrho
self.density_data[elem] = np.float_(data[d : (d + self.nr)])
d += self.nr
# reads in the r*phi data for each interaction between elements
self.rphi_data = np.zeros([self.Nelements, self.Nelements, self.nr])
for i in range(self.Nelements):
for j in range(i + 1):
self.rphi_data[j, i] = np.float_(data[d : (d + self.nr)])
d += self.nr
self.r = np.arange(0, self.nr) * self.dr
self.rho = np.arange(0, self.nrho) * self.drho
self.set_splines()
if self.form == "adp":
self.read_adp_data(data, d)
self.set_adp_splines()
def set_splines(self):
# this section turns the file data into three functions (and
# derivative functions) that define the potential
self.embedded_energy = np.empty(self.Nelements, object)
self.electron_density = np.empty(self.Nelements, object)
self.d_embedded_energy = np.empty(self.Nelements, object)
self.d_electron_density = np.empty(self.Nelements, object)
for i in range(self.Nelements):
self.embedded_energy[i] = spline(self.rho, self.embedded_data[i], k=3)
self.electron_density[i] = spline(self.r, self.density_data[i], k=3)
self.d_embedded_energy[i] = self.deriv(self.embedded_energy[i])
self.d_electron_density[i] = self.deriv(self.electron_density[i])
self.phi = np.empty([self.Nelements, self.Nelements], object)
self.d_phi = np.empty([self.Nelements, self.Nelements], object)
# ignore the first point of the phi data because it is forced
# to go through zero due to the r*phi format in alloy and adp
for i in range(self.Nelements):
for j in range(i, self.Nelements):
if self.form == "eam": # not stored as rphi
# should we ignore the first point for eam ?
raise RuntimeError(".eam format not yet supported")
self.phi[i, j] = spline(self.r[1:], self.rphi_data[i, j][1:], k=3)
else:
self.phi[i, j] = spline(self.r[1:], self.rphi_data[i, j][1:] / self.r[1:], k=3)
self.d_phi[i, j] = self.deriv(self.phi[i, j])
if j != i:
self.phi[j, i] = self.phi[i, j]
self.d_phi[j, i] = self.d_phi[i, j]
def set_adp_splines(self):
self.d = np.empty([self.Nelements, self.Nelements], object)
self.d_d = np.empty([self.Nelements, self.Nelements], object)
self.q = np.empty([self.Nelements, self.Nelements], object)
self.d_q = np.empty([self.Nelements, self.Nelements], object)
for i in range(self.Nelements):
for j in range(i, self.Nelements):
self.d[i, j] = spline(self.r[1:], self.d_data[i, j][1:], k=3)
self.d_d[i, j] = self.deriv(self.d[i, j])
self.q[i, j] = spline(self.r[1:], self.q_data[i, j][1:], k=3)
self.d_q[i, j] = self.deriv(self.q[i, j])
# make symmetrical
if j != i:
self.d[j, i] = self.d[i, j]
self.d_d[j, i] = self.d_d[i, j]
self.q[j, i] = self.q[i, j]
self.d_q[j, i] = self.d_q[i, j]
def read_adp_data(self, data, d):
"""read in the extra adp data from the potential file"""
self.d_data = np.zeros([self.Nelements, self.Nelements, self.nr])
# should be non symetrical combinations of 2
for i in range(self.Nelements):
for j in range(i + 1):
self.d_data[j, i] = data[d : d + self.nr]
d += self.nr
self.q_data = np.zeros([self.Nelements, self.Nelements, self.nr])
# should be non symetrical combinations of 2
for i in range(self.Nelements):
for j in range(i + 1):
self.q_data[j, i] = data[d : d + self.nr]
d += self.nr
def write_potential(self, filename, nc=1, numformat="%.8e"):
"""Writes out the potential in the format given by the form
variable to 'filename' with a data format that is nc columns
wide. Note: array lengths need to be an exact multiple of nc
"""
f = open(filename, "w")
assert self.nr % nc == 0
assert self.nrho % nc == 0
for line in self.header:
f.write(line)
f.write("%d " % self.Nelements)
for i in range(self.Nelements):
f.write("%s " % str(self.elements[i]))
f.write("\n")
f.write("%d %f %d %f %f \n" % (self.nrho, self.drho, self.nr, self.dr, self.cutoff))
# start of each section for each element
# rs = np.linspace(0, self.nr * self.dr, self.nr)
# rhos = np.linspace(0, self.nrho * self.drho, self.nrho)
rs = np.arange(0, self.nr) * self.dr
rhos = np.arange(0, self.nrho) * self.drho
for i in range(self.Nelements):
f.write("%d %f %f %s\n" % (self.Z[i], self.mass[i], self.a[i], str(self.lattice[i])))
np.savetxt(f, self.embedded_energy[i](rhos).reshape(self.nrho / nc, nc), fmt=nc * [numformat])
np.savetxt(f, self.electron_density[i](rs).reshape(self.nr / nc, nc), fmt=nc * [numformat])
# write out the pair potentials in Lammps DYNAMO setfl format
# as r*phi for alloy format
for i in range(self.Nelements):
for j in range(i, self.Nelements):
np.savetxt(f, (rs * self.phi[i, j](rs)).reshape(self.nr / nc, nc), fmt=nc * [numformat])
if self.form == "adp":
# these are the u(r) or dipole values
for i in range(self.Nelements):
for j in range(i + 1):
np.savetxt(f, self.d_data[i, j])
# these are the w(r) or quadrupole values
for i in range(self.Nelements):
for j in range(i + 1):
np.savetxt(f, self.q_data[i, j])
f.close()
def update(self, atoms):
# check all the elements are available in the potential
self.Nelements = len(self.elements)
elements = np.unique(atoms.get_chemical_symbols())
unavailable = np.logical_not(np.array([item in self.elements for item in elements]))
if np.any(unavailable):
raise RuntimeError("These elements are not in the potential: %s" % elements[unavailable])
# cutoffs need to be a vector for NeighborList
cutoffs = self.cutoff * np.ones(len(atoms))
# convert the elements to an index of the position
# in the eam format
self.index = np.array([self.elements.index(el) for el in atoms.get_chemical_symbols()])
self.pbc = atoms.get_pbc()
# since we need the contribution of all neighbors to the
# local electron density we cannot just calculate and use
# one way neighbors
self.neighbors = NeighborList(cutoffs, skin=self.parameters.skin, self_interaction=False, bothways=True)
self.neighbors.update(atoms)
def calculate(self, atoms=None, properties=["energy"], system_changes=all_changes):
"""EAM Calculator
atoms: Atoms object
Contains positions, unit-cell, ...
properties: list of str
List of what needs to be calculated. Can be any combination
of 'energy', 'forces'
system_changes: list of str
List of what has changed since last calculation. Can be
any combination of these five: 'positions', 'numbers', 'cell',
'pbc', 'initial_charges' and 'initial_magmoms'.
"""
Calculator.calculate(self, atoms, properties, system_changes)
# we shouldn't really recalc if charges or magmos change
if len(system_changes) > 0: # something wrong with this way
self.update(self.atoms)
self.calculate_energy(self.atoms)
if "forces" in properties:
self.calculate_forces(self.atoms)
# check we have all the properties requested
for property in properties:
if property not in self.results:
if property is "energy":
self.calculate_energy(self.atoms)
if property is "forces":
self.calculate_forces(self.atoms)
# we need to remember the previous state of parameters
# if 'potential' in parameter_changes and potential != None:
# self.read_potential(potential)
def calculate_energy(self, atoms):
"""Calculate the energy
the energy is made up of the ionic or pair interaction and
the embedding energy of each atom into the electron cloud
generated by its neighbors
"""
pair_energy = 0.0
embedding_energy = 0.0
mu_energy = 0.0
lam_energy = 0.0
trace_energy = 0.0
self.total_density = np.zeros(len(atoms))
if self.form == "adp":
self.mu = np.zeros([len(atoms), 3])
self.lam = np.zeros([len(atoms), 3, 3])
for i in range(len(atoms)): # this is the atom to be embedded
neighbors, offsets = self.neighbors.get_neighbors(i)
offset = np.dot(offsets, atoms.get_cell())
rvec = atoms.positions[neighbors] + offset - atoms.positions[i]
## calculate the distance to the nearest neighbors
r = np.sqrt(np.sum(np.square(rvec), axis=1)) # fast
# r = np.apply_along_axis(np.linalg.norm, 1, rvec) # sloow
nearest = np.arange(len(r))[r <= self.cutoff]
for j_index in range(self.Nelements):
use = self.index[neighbors[nearest]] == j_index
if not use.any():
continue
pair_energy += np.sum(self.phi[self.index[i], j_index](r[nearest][use])) / 2.0
density = np.sum(self.electron_density[j_index](r[nearest][use]))
self.total_density[i] += density
if self.form == "adp":
self.mu[i] += self.adp_dipole(r[nearest][use], rvec[nearest][use], self.d[self.index[i], j_index])
self.lam[i] += self.adp_quadrupole(
r[nearest][use], rvec[nearest][use], self.q[self.index[i], j_index]
)
# add in the electron embedding energy
embedding_energy += self.embedded_energy[self.index[i]](self.total_density[i])
components = dict(pair=pair_energy, embedding=embedding_energy)
if self.form == "adp":
mu_energy += np.sum(self.mu ** 2) / 2.0
lam_energy += np.sum(self.lam ** 2) / 2.0
for i in range(len(atoms)): # this is the atom to be embedded
trace_energy -= np.sum(self.lam[i].trace() ** 2) / 6.0
adp_result = dict(adp_mu=mu_energy, adp_lam=lam_energy, adp_trace=trace_energy)
components.update(adp_result)
self.positions = atoms.positions.copy()
self.cell = atoms.get_cell().copy()
energy = 0.0
for i in components.keys():
energy += components[i]
self.energy_free = energy
self.energy_zero = energy
self.results["energy_components"] = components
self.results["energy"] = energy
def calculate_forces(self, atoms):
# calculate the forces based on derivatives of the three EAM functions
self.update(atoms)
self.results["forces"] = np.zeros((len(atoms), 3))
for i in range(len(atoms)): # this is the atom to be embedded
neighbors, offsets = self.neighbors.get_neighbors(i)
offset = np.dot(offsets, atoms.get_cell())
# create a vector of relative positions of neighbors
rvec = atoms.positions[neighbors] + offset - atoms.positions[i]
r = np.sqrt(np.sum(np.square(rvec), axis=1))
nearest = np.arange(len(r))[r < self.cutoff]
d_embedded_energy_i = self.d_embedded_energy[self.index[i]](self.total_density[i])
urvec = rvec.copy() # unit directional vector
for j in np.arange(len(neighbors)):
urvec[j] = urvec[j] / r[j]
for j_index in range(self.Nelements):
use = self.index[neighbors[nearest]] == j_index
if not use.any():
continue
rnuse = r[nearest][use]
density_j = self.total_density[neighbors[nearest][use]]
scale = (
self.d_phi[self.index[i], j_index](rnuse)
+ (d_embedded_energy_i * self.d_electron_density[j_index](rnuse))
+ (self.d_embedded_energy[j_index](density_j) * self.d_electron_density[self.index[i]](rnuse))
)
self.results["forces"][i] += np.dot(scale, urvec[nearest][use])
if self.form == "adp":
adp_forces = self.angular_forces(
self.mu[i],
self.mu[neighbors[nearest][use]],
self.lam[i],
self.lam[neighbors[nearest][use]],
rnuse,
rvec[nearest][use],
self.index[i],
j_index,
)
self.results["forces"][i] += adp_forces
def angular_forces(self, mu_i, mu, lam_i, lam, r, rvec, form1, form2):
# calculate the extra components for the adp forces
# rvec are the relative positions to atom i
psi = np.zeros(mu.shape)
for gamma in range(3):
term1 = (mu_i[gamma] - mu[:, gamma]) * self.d[form1][form2](r)
term2 = np.sum(
(mu_i - mu)
* self.d_d[form1][form2](r)[:, np.newaxis]
* (rvec * rvec[:, gamma][:, np.newaxis] / r[:, np.newaxis]),
axis=1,
)
term3 = 2 * np.sum(
(lam_i[:, gamma] + lam[:, :, gamma]) * rvec * self.q[form1][form2](r)[:, np.newaxis], axis=1
)
term4 = 0.0
for alpha in range(3):
for beta in range(3):
rs = rvec[:, alpha] * rvec[:, beta] * rvec[:, gamma]
term4 += ((lam_i[alpha, beta] + lam[:, alpha, beta]) * self.d_q[form1][form2](r) * rs) / r
term5 = (
(lam_i.trace() + lam.trace(axis1=1, axis2=2))
* (self.d_q[form1][form2](r) * r + 2 * self.q[form1][form2](r))
* rvec[:, gamma]
) / 3.0
# the minus for term5 is a correction on the adp
# formulation given in the 2005 Mishin Paper and is posted
# on the NIST website with the AlH potential
psi[:, gamma] = term1 + term2 + term3 + term4 - term5
return np.sum(psi, axis=0)
def adp_dipole(self, r, rvec, d):
# calculate the dipole contribution
mu = np.sum((rvec * d(r)[:, np.newaxis]), axis=0)
return mu # sign to agree with lammps
def adp_quadrupole(self, r, rvec, q):
# slow way of calculating the quadrupole contribution
r = np.sqrt(np.sum(rvec ** 2, axis=1))
lam = np.zeros([rvec.shape[0], 3, 3])
qr = q(r)
for alpha in range(3):
for beta in range(3):
lam[:, alpha, beta] += qr * rvec[:, alpha] * rvec[:, beta]
return np.sum(lam, axis=0)
def deriv(self, spline):
"""Wrapper for extracting the derivative from a spline"""
def d_spline(aspline):
return spline(aspline, 1)
return d_spline
def plot(self, name=""):
"""Plot the individual curves"""
try:
import matplotlib.pyplot as plt
except ImportError:
raise NotAvailable("This needs matplotlib module.")
