def test_ewald():
""" Ewald Rydberg test """
from numpy import all, abs, sqrt
from pylada.crystal import Structure
from pylada.ewald import ewald
from quantities import angstrom, a0, Ry
structure = Structure([[1, 0, 0],
[0, 1, 0],
[0, 0, 1] ], scale=50 ) \
.add_atom(0, 0, 0, 'A', charge=1e0) \
.add_atom(float(a0.rescale(angstrom) / 50.0), 0, 0, 'A', charge=-1e0)
result = ewald(structure, cutoff=80)
assert abs(result.energy + 2e0 * Ry) < 1e-3
assert all(abs(abs(result[0].force) - [2e0, 0, 0] * Ry / a0) < 1e-3)
assert all(abs(abs(result[1].force) - [2e0, 0, 0] * Ry / a0) < 1e-3)
a = float(a0.rescale(angstrom) / 50.0) / sqrt(2.)
structure = Structure([[1, 0, 0],
[0, 1, 0],
[0, 0, 1] ], scale=50 ) \
.add_atom(0, 0, 0, 'A', charge=1e0) \
.add_atom(0, a, a, 'A', charge=-1e0)
result = ewald(structure, cutoff=80)
assert abs(result.energy + 2e0 * Ry) < 1e-3
assert all(
abs(abs(result[0].force) -
[0, 2. / sqrt(2), 2. / sqrt(2)] * Ry / a0) < 1e-3)
assert all(
abs(abs(result[1].force) -
[0, 2. / sqrt(2), 2. / sqrt(2)] * Ry / a0) < 1e-3)
def test():
from numpy import all, abs, sqrt
from pylada.crystal import Structure
from pylada.ewald import ewald
from quantities import angstrom, a0, Ry
structure = Structure( [ [1,0,0],
[0,1,0],
[0,0,1] ], scale=50 ) \
.add_atom(0, 0, 0, 'A', charge=1e0) \
.add_atom( float(a0.rescale(angstrom)/50.0), 0, 0, 'A',
charge=-1e0 )
result = ewald(structure, cutoff = 80)
assert abs(result.energy + 2e0*Ry) < 1e-3
assert all(abs(abs(result[0].force) - [2e0, 0, 0]*Ry/a0) < 1e-3)
assert all(abs(abs(result[1].force) - [2e0, 0, 0]*Ry/a0) < 1e-3)
a = float(a0.rescale(angstrom)/50.0) / sqrt(2.)
structure = Structure( [ [1,0,0],
[0,1,0],
[0,0,1] ], scale=50 ) \
.add_atom(0, 0, 0, 'A', charge=1e0) \
.add_atom(0, a, a, 'A', charge=-1e0 )
result = ewald(structure, cutoff = 80)
assert abs(result.energy + 2e0*Ry) < 1e-3
assert all(abs(abs(result[0].force) - [0, 2./sqrt(2), 2./sqrt(2)]*Ry/a0) < 1e-3)
assert all(abs(abs(result[1].force) - [0, 2./sqrt(2), 2./sqrt(2)]*Ry/a0) < 1e-3)
def get_madelungenergy(latt_vec_array, charge, epsilon, cutoff):
""" Function returns leading first order correction term, i.e.,
screened Madelung-like lattice energy of point charge
Reference: M. Leslie and M. J. Gillan, J. Phys. C: Solid State Phys. 18 (1985) 973
Parameters
defect = pylada.vasp.Extract object
charge = charge of point defect. Default 1e0 elementary charge
epsilon = dimensionless relative permittivity, SKW: isotropic average of dielectric constant
cutoff = Ewald cutoff parameter
Returns
Madelung (electrostatic) energy in eV
Note:
1. Units in this function are either handled by the module Quantities, or\
defaults to Angstrom and elementary charges
2. Function is adopted from Haowei Peng's version in pylada.defects modules
"""
ewald_cutoff = cutoff * Ry
cell_scale = 1.0 # SKW: In notebook workflow cell parameters are converted to Cartesians and units of Angstroms
# SKW: Create point charge in pylada.crystal.structure class (used for charge model)
# http://pylada.github.io/pylada/userguide/crystal.html
struc = Structure()
struc.cell = latt_vec_array
struc.scale = cell_scale
struc.add_atom(0., 0., 0., "P", charge=charge)
#Anuj_05/22/18: added "cutoff" in ewald syntax
result = ewald(struc, cutoff=ewald_cutoff).energy / epsilon
return -1 * result.rescale(eV)
def first_order_charge_correction(structure,
charge=None,
epsilon=1e0,
cutoff=20.0,
**kwargs):
""" First order charge correction of +1 charge in given supercell.
