def permittivity(base_dir="./", mode="df"):
curr_dir = os.path.dirname(os.path.abspath(__file__))
es_gpw = os.path.join(base_dir, "es.gpw")
param_file = os.path.join(curr_dir, "../parameters.json")
if os.path.exists(param_file):
params = json.load(open(param_file, "r"))
else:
raise FileNotFoundError("no parameter file!")
if not os.path.exists(es_gpw):
raise FileNotFoundError("Excited state not calculated!")
if mode not in ("df", "tetra"):
raise ValueError("Mode should be df or tetra")
data_file = os.path.join(base_dir, "polarizability_{}.npz".format(mode))
if os.path.exists(data_file):
parprint("Polarizability file exists!")
return 0
df = DielectricFunction(calc=es_gpw, **params[mode])
eps0x, epsx = df.get_dielectric_function(
q_c=[0, 0, 0],
direction="x",
#pbc=[True, True, False],
filename=None)
eps0y, epsy = df.get_dielectric_function(
q_c=[0, 0, 0],
direction="y",
#pbc=[True, True, False],
filename=None)
eps0z, epsz = df.get_dielectric_function(
q_c=[0, 0, 0],
direction="z",
#pbc=[True, True, False],
filename=None)
freq = df.get_frequencies()
data = dict(
frequencies=freq,
eps_x=epsx,
eps_y=epsy,
eps_z=epsz,
eps_x0=eps0x,
eps_y0=eps0y,
eps_z0=eps0z,
)
from ase.parallel import world
import numpy
if world.rank == 0:
numpy.savez_compressed(data_file, **data)
def dielectric(self, method="rpa"):
method = method.lower()
if method not in ("rpa", "gw"):
raise ValueError("Dielectric Method not known!")
if not os.path.exists(self.__es_file):
raise FileNotFoundError("Ground state not calculated!")
self.__eps_file = self.__eps_file_template.format(method)
if os.path.exists(self.__eps_file):
parprint(("Dielectricfunction using"
" method {} already calculated!").format(method))
return True
if os.path.exists(self.__es_file):
parprint("Excited state done, will use directly!")
if method == "rpa":
df = DielectricFunction(calc=self.__es_file, **self.params[method])
epsx0, epsx = df.get_dielectric_function(direction="x",
filename=None)
epsy0, epsy = df.get_dielectric_function(direction="y",
filename=None)
epsz0, epsz = df.get_dielectric_function(direction="z",
filename=None)
freq = df.get_frequencies()
data = dict(frequencies=freq,
eps_x=epsx,
eps_x0=epsx0,
eps_y=epsy,
eps_y0=epsy0,
eps_z=epsz,
eps_z0=epsz)
# write result
if rank == 0:
numpy.savez(self.__eps_file, **data)
parprint("Dielectric function using {} calculated!".format(method))
return True
else:
raise NotImplementedError("{} not implemented".format(method))
def get_hydrogen_chain_dielectric_function(NH, NK):
a = Atoms('H', cell=[1, 1, 1], pbc=True)
a.center()
a = a.repeat((1, 1, NH))
a.calc = GPAW(mode=PW(200), kpts={'size': (1, 1, NK), 'gamma': True},
parallel={'band': 1}, dtype=complex, gpts=(10, 10, 10 * NH))
a.get_potential_energy()
a.calc.diagonalize_full_hamiltonian(nbands=2 * NH)
a.calc.write('H_chain.gpw', 'all')
DF = DielectricFunction('H_chain.gpw', ecut=1e-3, hilbert=False,
omega2=np.inf, intraband=False)
eps_NLF, eps_LF = DF.get_dielectric_function(direction='z')
omega_w = DF.get_frequencies()
return omega_w, eps_LF
def get_hydrogen_chain_dielectric_function(NH, NK):
