def test_qmodel(self):
qm = QModel()
modqm = QModel(beta=2., expnorm=0.5, gamma=0.1)
# test rho_rec
self.assertEqual(qm.rho_rec(1.), 0.77880078307140488)
self.assertEqual(modqm.rho_rec(1.), 0.6814583156907158)
# test rho_rec_limit0
self.assertEqual(qm.rho_rec_limit0, -0.25)
self.assertEqual(modqm.rho_rec_limit0, -0.51)
def test_qmodel(self):
qm = QModel()
modqm = QModel(beta=2., expnorm=0.5, gamma=0.1)
# test rho_rec
self.assertEqual(qm.rho_rec(1.), 0.77880078307140488)
self.assertEqual(modqm.rho_rec(1.), 0.6814583156907158)
# test rho_rec_limit0
self.assertEqual(qm.rho_rec_limit0, -0.25)
self.assertEqual(modqm.rho_rec_limit0, -0.51)
class FreysoldtCorrection(DefectCorrection):
"""
A class for FreysoldtCorrection class. Largely adapated from PyCDT code
If this correction is used, please reference Freysoldt's original paper.
doi: 10.1103/PhysRevLett.102.016402
"""
def __init__(self,
dielectric_const,
q_model=None,
energy_cutoff=520,
madetol=0.0001,
axis=None):
"""
Initializes the FreysoldtCorrection class
Args:
dielectric_const (float or 3x3 matrix): Dielectric constant for the structure
q_model (QModel): instantiated QModel object or None.
Uses default parameters to instantiate QModel if None supplied
energy_cutoff (int): Maximum energy in eV in reciprocal space to perform
integration for potential correction.
madeltol(float): Convergence criteria for the Madelung energy for potential correction
axis (int): Axis to calculate correction.
If axis is None, then averages over all three axes is performed.
"""
self.q_model = QModel() if not q_model else q_model
self.energy_cutoff = energy_cutoff
self.madetol = madetol
self.dielectric_const = dielectric_const
if isinstance(dielectric_const, int) or \
isinstance(dielectric_const, float):
self.dielectric = float(dielectric_const)
else:
self.dielectric = float(np.mean(np.diag(dielectric_const)))
self.axis = axis
self.metadata = {"pot_plot_data": {}, "pot_corr_uncertainty_md": {}}
def get_correction(self, entry):
"""
Gets the Freysoldt correction for a defect entry
Args:
entry (DefectEntry): defect entry to compute Freysoldt correction on.
Requires following keys to exist in DefectEntry.parameters dict:
axis_grid (3 x NGX where NGX is the length of the NGX grid
in the x,y and z axis directions. Same length as planar
average lists):
A list of 3 numpy arrays which contain the cartesian axis
values (in angstroms) that correspond to each planar avg
potential supplied.
bulk_planar_averages (3 x NGX where NGX is the length of
the NGX grid in the x,y and z axis directions.):
A list of 3 numpy arrays which contain the planar averaged
electrostatic potential for the bulk supercell.
defect_planar_averages (3 x NGX where NGX is the length of
the NGX grid in the x,y and z axis directions.):
A list of 3 numpy arrays which contain the planar averaged
electrostatic potential for the defective supercell.