if self.form == "eam" or self.form == "alloy":
nrow = 2
elif self.form == "adp":
nrow = 3
else:
raise RuntimeError("Unknown form of potential: %s" % self.form)
if hasattr(self, "r"):
r = self.r
else:
r = np.linspace(0, self.cutoff, 50)
if hasattr(self, "rho"):
rho = self.rho
else:
rho = np.linspace(0, 10.0, 50)
plt.subplot(nrow, 2, 1)
self.elem_subplot(rho, self.embedded_energy, r"$\rho$", r"Embedding Energy $F(\bar\rho)$", name, plt)
plt.subplot(nrow, 2, 2)
self.elem_subplot(r, self.electron_density, r"$r$", r"Electron Density $\rho(r)$", name, plt)
plt.subplot(nrow, 2, 3)
self.multielem_subplot(r, self.phi, r"$r$", r"Pair Potential $\phi(r)$", name, plt)
plt.ylim(-1.0, 1.0) # need reasonable values
if self.form == "adp":
plt.subplot(nrow, 2, 5)
self.multielem_subplot(r, self.d, r"$r$", r"Dipole Energy", name, plt)
plt.subplot(nrow, 2, 6)
self.multielem_subplot(r, self.q, r"$r$", r"Quadrupole Energy", name, plt)
plt.plot()
def elem_subplot(self, curvex, curvey, xlabel, ylabel, name, plt):
plt.xlabel(xlabel)
plt.ylabel(ylabel)
for i in np.arange(self.Nelements):
label = name + " " + self.elements[i]
plt.plot(curvex, curvey[i](curvex), label=label)
plt.legend()
def multielem_subplot(self, curvex, curvey, xlabel, ylabel, name, plt):
plt.xlabel(xlabel)
plt.ylabel(ylabel)
for i in np.arange(self.Nelements):
for j in np.arange(i + 1):
label = name + " " + self.elements[i] + "-" + self.elements[j]
plt.plot(curvex, curvey[i, j](curvex), label=label)
plt.legend()
def check_min_dist(Optimizer, totalsol, type='Defect', nat=None, min_len=0.7, STR=''):
if type=='Defect' or type=='Crystal' or type=='Surface':
if nat==None:
nat=len(totalsol)
cutoffs=[2.0 for one in totalsol]
nl=NeighborList(cutoffs,bothways=True,self_interaction=False)
nl.update(totalsol)
for one in totalsol[0:nat]:
nbatoms=Atoms()
nbatoms.append(one)
indices, offsets=nl.get_neighbors(one.index)
for index, d in zip(indices,offsets):
index = int(index)
sym=totalsol[index].symbol
pos=totalsol[index].position + numpy.dot(d,totalsol.get_cell())
at=Atom(symbol=sym,position=pos)
nbatoms.append(at)
while True:
dflag=False
for i in range(1,len(nbatoms)):
d=nbatoms.get_distance(0,i)
if d < min_len:
nbatoms.set_distance(0,i,min_len+.01,fix=0.5)
STR+='--- WARNING: Atoms too close (<0.7A) - Implement Move ---\n'
dflag=True
if dflag==False:
break
for i in range(len(indices)):
totalsol[indices[i]].position=nbatoms[i+1].position
totalsol[one.index].position=nbatoms[0].position
nl.update(totalsol)
elif type=='Cluster':
if not 'LAMMPS' in Optimizer.modules:
for i in range(len(totalsol)):
for j in range(len(totalsol)):
if i != j:
d=totalsol.get_distance(i,j)
if d < min_len:
totalsol.set_distance(i,j,min_len,fix=0.5)
STR+='--- WARNING: Atoms too close (<0.7A) - Implement Move ---\n'
else:
rank = MPI.COMM_WORLD.Get_rank()
#logger = logging.getLogger(Optimizer.loggername)
R = totalsol.arrays['positions']
tol = 0.01
epsilon = 0.05
fix = 0.5
closelist = numpy.arange(len(totalsol))
iter = 0
while len(closelist) > 0 and iter<2:
iter+=1
closelist = []
dist=spatial.distance.cdist(R,R)
numpy.fill_diagonal(dist,1.0)
smalldist = numpy.where(dist < min_len-tol)
for ind in range(len(smalldist[0])):
i = smalldist[0][ind]
j = smalldist[1][ind]
if i < j and dist[i][j] < min_len-tol:
closelist.append(i)
closelist.append(j)
if dist[i][j] > epsilon:
x = 1.0 - min_len / dist[i][j]
D = R[j]-R[i]
R[i] += (x * fix) * D
R[j] -= (x * (1.0 - fix)) * D
else:
R[i] += [0.2, 0.0, 0.0]
R[j] -= [0.2, 0.0, 0.0]
R2P = [R[i],R[j]]
dist2P=spatial.distance.cdist(R2P,R)
dist[i] = dist2P[0]
dist[j] = dist2P[1]
for k in range(len(R)):
dist[k][i] = dist[i][k]
dist[k][j] = dist[j][k]
closelist=list(set(closelist))
closelist.sort()
#if len(closelist) != 0:
# logger.info('M:iter {0}, closelist size {1}'.format(iter,len(closelist)))
else:
print 'WARNING: In Check_Min_Dist in EvalEnergy: Structure Type not recognized'
return totalsol, STR
def newoverlap(wfs, spos_ac):
assert wfs.ksl.block_comm.size == wfs.gd.comm.size * wfs.bd.comm.size
even_part = EvenPartitioning(
wfs.gd.comm, #wfs.ksl.block_comm,
len(wfs.atom_partition.rank_a))
atom_partition = even_part.as_atom_partition()
tci = wfs.tci
gd = wfs.gd
kd = wfs.kd
nq = len(kd.ibzk_qc)
# New neighbor list because we want it "both ways", heh. Or do we?
neighbors = NeighborList(tci.cutoff_a,
skin=0,
sorted=True,
self_interaction=True,
bothways=False)
atoms = Atoms('X%d' % len(tci.cutoff_a), cell=gd.cell_cv, pbc=gd.pbc_c)
atoms.set_scaled_positions(spos_ac)
neighbors.update(atoms)
# XXX
pcutoff_a = []
phicutoff_a = []
for setup in wfs.setups:
if setup.pt_j:
pcutoff = max([pt.get_cutoff() for pt in setup.pt_j])
else:
pcutoff = 0.0
if setup.phit_j:
phicutoff = max([phit.get_cutoff() for phit in setup.phit_j])
else:
phicutoff = 0.0
pcutoff_a.append(pcutoff)
phicutoff_a.append(phicutoff)
# Calculate the projector--basis function overlaps:
#
# a1 ~a1
# P = < p | Phi > ,
# i mu i mu
#
# i.e. projector is on a1 and basis function is on what we will call a2.
overlapcalc = TwoCenterIntegralCalculator(wfs.kd.ibzk_qc, derivative=False)
P_aaqim = {} # keys: (a1, a2). Values: matrix blocks
dists_and_offsets = DistsAndOffsets(neighbors, spos_ac, gd.cell_cv)
#ng = 2**extra_parameters.get('log2ng', 10)
#transformer = FourierTransformer(rcmax, ng)
#tsoc = TwoSiteOverlapCalculator(transformer)
#msoc = ManySiteOverlapCalculator(tsoc, I_a, I_a)
msoc = wfs.tci.msoc
phit_Ij = [setup.phit_j for setup in tci.setups_I]
l_Ij = []
for phit_j in phit_Ij:
l_Ij.append([phit.get_angular_momentum_number() for phit in phit_j])
pt_l_Ij = [setup.l_j for setup in tci.setups_I]
pt_Ij = [setup.pt_j for setup in tci.setups_I]
phit_Ijq = msoc.transform(phit_Ij)
pt_Ijq = msoc.transform(pt_Ij)
#self.Theta_expansions = msoc.calculate_expansions(l_Ij, phit_Ijq,
# l_Ij, phit_Ijq)
#self.T_expansions = msoc.calculate_kinetic_expansions(l_Ij, phit_Ijq)
P_expansions = msoc.calculate_expansions(pt_l_Ij, pt_Ijq, l_Ij, phit_Ijq)
P_neighbors_a = {}
for a1 in atom_partition.my_indices:
for a2 in range(len(wfs.setups)):
R_ca_and_offset_a = dists_and_offsets.get(a1, a2)
if R_ca_and_offset_a is None: # No overlap between a1 and a2
continue
maxdistance = pcutoff_a[a1] + phicutoff_a[a2]
expansion = P_expansions.get(a1, a2)
P_qim = expansion.zeros((nq, ), dtype=wfs.dtype)
disp = None
for R_c, offset in R_ca_and_offset_a:
r = np.linalg.norm(R_c)
if r > maxdistance:
continue
# Below lines are meant to make use of symmetry. Will not
# be relevant for P.
#remainder = (a1 + a2) % 2
#if a1 < a2 and not remainder:
# continue
# if a1 > a2 and remainder:
# continue
phases = overlapcalc.phaseclass(overlapcalc.ibzk_qc, offset)
disp = AtomicDisplacement(None, a1, a2, R_c, offset, phases)
disp.evaluate_overlap(expansion, P_qim)
if disp is not None: # there was at least one non-zero overlap
assert (a1, a2) not in P_aaqim
P_aaqim[(a1, a2)] = P_qim
P_neighbors_a.setdefault(a1, []).append(a2)
Pkeys = P_aaqim.keys()
Pkeys.sort()
def get_M1M2(a):
M1 = wfs.setups.M_a[a]
M2 = M1 + wfs.setups[a].nao
return M1, M2
oldstyle_P_aqMi = None
if 0: #wfs.world.size == 1:
oldstyle_P_aqMi = {}
for a, setup in enumerate(wfs.setups):
oldstyle_P_aqMi[a] = np.zeros((nq, wfs.setups.nao, setup.ni),
dtype=wfs.dtype)
print([(s.ni, s.nao) for s in wfs.setups])
for a1, a2 in Pkeys:
M1, M2 = get_M1M2(a2)
Pconj_qmi = P_aaqim[(a1, a2)].transpose(0, 2, 1).conjugate()
oldstyle_P_aqMi[a1][:, M1:M2, :] = Pconj_qmi
# XXX mind distribution
return P_neighbors_a, P_aaqim, oldstyle_P_aqMi
def create_stucture(ratio, width, edge, key = 'top', a = 1.42):
vacuum = 10
length = get_length(ratio, width, edge)
length_b= int(length * .8)*2
width_b = width * 4
if edge == 'zz':
orig = [np.sqrt(3)*a, 2*a] # -> AB-stacking
b_l, b_w= 4, 3*width
if width % 2 == 1: raise
if edge == 'ac':
orig = [2*a, np.sqrt(3)*a] # -> AB-stacking
b_l, b_w= 2, 3*width
if width % 2 == 0: raise
bottom = graphene_nanoribbon2(length_b, width_b, edge_type=edge,
saturated=False,
C_H=1.09,
C_C=a,
vacuum=2.5,
sheet=False,
main_element='C',
saturate_element='H')
top = graphene_nanoribbon2(length, width, edge_type=edge,
saturated=True,
C_H=1.09,
C_C=a,
vacuum=2.5,
sheet=False,
main_element='C',
saturate_element='H')
base = graphene_nanoribbon2(b_l, b_w, edge_type=edge,
saturated=True,
C_H=1.09,
C_C=a,
vacuum=2.5,
sheet=False,
main_element='C',
saturate_element='H')
if key == 'top_bottom':
top.translate([orig[0],orig[1],3.4])
atoms = bottom
atoms.extend(top)
atoms.cell = [bottom.cell[0,0], bottom.cell[1,1], 2 * vacuum + 3.4]
atoms.center()
atoms.pbc = [True, True, False]
#view(atoms)
return atoms
if key == 'top':
atoms = top
L, W = top.cell[0,0], top.cell[1,1]
atoms.cell = [top.cell[0,0]*1.5, 2*top.cell[0,0] + top.cell[1,1], 2 * vacuum]
atoms.center()
atoms.positions[:,2] = 3.4
atoms.pbc = [False, False, False]
return atoms, L, W, length, None
if key == 'rib+base':
if edge == 'zz': base.translate([-base.cell[0,0], -base.cell[1,1]/3 ,0])
if edge == 'ac': base.translate([-base.cell[0,0], -base.cell[1,1]/3 + np.sqrt(3) / 2. * a,0])
atoms = top + base
rads = np.ones(len(atoms))*.3
nl = NeighborList(rads, self_interaction=False,
bothways=True)
nl.update(atoms)
coll = []
for i, atom in enumerate(atoms):
if atom.number == 1:
if 1 < len(nl.get_neighbors(i)[0]):
for j in nl.get_neighbors(i)[0]:
if atoms.numbers[j] == 1:
coll.append(j)
del atoms[coll]
atoms_base = []
for i, atom in enumerate(atoms):
if atom.position[0] < 0:
atoms_base.append(i)
rads = np.ones(len(atoms))*.7
nl = NeighborList(rads, self_interaction=False,
bothways=True)
nl.update(atoms)
new_pos = []
for i, atom in enumerate(atoms):
if len(nl.get_neighbors(i)[0]) == 2 and atom.number == 6 and i not in atoms_base:
pos = np.zeros(3)
for j in nl.get_neighbors(i)[0]:
pos += atoms.positions[j] - atoms.positions[i]
if atoms.numbers[j] != 6: raise
new_pos.append(atoms.positions[i] - pos)
for pos in new_pos:
atoms += Atom('C', position = pos)
rads = np.ones(len(atoms))*.7
nl = NeighborList(rads, self_interaction=False,
bothways=True)
nl.update(atoms)
h_pos = []
for i, atom in enumerate(atoms):
if len(nl.get_neighbors(i)[0]) == 2 and atom.number == 6:
pos = np.zeros(3)
for j in nl.get_neighbors(i)[0]:
pos += atoms.positions[j] - atoms.positions[i]
if atoms.numbers[j] != 6: raise
pos = pos/np.linalg.norm(pos)
h_pos.append(atoms.positions[i] - pos)
for pos in h_pos:
atoms += Atom('H', position = pos)
L, W = top.cell[0,0], top.cell[1,1]
atoms.cell = [top.cell[0,0]*1.5, 2*top.cell[0,0] + top.cell[1,1], 2 * vacuum]
atoms.center()
atoms.positions[:,2] = 3.4
atoms.pbc = [False, False, False]
return atoms, L, W, length, atoms_base
def newclus(ind1, ind2, Optimizer):
"""Select a box in the cluster configuration"""
if 'CX' in Optimizer.debug:
debug = True
else:
debug = False
Optimizer.output.write('Box Cluster Cx between individual ' +
repr(ind1.index) + ' and individual ' +
repr(ind2.index) + '\n')
#Perserve starting conditions of individual
solid1 = ind1[0].copy()
solid2 = ind2[0].copy()
cello1 = ind1[0].get_cell()
cello2 = ind2[0].get_cell()
cell1 = numpy.maximum.reduce(solid1.get_positions())
cell1m = numpy.minimum.reduce(solid1.get_positions())
cell2 = numpy.maximum.reduce(solid2.get_positions())
cell2m = numpy.minimum.reduce(solid2.get_positions())
cell = numpy.minimum(cell1, cell2)
pbc1 = solid1.get_pbc()
pbc2 = solid2.get_pbc()
#Get starting concentrations and number of atoms
nat1 = len(solid1)
nat2 = len(solid2)
# Pick a origin point for box in the cell
pt1 = random.choice(solid1)
pt1f = [(pt1.position[i] - cell1m[i]) / cell1[i] for i in range(3)]
pt2 = [pt1f[i] * cell2[i] + cell2m[i] for i in range(3)]
solid2.append(Atom(position=pt2))
pt2 = solid2[len(solid2) - 1]
#Find max neighborsize of circle cut
r = random.uniform(0, min(nat1, nat2) / 5.0)
if debug:
print 'DEBUG CX: Point one =', pt1.position
print 'DEBUG CX: Point two =', pt2.position
#Find atoms within sphere of neighborsize r for both individuals
#Make sure that crossover is only selection of atoms not all
while True:
ctoff = [r for on in solid1]
nl = NeighborList(ctoff, bothways=True, self_interaction=False)
nl.update(solid1)
indices1, offsets = nl.get_neighbors(pt1.index)
if len(indices1) == 0:
r = r * 1.2
elif len(indices1) < nat1 * .75:
break
else:
r = r * 0.8
if debug:
print 'Neighborsize of box = ' + repr(
r) + '\nPosition in solid1 = ' + repr(
pt1.position) + '\nPosition in solid2 = ' + repr(pt2.position)
group1 = Atoms(cell=solid1.get_cell(), pbc=solid1.get_pbc())
group1.append(pt1)
indices1a = [pt1.index]
for index, d in zip(indices1, offsets):
if index not in indices1a:
index = int(index)
pos = solid1[index].position + numpy.dot(d, solid1.get_cell())
group1.append(Atom(symbol=solid1[index].symbol, position=pos))
indices1a.append(index)
indices1 = indices1a
ctoff = [r for on in solid2]
nl = NeighborList(ctoff, bothways=True, self_interaction=False)
nl.update(solid2)
indices2, offsets = nl.get_neighbors(pt2.index)
group2 = Atoms(cell=solid2.get_cell(), pbc=solid2.get_pbc())
indices2a = []
for index, d in zip(indices2, offsets):
if index not in indices2a:
index = int(index)
pos = solid2[index].position + numpy.dot(d, solid2.get_cell())
group2.append(Atom(symbol=solid2[index].symbol, position=pos))
indices2a.append(index)
indices2 = indices2a
if len(indices2) == 0:
for one in group1:
while True:
sel = random.choice(solid2)
if sel.symbol == one.symbol:
if sel.index not in indices2:
group2.append(sel)
indices2.append(sel.index)
break
if Optimizer.forcing == 'Concentration':
symlist = list(set(group1.get_chemical_symbols()))
seplist = [[atm for atm in group2 if atm.symbol == sym]
for sym in symlist]
group2n = Atoms(cell=group2.get_cell(), pbc=group2.get_pbc())
indices2n = []
dellist = []
for one in group1:
sym1 = one.symbol
listpos = [i for i, s in enumerate(symlist) if s == sym1][0]
if len(seplist[listpos]) > 0:
pos = random.choice(range(len(seplist[listpos])))
group2n.append(seplist[listpos][pos])
indices2n.append(indices2[seplist[listpos][pos].index])
del seplist[listpos][pos]
else:
dellist.append(one.index)
if len(dellist) != 0:
dellist.sort(reverse=True)
for one in dellist:
del group1[one]
del indices1[one]
indices2n.append(pt2.index)
indices2 = indices2n
group2 = group2n.copy()
else:
dellist = []
while len(group2) < len(group1) - len(dellist):
#Too many atoms in group 1
dellist.append(random.choice(group1).index)
if len(dellist) != 0:
dellist.sort(reverse=True)
for one in dellist:
del group1[one]
del indices1[one]
dellist = []
while len(group1) < len(group2) - len(dellist):
#Too many atoms in group 2
dellist.append(random.choice(group2).index)
if len(dellist) != 0:
dellist.sort(reverse=True)
for one in dellist:
del group2[one]
del indices2[one]
other2 = Atoms(cell=solid2.get_cell(), pbc=solid2.get_pbc())
for one in solid2:
if one.index not in indices2:
other2.append(one)
other1 = Atoms(cell=solid1.get_cell(), pbc=solid1.get_pbc())
for one in solid1:
if one.index not in indices1:
other1.append(one)
#Exchange atoms in sphere and build new solids
nsolid1 = other1.copy()
nsolid1.extend(group2.copy())
