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"""Effective medium theory potential."""
from math import sqrt, exp, log
import numpy as np
from ase.data import chemical_symbols, atomic_numbers
from ase.units import Bohr
from ase.neighborlist import NeighborList
from ase.calculators.calculator import (Calculator, all_changes,
PropertyNotImplementedError)
parameters = {
# E0 s0 V0 eta2 kappa lambda n0
# eV bohr eV bohr^-1 bohr^-1 bohr^-1 bohr^-3
'Al': (-3.28, 3.00, 1.493, 1.240, 2.000, 1.169, 0.00700),
'Cu': (-3.51, 2.67, 2.476, 1.652, 2.740, 1.906, 0.00910),
'Ag': (-2.96, 3.01, 2.132, 1.652, 2.790, 1.892, 0.00547),
'Au': (-3.80, 3.00, 2.321, 1.674, 2.873, 2.182, 0.00703),
'Ni': (-4.44, 2.60, 3.673, 1.669, 2.757, 1.948, 0.01030),
'Pd': (-3.90, 2.87, 2.773, 1.818, 3.107, 2.155, 0.00688),
'Pt': (-5.85, 2.90, 4.067, 1.812, 3.145, 2.192, 0.00802),
# extra parameters - just for fun ...
'H': (-3.21, 1.31, 0.132, 2.652, 2.790, 3.892, 0.00547),
'C': (-3.50, 1.81, 0.332, 1.652, 2.790, 1.892, 0.01322),
'N': (-5.10, 1.88, 0.132, 1.652, 2.790, 1.892, 0.01222),
'O': (-4.60, 1.95, 0.332, 1.652, 2.790, 1.892, 0.00850)}
beta = 1.809 # (16 * pi / 3)**(1.0 / 3) / 2**0.5, preserve historical rounding
class EMT(Calculator):
"""Python implementation of the Effective Medium Potential.
Supports the following standard EMT metals:
Al, Cu, Ag, Au, Ni, Pd and Pt.
In addition, the following elements are supported.
They are NOT well described by EMT, and the parameters
are not for any serious use:
H, C, N, O
The potential takes a single argument, ``asap_cutoff``
(default: False). If set to True, the cutoff mimics
how Asap does it; most importantly the global cutoff
is chosen from the largest atom present in the simulation,
if False it is chosen from the largest atom in the parameter
table. True gives the behaviour of the Asap code and
older EMT implementations, although the results are not
bitwise identical.
"""
implemented_properties = ['energy', 'energies', 'forces',
'stress', 'magmom', 'magmoms']
nolabel = True
default_parameters = {'asap_cutoff': False}
def __init__(self, **kwargs):
Calculator.__init__(self, **kwargs)
def initialize(self, atoms):
self.par = {}
self.rc = 0.0
self.numbers = atoms.get_atomic_numbers()
if self.parameters.asap_cutoff:
relevant_pars = {}
for symb, p in parameters.items():
if atomic_numbers[symb] in self.numbers:
relevant_pars[symb] = p
else:
relevant_pars = parameters
maxseq = max(par[1] for par in relevant_pars.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)
if self.parameters.asap_cutoff:
self.rc_list = self.rc * 1.045
else:
self.rc_list = self.rc + 0.5
for Z in self.numbers:
if Z not in self.par:
sym = chemical_symbols[Z]
if sym not in parameters:
raise NotImplementedError('No EMT-potential for {0}'
.format(sym))
p = parameters[sym]
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}
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']
self.energies = np.empty(len(atoms))
self.forces = np.empty((len(atoms), 3))
self.stress = np.empty((3, 3))
self.sigma1 = np.empty(len(atoms))
self.deds = np.empty(len(atoms))
self.nl = NeighborList([0.5 * self.rc_list] * 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.energies[:] = 0
self.sigma1[:] = 0.0
self.forces[:] = 0.0
self.stress[:] = 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_list:
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']
self.energies[a] -= 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 += E
self.energies[a] += E
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_list:
Z2 = numbers[a2]
p2 = self.par[Z2]
self.interact2(a1, a2, d, r, p1, p2, ksi[Z2])
self.results['energy'] = self.energy
self.results['energies'] = self.energies
self.results['free_energy'] = self.energy
self.results['forces'] = self.forces
if 'stress' in properties:
if self.atoms.cell.rank == 3:
self.stress += self.stress.T.copy()
self.stress *= -0.5 / self.atoms.get_volume()
self.results['stress'] = self.stress.flat[[0, 4, 8, 5, 2, 1]]
else:
raise PropertyNotImplementedError
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
self.energies[a1] -= (y1 + y2) / 2
self.energies[a2] -= (y1 + y2) / 2
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.stress -= np.outer(f, d)
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
self.stress += np.outer(f, d)
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