initial_defect_structure (Structure) structure corresponding to
initial defect supercell structure (uses Lattice for charge correction)
defect_frac_sc_coords (3 x 1 array) Fractional co-ordinates of
defect location in supercell structure
Returns:
FreysoldtCorrection values as a dictionary
"""
if self.axis is None:
list_axis_grid = np.array(entry.parameters["axis_grid"])
list_bulk_plnr_avg_esp = np.array(
entry.parameters["bulk_planar_averages"])
list_defect_plnr_avg_esp = np.array(
entry.parameters["defect_planar_averages"])
list_axes = range(len(list_axis_grid))
else:
list_axes = np.array(self.axis)
list_axis_grid, list_bulk_plnr_avg_esp, list_defect_plnr_avg_esp = [], [], []
for ax in list_axes:
list_axis_grid.append(
np.array(entry.parameters["axis_grid"][ax]))
list_bulk_plnr_avg_esp.append(
np.array(entry.parameters["bulk_planar_averages"][ax]))
list_defect_plnr_avg_esp.append(
np.array(entry.parameters["defect_planar_averages"][ax]))
lattice = entry.parameters["initial_defect_structure"].lattice.copy()
defect_frac_coords = entry.parameters["defect_frac_sc_coords"]
q = entry.defect.charge
es_corr = self.perform_es_corr(lattice, entry.charge)
pot_corr_tracker = []
for x, pureavg, defavg, axis in zip(list_axis_grid,
list_bulk_plnr_avg_esp,
list_defect_plnr_avg_esp,
list_axes):
tmp_pot_corr = self.perform_pot_corr(x,
pureavg,
defavg,
lattice,
entry.charge,
defect_frac_coords,
axis,
widthsample=1.0)
pot_corr_tracker.append(tmp_pot_corr)
pot_corr = np.mean(pot_corr_tracker)
entry.parameters["freysoldt_meta"] = dict(self.metadata)
entry.parameters["potalign"] = pot_corr / (-q) if q else 0.
return {
"freysoldt_electrostatic": es_corr,
"freysoldt_potential_alignment": pot_corr
}
def perform_es_corr(self, lattice, q, step=1e-4):
"""
Peform Electrostatic Freysoldt Correction
Args:
lattice: Pymatgen lattice object
q (int): Charge of defect
step (float): step size for numerical integration
Return:
Electrostatic Point Charge contribution to Freysoldt Correction (float)
"""
logger.info("Running Freysoldt 2011 PC calculation (should be "
"equivalent to sxdefectalign)")
logger.debug("defect lattice constants are (in angstroms)" +
str(lattice.abc))
[a1, a2, a3] = ang_to_bohr * np.array(lattice.get_cartesian_coords(1))
logging.debug("In atomic units, lat consts are (in bohr):" +
str([a1, a2, a3]))
vol = np.dot(a1, np.cross(a2, a3)) # vol in bohr^3
def e_iso(encut):
gcut = eV_to_k(encut) # gcut is in units of 1/A
return scipy.integrate.quad(
lambda g: self.q_model.rho_rec(g * g)**2, step,
gcut)[0] * (q**2) / np.pi
def e_per(encut):
eper = 0
for g2 in generate_reciprocal_vectors_squared(a1, a2, a3, encut):
eper += (self.q_model.rho_rec(g2)**2) / g2
eper *= (q**2) * 2 * round(np.pi, 6) / vol
eper += (q**2) * 4 * round(np.pi,
6) * self.q_model.rho_rec_limit0 / vol
return eper
eiso = converge(e_iso, 5, self.madetol, self.energy_cutoff)
logger.debug("Eisolated : %f", round(eiso, 5))
eper = converge(e_per, 5, self.madetol, self.energy_cutoff)
logger.info("Eperiodic : %f hartree", round(eper, 5))
logger.info("difference (periodic-iso) is %f hartree",
round(eper - eiso, 6))
logger.info("difference in (eV) is %f",
round((eper - eiso) * hart_to_ev, 4))
es_corr = round((eiso - eper) / self.dielectric * hart_to_ev, 6)
logger.info("Defect Correction without alignment %f (eV): ", es_corr)
return es_corr
def perform_pot_corr(self,
axis_grid,
pureavg,
defavg,
lattice,
q,
defect_frac_position,
axis,
widthsample=1.0):
"""
For performing planar averaging potential alignment
Args:
axis_grid (1 x NGX where NGX is the length of the NGX grid
in the axis direction. Same length as pureavg list):
A numpy array which contain the cartesian axis
values (in angstroms) that correspond to each planar avg
potential supplied.
pureavg (1 x NGX where NGX is the length of the NGX grid in
the axis direction.):
A numpy array for the planar averaged
electrostatic potential of the bulk supercell.
defavg (1 x NGX where NGX is the length of the NGX grid in
the axis direction.):
A numpy array for the planar averaged
electrostatic potential of the defect supercell.
lattice: Pymatgen Lattice object of the defect supercell
q (float or int): charge of the defect
defect_frac_position: Fracitional Coordinates of the defect in the supercell
axis (int): axis for performing the freysoldt correction on
widthsample (float): width (in Angstroms) of the region in between defects
where the potential alignment correction is averaged. Default is 1 Angstrom.
