def test_make_grid():
# This unit test doesn't pass because the primitive translation vectors
# changed when I updated the code (I think).
grid_pts1 = [[0, 0, 0], [1, 1, 1], [0, 0, 2], [0, 2, 0], [0, 2, 2],
[2, 0, 0], [0, 2, 2], [2, 0, 2], [2, 2, 0], [2, 2, 2],
[1, 3, 3], [3, 1, 3], [3, 1, 1], [1, 1, 3], [1, 3, 1],
[3, 1, 1]]
grid_pts1 = np.asarray(grid_pts1) * 1. / 4
cell_centering = "prim"
cell_const = 1.
cell_const_list = [cell_const] * 3
cell_angles = [np.pi / 2] * 3
cell_vecs = make_ptvecs(cell_centering, cell_const_list, cell_angles)
grid_centering = "body"
grid_const = cell_const / 2
grid_const_list = [grid_const] * 3
grid_angles = [np.pi / 2] * 3
grid_vecs = make_ptvecs(grid_centering, grid_const_list, grid_angles)
offset = np.asarray([0., 0., 0.])
grid = make_grid(cell_vecs, grid_vecs, offset, False)
for g1 in grid_pts1:
check = False
for g2 in grid:
if np.allclose(g1, g2) == True:
check = True
assert check == True
lat_type_list = ["fcc", "bcc", "sc"]
lat_centering_list = ["face", "body", "prim"]
lat_const_list = [10, 10.1, 3 * np.pi]
lat_consts_list = [[l] * 3 for l in lat_const_list]
lat_angles = [np.pi / 2] * 3
offset_list = [[1.3, 1.1, 1.7], [11, 9, 8], [np.pi, np.pi, np.pi]]
r_list = [1, 2.3, np.pi]
for lat_centering in lat_centering_list:
for lat_consts in lat_consts_list:
lat_vecs = make_ptvecs(lat_centering, lat_consts, lat_angles)
lat_vecs = make_rptvecs(lat_vecs)
for offset in offset_list:
offset = np.asarray(offset)
for r in r_list:
total_grid = large_sphere_pts(lat_vecs, r, offset)
grid = sphere_pts(lat_vecs, r, offset)
contained = False
for tg in total_grid:
if np.dot(tg - offset, tg - offset) <= r:
contained = False
for g in grid:
if np.allclose(g, tg):
contained = True
assert contained == True
def test_make_grid():
grid_centering = "prim"
grid_consts = [1, 1, 1]
grid_angles = [np.pi / 2] * 3
grid_vecs = make_ptvecs(grid_centering, grid_consts, grid_angles)
lat_centering = "prim"
lat_consts = [2] * 3
lat_angles = [np.pi / 2] * 3
lat_vecs = make_ptvecs(lat_centering, lat_consts, lat_angles)
offset = [0] * 3
grid0 = [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 1, 1], [1, 0, 0], [1, 0, 1],
[1, 1, 0], [1, 1, 1]]
grid1 = make_grid(lat_vecs, grid_vecs, offset)
assert len(grid0) == len(grid1)
for g0 in grid0:
contained = False
for g1 in grid1:
if np.allclose(g0, g1):
contained = True
assert contained == True
grid_centering = "body"
grid_consts = [1.] * 3
grid_angles = [np.pi / 2] * 3
grid_vecs = make_ptvecs(grid_centering, grid_consts, grid_angles)
lat_centering = "body"
lat_consts = [2.] * 3
lat_angles = [np.pi / 2] * 3
lat_vecs = make_ptvecs(lat_centering, lat_consts, lat_angles)
offset = [0] * 3
a = 0.5
grid0 = [[0, 0, 0], [-a, a, a], [a, -a, a], [0, 0, 2 * a], [a, a, -a],
[0, 2 * a, 0], [2 * a, 0, 0], [a, a, a]]
grid1 = make_grid(lat_vecs, grid_vecs, offset)
assert len(grid0) == len(grid1)
for g0 in grid0:
contained = False
for g1 in grid1:
if np.allclose(g0, g1):
contained = True
assert contained == True
def __init__(self,
pseudo_potential=None,
cutoff=None,
cell_centering=None,
cell_constants=None,
cell_angles=None,
offset=None,
grid_types=None,
grid_constants=None,
integration_methods=None,
origin=None,
random=None):
self.pseudo_potential = pseudo_potential or Al_PP
self.cutoff = cutoff or 4.
self.cell_centering = cell_centering or "prim"
self.cell_constants = cell_constants or [1.] * 3
self.cell_angles = cell_angles or [np.pi / 2] * 3
self.cell_vectors = make_ptvecs(self.cell_centering,
self.cell_constants, self.cell_angles)
self.grid_centerings = grid_centerings or [
"prim", "base", "body", "face"
]
self.grid_constants = grid_constants or [1 / n for n in range(2, 11)]
self.offset = offset or [0., 0., 0.]