a = Atoms('H', cell=[1, 1, 1], pbc=True)
a.center()
a = a.repeat((1, 1, NH))
a.calc = GPAW(mode=PW(200, force_complex_dtype=True),
kpts={'size': (1, 1, NK), 'gamma': True},
parallel={'band': 1},
gpts=(10, 10, 10 * NH))
a.get_potential_energy()
a.calc.diagonalize_full_hamiltonian(nbands=2 * NH)
a.calc.write('H_chain.gpw', 'all')
DF = DielectricFunction('H_chain.gpw', ecut=1e-3, hilbert=False,
omega2=np.inf, intraband=False)
eps_NLF, eps_LF = DF.get_dielectric_function(direction='z')
omega_w = DF.get_frequencies()
return omega_w, eps_LF
import numpy as np
from ase.lattice import bulk
from gpaw import GPAW
from gpaw.response.df import DielectricFunction
# Part 1: Ground state calculation
atoms = bulk('Si', 'diamond', a=5.431) # Generate diamond crystal structure for silicon
calc = GPAW(mode='pw', kpts=(4,4,4)) # GPAW calculator initialization
atoms.set_calculator(calc)
atoms.get_potential_energy() # Ground state calculation is performed
calc.write('si.gpw', 'all') # Use 'all' option to write wavefunction
# Part 2 : Spectrum calculation # DF: dielectric function object
df = DielectricFunction(calc='si.gpw', # Ground state gpw file (with wavefunction) as input
domega0=0.05) # Using nonlinear frequency grid
df.get_dielectric_function() # By default, a file called 'df.csv' is generated
kpts=(4,4,4),
parallel={'band':1},
idiotproof=False, # allow uneven distribution of k-points
xc='LDA')
atoms.set_calculator(calc)
atoms.get_potential_energy()
t2 = time.time()
# Excited state calculation
q = np.array([1/4.,0.,0.])
w = np.linspace(0, 24, 241)
df = DielectricFunction(calc=calc, frequencies=w, eta=0.2, ecut=50)
eels_NLFC_w, eels_LFC_w = df.get_eels_spectrum(filename='EELS_Al', q_c=q)
df_NLFC_w, df_LFC_w = df.get_dielectric_function(q_c=q)
df.check_sum_rule(spectrum=np.imag(df_NLFC_w))
df.check_sum_rule(spectrum=np.imag(df_LFC_w))
df.check_sum_rule(spectrum=eels_NLFC_w)
df.check_sum_rule(spectrum=eels_LFC_w)
#df.write('Al.pckl')
t3 = time.time()
print('')
print('For ground state calc, it took', (t2 - t1) / 60, 'minutes')
print('For excited state calc, it took', (t3 - t2) / 60, 'minutes')
df = DielectricFunction('C.gpw',
frequencies=(0., ),
eta=0.001,
ecut=50,
hilbert=False)
eM1, eM2 = df.get_macroscopic_dielectric_constant()
equal(eM1, eM1_, 0.01)
equal(eM2, eM2_, 0.01)
# Absorption spectrum calculation RPA
df = DielectricFunction('C.gpw',
eta=0.25,
ecut=50,
frequencies=np.linspace(0, 24., 241),
hilbert=False)
a0, a = df.get_dielectric_function(filename=None)
df.check_sum_rule(a.imag)
equal(a0[0].real, eM1_, 0.01)
equal(a[0].real, eM2_, 0.01)
w, I = findpeak(np.linspace(0, 24., 241), a0.imag)
equal(w, w0_, 0.01)
equal(I / (4 * np.pi), I0_, 0.05)
w, I = findpeak(np.linspace(0, 24., 241), a.imag)
equal(w, w_, 0.01)
equal(I / (4 * np.pi), I_, 0.05)
a0, a = df.get_polarizability(filename=None)
w, I = findpeak(np.linspace(0, 24., 241), a0.imag)
equal(w, w0_, 0.01)
atoms.get_potential_energy() # Get ground state density
# Restart Calculation with fixed density and dense kpoint sampling
calc.set(
kpts={
'density': 15.0,
'gamma': False
}, # Dense kpoint sampling