Returns:
Potential Alignment contribution to Freysoldt Correction (float)
"""
logging.debug("run Freysoldt potential alignment method for axis " +
str(axis))
nx = len(axis_grid)
# shift these planar averages to have defect at origin
axfracval = defect_frac_position[axis]
axbulkval = axfracval * lattice.abc[axis]
if axbulkval < 0:
axbulkval += lattice.abc[axis]
elif axbulkval > lattice.abc[axis]:
axbulkval -= lattice.abc[axis]
if axbulkval:
for i in range(nx):
if axbulkval < axis_grid[i]:
break
rollind = len(axis_grid) - i
pureavg = np.roll(pureavg, rollind)
defavg = np.roll(defavg, rollind)
# if not self._silence:
logger.debug("calculating lr part along planar avg axis")
reci_latt = lattice.reciprocal_lattice
dg = reci_latt.abc[axis]
dg /= ang_to_bohr # convert to bohr to do calculation in atomic units
# Build background charge potential with defect at origin
v_G = np.empty(len(axis_grid), np.dtype("c16"))
v_G[0] = 4 * np.pi * -q / self.dielectric * self.q_model.rho_rec_limit0
g = np.roll(np.arange(-nx / 2, nx / 2, 1, dtype=int), int(nx / 2)) * dg
g2 = np.multiply(g, g)[1:]
v_G[1:] = 4 * np.pi / (self.dielectric *
g2) * -q * self.q_model.rho_rec(g2)
v_G[nx // 2] = 0 if not (nx % 2) else v_G[nx // 2]
# Get the real space potential by peforming a fft and grabbing the imaginary portion
v_R = np.fft.fft(v_G)
if abs(np.imag(v_R).max()) > self.madetol:
raise Exception("imaginary part found to be %s",
repr(np.imag(v_R).max()))
v_R /= (lattice.volume * ang_to_bohr**3)
v_R = np.real(v_R) * hart_to_ev
# get correction
short = (np.array(defavg) - np.array(pureavg) - np.array(v_R))
checkdis = int((widthsample / 2) / (axis_grid[1] - axis_grid[0]))
mid = int(len(short) / 2)
tmppot = [short[i] for i in range(mid - checkdis, mid + checkdis + 1)]
logger.debug("shifted defect position on axis (%s) to origin",
repr(axbulkval))
logger.debug("means sampling region is (%f,%f)",
axis_grid[mid - checkdis], axis_grid[mid + checkdis])
C = -np.mean(tmppot)
logger.debug("C = %f", C)
final_shift = [short[j] + C for j in range(len(v_R))]
v_R = [elmnt - C for elmnt in v_R]
logger.info("C value is averaged to be %f eV ", C)
logger.info(
"Potentital alignment energy correction (-q*delta V): %f (eV)",
-q * C)
self.pot_corr = -q * C
# log plotting data:
self.metadata["pot_plot_data"][axis] = {
"Vr": v_R,
"x": axis_grid,
"dft_diff": np.array(defavg) - np.array(pureavg),
"final_shift": final_shift,
"check": [mid - checkdis, mid + checkdis + 1]
}
# log uncertainty:
self.metadata["pot_corr_uncertainty_md"][axis] = {
"stats": stats.describe(tmppot)._asdict(),
"potcorr": -q * C
}
return self.pot_corr
def plot(self, axis, title=None, saved=False):
"""
Plots the planar average electrostatic potential against the Long range and
short range models from Freysoldt. Must run perform_pot_corr or get_correction
(to load metadata) before this can be used.