nsolid2 = other2.copy()
nsolid2.extend(group1.copy())
#DEBUG: Write crossover to file
if debug:
write_xyz(Optimizer.debugfile, nsolid1, 'CX(randalloybx):nsolid1')
write_xyz(Optimizer.debugfile, nsolid2, 'CX(randalloybx):nsolid2')
#DEBUG: Check structure of atoms exchanged
for sym, c, m, u in Optimizer.atomlist:
if Optimizer.structure == 'Defect':
nc = len([atm for atm in nsolid1 if atm.symbol == sym])
nc += len([atm for atm in ind1.bulki if atm.symbol == sym])
oc = len([atm for atm in solid1 if atm.symbol == sym])
oc += len([atm for atm in ind1.bulki if atm.symbol == sym])
else:
nc = len([atm for atm in nsolid1 if atm.symbol == sym])
oc = len([atm for atm in solid1 if atm.symbol == sym])
Optimizer.output.write('CX(clustbx):New solid1 contains ' + repr(nc) +
' ' + repr(sym) + ' atoms\n')
if debug:
print 'DEBUG CX: New solid1 contains ' + repr(nc) + ' ' + repr(
sym) + ' atoms'
if oc != nc:
#pdb.set_trace()
print 'CX: Issue in maintaining atom concentration\n Dropping new individual'
Optimizer.output.write(
'CX: Issue in maintaining atom concentration\n Dropping new individual 1\n'
)
nsolid1 = solid1
for sym, c, m, u in Optimizer.atomlist:
if Optimizer.structure == 'Defect':
nc = len([atm for atm in nsolid2 if atm.symbol == sym])
nc += len([atm for atm in ind2.bulki if atm.symbol == sym])
oc = len([atm for atm in solid2 if atm.symbol == sym])
oc += len([atm for atm in ind2.bulki if atm.symbol == sym])
else:
nc = len([atm for atm in nsolid2 if atm.symbol == sym])
oc = len([atm for atm in solid2 if atm.symbol == sym])
Optimizer.output.write('CX(clustbx):New solid2 contains ' + repr(nc) +
' ' + repr(sym) + ' atoms\n')
if debug:
print 'DEBUG CX: New solid2 contains ' + repr(nc) + ' ' + repr(
sym) + ' atoms'
if oc != nc:
#pdb.set_trace()
print 'CX: Issue in maintaining atom concentration\n Dropping new individual'
Optimizer.output.write(
'CX: Issue in maintaining atom concentration\n Dropping new individual 2\n'
)
solid2.pop()
nsolid2 = solid2
if Optimizer.forcing != 'Concentration':
for i in range(len(Optimizer.atomlist)):
atms1 = [
inds for inds in nsolid1
if inds.symbol == Optimizer.atomlist[i][0]
]
atms2 = [
inds for inds in nsolid2
if inds.symbol == Optimizer.atomlist[i][0]
]
if len(atms1) == 0:
if len(atms2) == 0:
nsolid1[random.randint(
0,
len(indi1) - 1)].symbol == Optimizer.atomlist[i][0]
nsolid2[random.randint(
0,
len(indi2) - 1)].symbol == Optimizer.atomlist[i][0]
else:
nsolid1.append(atms2[random.randint(0, len(atms2) - 1)])
nsolid1.pop(random.randint(0, len(nsolid1) - 2))
else:
if len(atms2) == 0:
nsolid2.append(atms1[random.randint(0, len(atms1) - 1)])
nsolid2.pop(random.randint(0, len(nsolid2) - 2))
nsolid1.set_cell(cello1)
nsolid2.set_cell(cello2)
nsolid1.set_pbc(pbc1)
nsolid2.set_pbc(pbc2)
ind1[0] = nsolid1.copy()
ind2[0] = nsolid2.copy()
return ind1, ind2
def eval_energy(input):
"""Function to evaluate energy of an individual
Inputs:
input = [Optimizer class object with parameters, Individual class structure to be evaluated]
Outputs:
energy, bul, individ, signal
energy = energy of Individual evaluated
bul = bulk structure of Individual if simulation structure is Defect
individ = Individual class structure evaluated
signal = string of information about evaluation
"""
if input[0]==None:
energy=0
bul=0
individ=0
rank = MPI.COMM_WORLD.Get_rank()
signal='Evaluated none individual on '+repr(rank)+'\n'
else:
[Optimizer, individ]=input
if Optimizer.calc_method=='MAST':
energy = individ.energy
bul = individ.energy
signal = 'Recieved MAST structure\n'
else:
if Optimizer.parallel: rank = MPI.COMM_WORLD.Get_rank()
if not Optimizer.genealogy:
STR='----Individual ' + str(individ.index)+ ' Optimization----\n'
else:
STR='----Individual ' + str(individ.history_index)+ ' Optimization----\n'
indiv=individ[0]
if 'EE' in Optimizer.debug:
debug = True
else:
debug = False
if debug:
write_xyz(Optimizer.debugfile,indiv,'Recieved by eval_energy')
Optimizer.debugfile.flush()
if Optimizer.structure=='Defect':
indi=indiv.copy()
if Optimizer.alloy==True:
bulk=individ.bulki
else:
bulk=individ.bulko
nat=indi.get_number_of_atoms()
csize=bulk.get_cell()
totalsol=Atoms(cell=csize, pbc=True)
totalsol.extend(indi)
totalsol.extend(bulk)
for sym,c,m,u in Optimizer.atomlist:
nc=len([atm for atm in totalsol if atm.symbol==sym])
STR+='Defect configuration contains '+repr(nc)+' '+repr(sym)+' atoms\n'
elif Optimizer.structure=='Surface':
totalsol=Atoms()
totalsol.extend(indiv)
nat=indiv.get_number_of_atoms()
totalsol.extend(individ.bulki)
for sym,c,m,u in Optimizer.atomlist:
nc=len([atm for atm in totalsol if atm.symbol==sym])
STR+='Surface-Bulk configuration contains '+repr(nc)+' '+repr(sym)+' atoms\n'
cell=numpy.maximum.reduce(indiv.get_cell())
totalsol.set_cell([cell[0],cell[1],500])
totalsol.set_pbc([True,True,False])
if Optimizer.constrain_position:
ts = totalsol.copy()
indc,indb,vacant,swap,stro = find_defects(ts,Optimizer.solidbulk,0)
sbulk = Optimizer.solidbulk.copy()
bcom = sbulk.get_center_of_mass()
#totalsol.translate(-bulkcom)
#indc.translate(-bulkcom)
#totalsol.append(Atom(position=[0,0,0]))
# for one in indc:
# index = [atm.index for atm in totalsol if atm.position[0]==one.position[0] and atm.position[1]==one.position[1] and atm.position[2]==one.position[2]][0]
# if totalsol.get_distance(-1,index) > Optimizer.sf:
# r = random.random()
# totalsol.set_distance(-1,index,Optimizer.sf*r,fix=0)
# totalsol.pop()
# totalsol.translate(bulkcom)
com = indc.get_center_of_mass()
dist = (sum((bcom[i] - com[i])**2 for i in range(3)))**0.5
if dist > Optimizer.sf:
STR+='Shifting structure to within region\n'
r = random.random()*Optimizer.sf
comv = numpy.linalg.norm(com)
ncom = [one*r/comv for one in com]
trans = [ncom[i]-com[i] for i in range(3)]
indices = []
for one in indc:
id = [atm.index for atm in totalsol if atm.position[0]==one.position[0] and atm.position[1]==one.position[1] and atm.position[2]==one.position[2]][0]
totalsol[id].position += trans
# Check for atoms that are too close
min_len=0.7
#pdb.set_trace()
if not Optimizer.fixed_region:
if Optimizer.structure=='Defect' or Optimizer.structure=='Surface':
cutoffs=[2.0 for one in totalsol]
nl=NeighborList(cutoffs,bothways=True,self_interaction=False)
nl.update(totalsol)
for one in totalsol[0:nat]:
nbatoms=Atoms()
nbatoms.append(one)
indices, offsets=nl.get_neighbors(one.index)
for index, d in zip(indices,offsets):
index = int(index)
sym=totalsol[index].symbol
pos=totalsol[index].position + numpy.dot(d,totalsol.get_cell())
at=Atom(symbol=sym,position=pos)
nbatoms.append(at)
while True:
dflag=False
for i in range(1,len(nbatoms)):
d=nbatoms.get_distance(0,i)
if d < min_len:
nbatoms.set_distance(0,i,min_len+.01,fix=0.5)
STR+='--- WARNING: Atoms too close (<0.7A) - Implement Move ---\n'
dflag=True
if dflag==False:
break
for i in range(len(indices)):
totalsol[indices[i]].position=nbatoms[i+1].position
totalsol[one.index].position=nbatoms[0].position
nl.update(totalsol)
if debug:
write_xyz(Optimizer.debugfile,totalsol,'After minlength check')
Optimizer.debugfile.flush()
else:
for i in range(len(indiv)):
for j in range(len(indiv)):
if i != j:
d=indiv.get_distance(i,j)
if d < min_len:
indiv.set_distance(i,j,min_len,fix=0.5)
STR+='--- WARNING: Atoms too close (<0.7A) - Implement Move ---\n'
if debug:
write_xyz(Optimizer.debugfile,indiv,'After minlength check')
Optimizer.debugfile.flush()
# Set calculator to use to get forces/energies
if Optimizer.parallel:
calc = setup_calculator(Optimizer)
if Optimizer.fixed_region:
pms=copy.deepcopy(calc.parameters)
try:
pms['mass'][len(pms['mass'])-1] += '\ngroup RO id >= '+repr(nat)+'\nfix freeze RO setforce 0.0 0.0 0.0\n'
except KeyError:
pms['pair_coeff'][0] += '\ngroup RO id >= '+repr(nat)+'\nfix freeze RO setforce 0.0 0.0 0.0\n'
calc = LAMMPS(parameters=pms, files=calc.files, keep_tmp_files=calc.keep_tmp_files, tmp_dir=calc.tmp_dir)
lmin = copy.copy(Optimizer.lammps_min)
Optimizer.lammps_min = None
Optimizer.static_calc = setup_calculator(Optimizer)
Optimizer.lammps_min = lmin
else:
calc=Optimizer.calc
if Optimizer.structure=='Defect' or Optimizer.structure=='Surface':
totalsol.set_calculator(calc)
totalsol.set_pbc(True)
else:
indiv.set_calculator(calc)
indiv.set_pbc(True) #Current bug in ASE optimizer-Lammps prevents pbc=false
if Optimizer.structure=='Cluster':
indiv.set_cell([500,500,500])
indiv.translate([250,250,250])
cwd=os.getcwd()
# Perform Energy Minimization
if not Optimizer.parallel:
Optimizer.output.flush()
if Optimizer.ase_min == True:
try:
if Optimizer.structure=='Defect' or Optimizer.structure=='Surface':
dyn=BFGS(totalsol)
else:
dyn=BFGS(indiv)
dyn.run(fmax=Optimizer.ase_min_fmax, steps=Optimizer.ase_min_maxsteps)