fixdensity=True)
atoms.get_potential_energy()
calc.diagonalize_full_hamiltonian(nbands=70) # Diagonalize Hamiltonian
calc.write('si_large.gpw', 'all') # Write wavefunctions
# Getting absorption spectrum
df = DielectricFunction(calc='si_large.gpw', eta=0.05, domega0=0.02, ecut=150)
df.get_dielectric_function(filename='si_abs.csv')
# Getting macroscopic constant
df = DielectricFunction(
calc='si_large.gpw',
frequencies=[0.0],
hilbert=False,
eta=0.0001,
ecut=150,
)
epsNLF, epsLF = df.get_macroscopic_dielectric_constant()
# Make table
epsrefNLF = 14.08 # From [1] in top
epsrefLF = 12.66 # From [1] in top
eigensolver='rmm-diis',
occupations=FermiDirac(0.01))
cluster.set_calculator(calc)
cluster.get_potential_energy()
calc.diagonalize_full_hamiltonian(nbands=24, scalapack=True)
calc.write('Au2.gpw', 'all')
if ABS:
df = DielectricFunction('Au2.gpw',
frequencies=np.linspace(0, 14, 141),
hilbert=not True,
eta=0.1,
ecut=10)
b0, b = df.get_dielectric_function(filename=None,
direction='z')
a0, a = df.get_polarizability(filename=None,
direction='z')
df_ws = DielectricFunction('Au2.gpw',
frequencies=np.linspace(0, 14, 141),
hilbert=not True,
eta=0.1,
ecut=10,
truncation='wigner-seitz')
a0_ws, a_ws = df_ws.get_polarizability(filename=None,
direction='z')
w0_ = 5.60491055
I0_ = 244.693028
w_ = 5.696528390
# Use twice as many bands for expanded structure
a1.calc.diagonalize_full_hamiltonian(nbands=20)
a2.calc.diagonalize_full_hamiltonian(nbands=40)
a1.calc.write('gs_Na_small.gpw', 'all')
a2.calc.write('gs_Na_large.gpw', 'all')
# Calculate the dielectric functions
df1 = DielectricFunction('gs_Na_small.gpw',
omegamax=15,
domega0=0.05,
hilbert=True,
ecut=150)
df1NLFCx, df1LFCx = df1.get_dielectric_function(direction='x')
df1NLFCy, df1LFCy = df1.get_dielectric_function(direction='y')
df1NLFCz, df1LFCz = df1.get_dielectric_function(direction='z')
df2 = DielectricFunction('gs_Na_large.gpw',
omegamax=15,
domega0=0.05,
hilbert=True,
ecut=150)
df2NLFCx, df2LFCx = df2.get_dielectric_function(direction='x')
df2NLFCy, df2LFCy = df2.get_dielectric_function(direction='y')
df2NLFCz, df2LFCz = df2.get_dielectric_function(direction='z')
# Compare plasmon frequencies and intensities
w_w = df1.chi0.omega_w
import numpy as np
from ase.lattice import bulk
from gpaw import GPAW
from gpaw.response.df import DielectricFunction
# Part 1: Ground state calculation
atoms = bulk('Si', 'diamond',
a=5.431) # Generate diamond crystal structure for silicon
calc = GPAW(mode='pw', kpts=(4, 4, 4)) # GPAW calculator initialization
atoms.set_calculator(calc)
atoms.get_potential_energy() # Ground state calculation is performed
calc.write('si.gpw', 'all') # Use 'all' option to write wavefunction
# Part 2 : Spectrum calculation # DF: dielectric function object
df = DielectricFunction(
calc='si.gpw', # Ground state gpw file (with wavefunction) as input
domega0=0.05) # Using nonlinear frequency grid
df.get_dielectric_function() # By default, a file called 'df.csv' is generated
from gpaw.response.df import DielectricFunction as DF
df = DF(
'LiF_fulldiag.gpw',
domega0=0.01, # grid-spacing at 0 eV