# self.integration_methods = integration_methods or [rectangle_method]
self.origin = origin or [0., 0., 0.]
self.random = random or False
def plot_grid(self, i, j):
"""Plot one of the grids in the convergence plot.
"""
grid_vecs = make_ptvecs(self.grid_types[i], self.grid_constants[j])
grid_pts = make_grid(self.rcell_vectors, gr_vecs, self.offset)
PlotMesh(grid_pts, self.rcell_vectors, self.offset)
def test_make_cell_points():
"""Verify the grid satisfies various properties, such as verifying
the neighbors of each point are withing the grid as long as the
neighbors lie within the unit cell. Also verify none of the points
lie outside the unit cell.
"""
# At the moment it only tests the cubic lattices.
grid_center_list = ["prim", "face", "body"]
grid_constants = np.array([1. / 2, 1. / 4]) * 2 * np.sqrt(2)
grid_consts_list = [[m] * 3 for m in grid_constants]
grid_angles = [np.pi / 2] * 3
cell_center_list = ["prim", "face", "body"]
cell_constants = [2 * np.sqrt(2)]
cell_consts_list = [[c] * 3 for c in cell_constants]
cell_angles = [np.pi / 2] * 3
offsets = [[0., 0., 0.], [1. / 2, 1. / 2, 1. / 2]]
# for grid_constant in grid_constants:
for grid_consts in grid_consts_list:
for grid_center in grid_center_list:
grid_vectors = make_ptvecs(grid_center, grid_consts, grid_angles)
grid_lengths = [np.linalg.norm(lv) for lv in grid_vectors]
for cell_consts in cell_consts_list:
for cell_center in cell_center_list:
cell_vectors = make_ptvecs(cell_center, cell_consts,
cell_angles)
cell_lengths = [np.linalg.norm(cv) for cv in cell_vectors]
for offset in offsets:
grid = make_cell_points(cell_vectors, grid_vectors,
offset)
grid2, null_grid = make_large_grid(
cell_vectors, grid_vectors, offset)
# Verify all the points in the cell for the large grid
# are contained in grid.
print(grid_consts)
print(grid_center)
print(cell_consts)
print(cell_center)
print(offset)
for g in grid:
included = False
for g2 in grid2:
if np.allclose(g, g2):
included = True
assert included == True
def test_rectangular():
"""This will test the rectangular methods of finding the total energy and the
Fermi level.
"""
degree_list = range(1,5)
for degree in degree_list:
# Verify the Fermi level of the free electron model.
lat_angles =[np.pi/2]*3
lat_consts = [1]*3
lat_centering = "prim"
lattice = Lattice(lat_centering, lat_consts, lat_angles)
free = FreeElectronModel(lattice, degree)
grid_consts = [40]*3
grid_angles = [np.pi/2]*3
grid_centering = "prim"
grid_vecs = make_ptvecs(grid_centering, grid_consts, grid_angles)
rgrid_vecs = make_rptvecs(grid_vecs)
offset = -np.dot(np.linalg.inv(rgrid_vecs),
np.dot(lattice.reciprocal_vectors, [.5]*3))
grid = make_grid(free.lattice.reciprocal_vectors, rgrid_vecs, offset)
weights = np.ones(len(grid))
free.fermi_level, temp = rectangular_method(free, grid, weights)
sphere_volume = 4./3*np.pi*free.fermi_level**(3./degree)
occupied_volume = free.lattice.reciprocal_volume*free.nvalence_electrons/2
fl_answer = (3*occupied_volume/(4*np.pi))**(degree/3.)