except OverflowError:
STR+='--- Error: Infinite Energy Calculated - Implement Random ---\n'
box=Atoms()
indiv=gen_pop_box(Optimizer.natoms, Optimizer.atomlist, Optimizer.size)
indiv.set_calculator(calc)
dyn=BFGS(indiv)
dyn.run(fmax=fmax, steps=steps)
except numpy.linalg.linalg.LinAlgError:
STR+='--- Error: Singular Matrix - Implement Random ---\n'
indiv=gen_pop_box(Optimizer.natoms, Optimizer.atomlist, Optimizer.size)
indiv.set_calculator(calc)
dyn=BFGS(indiv)
dyn.run(fmax=fmax, steps=steps)
# Get Energy of Minimized Structure
if Optimizer.structure=='Defect' or Optimizer.structure=='Surface':
en=totalsol.get_potential_energy()
#force=numpy.maximum.reduce(abs(totalsol.get_forces()))
if Optimizer.fitness_scheme == 'enthalpyfit':
pressure=totalsol.get_isotropic_pressure(totalsol.get_stress())
cell_max=numpy.maximum.reduce(totalsol.get_positions())
cell_min=numpy.minimum.reduce(totalsol.get_positions())
cell=cell_max-cell_min
volume=cell[0]*cell[1]*cell[2]
else:
pressure=0
volume=0
na=totalsol.get_number_of_atoms()
ena=en/na
energy=en
individ[0]=totalsol[0:nat]
bul=totalsol[(nat):len(totalsol)]
STR+='Number of positions = '+repr(len(bul)+len(individ[0]))+'\n'
individ[0].set_cell(csize)
indiv=individ[0]
else:
en=indiv.get_potential_energy()
if Optimizer.fitness_scheme == 'enthalpyfit':
pressure=indiv.get_isotropic_pressure(indiv.get_stress())
cell_max=numpy.maximum.reduce(indiv.get_positions())
cell_min=numpy.minimum.reduce(indiv.get_positions())
cell=cell_max-cell_min
volume=cell[0]*cell[1]*cell[2]
else:
pressure=0
volume=0
na=indiv.get_number_of_atoms()
ena=en/na
energy=ena
individ[0]=indiv
bul=0
else:
if Optimizer.structure=='Defect' or Optimizer.structure=='Surface':
if Optimizer.calc_method=='VASP':
en=totalsol.get_potential_energy()
calcb=Vasp(restart=True)
totalsol=calcb.get_atoms()
stress=calcb.read_stress()
else:
try:
totcop=totalsol.copy()
if debug: write_xyz(Optimizer.debugfile,totcop,'Individual sent to lammps')
OUT=totalsol.calc.calculate(totalsol)
totalsol=OUT['atoms']
totalsol.set_pbc(True)
if Optimizer.fixed_region:
if debug:
print 'Energy of fixed region calc = ', OUT['thermo'][-1]['pe']
totalsol.set_calculator(Optimizer.static_calc)
OUT=totalsol.calc.calculate(totalsol)
totalsol=OUT['atoms']
totalsol.set_pbc(True)
if debug:
print 'Energy of static calc = ', OUT['thermo'][-1]['pe']
en=OUT['thermo'][-1]['pe']
stress=numpy.array([OUT['thermo'][-1][i] for i in ('pxx','pyy','pzz','pyz','pxz','pxy')])*(-1e-4*GPa)
#force=numpy.maximum.reduce(abs(totalsol.get_forces()))
if debug:
write_xyz(Optimizer.debugfile,totalsol,'After Lammps Minimization')
Optimizer.debugfile.flush()
except Exception, e:
os.chdir(cwd)
STR+='WARNING: Exception during energy eval:\n'+repr(e)+'\n'
f=open('problem-structures.xyz','a')
write_xyz(f,totcop,data='Starting structure hindex='+individ.history_index)
write_xyz(f,totalsol,data='Lammps Min structure')
en=10
stress=0
f.close()
if Optimizer.fitness_scheme == 'enthalpyfit':
pressure=totalsol.get_isotropic_pressure(stress)
cell_max=numpy.maximum.reduce(totalsol.get_positions())
cell_min=numpy.minimum.reduce(totalsol.get_positions())
cell=cell_max-cell_min
volume=cell[0]*cell[1]*cell[2]
else:
pressure=totalsol.get_isotropic_pressure(stress)
volume=0
na=totalsol.get_number_of_atoms()
ena=en/na
energy=en
if Optimizer.structure=='Defect':
if Optimizer.fixed_region==True or Optimizer.finddefects==False:
individ[0]=totalsol[0:nat]
bul=totalsol[(nat):len(totalsol)]
individ[0].set_cell(csize)
else:
if 'FI' in Optimizer.debug:
outt=find_defects(totalsol,Optimizer.solidbulk,Optimizer.sf,atomlistcheck=Optimizer.atomlist,trackvacs=Optimizer.trackvacs,trackswaps=Optimizer.trackswaps,debug=Optimizer.debugfile)
else:
outt=find_defects(totalsol,Optimizer.solidbulk,Optimizer.sf,atomlistcheck=Optimizer.atomlist,trackvacs=Optimizer.trackvacs,trackswaps=Optimizer.trackswaps,debug=False)
individ[0]=outt[0]
bul=outt[1]
individ.vacancies = outt[2]
individ.swaps = outt[3]
STR += outt[4]
indiv=individ[0]
else:
top,bul=find_top_layer(totalsol,Optimizer.surftopthick)
indiv=top.copy()
individ[0]=top.copy()
else:
class EMT(Calculator):
implemented_properties = ['energy', 'forces']
nolabel = True
def __init__(self):
Calculator.__init__(self)
def initialize(self, atoms):
self.par = {}
self.rc = 0.0
self.numbers = atoms.get_atomic_numbers()
maxseq = max(par[1] for par in parameters.values()) * Bohr
rc = self.rc = beta * maxseq * 0.5 * (sqrt(3) + sqrt(4))
rr = rc * 2 * sqrt(4) / (sqrt(3) + sqrt(4))
self.acut = np.log(9999.0) / (rr - rc)
for Z in self.numbers:
if Z not in self.par:
p = parameters[chemical_symbols[Z]]
s0 = p[1] * Bohr
eta2 = p[3] / Bohr
kappa = p[4] / Bohr
x = eta2 * beta * s0
gamma1 = 0.0
gamma2 = 0.0
for i, n in enumerate([12, 6, 24]):
r = s0 * beta * sqrt(i + 1)
x = n / (12 * (1.0 + exp(self.acut * (r - rc))))
gamma1 += x * exp(-eta2 * (r - beta * s0))
gamma2 += x * exp(-kappa / beta * (r - beta * s0))
self.par[Z] = {'E0': p[0],
's0': s0,
'V0': p[2],
'eta2': eta2,
'kappa': kappa,
'lambda': p[5] / Bohr,
'n0': p[6] / Bohr**3,
'rc': rc,
'gamma1': gamma1,
'gamma2': gamma2}
#if rc + 0.5 > self.rc:
# self.rc = rc + 0.5
self.ksi = {}
for s1, p1 in self.par.items():
self.ksi[s1] = {}
for s2, p2 in self.par.items():
#self.ksi[s1][s2] = (p2['n0'] / p1['n0'] *
# exp(eta1 * (p1['s0'] - p2['s0'])))
self.ksi[s1][s2] = p2['n0'] / p1['n0']
self.forces = np.empty((len(atoms), 3))
self.sigma1 = np.empty(len(atoms))
self.deds = np.empty(len(atoms))
self.nl = NeighborList([0.5 * self.rc + 0.25] * len(atoms),
self_interaction=False)
def calculate(self, atoms=None, properties=['energy'],
system_changes=all_changes):
Calculator.calculate(self, atoms, properties, system_changes)
if 'numbers' in system_changes:
self.initialize(self.atoms)
positions = self.atoms.positions
numbers = self.atoms.numbers
cell = self.atoms.cell
self.nl.update(self.atoms)
self.energy = 0.0
self.sigma1[:] = 0.0
self.forces[:] = 0.0
natoms = len(self.atoms)
for a1 in range(natoms):
Z1 = numbers[a1]
p1 = self.par[Z1]
ksi = self.ksi[Z1]
neighbors, offsets = self.nl.get_neighbors(a1)
offsets = np.dot(offsets, cell)
for a2, offset in zip(neighbors, offsets):
d = positions[a2] + offset - positions[a1]
r = sqrt(np.dot(d, d))
if r < self.rc + 0.5:
Z2 = numbers[a2]
p2 = self.par[Z2]
self.interact1(a1, a2, d, r, p1, p2, ksi[Z2])
for a in range(natoms):
Z = numbers[a]
p = self.par[Z]
try:
ds = -log(self.sigma1[a] / 12) / (beta * p['eta2'])
except (OverflowError, ValueError):
self.deds[a] = 0.0
self.energy -= p['E0']
continue
x = p['lambda'] * ds
y = exp(-x)
z = 6 * p['V0'] * exp(-p['kappa'] * ds)
self.deds[a] = ((x * y * p['E0'] * p['lambda'] + p['kappa'] * z) /
(self.sigma1[a] * beta * p['eta2']))
self.energy += p['E0'] * ((1 + x) * y - 1) + z
for a1 in range(natoms):
Z1 = numbers[a1]
p1 = self.par[Z1]
ksi = self.ksi[Z1]
neighbors, offsets = self.nl.get_neighbors(a1)
offsets = np.dot(offsets, cell)
for a2, offset in zip(neighbors, offsets):
d = positions[a2] + offset - positions[a1]
r = sqrt(np.dot(d, d))
if r < self.rc + 0.5:
Z2 = numbers[a2]
p2 = self.par[Z2]
self.interact2(a1, a2, d, r, p1, p2, ksi[Z2])
self.results['energy'] = self.energy
self.results['forces'] = self.forces
def interact1(self, a1, a2, d, r, p1, p2, ksi):
x = exp(self.acut * (r - self.rc))
theta = 1.0 / (1.0 + x)
y1 = (0.5 * p1['V0'] * exp(-p2['kappa'] * (r / beta - p2['s0'])) *
ksi / p1['gamma2'] * theta)
y2 = (0.5 * p2['V0'] * exp(-p1['kappa'] * (r / beta - p1['s0'])) /
ksi / p2['gamma2'] * theta)
self.energy -= y1 + y2
f = ((y1 * p2['kappa'] + y2 * p1['kappa']) / beta +
(y1 + y2) * self.acut * theta * x) * d / r
self.forces[a1] += f
self.forces[a2] -= f
self.sigma1[a1] += (exp(-p2['eta2'] * (r - beta * p2['s0'])) *
ksi * theta / p1['gamma1'])
self.sigma1[a2] += (exp(-p1['eta2'] * (r - beta * p1['s0'])) /
ksi * theta / p2['gamma1'])
def interact2(self, a1, a2, d, r, p1, p2, ksi):
x = exp(self.acut * (r - self.rc))
theta = 1.0 / (1.0 + x)
y1 = (exp(-p2['eta2'] * (r - beta * p2['s0'])) *
ksi / p1['gamma1'] * theta * self.deds[a1])
y2 = (exp(-p1['eta2'] * (r - beta * p1['s0'])) /
ksi / p2['gamma1'] * theta * self.deds[a2])
f = ((y1 * p2['eta2'] + y2 * p1['eta2']) +
(y1 + y2) * self.acut * theta * x) * d / r
self.forces[a1] -= f
self.forces[a2] += f
C[5, 5] = 47.5 * GPa
# Surface energy computed with DFT (PBE-GGA)
surface_energy = 0.161 * (J / m**2) * 10
a = atoms.copy()
b = a * [nx, 1, 1]
b.center()
b.positions[:, 0] += 0.5
b.set_scaled_positions(b.get_scaled_positions())
mask = ((b.positions[:, 0] > 0.) & (b.positions[:, 0] < 2 * a.cell[0, 0]) &
(b.positions[:, 1] < (a.cell[1, 1] / 2.0 + final_height / 2.0)) &