Args:
axis (int): axis to plot
title (str): Title to be given to plot. Default is no title.
saved (bool): Whether to save file or not. If False then returns plot
object. If True then saves plot as str(title) + "FreyplnravgPlot.pdf"
"""
if not self.metadata["pot_plot_data"]:
raise ValueError(
"Cannot plot potential alignment before running correction!")
x = self.metadata['pot_plot_data'][axis]['x']
v_R = self.metadata['pot_plot_data'][axis]['Vr']
dft_diff = self.metadata['pot_plot_data'][axis]['dft_diff']
final_shift = self.metadata['pot_plot_data'][axis]['final_shift']
check = self.metadata['pot_plot_data'][axis]['check']
plt.figure()
plt.clf()
plt.plot(x, v_R, c="green", zorder=1, label="long range from model")
plt.plot(x, dft_diff, c="red", label="DFT locpot diff")
plt.plot(x, final_shift, c="blue", label="short range (aligned)")
tmpx = [x[i] for i in range(check[0], check[1])]
plt.fill_between(tmpx,
-100,
100,
facecolor="red",
alpha=0.15,
label="sampling region")
plt.xlim(round(x[0]), round(x[-1]))
ymin = min(min(v_R), min(dft_diff), min(final_shift))
ymax = max(max(v_R), max(dft_diff), max(final_shift))
plt.ylim(-0.2 + ymin, 0.2 + ymax)
plt.xlabel(r"distance along axis ($\AA$)", fontsize=15)
plt.ylabel("Potential (V)", fontsize=15)
plt.legend(loc=9)
plt.axhline(y=0, linewidth=0.2, color="black")
plt.title(str(title) + " defect potential", fontsize=18)
plt.xlim(0, max(x))
if saved:
plt.savefig(str(title) + "FreyplnravgPlot.pdf")
return
else:
return plt
class FreysoldtCorrection(DefectCorrection):
"""
A class for FreysoldtCorrection class. Largely adapated from PyCDT code
"""
def __init__(self, dielectric_const, q_model=None, energy_cutoff=520, madetol=0.0001, axis=None):
"""
Initializes the Freysoldt Correction
Args:
dielectric_const (float or 3x3 matrix): Dielectric constant for the structure
q_mode (QModel): instantiated QModel object or None. Uses default parameters to instantiate QModel if None supplied
energy_cutoff (int): Maximum energy in eV in recipripcol space to perform integration for potential correction
madeltol(float): Convergence criteria for the Madelung energy for potential correction
axis (int): Axis to calculate correction. Averages over all three if not supplied.
"""
self.q_model = QModel() if not q_model else q_model
self.energy_cutoff = energy_cutoff
self.madetol = madetol
self.dielectric_const = dielectric_const
if isinstance(dielectric_const, int) or \
isinstance(dielectric_const, float):
self.dielectric = float(dielectric_const)
else:
self.dielectric = float(np.mean(np.diag(dielectric_const)))
self.axis = axis
self.metadata = {"pot_plot_data": {}, "pot_corr_uncertainty_md": {}}
def get_correction(self, entry):
"""
Gets the Freysoldt correction for a defect entry
Args:
entry (DefectEntry): defect entry to compute Freysoldt correction on.
Requires following parameters in the DefectEntry to exist:
axis_grid (3 x NGX where NGX is the length of the NGX grid
in the x,y and z axis directions. Same length as planar
average lists):
A list of 3 numpy arrays which contain the cartesian axis
values (in angstroms) that correspond to each planar avg
potential supplied.
bulk_planar_averages (3 x NGX where NGX is the length of
the NGX grid in the x,y and z axis directions.):
A list of 3 numpy arrays which contain the planar averaged
electrostatic potential for the bulk supercell.
defect_planar_averages (3 x NGX where NGX is the length of
the NGX grid in the x,y and z axis directions.):
A list of 3 numpy arrays which contain the planar averaged
electrostatic potential for the defective supercell.
scaling_matrix (3 x 1 matrix): scaling matrix required to convert the
entry.defect.bulk_structure object into the lattice which is used by
the bulk_planar_average and defect_planar_average
"""
if not self.axis:
list_axis_grid = np.array(entry.parameters["axis_grid"])
list_bulk_plnr_avg_esp = np.array(entry.parameters["bulk_planar_averages"])
list_defect_plnr_avg_esp = np.array(entry.parameters["defect_planar_averages"])
list_axes = range(len(list_axis_grid))
else:
list_axes = np.array(self.axis)
list_axis_grid, list_bulk_plnr_avg_esp, list_defect_plnr_avg_esp = [], [], []
for ax in list_axes:
list_axis_grid.append(np.array(entry.parameters["axis_grid"][ax]))
list_bulk_plnr_avg_esp.append(np.array(entry.parameters["bulk_planar_averages"][ax]))
list_defect_plnr_avg_esp.append(np.array(entry.parameters["defect_planar_averages"][ax]))
bulk_struct = entry.defect.bulk_structure.copy()
if "scaling_matrix" in entry.parameters.keys():
bulk_struct.make_supercell(entry.parameters["scaling_matrix"])
lattice = bulk_struct.lattice
q = entry.defect.charge
es_corr = self.perform_es_corr(lattice, entry.charge)
pot_corr_tracker = []
for x, pureavg, defavg, axis in zip(list_axis_grid, list_bulk_plnr_avg_esp, list_defect_plnr_avg_esp,
list_axes):
tmp_pot_corr = self.perform_pot_corr(
x, pureavg, defavg, lattice, entry.charge, entry.site.coords, axis, widthsample=1.0)
pot_corr_tracker.append(tmp_pot_corr)
pot_corr = np.mean(pot_corr_tracker)
entry.parameters["freysoldt_meta"] = dict(self.metadata)
entry.parameters["potalign"] = pot_corr / (-q) if q else 0.
return {"freysoldt_electrostatic": es_corr, "freysoldt_potential_alignment": pot_corr}
def perform_es_corr(self, lattice, q, step=1e-4):
"""
Peform Electrostatic Freysoldt Correction
"""
logger.info("Running Freysoldt 2011 PC calculation (should be " "equivalent to sxdefectalign)")
logger.debug("defect lattice constants are (in angstroms)" + str(lattice.abc))
[a1, a2, a3] = ang_to_bohr * np.array(lattice.get_cartesian_coords(1))
logging.debug("In atomic units, lat consts are (in bohr):" + str([a1, a2, a3]))
vol = np.dot(a1, np.cross(a2, a3)) # vol in bohr^3
def e_iso(encut):
gcut = eV_to_k(encut) # gcut is in units of 1/A
return scipy.integrate.quad(lambda g: self.q_model.rho_rec(g * g)**2, step, gcut)[0] * (q**2) / np.pi
def e_per(encut):
eper = 0
for g2 in generate_reciprocal_vectors_squared(a1, a2, a3, encut):
eper += (self.q_model.rho_rec(g2)**2) / g2
eper *= (q**2) * 2 * round(np.pi, 6) / vol
eper += (q**2) * 4 * round(np.pi, 6) \
* self.q_model.rho_rec_limit0 / vol
return eper
eiso = converge(e_iso, 5, self.madetol, self.energy_cutoff)
logger.debug("Eisolated : %f", round(eiso, 5))
eper = converge(e_per, 5, self.madetol, self.energy_cutoff)
logger.info("Eperiodic : %f hartree", round(eper, 5))
logger.info("difference (periodic-iso) is %f hartree", round(eper - eiso, 6))
logger.info("difference in (eV) is %f", round((eper - eiso) * hart_to_ev, 4))
es_corr = round((eiso - eper) / self.dielectric * hart_to_ev, 6)
logger.info("Defect Correction without alignment %f (eV): ", es_corr)
return es_corr
def perform_pot_corr(self,
axis_grid,
pureavg,
defavg,
lattice,
q,
defect_position,
axis,
madetol=0.0001,
widthsample=1.0):
"""
For performing planar averaging potential alignment
title is for name of plot, if you dont want a plot then leave it as None
widthsample is the width (in Angstroms) of the region in between defects where the potential alignment correction is averaged
"""
logging.debug("run Freysoldt potential alignment method for axis " + str(axis))
nx = len(axis_grid)