Units in this function are either handled by the module Quantities, or
defaults to Angstroems and elementary charges.
:Parameters:
structure : `pylada.crystal.Structure`
Defect supercell, with cartesian positions in angstrom.
charge
Charge of the point-defect. Defaults to 1e0 elementary charge. If no
units are attached, expects units of elementary charges.
epsilon
dimensionless relative permittivity.
cutoff
Ewald cutoff parameter.
:return: Electrostatic energy in eV.
"""
from quantities import elementary_charge, eV
from pylada.crystal import Structure
from pylada.physics import Ry
from pylada.ewald import ewald
if charge is None:
charge = 1
elif charge == 0:
return 0e0 * eV
if hasattr(charge, "units"):
charge = float(charge.rescale(elementary_charge))
ewald_cutoff = cutoff * Ry
struc = Structure()
struc.cell = structure.cell
struc.scale = structure.scale
struc.add_atom(0e0, 0, 0, "A", charge=charge)
result = ewald(struc, ewald_cutoff).energy / epsilon
return -result.rescale(eV)
def get_madelungenergy(defect, charge=None, epsilon=1e0, cutoff=100.0):
""" Function returns leading first order correction term, i.e.,
screened Madelung-like lattice energy of point charge
Reference: M. Leslie and M. J. Gillan, J. Phys. C: Solid State Phys. 18 (1985) 973
Parameters
defect = pylada.vasp.Extract object
charge = charge of point defect. Default 1e0 elementary charge
epsilon = dimensionless relative permittivity
cutoff = Ewald cutoff parameter
Returns
Madelung (electrostatic) energy in eV
Note:
1. Units in this function are either handled by the module Quantities, or\
defaults to Angstrom and elementary charges
2. Function is adopted from Haowei Peng's version in pylada.defects modules
"""
from quantities import elementary_charge, eV
from pylada.crystal import Structure
from pylada.physics import Ry
from pylada.ewald import ewald
if charge is None: charge = 1
elif charge == 0: return 0e0 * eV
if hasattr(charge, "units"):
charge = float(charge.rescale(elementary_charge))
ewald_cutoff = cutoff * Ry
structure = defect.structure
struc = Structure()
struc.cell = structure.cell
struc.scale = structure.scale
struc.add_atom(0., 0., 0., "P", charge=charge)
#Anuj_05/22/18: added "cutoff" in ewald syntax
result = ewald(struc, cutoff=ewald_cutoff).energy / epsilon
return -1 * result.rescale(eV)
def first_order_charge_correction(structure, charge=None, epsilon=1e0, cutoff=20.0, **kwargs):
""" First order charge correction of +1 charge in given supercell.
Units in this function are either handled by the module Quantities, or
defaults to Angstroems and elementary charges.
:Parameters:
structure : `pylada.crystal.Structure`
Defect supercell, with cartesian positions in angstrom.
charge
Charge of the point-defect. Defaults to 1e0 elementary charge. If no
units are attached, expects units of elementary charges.
epsilon
dimensionless relative permittivity.
cutoff
Ewald cutoff parameter.
:return: Electrostatic energy in eV.
"""
from quantities import elementary_charge, eV
from pylada.crystal import Structure
from pylada.physics import Ry
from pylada.ewald import ewald
if charge is None:
charge = 1
elif charge == 0:
return 0e0 * eV
if hasattr(charge, "units"):
charge = float(charge.rescale(elementary_charge))
ewald_cutoff = cutoff * Ry
struc = Structure()
struc.cell = structure.cell
struc.scale = structure.scale
struc.add_atom(0e0, 0, 0, "A", charge=charge)
result = ewald(struc, ewald_cutoff).energy / epsilon
return -result.rescale(eV)