(b.positions[:, 1] > (a.cell[1, 1] / 2.0 - final_height / 2.0)))
nl = NeighborList([1.0] * len(b), self_interaction=False, bothways=True)
nl.update(b)
term = Atoms()
if tetra:
for i in range(len(b)):
if not mask[i]:
continue
indices, offsets = nl.get_neighbors(i)
if b.numbers[i] == 8 and mask[indices].sum() == 0:
mask[i] = False
if b.numbers[i] == 14:
# complete tetrahedra
for (j, o) in zip(indices, offsets):
if b.numbers[j] == 8:
class EAM(Calculator):
r"""
EAM Interface Documentation
Introduction
============
The Embedded Atom Method (EAM) [1]_ is a classical potential which is
good for modelling metals particularly or fcc materials. Because it is
an equiaxial potential the EAM does not model directional bonds
well. However, the Angular Dependent Potential (ADP) [2]_ which is an
extended version of EAM is able to model directional bonds is part of
the EAM calculator.
A single element EAM potential is defined by three functions: the
embedded energy, electron density and the pair potential (phi).
A two element alloy contains the individual three functions
for each element plus cross pair interactions.
The ADP potential has additional two additional sets of data to
define the dipole and quadrupole directional terms for each alloy
and their cross interactions.
The files containing the potentials for this calculator are not
included but many suitable potentials can be downloaded from The
Interatomic Potentials Repository Project at
http://www.ctcms.nist.gov/potentials/
Running the Calculator
======================
EAM calculates the cohesive atom energy and forces. Internally the
potential functions are defined by splines which may be directly
supplied or created by reading the spline points from a data file from
which a slpline function is created. The LAMMPS compatible ``.alloy``
and ``.adp`` formats are supported. The LAMMPS ``.eam`` format is
slightly different from the ``.alloy`` format and is currently not
supported.
For example::
from eam import EAM
mishin = EAM('Al99.eam.alloy')
mishin.write_file('new.eam.alloy')
mishin.plot()
slab.set_calculator(mishin)
slab.get_potential_energy()
slab.get_forces()
Arguments
=========
========================= ====================================================
Keyword Description
========================= ====================================================
``fileobj`` file of potential in ``.alloy`` or ``.adp`` format
(This is generally all you need to supply)
``elements[N]`` array of N element abreviations
``embedded_energy[N]`` arrays of embedded energy functions
``electron_density[N]`` arrays of electron density functions
``phi[N,N]`` arrays of pair potential funtions
``d_embedded_energy[N]`` arrays of derivative embedded energy functions
``d_electron_density[N]`` arrays of derivative electron density functions
``d_phi[N,N]`` arrays of derivative pair potentials functions
``d[N], q[N,N]`` ADP dipole and quadrupole function
``d_d[N,N], d_q[N,N]`` ADP dipole and quadrupole derivative functions
========================= ====================================================
Additional parameters for writing potential files
=================================================
The following parameters are only required for writing a potential in
``.alloy`` or ``.adp`` format file.
========================= ====================================================
Keyword Description
========================= ====================================================
``Z[N]`` Array of atomic number of each element
``mass[N]`` Atomic mass of each element
``a[N]`` Array of lattice parameters for each element
``lattice[N]`` Lattice type
``nrho`` No. of rho samples
``drho`` Increment for sampling density
``nr`` No. of radial points
``dr`` Increment for sampling radius
========================= ====================================================
Special features
================
``.plot()``
Plots the individual funtions. This may be called from multiple EAM
potentials to compare the shape of the individual curves. This
function requires the installation of the Matplotlib libraries.
Notes/Issues
=============
* Although currently not fast, this calculator can be good for trying
small calculations or for creating new potentials by matching baseline
data such as from DFT results. The format for these potentials is
compatable with LAMMPS_ and so can be used either directly by LAMMPS or
with the ASE LAMMPS calculator interface.
* Supported formats are the LAMMPS_ ``.alloy`` and ``.adp``. The
``.eam`` format is currently not supported.
* Any supplied values will overide values read from the file.
* The derivative functions, if supplied, are only used to calculate
forces.
.. _LAMMPS: http://lammps.sandia.gov/
.. [1] M.S. Daw and M.I. Baskes, Phys. Rev. Letters 50 (1983)
1285.
.. [2] Y. Mishin, M.J. Mehl, and D.A. Papaconstantopoulos,
Acta Materialia 53 2005 4029--4041.
End EAM Interface Documentation
"""
def __init__(self, fileobj=None, **kwargs):
if fileobj != None:
self.read_file(fileobj)
valid_args = ('elements', 'header', 'drho', 'dr', 'cutoff',
'atomic_number', 'mass', 'a', 'lattice',
'embedded_energy', 'electron_density', 'phi',
# adp terms
'd', 'q', 'd_d', 'd_q',
# derivatives
'd_embedded_energy', 'd_electron_density', 'd_phi',
'skin', 'form', 'Z', 'nr', 'nrho', 'mass')
# these variables need to be set, but are not read in
if 'skin' not in kwargs:
self.skin = 1.0
# set any additional keyword arguments
for arg, val in kwargs.iteritems():
if arg in valid_args:
setattr(self, arg, val)
else:
raise RuntimeError('unknown keyword arg "%s" : not in %s'
% (arg, valid_args))
# initialise the state of the calculation
self.Nelements = len(self.elements)
self.energy = 0.0
self.positions = None
self.cell = None
self.pbc = None
def set_form(self, fileobj):
extension = os.path.splitext(fileobj)[1]
if extension == '.eam':
self.form = 'eam'
raise NotImplementedError
elif extension == '.alloy':
self.form = 'alloy'
elif extension == '.adp':
self.form = 'adp'
else:
raise RuntimeError('unknown file extension type: %s' % extension)
def read_file(self, fileobj):
"""Reads a LAMMPS EAM file in alloy format
and creates the interpolation functions from the data
"""
if isinstance(fileobj, str):
f = open(fileobj)
self.set_form(fileobj)
else:
f = fileobj
lines = f.readlines()
self.header = lines[:3]
i = 3
# make the data one long line so as not to care how its formatted
data = []
for line in lines[i:]:
data.extend(line.split())
self.Nelements = int(data[0])
d = 1
self.elements = data[d:(d + self.Nelements)]
d += self.Nelements
self.nrho = int(data[d])
self.drho = float(data[d + 1])
self.nr = int(data[d + 2])
self.dr = float(data[d + 3])
self.cutoff = float(data[d + 4])
self.embedded_data = np.zeros([self.Nelements, self.nrho])
self.density_data = np.zeros([self.Nelements, self.nr])
self.Z = np.zeros([self.Nelements], dtype=int)
self.mass = np.zeros([self.Nelements])
self.a = np.zeros([self.Nelements])
self.lattice = []
d += 5
# reads in the part of the eam file for each element
for elem in range(self.Nelements):
self.Z[elem] = int(data[d])
self.mass[elem] = float(data[d + 1])
self.a[elem] = float(data[d + 2])
self.lattice.append(data[d + 3])
d += 4
self.embedded_data[elem] = np.float_(data[d:(d + self.nrho)])
d += self.nrho
self.density_data[elem] = np.float_(data[d:(d + self.nr)])
d += self.nr
# reads in the r*phi data for each interaction between elements
self.rphi_data = np.zeros([self.Nelements, self.Nelements, self.nr])
for i in range(self.Nelements):
for j in range(i, self.Nelements):
self.rphi_data[i, j] = np.float_(data[d:(d + self.nr)])
d += self.nr
self.r = np.arange(0, self.nr) * self.dr
self.rho = np.arange(0, self.nrho) * self.drho
# this section turns the file data into three functions (and
# derivative functions) that define the potential
self.embedded_energy = np.zeros(self.Nelements, object)
self.electron_density = np.zeros(self.Nelements, object)
self.d_embedded_energy = np.zeros(self.Nelements, object)
self.d_electron_density = np.zeros(self.Nelements, object)
for i in range(self.Nelements):
self.embedded_energy[i] = spline(self.rho,
self.embedded_data[i], k=3)
self.electron_density[i] = spline(self.r,
self.density_data[i], k=3)
self.d_embedded_energy[i] = self.deriv(self.embedded_energy[i])
self.d_electron_density[i] = self.deriv(self.electron_density[i])
self.phi = np.zeros([self.Nelements, self.Nelements], object)
self.d_phi = np.zeros([self.Nelements, self.Nelements], object)
# ignore the first point of the phi data because it is forced
# to go through zero due to the r*phi format in alloy and adp
for i in range(self.Nelements):
for j in range(i, self.Nelements):