# shift these planar averages to have defect at origin
axfracval = lattice.get_fractional_coords(defect_position)[axis]
axbulkval = axfracval * lattice.abc[axis]
if axbulkval < 0:
axbulkval += lattice.abc[axis]
elif axbulkval > lattice.abc[axis]:
axbulkval -= lattice.abc[axis]
if axbulkval:
for i in range(nx):
if axbulkval < axis_grid[i]:
break
rollind = len(axis_grid) - i
pureavg = np.roll(pureavg, rollind)
defavg = np.roll(defavg, rollind)
# if not self._silence:
logger.debug("calculating lr part along planar avg axis")
reci_latt = lattice.reciprocal_lattice
dg = reci_latt.abc[axis]
dg /= ang_to_bohr # convert to bohr to do calculation in atomic units
# Build background charge potential with defect at origin
v_G = np.empty(len(axis_grid), np.dtype("c16"))
v_G[0] = 4 * np.pi * -q / self.dielectric * self.q_model.rho_rec_limit0
g = np.roll(np.arange(-nx / 2, nx / 2, 1, dtype=int), int(nx / 2)) * dg
g2 = np.multiply(g, g)[1:]
v_G[1:] = 4 * np.pi / (self.dielectric * g2) * -q * self.q_model.rho_rec(g2)
v_G[nx // 2] = 0 if not (nx % 2) else v_G[nx // 2]
# Get the real space potential by peforming a fft and grabbing the imaginary portion
v_R = np.fft.fft(v_G)
if abs(np.imag(v_R).max()) > self.madetol:
raise Exception("imaginary part found to be %s", repr(np.imag(v_R).max()))
v_R /= (lattice.volume * ang_to_bohr**3)
v_R = np.real(v_R) * hart_to_ev
# get correction
short = (defavg - pureavg - v_R)
checkdis = int((widthsample / 2) / (axis_grid[1] - axis_grid[0]))
mid = int(len(short) / 2)
tmppot = [short[i] for i in range(mid - checkdis, mid + checkdis + 1)]
logger.debug("shifted defect position on axis (%s) to origin", repr(axbulkval))
logger.debug("means sampling region is (%f,%f)", axis_grid[mid - checkdis], axis_grid[mid + checkdis])
C = -np.mean(tmppot)
logger.debug("C = %f", C)
final_shift = [short[j] + C for j in range(len(v_R))]
v_R = [elmnt - C for elmnt in v_R]
logger.info("C value is averaged to be %f eV ", C)
logger.info("Potentital alignment energy correction (-q*delta V): %f (eV)", -q * C)
self.pot_corr = -q * C
# log plotting data:
self.metadata["pot_plot_data"][axis] = {
"Vr": v_R,
"x": axis_grid,
"dft_diff": defavg - pureavg,
"final_shift": final_shift,
"check": [mid - checkdis, mid + checkdis + 1]
}
# log uncertainty:
self.metadata["pot_corr_uncertainty_md"][axis] = {"stats": stats.describe(tmppot)._asdict(), "potcorr": -q * C}
return self.pot_corr
def plot(self, axis, title=None, saved=False):
"""
Plots the planar average electrostatic potential against the Long range and short range models from Freysoldt
"""
x = self.metadata['pot_plot_data'][axis]['x']
v_R = self.metadata['pot_plot_data'][axis]['Vr']
dft_diff = self.metadata['pot_plot_data'][axis]['dft_diff']
final_shift = self.metadata['pot_plot_data'][axis]['final_shift']
check = self.metadata['pot_plot_data'][axis]['check']
plt.figure()
plt.clf()
plt.plot(x, v_R, c="green", zorder=1, label="long range from model")
plt.plot(x, dft_diff, c="red", label="DFT locpot diff")
plt.plot(x, final_shift, c="blue", label="short range (aligned)")
tmpx = [x[i] for i in range(check[0], check[1])]
plt.fill_between(tmpx, -100, 100, facecolor="red", alpha=0.15, label="sampling region")
plt.xlim(round(x[0]), round(x[-1]))
ymin = min(min(v_R), min(dft_diff), min(final_shift))
ymax = max(max(v_R), max(dft_diff), max(final_shift))
plt.ylim(-0.2 + ymin, 0.2 + ymax)
plt.xlabel("distance along axis ($\AA$)", fontsize=15)
plt.ylabel("Potential (V)", fontsize=15)
plt.legend(loc=9)
plt.axhline(y=0, linewidth=0.2, color="black")
plt.title(str(title) + " defect potential", fontsize=18)
plt.xlim(0, max(x))
if saved:
plt.savefig(str(title) + "FreyplnravgPlot.pdf")
else:
return plt