print("degree ", degree)
print("shere volume ", sphere_volume)
print("occupied_volume ", occupied_volume)
assert np.isclose(sphere_volume, occupied_volume, 1e-1, 1e-1)
assert np.isclose(free.fermi_level, fl_answer, 1e-2,1e-2)
weights = np.ones(len(grid))
temp, total_energy = rectangular_method(free, grid, weights)
rf = free.fermi_level**(1./degree)
te_answer = 4*np.pi*(rf**(3 + degree)/(3. + degree))
assert np.isclose(total_energy, te_answer, 1e-1, 1e-1)
def compare_grids(self, answer, plot=False, save=False):
self.answer = answer
if self.random:
nm = len(self.grid_types)
self.nspts = [[] for _ in range(nm + 1)]
self.errors = [[] for _ in range(nm + 1)]
self.integrals = [[] for _ in range(nm + 1)]
self.times = [[] for _ in range(nm + 1)]
npts_list = [2**n for n in range(8, 14)]
for npts in npts_list:
time1 = time.time()
integral = monte_carlo(self.pseudo_potential,
self.cell_vectors, npts, self.cutoff)
self.nspts[nm].append(npts)
self.integrals[nm].append(integral)
self.times[nm].append((time.time() - time1))
self.errors[nm].append(np.abs(self.integrals[nm][-1] - answer))
else:
self.nspts = [[] for _ in range(len(self.grid_types))]
self.errors = [[] for _ in range(len(self.grid_types))]
self.integrals = [[] for _ in range(len(self.grid_types))]
self.times = [[] for _ in range(len(self.grid_types))]
integration_method = self.integration_methods[0]
for (i, grid_centering) in enumerate(self.grid_centering_list):
for grid_consts in self.grid_constants_list:
for grid_angles in grid_angles_list:
grid_vecs = make_ptvecs(grid_centering, grid_consts,
grid_angles)
time1 = time.time()
npts, integral = integration_method(
self.pseudo_potential, self.cell_vectors, grid_vecs,
self.offset, self.origin, self.cutoff)
self.nspts[i].append(npts)
self.integrals[i].append(integral)
self.times[i].append((time.time() - time1))
self.errors[i].append(np.abs(self.integrals[i][-1] - answer))
if save:
np.save("%s_times" % self.pseudo_potential, self.times)
np.save("%s_integrals" % self.pseudo_potential, self.integrals)
np.save("%s_errors" % self.pseudo_potential, self.errors)
if plot:
if self.random:
plt.loglog(self.nspts[nm],
self.errors[nm],
label="random",
color="orange")
for i in range(len(self.grid_types)):
plt.loglog(self.nspts[i],
self.errors[i],
label=self.grid_types[i])
plt.xlabel("Number of samping points")
plt.ylabel("Error")
test = [1. / n**(2. / 3) for n in self.nspts[0]]
plt.loglog(self.nspts[0], test, label="1/n**(2/3)")
lgd = plt.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.grid()
plt.show()
plt.close()
for i in range(len(self.grid_types)):
plt.loglog(self.nspts[i],
self.times[i],
label=self.grid_types[i])
plt.xlabel("Number of samping points")
plt.ylabel("Time (s)")
lgd = plt.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.grid()
plt.show()
plt.close()
def PlotVaspBandStructure(file_loc,
material,
lat_type,
lat_consts,
lat_angles,
energy_shift=0.0,
fermi_level=False,
elimits=False,
save=False,
show=True):
"""Plot the band structure from a VASP INCAR, KPOINT, and OUTCAR file.
Args:
file_loc (str): the location of the directory with the VASP output files.
The KPOINTS file MUST be in a very particular format: there must be
4 introductory lines, each k-point must be on its own line and there
must only be one space between pairs of k-points. There mustn't be
any space after the last entered k-point.
material (str): the material whose band structure is being plotted.
lat_type (str): the lattice type
energy_shift (float): energy shift for band structure
fermi_level (bool): if true, plot the Fermi level.
elimits (list): the energy window for the plot.
save (bool): if true, the band structure will be saved.
show (bool): if false, return none. This is useful for showing multiple
plots.
Returns:
Display or save the band structure.
"""
# Get the correct symmetry point dictionary.
if lat_type == "fcc":
sympt_dict = fcc_sympts
lat_centering = "face"
elif lat_type == "bcc":
sympt_dict = bcc_sympts
lat_centering = "body"
elif lat_type == "sc":
sympt_dict = sc_sympts
lat_centering = "prim"
else:
raise ValueError("Invalid lattice type")
# Extract the lattice constant from the POSCAR file.
sympt_list = []
with open(file_loc + "POSCAR", "r") as file:
lat_const = ""
f = file.readlines()
for c in f[1]:
try:
int(c)
lat_const += c
except:
if c == ".":
lat_const += c
if c == "!":
break
continue
lat_const = float(lat_const)
angstrom_to_Bohr = 1.889725989
lat_const *= angstrom_to_Bohr
lat_vecs = make_ptvecs(lat_centering, lat_consts, lat_angles)
rlat_vecs = make_rptvecs(lat_vecs)
nbands = ""
with open(file_loc + "INCAR", "r") as file:
f = file.readlines()
for line in f:
if "NBANDS" in line:
for l in line:
try:
int(l)
nbands += l
except ValueError:
continue
# nbands = int(nbands)
nbands = 10
# Extract the total number of k-points, number of k-points per path,
# the number of paths and the symmetry points from the KPOINTs file.
with open(file_loc + "KPOINTS", "r") as file:
f = file.readlines()
npts_path = int(f[1].split()[0])
npaths = (len(f) - 3) / 3
nkpoints = int(npts_path * npaths)
sympt_list = []
f = f[4:]
for line in f:
spt = ""
sline = line.strip()
for l in sline:
if (l == " " or l == "!" or l == "." or l == "\t"):
continue
else:
try:
int(l)
except:
spt += l
if spt != "":
sympt_list.append(spt)
for i, sympt in enumerate(sympt_list):
if sympt == "gamma" or sympt == "Gamma":
sympt_list[i] = "G"
# Remove all duplicate symmetry points
unique_sympts = [sympt_list[i]
for i in range(0, len(sympt_list), 2)] + [sympt_list[-1]]
# Replace symbols representing points with their lattice coordinates.
lat_sympt_coords = [sympt_dict[sp] for sp in unique_sympts]
car_sympt_coords = [np.dot(rlat_vecs, k) for k in lat_sympt_coords]
with open(file_loc + "OUTCAR", "r") as file:
f = file.readlines()
EFERMI = ""
for line in f:
sline = line.strip()
if "EFERMI" in sline:
for c in sline:
try:
int(c)
EFERMI += c
except:
if c == ".":
EFERMI += c
EFERMI = float(EFERMI)
id_line = " band No. band energies occupation \n"
with open(file_loc + "OUTCAR", "r") as file:
f = file.readlines()
energies = []
occupancies = []
en_occ = []
lat_kpoints = []
nkpt = 0
nkpts_dr = 0 # number of kpoints with duplicates removed
for i, line in enumerate(f):
if line == id_line:
nkpt += 1
if nkpt % npts_path == 0 and nkpt != nkpoints:
continue
else:
nkpts_dr += 1
energies.append([])
occupancies.append([])
en_occ.append([])
lat_kpoints.append(list(map(float, f[i - 1].split()[3:6])))
for j in range(1, nbands + 1):
energies[nkpts_dr - 1].append(
float(f[i + j].split()[1]) - energy_shift)
occupancies[nkpts_dr - 1].append(
float(f[i + j].split()[2]))
en_occ[nkpts_dr -
1].append(energies[nkpts_dr - 1][-1] *
(occupancies[nkpts_dr - 1][-1] / 2))
car_kpoints = [np.dot(rlat_vecs, k) for k in lat_kpoints]
# Find the distances between symmetry points.
nsympts = len(unique_sympts)
sympt_dist = [0] + [
norm(car_sympt_coords[i + 1] - car_sympt_coords[i])
for i in range(nsympts - 1)
]
# Create coordinates for plotting
lines = []
for i in range(nsympts - 1):
start = np.sum(sympt_dist[:i + 1])
stop = np.sum(sympt_dist[:i + 2])
if i == (nsympts - 2):
lines += list(np.linspace(start, stop, npts_path))
else:
lines += list(np.delete(np.linspace(start, stop, npts_path), -1))
for nb in range(nbands):
ienergy = []
for nk in range(len(car_kpoints)):
ienergy.append(energies[nk][nb])
if nb == 0:
plt.plot(lines, ienergy, label="VASP Band structure", color="blue")
else:
plt.plot(lines, ienergy, color="blue")
# Plot a vertical line at the symmetry points with proper labels.
for i in range(nsympts):
pos = np.sum(sympt_dist[:i + 1])
plt.axvline(x=pos, c="gray")
tick_labels = unique_sympts
tick_locs = [np.sum(sympt_dist[:i + 1]) for i in range(nsympts)]
plt.xticks(tick_locs, tick_labels)
# Adjust the energy range if one was provided.
if elimits:
plt.ylim(elimits)
if fermi_level:
plt.axhline(y=EFERMI, c="yellow", label="Fermi level")
# Adjust the legend.
lgd = plt.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.xlim([0, np.sum(sympt_dist)])
plt.xlabel("Symmetry points")
plt.ylabel("Energy (eV)")
plt.title("%s Band Structure" % material)
plt.grid(linestyle="dotted")
if save:
plt.savefig("%s_band_struct.pdf" % material,
bbox_extra_artists=(lgd, ),
bbox_inches='tight')
elif show:
plt.show()
else:
return None