if self.form == 'eam': # not stored as rphi
# should we igore the first point for eam ?
raise RuntimeError('.eam format not yet supported')
self.phi[i, j] = spline(
self.r[1:], self.rphi_data[i, j][1:], k=3)
else:
self.phi[i, j] = spline(
self.r[1:],
self.rphi_data[i, j][1:] / self.r[1:], k=3)
self.d_phi[i, j] = self.deriv(self.phi[i, j])
if j != i:
self.phi[j, i] = self.phi[i, j]
self.d_phi[j, i] = self.d_phi[i, j]
if (self.form == 'adp'):
self.read_adp_data(data, d)
def read_adp_data(self, data, d):
"""reads in the extra data fro the adp format"""
self.d_data = np.zeros([self.Nelements, self.Nelements, self.nr])
# should be non symetrical combinations of 2
for i in range(self.Nelements):
for j in range(i, self.Nelements):
self.d_data[i, j] = data[d:d + self.nr]
d += self.nr
self.q_data = np.zeros([self.Nelements, self.Nelements, self.nr])
# should be non symetrical combinations of 2
for i in range(self.Nelements):
for j in range(i, self.Nelements):
self.q_data[i, j] = data[d:d + self.nr]
d += self.nr
self.d = np.zeros([self.Nelements, self.Nelements], object)
self.d_d = np.zeros([self.Nelements, self.Nelements], object)
self.q = np.zeros([self.Nelements, self.Nelements], object)
self.d_q = np.zeros([self.Nelements, self.Nelements], object)
for i in range(self.Nelements):
for j in range(i, self.Nelements):
self.d[i, j] = spline(self.r[1:], self.d_data[i, j][1:], k=3)
self.d_d[i, j] = self.deriv(self.d[i, j])
self.q[i, j] = spline(self.r[1:], self.q_data[i, j][1:], k=3)
self.d_q[i, j] = self.deriv(self.q[i, j])
# make symmetrical
if j != i:
self.d[j, i] = self.d[i, j]
self.d_d[j, i] = self.d_d[i, j]
self.q[j, i] = self.q[i, j]
self.d_q[j, i] = self.d_q[i, j]
def write_file(self, filename, nc=1, form='%.8e'):
"""Writes out the model of the eam_alloy in lammps alloy
format to file with name = 'filename' with a data format that
is nc columns wide. Note: array lengths need to be an exact
multiple of nc
"""
f = open(filename, 'w')
assert self.nr % nc == 0
assert self.nrho % nc == 0
if not hasattr(self, 'header'):
self.header = """Unknown EAM potential file
Generated from eam.py
blank
"""
for line in self.header:
f.write(line)
f.write('%d ' % self.Nelements)
for i in range(self.Nelements):
f.write('%s ' % str(self.elements[i]))
f.write('\n')
f.write('%d %f %d %f %f \n' %
(self.nrho, self.drho, self.nr, self.dr, self.cutoff))
# start of each section for each element
# rs = np.linspace(0, self.nr * self.dr, self.nr)
# rhos = np.linspace(0, self.nrho * self.drho, self.nrho)
rs = np.arange(0, self.nr) * self.dr
rhos = np.arange(0, self.nrho) * self.drho
for i in range(self.Nelements):
f.write('%d %f %f %s\n' % (self.Z[i], self.mass[i],
self.a[i], str(self.lattice[i])))
np.savetxt(f,
self.embedded_energy[i](rhos).reshape(self.nrho / nc,
nc),
fmt=nc * [form])
np.savetxt(f,
self.electron_density[i](rs).reshape(self.nr / nc,
nc),
fmt=nc * [form])
# write out the pair potentials in Lammps DYNAMO setfl format
# as r*phi for alloy format
for i in range(self.Nelements):
for j in range(i, self.Nelements):
np.savetxt(f,
(rs * self.phi[i, j](rs)).reshape(self.nr / nc,
nc),
fmt=nc * [form])
if self.form == 'adp':
# these are the u(r) values
for i in range(self.Nelements):
for j in range(i + 1):
np.savetxt(f, self.d_data[i, j])
# these are the w(r) values
for i in range(self.Nelements):
for j in range(i + 1):
np.savetxt(f, self.q_data[i, j])
f.close()
def update(self, atoms):
# check all the elements are available in the potential
elements = np.unique(atoms.get_chemical_symbols())
unavailable = np.logical_not(
np.array([item in self.elements for item in elements]))
if np.any(unavailable):
raise RuntimeError('These elements are not in the potential: %s' %
elements[unavailable])
# check if anything has changed to require re-calculation
if (self.positions is None or
len(self.positions) != len(atoms.get_positions()) or
(self.positions != atoms.get_positions()).any() or
(self.cell != atoms.get_cell()).any() or
(self.pbc != atoms.get_pbc()).any()):
# cutoffs need to be a vector for NeighborList
cutoffs = self.cutoff * np.ones(len(atoms))
# convert the elements to an index of the position
# in the eam format
self.index = np.array([atoms.calc.elements.index(el)
for el in atoms.get_chemical_symbols()])
self.pbc = atoms.get_pbc()
# since we need the contribution of all neighbors to the
# local electron density we cannot just calculate and use
# one way neighbors
self.neighbors = NeighborList(cutoffs, skin=self.skin,
self_interaction=False,
bothways=True)
self.neighbors.update(atoms)
self.calculate(atoms)
def get_forces(self, atoms):
# calculate the forces based on derivatives of the three EAM functions
self.update(atoms)
self.forces = np.zeros((len(atoms), 3))
for i in range(len(atoms)): # this is the atom to be embedded
neighbors, offsets = self.neighbors.get_neighbors(i)
offset = np.dot(offsets, atoms.get_cell())
# create a vector of relative positions of neighbors
rvec = atoms.positions[neighbors] + offset - atoms.positions[i]
r = np.sqrt(np.sum(np.square(rvec), axis=1))
nearest = np.arange(len(r))[r < self.cutoff]
d_embedded_energy_i = self.d_embedded_energy[
self.index[i]](self.total_density[i])
urvec = rvec.copy() # unit directional vector
for j in np.arange(len(neighbors)):
urvec[j] = urvec[j] / r[j]
for j_index in range(self.Nelements):
use = self.index[neighbors[nearest]] == j_index
if not use.any():
continue
rnuse = r[nearest][use]
density_j = self.total_density[neighbors[nearest][use]]
scale = (self.d_phi[self.index[i], j_index](rnuse) +
(d_embedded_energy_i *
self.d_electron_density[j_index](rnuse)) +
(self.d_embedded_energy[j_index](density_j) *
self.d_electron_density[self.index[i]](rnuse)))
self.forces[i] += np.dot(scale, urvec[nearest][use])
if (self.form == 'adp'):
adp_forces = self.angular_forces(
self.mu[i],
self.mu[neighbors[nearest][use]],
self.lam[i],
self.lam[neighbors[nearest][use]],
rnuse,
rvec[nearest][use],
self.index[i],
j_index)
self.forces[i] += adp_forces
return self.forces.copy()
def get_stress(self, atoms):
## currently not implemented
raise NotImplementedError
def calculate(self, atoms):
# calculate the energy
# the energy is made up of the ionic or pair interaction and
# the embedding energy of each atom into the electron cloud
# generated by its neighbors
energy = 0.0
adp_energy = 0.0
self.total_density = np.zeros(len(atoms))
if (self.form == 'adp'):
self.mu = np.zeros([len(atoms), 3])
self.lam = np.zeros([len(atoms), 3, 3])
for i in range(len(atoms)): # this is the atom to be embedded
neighbors, offsets = self.neighbors.get_neighbors(i)
offset = np.dot(offsets, atoms.get_cell())
rvec = (atoms.positions[neighbors] + offset -
atoms.positions[i])
## calculate the distance to the nearest neighbors
r = np.sqrt(np.sum(np.square(rvec), axis=1)) # fast
# r = np.apply_along_axis(np.linalg.norm, 1, rvec) # sloow
nearest = np.arange(len(r))[r <= self.cutoff]
for j_index in range(self.Nelements):
use = self.index[neighbors[nearest]] == j_index
if not use.any():
continue
pair_energy = np.sum(self.phi[self.index[i], j_index](
r[nearest][use])) / 2.
energy += pair_energy
density = np.sum(
self.electron_density[j_index](r[nearest][use]))
self.total_density[i] += density
if self.form == 'adp':
self.mu[i] += self.eam_dipole(
r[nearest][use],
rvec[nearest][use],
self.d[self.index[i], j_index])
self.lam[i] += self.eam_quadrupole(
r[nearest][use],
rvec[nearest][use],
self.q[self.index[i], j_index])
# add in the electron embedding energy
embedding_energy = self.embedded_energy[self.index[i]](
self.total_density[i])
# print 'pair energy',energy
# print 'embed energy',embedding_energy
energy += embedding_energy
if self.form == 'adp':
mu_energy = np.sum(self.mu**2) / 2.
adp_energy += mu_energy
# print 'adp mu', mu_energy
lam_energy = np.sum(self.lam**2) / 2.
adp_energy += lam_energy
# print 'adp lam', lam_energy
for i in range(len(atoms)): # this is the atom to be embedded
adp_energy -= np.sum(self.lam[i].trace()**2) / 6.