omega2=10.0, # frequency where grid-spacing has doubled to 0.02 eV
eta=0.1, # broadening parameter
nbands=60, # number of bands to consider for building chi
ecut=30, # energy cutoff for planewaves
txt='LiF_RPA_out2.txt')
# Calculate the dielectric function without and with local field effects:
df.get_dielectric_function()
ecut = 50
eshift = 0.8
eta = 0.2
df = DielectricFunction('gs_Si.gpw',
ecut=ecut,
frequencies=np.linspace(0., 10., 1001),
nbands=8,
intraband=False,
hilbert=False,
eta=eta,
eshift=eshift,
txt='rpa_Si.txt')
df.get_dielectric_function(filename='eps_rpa_Si.csv')
bse = BSE('gs_Si.gpw',
ecut=ecut,
valence_bands=range(0, 4),
conduction_bands=range(4, 8),
nbands=50,
eshift=eshift,
mode='BSE',
integrate_gamma=0,
txt='bse_Si.txt')
bse.get_dielectric_function(filename='eps_bse_Si.csv',
eta=eta,
write_eig='bse_Si_eig.dat',
w_w=np.linspace(0.0, 10.0, 10001))
from gpaw.response.df import DielectricFunction as DF
df = DF('LiF_fulldiag.gpw',
domega0=0.01, # grid-spacing at 0 eV
omega2=10.0, # frequency where grid-spacing has doubled to 0.02 eV
eta=0.1, # broadening parameter
nbands=60, # number of bands to consider for building chi
ecut=30, # energy cutoff for planewaves
txt='LiF_RPA_out2.txt')
# Calculate the dielectric function without and with local field effects:
df.get_dielectric_function()
atoms.set_calculator(calc)
atoms.get_potential_energy() # Get ground state density
# Restart Calculation with fixed density and dense kpoint sampling
calc.set(kpts={'density': 15.0, 'gamma': False}, # Dense kpoint sampling
fixdensity=True)
atoms.get_potential_energy()
calc.diagonalize_full_hamiltonian(nbands=70) # Diagonalize Hamiltonian
calc.write('si_large.gpw', 'all') # Write wavefunctions
# Getting absorption spectrum
df = DielectricFunction(calc='si_large.gpw',
eta=0.05,
domega0=0.02,
ecut=150)
df.get_dielectric_function(filename='si_abs.csv')
# Getting macroscopic constant
df = DielectricFunction(calc='si_large.gpw',
frequencies=[0.0],
hilbert=False,
eta=0.0001,
ecut=150,
)
epsNLF, epsLF = df.get_macroscopic_dielectric_constant()
# Make table
epsrefNLF = 14.08 # From [1] in top
epsrefLF = 12.66 # From [1] in top
kpts=kpts,
parallel={'band': 1},
nbands=60,
convergence={'bands': 50})
responseGS.get_potential_energy()
responseGS.write('TaS2-gsresponse.gpw', 'all')
# 3) Dielectric function
df = DielectricFunction('TaS2-gsresponse.gpw',
eta=25e-3,
domega0=0.01,
integrationmode='tetrahedron integration')
df1tetra_w, df2tetra_w = df.get_dielectric_function(direction='x')
df = DielectricFunction('TaS2-gsresponse.gpw', eta=25e-3, domega0=0.01)
df1_w, df2_w = df.get_dielectric_function(direction='x')
omega_w = df.get_frequencies()
if world.rank == 0:
plt.figure(figsize=(6, 6))
plt.plot(omega_w, df2tetra_w.real, label='tetra Re')
plt.plot(omega_w, df2tetra_w.imag, label='tetra Im')
plt.plot(omega_w, df2_w.real, label='Re')
plt.plot(omega_w, df2_w.imag, label='Im')
plt.xlabel('Frequency (eV)')
plt.ylabel('$\\varepsilon$')
plt.xlim(0, 10)
plt.ylim(-20, 20)
pbc=pbc)
responseGS = GPAW('gs.gpw',
fixdensity=True,
kpts=kpts,