# print 'energy no adp', energy
energy += adp_energy
self.positions = atoms.positions.copy()
self.cell = atoms.get_cell().copy()
self.energy_free = energy
self.energy_zero = energy
def plot(self, name=''):
"""Plot the individual curves"""
try:
import matplotlib.pyplot as plt
except ImportError:
raise NotAvailable('This needs matplotlib module.')
if self.form == 'eam' or self.form == 'alloy':
nrow = 2
elif self.form == 'adp':
nrow = 3
else:
raise RuntimeError('Unknown form of potential: %s' % self.form)
if hasattr(self, 'r'):
r = self.r
else:
r = np.linspace(0, self.cutoff, 50)
if hasattr(self, 'rho'):
rho = self.rho
else:
rho = np.linspace(0, 10.0, 50)
plt.subplot(nrow, 2, 1)
self.elem_subplot(rho, self.embedded_energy,
r'$\rho$', r'Embedding Energy $F(\bar\rho)$',
name, plt)
plt.subplot(nrow, 2, 2)
self.elem_subplot(r, self.electron_density,
r'$r$', r'Electron Density $\rho(r)$', name, plt)
plt.subplot(nrow, 2, 3)
self.multielem_subplot(r, self.phi,
r'$r$', r'Pair Potential $\phi(r)$', name, plt)
plt.ylim(-1.0, 1.0) # need reasonable values
if self.form == 'adp':
plt.subplot(nrow, 2, 5)
self.multielem_subplot(r, self.d,
r'$r$', r'Dipole Energy', name, plt)
plt.subplot(nrow, 2, 6)
self.multielem_subplot(r, self.q,
r'$r$', r'Quadrupole Energy', name, plt)
plt.plot()
def elem_subplot(self, curvex, curvey, xlabel, ylabel, name, plt):
plt.xlabel(xlabel)
plt.ylabel(ylabel)
for i in np.arange(self.Nelements):
label = name + ' ' + self.elements[i]
plt.plot(curvex, curvey[i](curvex), label=label)
plt.legend()
def multielem_subplot(self, curvex, curvey, xlabel, ylabel, name, plt):
plt.xlabel(xlabel)
plt.ylabel(ylabel)
for i in np.arange(self.Nelements):
for j in np.arange(i + 1):
label = name + ' ' + self.elements[i] + '-' + self.elements[j]
plt.plot(curvex, curvey[i, j](curvex), label=label)
plt.legend()
def angular_forces(self, mu_i, mu, lam_i, lam, r, rvec, form1, form2):
# calculate the extra components for the adp forces
# rvec are the relative positions to atom i
psi = np.zeros(mu.shape)
for gamma in range(3):
term1 = (mu_i[gamma] - mu[:, gamma]) * self.d[form1][form2](r)
term2 = np.sum((mu_i - mu) * self.d_d[form1][form2](r)[:, np.newaxis]
* (rvec * rvec[:, gamma][:, np.newaxis]
/ r[:, np.newaxis]), axis=1)
term3 = 2 * np.sum((lam_i[:, gamma] + lam[:, :, gamma])
* rvec * self.q[form1][form2](r)[:, np.newaxis],
axis=1)
term4 = 0.0
for alpha in range(3):
for beta in range(3):
rs = rvec[:, alpha] * rvec[:, beta] * rvec[:, gamma]
term4 += ((lam_i[alpha, beta] + lam[:, alpha, beta]) *
self.d_q[form1][form2](r) * rs) / r
term5 = ((lam_i.trace() + lam.trace(axis1=1, axis2=2)) *
(self.d_q[form1][form2](r) * r
+ 2 * self.q[form1][form2](r)) * rvec[:, gamma]) / 3.
# the minus for term5 is a correction on the adp
# formulation given in the 2005 Mishin Paper and is posted
# on the NIST website with the AlH potential
psi[:, gamma] = term1 + term2 + term3 + term4 - term5
return np.sum(psi, axis=0)
def eam_dipole(self, r, rvec, d):
# calculate the dipole contribution
mu = np.sum((rvec * d(r)[:, np.newaxis]), axis=0)
return mu # sign to agree with lammps
def eam_quadrupole(self, r, rvec, q):
# slow way of calculating the quadrupole contribution
r = np.sqrt(np.sum(rvec**2, axis=1))
lam = np.zeros([rvec.shape[0], 3, 3])
qr = q(r)
for alpha in range(3):
for beta in range(3):
lam[:, alpha, beta] += qr * rvec[:, alpha] * rvec[:, beta]
return np.sum(lam, axis=0)
def deriv(self, spline):
"""Wrapper for extracting the derivative from a spline"""
def d_spline(aspline):
return spline(aspline, 1)
return d_spline
d = 0.0
for a in range(len(atoms)):
i, offsets = nl.get_neighbors(a)
for j in i:
c[j] += 1
c[a] += len(i)
d += (((R[i] + np.dot(offsets, cell) - R[a])**2).sum(1)**0.5).sum()
return d, c
for sorted in [False, True]:
for p1 in range(2):
for p2 in range(2):
for p3 in range(2):
print(p1, p2, p3)
atoms.set_pbc((p1, p2, p3))
nl = NeighborList(atoms.numbers * 0.2 + 0.5,
skin=0.0, sorted=sorted)
nl.update(atoms)
d, c = count(nl, atoms)
atoms2 = atoms.repeat((p1 + 1, p2 + 1, p3 + 1))
nl2 = NeighborList(atoms2.numbers * 0.2 + 0.5,
skin=0.0, sorted=sorted)
nl2.update(atoms2)
d2, c2 = count(nl2, atoms2)
c2.shape = (-1, 10)
dd = d * (p1 + 1) * (p2 + 1) * (p3 + 1) - d2
print(dd)
print(c2 - c)
assert abs(dd) < 1e-10
assert not (c2 - c).any()
h2 = Atoms('H2', positions=[(0, 0, 0), (0, 0, 1)])
class EMT(Calculator):
implemented_properties = ['energy', 'forces']
nolabel = True
def __init__(self):
Calculator.__init__(self)
def initialize(self, atoms):
self.par = {}
self.rc = 0.0
self.numbers = atoms.get_atomic_numbers()
maxseq = max(par[1] for par in parameters.values()) * Bohr
rc = self.rc = beta * maxseq * 0.5 * (sqrt(3) + sqrt(4))
rr = rc * 2 * sqrt(4) / (sqrt(3) + sqrt(4))
self.acut = np.log(9999.0) / (rr - rc)
for Z in self.numbers:
if Z not in self.par:
p = parameters[chemical_symbols[Z]]
s0 = p[1] * Bohr
eta2 = p[3] / Bohr
kappa = p[4] / Bohr
x = eta2 * beta * s0
gamma1 = 0.0
gamma2 = 0.0
for i, n in enumerate([12, 6, 24]):
r = s0 * beta * sqrt(i + 1)
x = n / (12 * (1.0 + exp(self.acut * (r - rc))))
gamma1 += x * exp(-eta2 * (r - beta * s0))
gamma2 += x * exp(-kappa / beta * (r - beta * s0))
self.par[Z] = {
'E0': p[0],
's0': s0,
'V0': p[2],
'eta2': eta2,
'kappa': kappa,
'lambda': p[5] / Bohr,
'n0': p[6] / Bohr**3,
'rc': rc,
'gamma1': gamma1,
'gamma2': gamma2
}
#if rc + 0.5 > self.rc:
# self.rc = rc + 0.5
self.ksi = {}
for s1, p1 in self.par.items():
self.ksi[s1] = {}
for s2, p2 in self.par.items():
#self.ksi[s1][s2] = (p2['n0'] / p1['n0'] *
# exp(eta1 * (p1['s0'] - p2['s0'])))
self.ksi[s1][s2] = p2['n0'] / p1['n0']
self.forces = np.empty((len(atoms), 3))
self.sigma1 = np.empty(len(atoms))
self.deds = np.empty(len(atoms))
self.nl = NeighborList([0.5 * self.rc + 0.25] * len(atoms),
self_interaction=False)
def calculate(self,
atoms=None,
properties=['energy'],
system_changes=[
'positions', 'numbers', 'cell', 'pbc', 'charges',
'magmoms'
]):
Calculator.calculate(self, atoms, properties, system_changes)
if 'numbers' in system_changes:
self.initialize(self.atoms)
positions = self.atoms.positions
numbers = self.atoms.numbers
cell = self.atoms.cell
self.nl.update(self.atoms)
self.energy = 0.0
self.sigma1[:] = 0.0
self.forces[:] = 0.0
natoms = len(self.atoms)
for a1 in range(natoms):
Z1 = numbers[a1]
p1 = self.par[Z1]
ksi = self.ksi[Z1]
neighbors, offsets = self.nl.get_neighbors(a1)
offsets = np.dot(offsets, cell)
for a2, offset in zip(neighbors, offsets):
d = positions[a2] + offset - positions[a1]
r = sqrt(np.dot(d, d))
if r < self.rc + 0.5:
Z2 = numbers[a2]
p2 = self.par[Z2]
self.interact1(a1, a2, d, r, p1, p2, ksi[Z2])
for a in range(natoms):
Z = numbers[a]
p = self.par[Z]
try:
ds = -log(self.sigma1[a] / 12) / (beta * p['eta2'])
except (OverflowError, ValueError):
self.deds[a] = 0.0
self.energy -= p['E0']
continue
x = p['lambda'] * ds
y = exp(-x)
z = 6 * p['V0'] * exp(-p['kappa'] * ds)
self.deds[a] = ((x * y * p['E0'] * p['lambda'] + p['kappa'] * z) /
(self.sigma1[a] * beta * p['eta2']))
self.energy += p['E0'] * ((1 + x) * y - 1) + z
for a1 in range(natoms):
Z1 = numbers[a1]
p1 = self.par[Z1]
ksi = self.ksi[Z1]
neighbors, offsets = self.nl.get_neighbors(a1)
offsets = np.dot(offsets, cell)
for a2, offset in zip(neighbors, offsets):
d = positions[a2] + offset - positions[a1]
r = sqrt(np.dot(d, d))
if r < self.rc + 0.5:
Z2 = numbers[a2]
p2 = self.par[Z2]
self.interact2(a1, a2, d, r, p1, p2, ksi[Z2])
self.results['energy'] = self.energy
self.results['forces'] = self.forces
def interact1(self, a1, a2, d, r, p1, p2, ksi):
x = exp(self.acut * (r - self.rc))
theta = 1.0 / (1.0 + x)
y1 = (0.5 * p1['V0'] * exp(-p2['kappa'] * (r / beta - p2['s0'])) *
ksi / p1['gamma2'] * theta)
y2 = (0.5 * p2['V0'] * exp(-p1['kappa'] * (r / beta - p1['s0'])) /
ksi / p2['gamma2'] * theta)
self.energy -= y1 + y2
f = ((y1 * p2['kappa'] + y2 * p1['kappa']) / beta +
(y1 + y2) * self.acut * theta * x) * d / r
self.forces[a1] += f
self.forces[a2] -= f
self.sigma1[a1] += (exp(-p2['eta2'] * (r - beta * p2['s0'])) * ksi *
theta / p1['gamma1'])
self.sigma1[a2] += (exp(-p1['eta2'] * (r - beta * p1['s0'])) / ksi *
theta / p2['gamma1'])
def interact2(self, a1, a2, d, r, p1, p2, ksi):
x = exp(self.acut * (r - self.rc))
theta = 1.0 / (1.0 + x)
y1 = (exp(-p2['eta2'] * (r - beta * p2['s0'])) * ksi / p1['gamma1'] *
theta * self.deds[a1])
y2 = (exp(-p1['eta2'] * (r - beta * p1['s0'])) / ksi / p2['gamma1'] *
theta * self.deds[a2])
f = ((y1 * p2['eta2'] + y2 * p1['eta2']) +
(y1 + y2) * self.acut * theta * x) * d / r
self.forces[a1] -= f
self.forces[a2] += f