parallel={'band': 1},
nbands=30,
occupations=FermiDirac(0.001),
convergence={'bands': 20})
responseGS.get_potential_energy()
responseGS.write('gsresponse.gpw', 'all')
df = DielectricFunction('gsresponse.gpw', eta=25e-3,
pbc=pbc, domega0=0.01,
integrationmode='tetrahedron integration')
df1tetra, df2tetra = df.get_dielectric_function(q_c=[0, 0, 0])
df = DielectricFunction('gsresponse.gpw',
domega0=0.01,
eta=25e-3)
df1, df2 = df.get_dielectric_function(q_c=[0, 0, 0])
omega_w = df.get_frequencies()
if world.rank == 0:
plt.figure(figsize=(6, 6))
plt.plot(omega_w, df2.imag * 2, label='Point sampling')
plt.plot(omega_w, df2tetra.imag * 2, label='Tetrahedron')
# Analytical result for graphene
sigmainter = 1 / 4. # The surface conductivity of graphene
with seterr(divide='ignore', invalid='ignore'):
dfanalytic = 1 + (4 * np.pi * 1j / (omega_w / Hartree) *
eigensolver='rmm-diis',
occupations=FermiDirac(0.01))
cluster.set_calculator(calc)
cluster.get_potential_energy()
calc.diagonalize_full_hamiltonian(nbands=24, scalapack=True)
calc.write('Au2.gpw', 'all')
if ABS:
df = DielectricFunction('Au2.gpw',
frequencies=np.linspace(0, 14, 141),
hilbert=not True,
eta=0.1,
ecut=10)
b0, b = df.get_dielectric_function(filename=None, direction='z')
a0, a = df.get_polarizability(filename=None, direction='z')
df_ws = DielectricFunction('Au2.gpw',
frequencies=np.linspace(0, 14, 141),
hilbert=not True,
eta=0.1,
ecut=10,
truncation='wigner-seitz')
a0_ws, a_ws = df_ws.get_polarizability(filename=None, direction='z')
w0_ = 5.60491055
I0_ = 244.693028
w_ = 5.696528390
I_ = 207.8
# Macroscopic dielectric constant calculation
df = DielectricFunction('C.gpw', frequencies=(0.,), eta=0.001, ecut=200,
hilbert=False)
eM1, eM2 = df.get_macroscopic_dielectric_constant()
eM1_ = 9.725
eM2_ = 9.068
equal(eM1, eM1_, 0.01)
equal(eM2, eM2_, 0.01)
# Absorption spectrum calculation
df = DielectricFunction('C.gpw', eta=0.25, ecut=200,
frequencies=np.linspace(0, 24., 241), hilbert=False)
b0, b = df.get_dielectric_function(filename=None)
df.check_sum_rule(b.imag)
equal(b0[0].real, eM1_, 0.01)
equal(b[0].real, eM2_, 0.01)
a0, a = df.get_polarizability(filename=None)
df_ws = DielectricFunction('C.gpw', eta=0.25, ecut=200,
frequencies=np.linspace(0, 24., 241), hilbert=False,
truncation='wigner-seitz')
a0_ws, a_ws = df_ws.get_polarizability(filename=None)
w0_ = 10.778232265664668
I0_ = 5.5467658790816268
mode=PW(600),
occupations=FermiDirac(0.2),
**GSkwargs)
atoms.set_calculator(calc)
atoms.get_potential_energy()
calc.write('gr.gpw', 'all')
dfs = []
for kwargs in DFsettings:
DF = DielectricFunction(calc='gr.gpw',
domega0=0.2,
eta=0.2,
ecut=40.0,
**kwargs)
df1, df2 = DF.get_dielectric_function()
if world.rank == 0:
dfs.append(df1)
# Check the calculated dielectric functions against
# each other.
while len(dfs):
df = dfs.pop()
for DFkwargs, df2 in zip(DFsettings[-len(dfs):], dfs):
try:
assert np.allclose(df, df2)
print('Ground state settings:', GSkwargs)
print('DFkwargs1:', DFsettings[-len(dfs) - 1])
print('DFkwargs2:', DFkwargs)
print(np.max(np.abs((df - df2) / df)))
except AssertionError:
