def __init__(self, calc, omega_w, ecut=50, hilbert=False,
timeordered=False, eta=0.2, ftol=1e-6,
real_space_derivatives=False,
world=mpi.world, txt=sys.stdout):
PairDensity.__init__(self, calc, ecut, ftol,
real_space_derivatives, world, txt)
eta /= Hartree
self.omega_w = omega_w = np.asarray(omega_w) / Hartree
self.hilbert = hilbert
self.timeordered = bool(timeordered)
self.eta = eta
if eta == 0.0:
assert not hilbert
assert not timeordered
assert not omega_w.real.any()
self.mysKn1n2 = None # my (s, K, n1, n2) indices
self.distribute_k_points_and_bands(self.nocc2)
self.mykpts = [self.get_k_point(s, K, n1, n2)
for s, K, n1, n2 in self.mysKn1n2]
wfs = self.calc.wfs
self.prefactor = 2 / self.vol / wfs.kd.nbzkpts / wfs.nspins
def __init__(self, calc,
frequencies=None, domega0=0.1, omega2=10.0, omegamax=None,
ecut=50, hilbert=True, nbands=None,
timeordered=False, eta=0.2, ftol=1e-6, threshold=1,
real_space_derivatives=False, intraband=True,
world=mpi.world, txt=sys.stdout, timer=None,
nblocks=1, no_optical_limit=False,
keep_occupied_states=False, gate_voltage=None,
disable_point_group=False, disable_time_reversal=False,
use_more_memory=0, unsymmetrized=True, eshift=None):
PairDensity.__init__(self, calc, ecut, ftol, threshold,
real_space_derivatives, world, txt, timer,
nblocks=nblocks,
gate_voltage=gate_voltage, eshift=eshift)
self.eta = eta / Hartree
self.domega0 = domega0 / Hartree
self.omega2 = omega2 / Hartree
self.omegamax = None if omegamax is None else omegamax / Hartree
self.nbands = nbands or self.calc.wfs.bd.nbands
self.keep_occupied_states = keep_occupied_states
self.intraband = intraband
self.no_optical_limit = no_optical_limit
self.disable_point_group = disable_point_group
self.disable_time_reversal = disable_time_reversal
self.use_more_memory = use_more_memory
self.unsymmetrized = unsymmetrized
omax = self.find_maximum_frequency()
if frequencies is None:
if self.omegamax is None:
self.omegamax = omax
print('Using nonlinear frequency grid from 0 to %.3f eV' %
(self.omegamax * Hartree), file=self.fd)
self.omega_w = frequency_grid(self.domega0, self.omega2,
self.omegamax)
else:
self.omega_w = np.asarray(frequencies) / Hartree
assert not hilbert
self.hilbert = hilbert
self.timeordered = bool(timeordered)
if self.eta == 0.0:
assert not hilbert
assert not timeordered
assert not self.omega_w.real.any()
# Occupied states:
wfs = self.calc.wfs
self.mysKn1n2 = None # my (s, K, n1, n2) indices
self.distribute_k_points_and_bands(0, self.nocc2,
kpts=range(wfs.kd.nibzkpts))
self.mykpts = None
self.prefactor = 2 / self.vol / wfs.kd.nbzkpts / wfs.nspins
self.chi0_vv = None # strength of intraband peak
def __init__(self, calc,
frequencies=None, domega0=0.1, omega2=10.0, omegamax=None,
ecut=50, hilbert=True, nbands=None,
timeordered=False, eta=0.2, ftol=1e-6, threshold=1,
real_space_derivatives=False, intraband=True,
world=mpi.world, txt=sys.stdout, timer=None,
nblocks=1, no_optical_limit=False,
keep_occupied_states=False, gate_voltage=None):
PairDensity.__init__(self, calc, ecut, ftol, threshold,
real_space_derivatives, world, txt, timer,
nblocks=nblocks,
gate_voltage=gate_voltage)
self.eta = eta / Hartree
self.domega0 = domega0 / Hartree
self.omega2 = omega2 / Hartree
self.omegamax = None if omegamax is None else omegamax / Hartree
self.nbands = nbands or self.calc.wfs.bd.nbands
self.keep_occupied_states = keep_occupied_states
self.intraband = intraband
self.no_optical_limit = no_optical_limit
omax = self.find_maximum_frequency()
if frequencies is None:
if self.omegamax is None:
self.omegamax = omax
print('Using nonlinear frequency grid from 0 to %.3f eV' %
(self.omegamax * Hartree), file=self.fd)
self.omega_w = frequency_grid(self.domega0, self.omega2,
self.omegamax)
else:
self.omega_w = np.asarray(frequencies) / Hartree
assert not hilbert
self.hilbert = hilbert
self.timeordered = bool(timeordered)
if self.eta == 0.0:
assert not hilbert
assert not timeordered
assert not self.omega_w.real.any()
# Occupied states:
self.mysKn1n2 = None # my (s, K, n1, n2) indices
self.distribute_k_points_and_bands(0, self.nocc2)
self.mykpts = None
wfs = self.calc.wfs
self.prefactor = 2 / self.vol / wfs.kd.nbzkpts / wfs.nspins
self.chi0_vv = None # strength of intraband peak
def update_optical_limit(self, n, m, kpt1, kpt2, deps_m, df_m, n_mG,
chi0_wxvG, chi0_wvv):
n0_mv = PairDensity.update_optical_limit(self, n, m, kpt1, kpt2,
deps_m, df_m, n_mG)
if self.hilbert:
self.update_optical_limit_hilbert(n0_mv, deps_m, df_m, n_mG,
chi0_wxvG, chi0_wvv)
return
if self.timeordered:
# avoid getting a zero from np.sign():
deps1_m = deps_m + 1j * self.eta * np.sign(deps_m + 1e-20)
deps2_m = deps1_m
else:
deps1_m = deps_m + 1j * self.eta
deps2_m = deps_m - 1j * self.eta
for w, omega in enumerate(self.omega_w):
x_m = self.prefactor * df_m * (1 / (omega + deps1_m) -
1 / (omega - deps2_m))
chi0_wvv[w] += np.dot(x_m * n0_mv.T, n0_mv.conj())
chi0_wxvG[w, 0, :, 1:] += np.dot(x_m * n0_mv.T, n_mG[:, 1:].conj())
chi0_wxvG[w, 1, :, 1:] += np.dot(x_m * n0_mv.T.conj(), n_mG[:, 1:])
def update_optical_limit(self, n, m, kpt1, kpt2, deps_m, df_m, n_mG,
chi0_wxvG, chi0_wvv):
n0_mv = PairDensity.update_optical_limit(self, n, m, kpt1, kpt2,
deps_m, df_m, n_mG)
if self.hilbert:
self.update_optical_limit_hilbert(n0_mv, deps_m, df_m, n_mG,
chi0_wxvG, chi0_wvv)
return
if self.timeordered:
# avoid getting a zero from np.sign():
deps1_m = deps_m + 1j * self.eta * np.sign(deps_m + 1e-20)
deps2_m = deps1_m
else:
deps1_m = deps_m + 1j * self.eta
deps2_m = deps_m - 1j * self.eta
for w, omega in enumerate(self.omega_w):
x_m = self.prefactor * df_m * (1 / (omega + deps1_m) - 1 /
(omega - deps2_m))
chi0_wvv[w] += np.dot(x_m * n0_mv.T, n0_mv.conj())
chi0_wxvG[w, 0, :, 1:] += np.dot(x_m * n0_mv.T, n_mG[:, 1:].conj())
chi0_wxvG[w, 1, :, 1:] += np.dot(x_m * n0_mv.T.conj(), n_mG[:, 1:])
def get_bz_transitions(filename,
q_c,
bzk_kc,
response='density',
spins='all',
ecut=50,
txt=sys.stdout):
"""
Get transitions in the Brillouin zone from kpoints bzk_kv
contributing to the linear response at wave vector q_c.
"""
pair = PairDensity(filename, ecut=ecut, response=response, txt=txt)
pd = get_pw_descriptor(q_c, pair.calc, pair.ecut)
bzk_kv = np.dot(bzk_kc, pd.gd.icell_cv) * 2 * np.pi
if spins == 'all':
spins = range(pair.calc.wfs.nspins)
else:
for spin in spins:
assert spin in range(pair.calc.wfs.nspins)
domain_dl = (bzk_kv, spins)
domainsize_d = [len(domain_l) for domain_l in domain_dl]
nterms = np.prod(domainsize_d)
domainarg_td = []
for t in range(nterms):
unravelled_d = np.unravel_index(t, domainsize_d)
arg = []
for domain_l, index in zip(domain_dl, unravelled_d):
arg.append(domain_l[index])
domainarg_td.append(tuple(arg))
return pair, pd, domainarg_td
def update_intraband(self, kpt, chi0_wvv):
"""Check whether there are any partly occupied bands."""
width = self.calc.occupations.width
if width == 0.0:
return
assert isinstance(self.calc.occupations, FermiDirac)
dfde_m = -1.0 / width * (kpt.f_n - kpt.f_n ** 2.0)
partocc_m = np.abs(dfde_m) > 1e-5
if not partocc_m.any():
return
# Break bands into degenerate chunks
deginds_cm = [] # indexing c as chunk number
for m in range(kpt.n2 - kpt.n1):
inds_m = np.nonzero(np.abs(kpt.eps_n[m] - kpt.eps_n) < 1e-5)[0]
if m == np.min(inds_m) and partocc_m[m]:
deginds_cm.append((inds_m))
# Sum over the chunks of degenerate bands
for inds_m in deginds_cm:
deg = len(inds_m)
vel_mmv = -1j * PairDensity.update_intraband(self, inds_m, kpt)
vel_mv = np.zeros((deg, 3), dtype=complex)
for iv in range(3):
w, v = np.linalg.eig(vel_mmv[..., iv])
vel_mv[:, iv] = w
for m in range(deg):
velm_v = vel_mv[m]
x_vv = -self.prefactor * dfde_m[inds_m[m]] * np.outer(velm_v.conj(), velm_v)
self.chi0_vv += x_vv
def update_optical_limit(self, n, kpt1, kpt2, deps_m, df_m, n_mG,
chi0_wxvG):
n0_mv = PairDensity.update_optical_limit(self, n, kpt1, kpt2,
deps_m, df_m, n_mG)
for w, omega in enumerate(self.omega_w):
x_m = (self.prefactor *
df_m * (1.0 / (omega + deps_m + 1j * self.eta) -
1.0 / (omega - deps_m + 1j * self.eta)))
chi0_wxvG[w, :, :, 0] += np.dot(x_m, n0_mv * n0_mv.conj())
chi0_wxvG[w, 0, :, 1:] += np.dot(x_m * n0_mv.T, n_mG[:, 1:].conj())
chi0_wxvG[w, 1, :, 1:] += np.dot(x_m * n0_mv.T.conj(), n_mG[:, 1:])
def update_intraband(self, kpt):
"""Check whether there are any partly occupied bands."""
width = self.calc.occupations.width
if width == 0.0:
return
assert isinstance(self.calc.occupations, FermiDirac)
dfde_m = -1. / width * (kpt.f_n - kpt.f_n**2.0)
partocc_m = np.abs(dfde_m) > 1e-5
if not partocc_m.any():
return
# Break bands into degenerate chunks
deginds_cm = [] # indexing c as chunk number
for m in range(kpt.nb - kpt.na):
inds_m = np.nonzero(np.abs(kpt.eps_n[m] - kpt.eps_n) < 1e-5)[0]
if m == np.min(inds_m) and partocc_m[m]:
deginds_cm.append((inds_m))
# Sum over the chunks of degenerate bands
for inds_m in deginds_cm:
deg = len(inds_m)
vel_mmv = -1j * PairDensity.update_intraband(self, inds_m, kpt)
vel_mv = np.zeros((deg, 3), dtype=complex)
for iv in range(3):
w, v = np.linalg.eig(vel_mmv[..., iv])
vel_mv[:, iv] = w
for m in range(deg):
velm_v = vel_mv[m]
x_vv = (-self.prefactor * dfde_m[inds_m[m]] *
np.outer(velm_v.conj(), velm_v))
self.chi0_vv += x_vv
def __init__(self, calc, filename='gw',
kpts=None, bands=None, nbands=None, ppa=False,
wstc=False,
ecut=150.0, eta=0.1, E0=1.0 * Hartree,
domega0=0.025, omega2=10.0,
world=mpi.world):
PairDensity.__init__(self, calc, ecut, world=world,
txt=filename + '.txt')
self.filename = filename
ecut /= Hartree
self.ppa = ppa
self.wstc = wstc
self.eta = eta / Hartree
self.E0 = E0 / Hartree
self.domega0 = domega0 / Hartree
self.omega2 = omega2 / Hartree
print(' ___ _ _ _ ', file=self.fd)
print(' | || | | |', file=self.fd)
print(' | | || | | |', file=self.fd)
print(' |__ ||_____|', file=self.fd)
print(' |___| ', file=self.fd)
print(file=self.fd)
self.kpts = select_kpts(kpts, self.calc)
if bands is None:
bands = [0, self.nocc2]
self.bands = bands
b1, b2 = bands
self.shape = shape = (self.calc.wfs.nspins, len(self.kpts), b2 - b1)
self.eps_sin = np.empty(shape) # KS-eigenvalues
self.f_sin = np.empty(shape) # occupation numbers
self.sigma_sin = np.zeros(shape) # self-energies
self.dsigma_sin = np.zeros(shape) # derivatives of self-energies
self.vxc_sin = None # KS XC-contributions
self.exx_sin = None # exact exchange contributions
self.Z_sin = None # renormalization factors
if nbands is None:
nbands = int(self.vol * ecut**1.5 * 2**0.5 / 3 / pi**2)
self.nbands = nbands
kd = self.calc.wfs.kd
self.mysKn1n2 = None # my (s, K, n1, n2) indices
self.distribute_k_points_and_bands(b1, b2, kd.ibz2bz_k[self.kpts])
# Find q-vectors and weights in the IBZ:
assert -1 not in kd.bz2bz_ks
offset_c = 0.5 * ((kd.N_c + 1) % 2) / kd.N_c
bzq_qc = monkhorst_pack(kd.N_c) + offset_c
self.qd = KPointDescriptor(bzq_qc)
self.qd.set_symmetry(self.calc.atoms, self.calc.wfs.setups,
usesymm=self.calc.input_parameters.usesymm,
N_c=self.calc.wfs.gd.N_c)
assert self.calc.wfs.nspins == 1
G = (kpts[ik1] + 1.0 * j * direction[i, :] /
nk_size) - kpts[ik2]
if j >= 0:
G = (kpts[ik1] + 1.0 * (j + 1) * direction[i, :] /
nk_size) - kpts[ik2]
bG_c = kpts[ik2] - kpts[ik1] + G
bG_v = np.dot(bG_c, icell_cv)
u2_nG = u_knG[ik2] * np.exp(
-1j * np.inner(r_g.T, bG_v).T)
S[ik1, i, j, :, :] = get_overlap(
calc, bands, np.reshape(u1_nG, (len(u1_nG), Ng)),
np.reshape(u2_nG, (len(u2_nG), Ng)), P_kani[ik1],
P_kani[ik2], dO_aii, bG_v)[:nb, :nb]
np.save(output_directory + case + ".gpaw.S.npy", S)
pair = PairDensity(calc=calc)
momentum = np.zeros((nkpts, nb, nb, 3), dtype=np.complex)
for i in range(nkpts):
#k = b1*calc.wfs.kd.bzk_kc[i][0] + b2*calc.wfs.kd.bzk_kc[i][1] +b3*calc.wfs.kd.bzk_kc[i][2]
q_c = [0.0, 0.0, 0.0]
qd = KPointDescriptor([q_c])
pd = PWDescriptor(pair.ecut, calc.wfs.gd, complex, qd)
kptpair = pair.get_kpoint_pair(pd,
s=0,
K=i,
n1=0,
n2=nb,
m1=0,
m2=nb)
ol = np.allclose(q_c, 0.0)
n_nmvG = pair.get_pair_momentum(pd, kptpair, np.arange(0, nb),
def __init__(self, calc, xc=None, kpts=None, bands=None, ecut=None,
omega=None, world=mpi.world, txt=sys.stdout, timer=None):
PairDensity.__init__(self, calc, ecut, world=world, txt=txt,
timer=timer)
if xc is None or xc == 'EXX':
self.exx_fraction = 1.0
xc = XC(XCNull())
elif xc == 'PBE0':
self.exx_fraction = 0.25
xc = XC('HYB_GGA_XC_PBEH')
elif xc == 'HSE03':
omega = 0.106
self.exx_fraction = 0.25
xc = XC('HYB_GGA_XC_HSE03')
elif xc == 'HSE06':
omega = 0.11
self.exx_fraction = 0.25
xc = XC('HYB_GGA_XC_HSE06')
elif xc == 'B3LYP':
self.exx_fraction = 0.2
xc = XC('HYB_GGA_XC_B3LYP')
self.xc = xc
self.omega = omega
self.exc = np.nan # density dependent part of xc-energy
self.kpts = select_kpts(kpts, self.calc)
if bands is None:
# Do all occupied bands:
bands = [0, self.nocc2]
prnt('Calculating exact exchange contributions for band index',
'%d-%d' % (bands[0], bands[1] - 1), file=self.fd)
prnt('for IBZ k-points with indices:',
', '.join(str(i) for i in self.kpts), file=self.fd)
self.bands = bands
if self.ecut is None:
self.ecut = self.calc.wfs.pd.ecut
prnt('Plane-wave cutoff: %.3f eV' % (self.ecut * Hartree),
file=self.fd)
shape = (self.calc.wfs.nspins, len(self.kpts), bands[1] - bands[0])
self.exxvv_sin = np.zeros(shape) # valence-valence exchange energies
self.exxvc_sin = np.zeros(shape) # valence-core exchange energies
self.f_sin = np.empty(shape) # occupation numbers
# The total EXX energy will not be calculated if we are only
# interested in a few eigenvalues for a few k-points
self.exx = np.nan # total EXX energy
self.exxvv = np.nan # valence-valence
self.exxvc = np.nan # valence-core
self.exxcc = 0.0 # core-core
self.mysKn1n2 = None # my (s, K, n1, n2) indices
self.distribute_k_points_and_bands(0, self.nocc2)
# All occupied states:
self.mykpts = [self.get_k_point(s, K, n1, n2)
for s, K, n1, n2 in self.mysKn1n2]
prnt('Using Wigner-Seitz truncated coulomb interaction.',
file=self.fd)
self.wstc = WignerSeitzTruncatedCoulomb(self.calc.wfs.gd.cell_cv,
self.calc.wfs.kd.N_c,
self.fd)
self.iG_qG = {} # cache
# PAW matrices:
self.V_asii = [] # valence-valence correction
self.C_aii = [] # valence-core correction
self.initialize_paw_exx_corrections()
def __init__(self,
calc,
xc=None,
kpts=None,
bands=None,
ecut=None,
omega=None,
world=mpi.world,
txt=sys.stdout,
timer=None):
PairDensity.__init__(self,
calc,
ecut,
world=world,
txt=txt,
timer=timer)
if xc is None or xc == 'EXX':
self.exx_fraction = 1.0
xc = XC(XCNull())
elif xc == 'PBE0':
self.exx_fraction = 0.25
xc = XC('HYB_GGA_XC_PBEH')
elif xc == 'HSE03':
omega = 0.106
self.exx_fraction = 0.25
xc = XC('HYB_GGA_XC_HSE03')
elif xc == 'HSE06':
omega = 0.11
self.exx_fraction = 0.25
xc = XC('HYB_GGA_XC_HSE06')
elif xc == 'B3LYP':
self.exx_fraction = 0.2
xc = XC('HYB_GGA_XC_B3LYP')
self.xc = xc
self.omega = omega
self.exc = np.nan # density dependent part of xc-energy
self.kpts = select_kpts(kpts, self.calc)
if bands is None:
# Do all occupied bands:
bands = [0, self.nocc2]
prnt('Calculating exact exchange contributions for band index',
'%d-%d' % (bands[0], bands[1] - 1),
file=self.fd)
prnt('for IBZ k-points with indices:',
', '.join(str(i) for i in self.kpts),
file=self.fd)
self.bands = bands
if self.ecut is None:
self.ecut = self.calc.wfs.pd.ecut
prnt('Plane-wave cutoff: %.3f eV' % (self.ecut * Hartree),
file=self.fd)
shape = (self.calc.wfs.nspins, len(self.kpts), bands[1] - bands[0])
self.exxvv_sin = np.zeros(shape) # valence-valence exchange energies
self.exxvc_sin = np.zeros(shape) # valence-core exchange energies
self.f_sin = np.empty(shape) # occupation numbers
# The total EXX energy will not be calculated if we are only
# interested in a few eigenvalues for a few k-points
self.exx = np.nan # total EXX energy
self.exxvv = np.nan # valence-valence
self.exxvc = np.nan # valence-core
self.exxcc = 0.0 # core-core
self.mysKn1n2 = None # my (s, K, n1, n2) indices
self.distribute_k_points_and_bands(0, self.nocc2)
# All occupied states:
self.mykpts = [
self.get_k_point(s, K, n1, n2) for s, K, n1, n2 in self.mysKn1n2
]
prnt('Using Wigner-Seitz truncated coulomb interaction.', file=self.fd)
self.wstc = WignerSeitzTruncatedCoulomb(self.calc.wfs.gd.cell_cv,
self.calc.wfs.kd.N_c, self.fd)
self.iG_qG = {} # cache
# PAW matrices:
self.V_asii = [] # valence-valence correction
self.C_aii = [] # valence-core correction
self.initialize_paw_exx_corrections()
def __init__(self, calc, xc=None, kpts=None, bands=None, ecut=150.0,
alpha=0.0, skip_gamma=False,
world=mpi.world, txt=sys.stdout):
alpha /= Bohr**2
PairDensity.__init__(self, calc, ecut, world=world, txt=txt)
ecut /= Hartree
if xc is None:
self.exx_fraction = 1.0
xc = XC(XCNull())
if xc == 'PBE0':
self.exx_fraction = 0.25
xc = XC('HYB_GGA_XC_PBEH')
elif xc == 'B3LYP':
self.exx_fraction = 0.2
xc = XC('HYB_GGA_XC_B3LYP')
self.xc = xc
self.exc = np.nan # density dependent part of xc-energy
if kpts is None:
# Do all k-points in the IBZ:
kpts = range(self.calc.wfs.kd.nibzkpts)
if bands is None:
# Do all occupied bands:
bands = [0, self.nocc2]
prnt('Calculating exact exchange contributions for band index',
'%d-%d' % (bands[0], bands[1] - 1), file=self.fd)
prnt('for IBZ k-points with indices:',
', '.join(str(i) for i in kpts), file=self.fd)
self.kpts = kpts
self.bands = bands
shape = (self.calc.wfs.nspins, len(kpts), bands[1] - bands[0])
self.exxvv_sin = np.zeros(shape) # valence-valence exchange energies
self.exxvc_sin = np.zeros(shape) # valence-core exchange energies
self.f_sin = np.empty(shape) # occupation numbers
# The total EXX energy will not be calculated if we are only
# interested in a few eigenvalues for a few k-points
self.exx = np.nan # total EXX energy
self.exxvv = np.nan # valence-valence
self.exxvc = np.nan # valence-core
self.exxcc = 0.0 # core-core
self.mysKn1n2 = None # my (s, K, n1, n2) indices
self.distribute_k_points_and_bands(self.nocc2)
# All occupied states:
self.mykpts = [self.get_k_point(s, K, n1, n2)
for s, K, n1, n2 in self.mysKn1n2]
# Compensation charge used for molecular calculations only:
self.beta = None # e^(-beta*r^2)
self.ngauss_G = None # density
self.vgauss_G = None # potential
self.G0 = None # effective value for |G+q| when |G+q|=0
self.skip_gamma = skip_gamma
if not self.calc.atoms.pbc.any():
# Set exponent of exp-function to -19 on the boundary:
self.beta = 4 * 19 * (self.calc.wfs.gd.icell_cv**2).sum(1).max()
prnt('Gaussian for electrostatic decoupling: e^(-beta*r^2),',
'beta=%.3f 1/Ang^2' % (self.beta / Bohr**2), file=self.fd)
elif skip_gamma:
prnt('Skip |G+q|=0 term', file=self.fd)
else:
# Volume per q-point:
dvq = (2 * pi)**3 / self.vol / self.calc.wfs.kd.nbzkpts
qcut = (dvq / (4 * pi / 3))**(1 / 3)
if alpha == 0.0:
self.G0 = (4 * pi * qcut / dvq)**-0.5
else:
self.G0 = (2 * pi**1.5 * erf(alpha**0.5 * qcut) / alpha**0.5 /
dvq)**-0.5
prnt('G+q=0 term: Integrate e^(-alpha*q^2)/q^2 for',
'q<%.3f 1/Ang and alpha=%.3f Ang^2' %
(qcut / Bohr, alpha * Bohr**2), file=self.fd)
# PAW matrices:
self.V_asii = [] # valence-valence correction
self.C_aii = [] # valence-core correction
self.initialize_paw_exx_corrections()
from gpaw.response.pair import PairDensity
from gpaw.response.math_func import two_phi_nabla_planewave_integrals
np.set_printoptions(precision=1)
nb = 6
a = Atoms('H', cell=(3 * np.eye(3)), pbc=True)
calc = GPAW(mode=PW(600), kpts=[[0, 0, 0], [0.25, 0, 0]])
a.calc = calc
a.get_potential_energy()
calc.diagonalize_full_hamiltonian(nbands=nb, expert=True)
calc.write('a.gpw', 'all')
pair = PairDensity('a.gpw', ecut=100)
# Check continuity eq.
for q_c in [[0, 0, 0], [1. / 4, 0, 0]]:
ol = np.allclose(q_c, 0.0)
qd = KPointDescriptor([q_c])
pd = PWDescriptor(pair.ecut, calc.wfs.gd, complex, qd)
kptpair = pair.get_kpoint_pair(pd, s=0, K=0, n1=0, n2=nb, m1=0, m2=nb)
deps_nm = kptpair.get_transition_energies(np.arange(0, nb),
np.arange(0, nb))
n_nmG, n_nmv, _ = pair.get_pair_density(pd,
kptpair,
np.arange(0, nb),
np.arange(0, nb),
optical_limit=ol)
class BSE:
def __init__(self,
calc=None,
spinors=False,
ecut=10.,
scale=1.0,
nbands=None,
valence_bands=None,
conduction_bands=None,
eshift=None,
gw_skn=None,
truncation=None,
integrate_gamma=1,
txt=sys.stdout,
mode='BSE',
wfile=None,
write_h=False,
write_v=False):
"""Creates the BSE object
calc: str or calculator object
The string should refer to the .gpw file contaning KS orbitals
ecut: float
Plane wave cutoff energy (eV)
nbands: int
Number of bands used for the screened interaction
valence_bands: list
Valence bands used in the BSE Hamiltonian
conduction_bands: list
Conduction bands used in the BSE Hamiltonian
eshift: float
Scissors operator opening the gap (eV)
gw_skn: list / array
List or array defining the gw quasiparticle energies used in
the BSE Hamiltonian. Should match spin, k-points and
valence/conduction bands
truncation: str
Coulomb truncation scheme. Can be either wigner-seitz,
2D, 1D, or 0D
integrate_gamma: int
Method to integrate the Coulomb interaction. 1 is a numerical
integration at all q-points with G=[0,0,0] - this breaks the
symmetry slightly. 0 is analytical integration at q=[0,0,0] only -
this conserves the symmetry. integrate_gamma=2 is the same as 1,
but the average is only carried out in the non-periodic directions.
txt: str
txt output
mode: str
Theory level used. can be RPA TDHF or BSE. Only BSE is screened.
wfile: str
File for saving screened interaction and some other stuff
needed later
write_h: bool
If True, write the BSE Hamiltonian to H_SS.ulm.
write_v: bool
If True, write eigenvalues and eigenstates to v_TS.ulm
"""
# Calculator
if isinstance(calc, str):
calc = GPAW(calc, txt=None, communicator=serial_comm)
self.calc = calc
self.spinors = spinors
self.scale = scale
assert mode in ['RPA', 'TDHF', 'BSE']
# assert calc.wfs.kd.nbzkpts % world.size == 0
# txt file
if world.rank != 0:
txt = devnull
elif isinstance(txt, str):
txt = open(txt, 'w', 1)
self.fd = txt
self.ecut = ecut / Hartree
self.nbands = nbands
self.mode = mode
self.truncation = truncation
if integrate_gamma == 0 and truncation is not None:
print('***WARNING*** Analytical Coulomb integration is ' +
'not expected to work with Coulomb truncation. ' +
'Use integrate_gamma=1', file=self.fd)
self.integrate_gamma = integrate_gamma
self.wfile = wfile
self.write_h = write_h
self.write_v = write_v
# Find q-vectors and weights in the IBZ:
self.kd = calc.wfs.kd
if -1 in self.kd.bz2bz_ks:
print('***WARNING*** Symmetries may not be right ' +
'Use gamma-centered grid to be sure', file=self.fd)
offset_c = 0.5 * ((self.kd.N_c + 1) % 2) / self.kd.N_c
bzq_qc = monkhorst_pack(self.kd.N_c) + offset_c
self.qd = KPointDescriptor(bzq_qc)
self.qd.set_symmetry(self.calc.atoms, self.kd.symmetry)
self.vol = abs(np.linalg.det(calc.wfs.gd.cell_cv))
# bands
self.spins = self.calc.wfs.nspins
if self.spins == 2:
if self.spinors:
self.spinors = False
print('***WARNING*** Presently the spinor version' +
'does not work for spin-polarized calculations.' +
'Performing scalar calculation', file=self.fd)
assert len(valence_bands[0]) == len(valence_bands[1])
assert len(conduction_bands[0]) == len(conduction_bands[1])
if valence_bands is None:
nv = self.calc.wfs.setups.nvalence
valence_bands = [[nv // 2 - 1]]
if self.spins == 2:
valence_bands *= 2
if conduction_bands is None:
conduction_bands = [[valence_bands[-1] + 1]]
if self.spins == 2:
conduction_bands *= 2
self.val_sn = np.array(valence_bands)
if len(np.shape(self.val_sn)) == 1:
self.val_sn = np.array([self.val_sn])
self.con_sn = np.array(conduction_bands)
if len(np.shape(self.con_sn)) == 1:
self.con_sn = np.array([self.con_sn])
self.td = True
for n in self.val_sn[0]:
if n in self.con_sn[0]:
self.td = False
if len(self.val_sn) == 2:
for n in self.val_sn[1]:
if n in self.con_sn[1]:
self.td = False
self.nv = len(self.val_sn[0])
self.nc = len(self.con_sn[0])
if eshift is not None:
eshift /= Hartree
if gw_skn is not None:
assert self.nv + self.nc == len(gw_skn[0, 0])
assert self.kd.nibzkpts == len(gw_skn[0])
gw_skn = gw_skn[:, self.kd.bz2ibz_k]
# assert self.kd.nbzkpts == len(gw_skn[0])
gw_skn /= Hartree
self.gw_skn = gw_skn
self.eshift = eshift
# Number of pair orbitals
self.nS = self.kd.nbzkpts * self.nv * self.nc * self.spins
self.nS *= (self.spinors + 1)**2
# Wigner-Seitz stuff
if self.truncation == 'wigner-seitz':
self.wstc = WignerSeitzTruncatedCoulomb(self.calc.wfs.gd.cell_cv,
self.kd.N_c, self.fd)
else:
self.wstc = None
self.print_initialization(self.td, self.eshift, self.gw_skn)
def calculate(self, optical=True, ac=1.0):
if self.spinors:
"""Calculate spinors. Here m is index of eigenvalues with SOC
and n is the basis of eigenstates withour SOC. Below m is used
for unoccupied states and n is used for occupied states so be
careful!"""
print('Diagonalizing spin-orbit Hamiltonian', file=self.fd)
param = self.calc.parameters
if not param['symmetry'] == 'off':
print('Calculating KS wavefunctions without symmetry ' +
'for spin-orbit', file=self.fd)
if not op.isfile('gs_nosym.gpw'):
calc_so = GPAW(**param)
calc_so.set(symmetry='off',
fixdensity=True,
txt='gs_nosym.txt')
calc_so.atoms = self.calc.atoms
calc_so.density = self.calc.density
calc_so.get_potential_energy()
calc_so.write('gs_nosym.gpw')
calc_so = GPAW('gs_nosym.gpw', txt=None,
communicator=serial_comm)
e_mk, v_knm = get_spinorbit_eigenvalues(calc_so,
return_wfs=True,
scale=self.scale)
del calc_so
else:
e_mk, v_knm = get_spinorbit_eigenvalues(self.calc,
return_wfs=True,
scale=self.scale)
e_mk /= Hartree
# Parallelization stuff
nK = self.kd.nbzkpts
myKrange, myKsize, mySsize = self.parallelisation_sizes()
# Calculate exchange interaction
qd0 = KPointDescriptor([self.q_c])
pd0 = PWDescriptor(self.ecut, self.calc.wfs.gd, complex, qd0)
ikq_k = self.kd.find_k_plus_q(self.q_c)
v_G = get_coulomb_kernel(pd0, self.kd.N_c, truncation=self.truncation,
wstc=self.wstc)
if optical:
v_G[0] = 0.0
self.pair = PairDensity(self.calc, self.ecut, world=serial_comm,
txt='pair.txt')
# Calculate direct (screened) interaction and PAW corrections
if self.mode == 'RPA':
Q_aGii = self.pair.initialize_paw_corrections(pd0)
else:
self.get_screened_potential(ac=ac)
if (self.qd.ibzk_kc - self.q_c < 1.0e-6).all():
iq0 = self.qd.bz2ibz_k[self.kd.where_is_q(self.q_c,
self.qd.bzk_kc)]
Q_aGii = self.Q_qaGii[iq0]
else:
Q_aGii = self.pair.initialize_paw_corrections(pd0)
# Calculate pair densities, eigenvalues and occupations
so = self.spinors + 1
Nv, Nc = so * self.nv, so * self.nc
Ns = self.spins
rhoex_KsmnG = np.zeros((nK, Ns, Nv, Nc, len(v_G)), complex)
# rhoG0_Ksmn = np.zeros((nK, Ns, Nv, Nc), complex)
df_Ksmn = np.zeros((nK, Ns, Nv, Nc), float) # -(ev - ec)
deps_ksmn = np.zeros((myKsize, Ns, Nv, Nc), float) # -(fv - fc)
if np.allclose(self.q_c, 0.0):
optical_limit = True
else:
optical_limit = False
get_pair = self.pair.get_kpoint_pair
get_rho = self.pair.get_pair_density
if self.spinors:
# Get all pair densities to allow for SOC mixing
# Use twice as many no-SOC states as BSE bands to allow mixing
vi_s = [2 * self.val_sn[0, 0] - self.val_sn[0, -1] - 1]
vf_s = [2 * self.con_sn[0, -1] - self.con_sn[0, 0] + 2]
if vi_s[0] < 0:
vi_s[0] = 0
ci_s, cf_s = vi_s, vf_s
ni, nf = vi_s[0], vf_s[0]
mvi = 2 * self.val_sn[0, 0]
mvf = 2 * (self.val_sn[0, -1] + 1)
mci = 2 * self.con_sn[0, 0]
mcf = 2 * (self.con_sn[0, -1] + 1)
else:
vi_s, vf_s = self.val_sn[:, 0], self.val_sn[:, -1] + 1
ci_s, cf_s = self.con_sn[:, 0], self.con_sn[:, -1] + 1
for ik, iK in enumerate(myKrange):
for s in range(Ns):
pair = get_pair(pd0, s, iK,
vi_s[s], vf_s[s], ci_s[s], cf_s[s])
m_m = np.arange(vi_s[s], vf_s[s])
n_n = np.arange(ci_s[s], cf_s[s])
if self.gw_skn is not None:
iKq = self.calc.wfs.kd.find_k_plus_q(self.q_c, [iK])[0]
epsv_m = self.gw_skn[s, iK, :self.nv]
epsc_n = self.gw_skn[s, iKq, self.nv:]
deps_ksmn[ik] = -(epsv_m[:, np.newaxis] - epsc_n)
elif self.spinors:
iKq = self.calc.wfs.kd.find_k_plus_q(self.q_c, [iK])[0]
epsv_m = e_mk[mvi:mvf, iK]
epsc_n = e_mk[mci:mcf, iKq]
deps_ksmn[ik, s] = -(epsv_m[:, np.newaxis] - epsc_n)
else:
deps_ksmn[ik, s] = -pair.get_transition_energies(m_m, n_n)
df_mn = pair.get_occupation_differences(self.val_sn[s],
self.con_sn[s])
rho_mnG = get_rho(pd0, pair,
m_m, n_n,
optical_limit=optical_limit,
direction=self.direction,
Q_aGii=Q_aGii,
extend_head=False)
if self.spinors:
if optical_limit:
deps0_mn = -pair.get_transition_energies(m_m, n_n)
rho_mnG[:, :, 0] *= deps0_mn
df_Ksmn[iK, s, ::2, ::2] = df_mn
df_Ksmn[iK, s, ::2, 1::2] = df_mn
df_Ksmn[iK, s, 1::2, ::2] = df_mn
df_Ksmn[iK, s, 1::2, 1::2] = df_mn
vecv0_nm = v_knm[iK][::2][ni:nf, mvi:mvf]
vecc0_nm = v_knm[iKq][::2][ni:nf, mci:mcf]
rho_0mnG = np.dot(vecv0_nm.T.conj(),
np.dot(vecc0_nm.T, rho_mnG))
vecv1_nm = v_knm[iK][1::2][ni:nf, mvi:mvf]
vecc1_nm = v_knm[iKq][1::2][ni:nf, mci:mcf]
rho_1mnG = np.dot(vecv1_nm.T.conj(),
np.dot(vecc1_nm.T, rho_mnG))
rhoex_KsmnG[iK, s] = rho_0mnG + rho_1mnG
if optical_limit:
rhoex_KsmnG[iK, s, :, :, 0] /= deps_ksmn[ik, s]
else:
df_Ksmn[iK, s] = pair.get_occupation_differences(m_m, n_n)
rhoex_KsmnG[iK, s] = rho_mnG
if self.eshift is not None:
deps_ksmn[np.where(df_Ksmn[myKrange] > 1.0e-3)] += self.eshift
deps_ksmn[np.where(df_Ksmn[myKrange] < -1.0e-3)] -= self.eshift
world.sum(df_Ksmn)
world.sum(rhoex_KsmnG)
self.rhoG0_S = np.reshape(rhoex_KsmnG[:, :, :, :, 0], -1)
if hasattr(self, 'H_sS'):
return
# Calculate Hamiltonian
t0 = time()
print('Calculating %s matrix elements at q_c = %s'
% (self.mode, self.q_c), file=self.fd)
H_ksmnKsmn = np.zeros((myKsize, Ns, Nv, Nc, nK, Ns, Nv, Nc), complex)
for ik1, iK1 in enumerate(myKrange):
for s1 in range(Ns):
kptv1 = self.pair.get_k_point(s1, iK1, vi_s[s1], vf_s[s1])
kptc1 = self.pair.get_k_point(s1, ikq_k[iK1], ci_s[s1],
cf_s[s1])
rho1_mnG = rhoex_KsmnG[iK1, s1]
#rhoG0_Ksmn[iK1, s1] = rho1_mnG[:, :, 0]
rho1ccV_mnG = rho1_mnG.conj()[:, :] * v_G
for s2 in range(Ns):
for Q_c in self.qd.bzk_kc:
iK2 = self.kd.find_k_plus_q(Q_c, [kptv1.K])[0]
rho2_mnG = rhoex_KsmnG[iK2, s2]
rho2_mGn = np.swapaxes(rho2_mnG, 1, 2)
H_ksmnKsmn[ik1, s1, :, :, iK2, s2, :, :] += (
np.dot(rho1ccV_mnG, rho2_mGn))
if not self.mode == 'RPA' and s1 == s2:
ikq = ikq_k[iK2]
kptv2 = self.pair.get_k_point(s1, iK2, vi_s[s1],
vf_s[s1])
kptc2 = self.pair.get_k_point(s1, ikq, ci_s[s1],
cf_s[s1])
rho3_mmG, iq = self.get_density_matrix(kptv1,
kptv2)
rho4_nnG, iq = self.get_density_matrix(kptc1,
kptc2)
if self.spinors:
vec0_nm = v_knm[iK1][::2][ni:nf, mvi:mvf]
vec1_nm = v_knm[iK1][1::2][ni:nf, mvi:mvf]
vec2_nm = v_knm[iK2][::2][ni:nf, mvi:mvf]
vec3_nm = v_knm[iK2][1::2][ni:nf, mvi:mvf]
rho_0mnG = np.dot(vec0_nm.T.conj(),
np.dot(vec2_nm.T, rho3_mmG))
rho_1mnG = np.dot(vec1_nm.T.conj(),
np.dot(vec3_nm.T, rho3_mmG))
rho3_mmG = rho_0mnG + rho_1mnG
vec0_nm = v_knm[ikq_k[iK1]][::2][ni:nf, mci:mcf]
vec1_nm = v_knm[ikq_k[iK1]][1::2][ni:nf,mci:mcf]
vec2_nm = v_knm[ikq][::2][ni:nf, mci:mcf]
vec3_nm = v_knm[ikq][1::2][ni:nf, mci:mcf]
rho_0mnG = np.dot(vec0_nm.T.conj(),
np.dot(vec2_nm.T, rho4_nnG))
rho_1mnG = np.dot(vec1_nm.T.conj(),
np.dot(vec3_nm.T, rho4_nnG))
rho4_nnG = rho_0mnG + rho_1mnG
rho3ccW_mmG = np.dot(rho3_mmG.conj(),
self.W_qGG[iq])
W_mmnn = np.dot(rho3ccW_mmG,
np.swapaxes(rho4_nnG, 1, 2))
W_mnmn = np.swapaxes(W_mmnn, 1, 2) * Ns * so
H_ksmnKsmn[ik1, s1, :, :, iK2, s1] -= 0.5 * W_mnmn
if iK1 % (myKsize // 5 + 1) == 0:
dt = time() - t0
tleft = dt * myKsize / (iK1 + 1) - dt
print(' Finished %s pair orbitals in %s - Estimated %s left' %
((iK1 + 1) * Nv * Nc * Ns * world.size,
timedelta(seconds=round(dt)),
timedelta(seconds=round(tleft))), file=self.fd)
#if self.mode == 'BSE':
# del self.Q_qaGii, self.W_qGG, self.pd_q
H_ksmnKsmn /= self.vol
mySsize = myKsize * Nv * Nc * Ns
if myKsize > 0:
iS0 = myKrange[0] * Nv * Nc * Ns
#world.sum(rhoG0_Ksmn)
#self.rhoG0_S = np.reshape(rhoG0_Ksmn, -1)
self.df_S = np.reshape(df_Ksmn, -1)
if not self.td:
self.excludef_S = np.where(np.abs(self.df_S) < 0.001)[0]
# multiply by 2 when spin-paired and no SOC
self.df_S *= 2.0 / nK / Ns / so
self.deps_s = np.reshape(deps_ksmn, -1)
H_sS = np.reshape(H_ksmnKsmn, (mySsize, self.nS))
for iS in range(mySsize):
# Multiply by occupations and adiabatic coupling
H_sS[iS] *= self.df_S[iS0 + iS] * ac
# add bare transition energies
H_sS[iS, iS0 + iS] += self.deps_s[iS]
self.H_sS = H_sS
if self.write_h:
self.par_save('H_SS.ulm', 'H_SS', self.H_sS)
def get_density_matrix(self, kpt1, kpt2):
Q_c = self.kd.bzk_kc[kpt2.K] - self.kd.bzk_kc[kpt1.K]
iQ = self.qd.where_is_q(Q_c, self.qd.bzk_kc)
iq = self.qd.bz2ibz_k[iQ]
q_c = self.qd.ibzk_kc[iq]
# Find symmetry that transforms Q_c into q_c
sym = self.qd.sym_k[iQ]
U_cc = self.qd.symmetry.op_scc[sym]
time_reversal = self.qd.time_reversal_k[iQ]
sign = 1 - 2 * time_reversal
d_c = sign * np.dot(U_cc, q_c) - Q_c
assert np.allclose(d_c.round(), d_c)
pd = self.pd_q[iq]
N_c = pd.gd.N_c
i_cG = sign * np.dot(U_cc, np.unravel_index(pd.Q_qG[0], N_c))
shift0_c = Q_c - sign * np.dot(U_cc, q_c)
assert np.allclose(shift0_c.round(), shift0_c)
shift0_c = shift0_c.round().astype(int)
shift_c = kpt1.shift_c - kpt2.shift_c - shift0_c
I_G = np.ravel_multi_index(i_cG + shift_c[:, None], N_c, 'wrap')
G_Gv = pd.get_reciprocal_vectors()
pos_ac = self.calc.spos_ac
pos_av = np.dot(pos_ac, pd.gd.cell_cv)
M_vv = np.dot(pd.gd.cell_cv.T, np.dot(U_cc.T,
np.linalg.inv(pd.gd.cell_cv).T))
Q_aGii = []
for a, Q_Gii in enumerate(self.Q_qaGii[iq]):
x_G = np.exp(1j * np.dot(G_Gv, (pos_av[a] -
np.dot(M_vv, pos_av[a]))))
U_ii = self.calc.wfs.setups[a].R_sii[sym]
Q_Gii = np.dot(np.dot(U_ii, Q_Gii * x_G[:, None, None]),
U_ii.T).transpose(1, 0, 2)
if sign == -1:
Q_Gii = Q_Gii.conj()
Q_aGii.append(Q_Gii)
rho_mnG = np.zeros((len(kpt1.eps_n), len(kpt2.eps_n), len(G_Gv)),
complex)
for m in range(len(rho_mnG)):
C1_aGi = [np.dot(Qa_Gii, P1_ni[m].conj())
for Qa_Gii, P1_ni in zip(Q_aGii, kpt1.P_ani)]
ut1cc_R = kpt1.ut_nR[m].conj()
rho_mnG[m] = self.pair.calculate_pair_densities(ut1cc_R, C1_aGi,
kpt2, pd, I_G)
return rho_mnG, iq
def get_screened_potential(self, ac=1.0):
if hasattr(self, 'W_qGG'):
return
if self.wfile is not None:
# Read screened potential from file
try:
data = np.load(self.wfile + '.npz')
self.Q_qaGii = data['Q']
self.W_qGG = data['W']
self.pd_q = data['pd']
print('Reading screened potential from % s' % self.wfile,
file=self.fd)
except:
self.calculate_screened_potential(ac)
print('Saving screened potential to % s' % self.wfile,
file=self.fd)
if world.rank == 0:
np.savez(self.wfile,
Q=self.Q_qaGii, pd=self.pd_q, W=self.W_qGG)
else:
self.calculate_screened_potential(ac)
def calculate_screened_potential(self, ac):
"""Calculate W_GG(q)"""
chi0 = Chi0(self.calc,
frequencies=[0.0],
eta=0.001,
ecut=self.ecut,
intraband=False,
hilbert=False,
nbands=self.nbands,
txt='chi0.txt',
world=world,
)
self.blockcomm = chi0.blockcomm
wfs = self.calc.wfs
self.Q_qaGii = []
self.W_qGG = []
self.pd_q = []
t0 = time()
print('Calculating screened potential', file=self.fd)
for iq, q_c in enumerate(self.qd.ibzk_kc):
thisqd = KPointDescriptor([q_c])
pd = PWDescriptor(self.ecut, wfs.gd, complex, thisqd)
nG = pd.ngmax
chi0.Ga = self.blockcomm.rank * nG
chi0.Gb = min(chi0.Ga + nG, nG)
chi0_wGG = np.zeros((1, nG, nG), complex)
if np.allclose(q_c, 0.0):
chi0_wxvG = np.zeros((1, 2, 3, nG), complex)
chi0_wvv = np.zeros((1, 3, 3), complex)
else:
chi0_wxvG = None
chi0_wvv = None
chi0._calculate(pd, chi0_wGG, chi0_wxvG, chi0_wvv,
0, self.nbands, spins='all', extend_head=False)
chi0_GG = chi0_wGG[0]
# Calculate eps^{-1}_GG
if pd.kd.gamma:
# Generate fine grid in vicinity of gamma
kd = self.calc.wfs.kd
N = 4
N_c = np.array([N, N, N])
if self.truncation is not None:
# Only average periodic directions if trunction is used
N_c[kd.N_c == 1] = 1
qf_qc = monkhorst_pack(N_c) / kd.N_c
qf_qc *= 1.0e-6
U_scc = kd.symmetry.op_scc
qf_qc = kd.get_ibz_q_points(qf_qc, U_scc)[0]
weight_q = kd.q_weights
qf_qv = 2 * np.pi * np.dot(qf_qc, pd.gd.icell_cv)
a_q = np.sum(np.dot(chi0_wvv[0], qf_qv.T) * qf_qv.T, axis=0)
a0_qG = np.dot(qf_qv, chi0_wxvG[0, 0])
a1_qG = np.dot(qf_qv, chi0_wxvG[0, 1])
einv_GG = np.zeros((nG, nG), complex)
# W_GG = np.zeros((nG, nG), complex)
for iqf in range(len(qf_qv)):
chi0_GG[0] = a0_qG[iqf]
chi0_GG[:, 0] = a1_qG[iqf]
chi0_GG[0, 0] = a_q[iqf]
sqrV_G = get_coulomb_kernel(pd,
kd.N_c,
truncation=self.truncation,
wstc=self.wstc,
q_v=qf_qv[iqf])**0.5
sqrV_G *= ac**0.5 # Multiply by adiabatic coupling
e_GG = np.eye(nG) - chi0_GG * sqrV_G * sqrV_G[:,
np.newaxis]
einv_GG += np.linalg.inv(e_GG) * weight_q[iqf]
# einv_GG = np.linalg.inv(e_GG) * weight_q[iqf]
# W_GG += (einv_GG * sqrV_G * sqrV_G[:, np.newaxis]
# * weight_q[iqf])
else:
sqrV_G = get_coulomb_kernel(pd,
self.kd.N_c,
truncation=self.truncation,
wstc=self.wstc)**0.5
sqrV_G *= ac**0.5 # Multiply by adiabatic coupling
e_GG = np.eye(nG) - chi0_GG * sqrV_G * sqrV_G[:, np.newaxis]
einv_GG = np.linalg.inv(e_GG)
# W_GG = einv_GG * sqrV_G * sqrV_G[:, np.newaxis]
# Now calculate W_GG
if pd.kd.gamma:
# Reset bare Coulomb interaction
sqrV_G = get_coulomb_kernel(pd,
self.kd.N_c,
truncation=self.truncation,
wstc=self.wstc)**0.5
W_GG = einv_GG * sqrV_G * sqrV_G[:, np.newaxis]
if self.integrate_gamma != 0:
# Numerical integration of Coulomb interaction at all q-points
if self.integrate_gamma == 2:
reduced = True
else:
reduced = False
V0, sqrV0 = get_integrated_kernel(pd,
self.kd.N_c,
truncation=self.truncation,
reduced=reduced,
N=100)
W_GG[0, 0] = einv_GG[0, 0] * V0
W_GG[0, 1:] = einv_GG[0, 1:] * sqrV0 * sqrV_G[1:]
W_GG[1:, 0] = einv_GG[1:, 0] * sqrV_G[1:] * sqrV0
elif self.integrate_gamma == 0 and pd.kd.gamma:
# Analytical integration at gamma
bzvol = (2 * np.pi)**3 / self.vol / self.qd.nbzkpts
Rq0 = (3 * bzvol / (4 * np.pi))**(1. / 3.)
V0 = 16 * np.pi**2 * Rq0 / bzvol
sqrV0 = (4 * np.pi)**(1.5) * Rq0**2 / bzvol / 2
W_GG[0, 0] = einv_GG[0, 0] * V0
W_GG[0, 1:] = einv_GG[0, 1:] * sqrV0 * sqrV_G[1:]
W_GG[1:, 0] = einv_GG[1:, 0] * sqrV_G[1:] * sqrV0
else:
pass
if pd.kd.gamma:
e = 1 / einv_GG[0, 0].real
print(' RPA dielectric constant is: %3.3f' % e,
file=self.fd)
self.Q_qaGii.append(chi0.Q_aGii)
self.pd_q.append(pd)
self.W_qGG.append(W_GG)
if iq % (self.qd.nibzkpts // 5 + 1) == 2:
dt = time() - t0
tleft = dt * self.qd.nibzkpts / (iq + 1) - dt
print(' Finished %s q-points in %s - Estimated %s left' %
(iq + 1, timedelta(seconds=round(dt)),
timedelta(seconds=round(tleft))), file=self.fd)
def diagonalize(self):
print('Diagonalizing Hamiltonian', file=self.fd)
"""The t and T represent local and global
eigenstates indices respectively
"""
# Non-Hermitian matrix can only use linalg.eig
if not self.td:
print(' Using numpy.linalg.eig...', file=self.fd)
print(' Eliminated %s pair orbitals' % len(self.excludef_S),
file=self.fd)
self.H_SS = self.collect_A_SS(self.H_sS)
self.w_T = np.zeros(self.nS - len(self.excludef_S), complex)
if world.rank == 0:
self.H_SS = np.delete(self.H_SS, self.excludef_S, axis=0)
self.H_SS = np.delete(self.H_SS, self.excludef_S, axis=1)
self.w_T, self.v_ST = np.linalg.eig(self.H_SS)
world.broadcast(self.w_T, 0)
self.df_S = np.delete(self.df_S, self.excludef_S)
self.rhoG0_S = np.delete(self.rhoG0_S, self.excludef_S)
# Here the eigenvectors are returned as complex conjugated rows
else:
if world.size == 1:
print(' Using lapack...', file=self.fd)
from gpaw.utilities.lapack import diagonalize
self.w_T = np.zeros(self.nS)
diagonalize(self.H_sS, self.w_T)
self.v_St = self.H_sS.conj().T
else:
print(' Using scalapack...', file=self.fd)
nS = self.nS
ns = -(-self.kd.nbzkpts // world.size) * (self.nv * self.nc *
self.spins *
(self.spinors + 1)**2)
grid = BlacsGrid(world, world.size, 1)
desc = grid.new_descriptor(nS, nS, ns, nS)
desc2 = grid.new_descriptor(nS, nS, 2, 2)
H_tmp = desc2.zeros(dtype=complex)
r = Redistributor(world, desc, desc2)
r.redistribute(self.H_sS, H_tmp)
self.w_T = np.empty(nS)
v_tmp = desc2.empty(dtype=complex)
desc2.diagonalize_dc(H_tmp, v_tmp, self.w_T)
r = Redistributor(grid.comm, desc2, desc)
self.v_St = desc.zeros(dtype=complex)
r.redistribute(v_tmp, self.v_St)
self.v_St = self.v_St.conj().T
if self.write_v and self.td:
# Cannot use par_save without td
self.par_save('v_TS.ulm', 'v_TS', self.v_St.T)
return
def get_bse_matrix(self, q_c=[0.0, 0.0, 0.0], direction=0, ac=1.0,
readfile=None, optical=True, write_eig=None):
"""Calculate and diagonalize BSE matrix"""
self.q_c = q_c
self.direction = direction
if readfile is None:
self.calculate(optical=optical, ac=ac)
if hasattr(self, 'w_T'):
return
self.diagonalize()
elif readfile == 'H_SS':
print('Reading Hamiltonian from file', file=self.fd)
self.par_load('H_SS.ulm', 'H_SS')
self.diagonalize()
elif readfile == 'v_TS':
print('Reading eigenstates from file', file=self.fd)
self.par_load('v_TS.ulm', 'v_TS')
else:
raise ValueError('%s array not recognized' % readfile)
# TODO: Move write_eig here
return
def get_vchi(self, w_w=None, eta=0.1, q_c=[0.0, 0.0, 0.0],
direction=0, ac=1.0, readfile=None, optical=True,
write_eig=None):
"""Returns v * \chi where v is the bare Coulomb interaction"""
self.get_bse_matrix(q_c=q_c, direction=direction, ac=ac,
readfile=readfile, optical=optical,
write_eig=write_eig)
w_T = self.w_T
rhoG0_S = self.rhoG0_S
df_S = self.df_S
print('Calculating response function at %s frequency points' %
len(w_w), file=self.fd)
vchi_w = np.zeros(len(w_w), dtype=complex)
if not self.td:
C_T = np.zeros(self.nS - len(self.excludef_S), complex)
if world.rank == 0:
A_T = np.dot(rhoG0_S, self.v_ST)
B_T = np.dot(rhoG0_S * df_S, self.v_ST)
tmp = np.dot(self.v_ST.conj().T, self.v_ST)
overlap_tt = np.linalg.inv(tmp)
C_T = np.dot(B_T.conj(), overlap_tt.T) * A_T
world.broadcast(C_T, 0)
else:
A_t = np.dot(rhoG0_S, self.v_St)
B_t = np.dot(rhoG0_S * df_S, self.v_St)
if world.size == 1:
C_T = B_t.conj() * A_t
else:
Nv = self.nv * (self.spinors + 1)
Nc = self.nc * (self.spinors + 1)
Ns = self.spins
nS = self.nS
ns = -(-self.kd.nbzkpts // world.size) * Nv * Nc * Ns
grid = BlacsGrid(world, world.size, 1)
desc = grid.new_descriptor(nS, 1, ns, 1)
C_t = desc.empty(dtype=complex)
C_t[:, 0] = B_t.conj() * A_t
C_T = desc.collect_on_master(C_t)[:, 0]
if world.rank != 0:
C_T = np.empty(nS, dtype=complex)
world.broadcast(C_T, 0)
eta /= Hartree
for iw, w in enumerate(w_w / Hartree):
tmp_T = 1. / (w - w_T + 1j * eta)
vchi_w[iw] += np.dot(tmp_T, C_T)
vchi_w *= 4 * np.pi / self.vol
if not np.allclose(self.q_c, 0.0):
cell_cv = self.calc.wfs.gd.cell_cv
B_cv = 2 * np.pi * np.linalg.inv(cell_cv).T
q_v = np.dot(q_c, B_cv)
vchi_w /= np.dot(q_v, q_v)
"""Check f-sum rule."""
nv = self.calc.wfs.setups.nvalence
dw_w = (w_w[1:] - w_w[:-1]) / Hartree
wchi_w = (w_w[1:] * vchi_w[1:] + w_w[:-1] * vchi_w[:-1]) / Hartree / 2
N = -np.dot(dw_w, wchi_w.imag) * self.vol / (2 * np.pi**2)
print(file=self.fd)
print('Checking f-sum rule:', file=self.fd)
print(' Valence = %s, N = %f' % (nv, N), file=self.fd)
print(file=self.fd)
if write_eig is not None:
if world.rank == 0:
f = open(write_eig, 'w')
print('# %s eigenvalues in eV' % self.mode, file=f)
for iw, w in enumerate(self.w_T * Hartree):
print('%8d %12.6f %12.16f' % (iw, w.real, C_T[iw].real),
file=f)
f.close()
return vchi_w * ac
def get_dielectric_function(self, w_w=None, eta=0.1,
q_c=[0.0, 0.0, 0.0], direction=0,
filename='df_bse.csv', readfile=None,
write_eig='eig.dat'):
"""Returns and writes real and imaginary part of the dielectric
function.
w_w: list of frequencies (eV)
Dielectric function is calculated at these frequencies
eta: float
Lorentzian broadening of the spectrum (eV)
q_c: list of three floats
Wavevector in reduced units on which the response is calculated
direction: int
if q_c = [0, 0, 0] this gives the direction in cartesian
coordinates - 0=x, 1=y, 2=z
filename: str
data file on which frequencies, real and imaginary part of
dielectric function is written
readfile: str
If H_SS is given, the method will load the BSE Hamiltonian
from H_SS.ulm. If v_TS is given, the method will load the
eigenstates from v_TS.ulm
write_eig: str
File on which the BSE eigenvalues are written
"""
epsilon_w = -self.get_vchi(w_w=w_w, eta=eta, q_c=q_c,
direction=direction,
readfile=readfile, optical=True,
write_eig=write_eig)
epsilon_w += 1.0
if world.rank == 0 and filename is not None:
f = open(filename, 'w')
for iw, w in enumerate(w_w):
print('%.9f, %.9f, %.9f' %
(w, epsilon_w[iw].real, epsilon_w[iw].imag), file=f)
f.close()
world.barrier()
print('Calculation completed at:', ctime(), file=self.fd)
print(file=self.fd)
return w_w, epsilon_w
def get_eels_spectrum(self, w_w=None, eta=0.1,
q_c=[0.0, 0.0, 0.0], direction=0,
filename='df_bse.csv', readfile=None,
write_eig='eig.dat'):
"""Returns and writes real and imaginary part of the dielectric
function.
w_w: list of frequencies (eV)
Dielectric function is calculated at these frequencies
eta: float
Lorentzian broadening of the spectrum (eV)
q_c: list of three floats
Wavevector in reduced units on which the response is calculated
direction: int
if q_c = [0, 0, 0] this gives the direction in cartesian
coordinates - 0=x, 1=y, 2=z
filename: str
data file on which frequencies, real and imaginary part of
dielectric function is written
readfile: str
If H_SS is given, the method will load the BSE Hamiltonian
from H_SS.ulm. If v_TS is given, the method will load the
eigenstates from v_TS.ulm
write_eig: str
File on which the BSE eigenvalues are written
"""
eels_w = -self.get_vchi(w_w=w_w, eta=eta, q_c=q_c, direction=direction,
readfile=readfile, optical=False,
write_eig=write_eig).imag
if world.rank == 0 and filename is not None:
f = open(filename, 'w')
for iw, w in enumerate(w_w):
print('%.9f, %.9f' % (w, eels_w[iw]), file=f)
f.close()
world.barrier()
print('Calculation completed at:', ctime(), file=self.fd)
print(file=self.fd)
return w_w, eels_w
def get_polarizability(self, w_w=None, eta=0.1,
q_c=[0.0, 0.0, 0.0], direction=0,
filename='pol_bse.csv', readfile=None, pbc=None,
write_eig='eig.dat'):
"""Calculate the polarizability alpha.
In 3D the imaginary part of the polarizability is related to the
dielectric function by Im(eps_M) = 4 pi * Im(alpha). In systems
with reduced dimensionality the converged value of alpha is
independent of the cell volume. This is not the case for eps_M,
which is ill defined. A truncated Coulomb kernel will always give
eps_M = 1.0, whereas the polarizability maintains its structure.
pbs should be a list of booleans giving the periodic directions.
By default, generate a file 'pol_bse.csv'. The three colomns are:
frequency (eV), Real(alpha), Imag(alpha). The dimension of alpha
is \AA to the power of non-periodic directions.
"""
cell_cv = self.calc.wfs.gd.cell_cv
if not pbc:
pbc_c = self.calc.atoms.pbc
else:
pbc_c = np.array(pbc)
if pbc_c.all():
V = 1.0
else:
V = np.abs(np.linalg.det(cell_cv[~pbc_c][:, ~pbc_c]))
if self.truncation is None:
optical = True
else:
optical = False
vchi_w = self.get_vchi(w_w=w_w, eta=eta, q_c=q_c, direction=direction,
readfile=readfile, optical=optical,
write_eig=write_eig)
alpha_w = -V * vchi_w / (4 * np.pi)
alpha_w *= Bohr**(sum(~pbc_c))
if world.rank == 0 and filename is not None:
fd = open(filename, 'w')
for iw, w in enumerate(w_w):
print('%.9f, %.9f, %.9f' %
(w, alpha_w[iw].real, alpha_w[iw].imag), file=fd)
fd.close()
print('Calculation completed at:', ctime(), file=self.fd)
print(file=self.fd)
return w_w, alpha_w
def get_2d_absorption(self, w_w=None, eta=0.1,
q_c=[0.0, 0.0, 0.0], direction=0,
filename='abs_bse.csv', readfile=None, pbc=None,
write_eig='eig.dat'):
"""Calculate the dimensionless absorption for 2d materials.
It is essentially related to the 2D polarizability \alpha_2d as
ABS = 4 * np.pi * \omega * \alpha_2d / c
where c is the velocity of light
"""
from ase.units import alpha
c = 1.0 / alpha
cell_cv = self.calc.wfs.gd.cell_cv
if not pbc:
pbc_c = self.calc.atoms.pbc
else:
pbc_c = np.array(pbc)
assert np.sum(pbc_c) == 2
V = np.abs(np.linalg.det(cell_cv[~pbc_c][:, ~pbc_c]))
vchi_w = self.get_vchi(w_w=w_w, eta=eta, q_c=q_c, direction=direction,
readfile=readfile, optical=True,
write_eig=write_eig)
abs_w = -V * vchi_w.imag * w_w / Hartree / c
if world.rank == 0 and filename is not None:
fd = open(filename, 'w')
for iw, w in enumerate(w_w):
print('%.9f, %.9f' % (w, abs_w[iw]), file=fd)
fd.close()
print('Calculation completed at:', ctime(), file=self.fd)
print(file=self.fd)
return w_w, abs_w
def par_save(self, filename, name, A_sS):
import ase.io.ulm as ulm
if world.size == 1:
A_XS = A_sS
else:
A_XS = self.collect_A_SS(A_sS)
if world.rank == 0:
w = ulm.open(filename, 'w')
if name == 'v_TS':
w.write(w_T=self.w_T)
# w.write(nS=self.nS)
w.write(rhoG0_S=self.rhoG0_S)
w.write(df_S=self.df_S)
w.write(A_XS=A_XS)
w.close()
world.barrier()
def par_load(self, filename, name):
import ase.io.ulm as ulm
if world.rank == 0:
r = ulm.open(filename, 'r')
if name == 'v_TS':
self.w_T = r.w_T
self.rhoG0_S = r.rhoG0_S
self.df_S = r.df_S
A_XS = r.A_XS
r.close()
else:
if name == 'v_TS':
self.w_T = np.zeros((self.nS), dtype=float)
self.rhoG0_S = np.zeros((self.nS), dtype=complex)
self.df_S = np.zeros((self.nS), dtype=float)
A_XS = None
world.broadcast(self.rhoG0_S, 0)
world.broadcast(self.df_S, 0)
if name == 'H_SS':
self.H_sS = self.distribute_A_SS(A_XS)
if name == 'v_TS':
world.broadcast(self.w_T, 0)
self.v_St = self.distribute_A_SS(A_XS, transpose=True)
def collect_A_SS(self, A_sS):
if world.rank == 0:
A_SS = np.zeros((self.nS, self.nS), dtype=complex)
A_SS[:len(A_sS)] = A_sS
Ntot = len(A_sS)
for rank in range(1, world.size):
nkr, nk, ns = self.parallelisation_sizes(rank)
buf = np.empty((ns, self.nS), dtype=complex)
world.receive(buf, rank, tag=123)
A_SS[Ntot:Ntot + ns] = buf
Ntot += ns
else:
world.send(A_sS, 0, tag=123)
world.barrier()
if world.rank == 0:
return A_SS
def distribute_A_SS(self, A_SS, transpose=False):
if world.rank == 0:
for rank in range(0, world.size):
nkr, nk, ns = self.parallelisation_sizes(rank)
if rank == 0:
A_sS = A_SS[0:ns]
Ntot = ns
else:
world.send(A_SS[Ntot:Ntot + ns], rank, tag=123)
Ntot += ns
else:
nkr, nk, ns = self.parallelisation_sizes()
A_sS = np.empty((ns, self.nS), dtype=complex)
world.receive(A_sS, 0, tag=123)
world.barrier()
if transpose:
A_sS = A_sS.T
return A_sS
def parallelisation_sizes(self, rank=None):
if rank is None:
rank = world.rank
nK = self.kd.nbzkpts
myKsize = -(-nK // world.size)
myKrange = range(rank * myKsize,
min((rank + 1) * myKsize, nK))
myKsize = len(myKrange)
mySsize = myKsize * self.nv * self.nc * self.spins
mySsize *= (1 + self.spinors)**2
return myKrange, myKsize, mySsize
def get_bse_wf(self):
pass
# asd = 1.0
def print_initialization(self, td, eshift, gw_skn):
p = functools.partial(print, file=self.fd)
p('----------------------------------------------------------')
p('%s Hamiltonian' % self.mode)
p('----------------------------------------------------------')
p('Started at: ', ctime())
p()
p('Atoms :',
self.calc.atoms.get_chemical_formula(mode='hill'))
p('Ground state XC functional :', self.calc.hamiltonian.xc.name)
p('Valence electrons :', self.calc.wfs.setups.nvalence)
p('Spinor calculations :', self.spinors)
p('Number of bands :', self.calc.wfs.bd.nbands)
p('Number of spins :', self.calc.wfs.nspins)
p('Number of k-points :', self.kd.nbzkpts)
p('Number of irreducible k-points :', self.kd.nibzkpts)
p('Number of q-points :', self.qd.nbzkpts)
p('Number of irreducible q-points :', self.qd.nibzkpts)
p()
for q in self.qd.ibzk_kc:
p(' q: [%1.4f %1.4f %1.4f]' % (q[0], q[1], q[2]))
p()
if gw_skn is not None:
p('User specified BSE bands')
p('Response PW cutoff :', self.ecut * Hartree, 'eV')
p('Screening bands included :', self.nbands)
if len(self.val_sn) == 1:
p('Valence bands :', self.val_sn[0])
p('Conduction bands :', self.con_sn[0])
else:
p('Valence bands :', self.val_sn[0],self.val_sn[1])
p('Conduction bands :', self.con_sn[0],self.con_sn[1])
if eshift is not None:
p('Scissors operator :', eshift * Hartree, 'eV')
p('Tamm-Dancoff approximation :', td)
p('Number of pair orbitals :', self.nS)
p()
p('Truncation of Coulomb kernel :', self.truncation)
if self.integrate_gamma == 0:
p('Coulomb integration scheme :', 'Analytical - gamma only')
elif self.integrate_gamma == 1:
p('Coulomb integration scheme :', 'Numerical - all q-points')
else:
pass
p()
p('----------------------------------------------------------')
p('----------------------------------------------------------')
p()
p('Parallelization - Total number of CPUs : % s' % world.size)
p(' Screened potential')
p(' K-point/band decomposition : % s' % world.size)
p(' Hamiltonian')
p(' Pair orbital decomposition : % s' % world.size)
p()
def calculate(self, optical=True, ac=1.0):
if self.spinors:
"""Calculate spinors. Here m is index of eigenvalues with SOC
and n is the basis of eigenstates withour SOC. Below m is used
for unoccupied states and n is used for occupied states so be
careful!"""
print('Diagonalizing spin-orbit Hamiltonian', file=self.fd)
param = self.calc.parameters
if not param['symmetry'] == 'off':
print('Calculating KS wavefunctions without symmetry ' +
'for spin-orbit', file=self.fd)
if not op.isfile('gs_nosym.gpw'):
calc_so = GPAW(**param)
calc_so.set(symmetry='off',
fixdensity=True,
txt='gs_nosym.txt')
calc_so.atoms = self.calc.atoms
calc_so.density = self.calc.density
calc_so.get_potential_energy()
calc_so.write('gs_nosym.gpw')
calc_so = GPAW('gs_nosym.gpw', txt=None,
communicator=serial_comm)
e_mk, v_knm = get_spinorbit_eigenvalues(calc_so,
return_wfs=True,
scale=self.scale)
del calc_so
else:
e_mk, v_knm = get_spinorbit_eigenvalues(self.calc,
return_wfs=True,
scale=self.scale)
e_mk /= Hartree
# Parallelization stuff
nK = self.kd.nbzkpts
myKrange, myKsize, mySsize = self.parallelisation_sizes()
# Calculate exchange interaction
qd0 = KPointDescriptor([self.q_c])
pd0 = PWDescriptor(self.ecut, self.calc.wfs.gd, complex, qd0)
ikq_k = self.kd.find_k_plus_q(self.q_c)
v_G = get_coulomb_kernel(pd0, self.kd.N_c, truncation=self.truncation,
wstc=self.wstc)
if optical:
v_G[0] = 0.0
self.pair = PairDensity(self.calc, self.ecut, world=serial_comm,
txt='pair.txt')
# Calculate direct (screened) interaction and PAW corrections
if self.mode == 'RPA':
Q_aGii = self.pair.initialize_paw_corrections(pd0)
else:
self.get_screened_potential(ac=ac)
if (self.qd.ibzk_kc - self.q_c < 1.0e-6).all():
iq0 = self.qd.bz2ibz_k[self.kd.where_is_q(self.q_c,
self.qd.bzk_kc)]
Q_aGii = self.Q_qaGii[iq0]
else:
Q_aGii = self.pair.initialize_paw_corrections(pd0)
# Calculate pair densities, eigenvalues and occupations
so = self.spinors + 1
Nv, Nc = so * self.nv, so * self.nc
Ns = self.spins
rhoex_KsmnG = np.zeros((nK, Ns, Nv, Nc, len(v_G)), complex)
# rhoG0_Ksmn = np.zeros((nK, Ns, Nv, Nc), complex)
df_Ksmn = np.zeros((nK, Ns, Nv, Nc), float) # -(ev - ec)
deps_ksmn = np.zeros((myKsize, Ns, Nv, Nc), float) # -(fv - fc)
if np.allclose(self.q_c, 0.0):
optical_limit = True
else:
optical_limit = False
get_pair = self.pair.get_kpoint_pair
get_rho = self.pair.get_pair_density
if self.spinors:
# Get all pair densities to allow for SOC mixing
# Use twice as many no-SOC states as BSE bands to allow mixing
vi_s = [2 * self.val_sn[0, 0] - self.val_sn[0, -1] - 1]
vf_s = [2 * self.con_sn[0, -1] - self.con_sn[0, 0] + 2]
if vi_s[0] < 0:
vi_s[0] = 0
ci_s, cf_s = vi_s, vf_s
ni, nf = vi_s[0], vf_s[0]
mvi = 2 * self.val_sn[0, 0]
mvf = 2 * (self.val_sn[0, -1] + 1)
mci = 2 * self.con_sn[0, 0]
mcf = 2 * (self.con_sn[0, -1] + 1)
else:
vi_s, vf_s = self.val_sn[:, 0], self.val_sn[:, -1] + 1
ci_s, cf_s = self.con_sn[:, 0], self.con_sn[:, -1] + 1
for ik, iK in enumerate(myKrange):
for s in range(Ns):
pair = get_pair(pd0, s, iK,
vi_s[s], vf_s[s], ci_s[s], cf_s[s])
m_m = np.arange(vi_s[s], vf_s[s])
n_n = np.arange(ci_s[s], cf_s[s])
if self.gw_skn is not None:
iKq = self.calc.wfs.kd.find_k_plus_q(self.q_c, [iK])[0]
epsv_m = self.gw_skn[s, iK, :self.nv]
epsc_n = self.gw_skn[s, iKq, self.nv:]
deps_ksmn[ik] = -(epsv_m[:, np.newaxis] - epsc_n)
elif self.spinors:
iKq = self.calc.wfs.kd.find_k_plus_q(self.q_c, [iK])[0]
epsv_m = e_mk[mvi:mvf, iK]
epsc_n = e_mk[mci:mcf, iKq]
deps_ksmn[ik, s] = -(epsv_m[:, np.newaxis] - epsc_n)
else:
deps_ksmn[ik, s] = -pair.get_transition_energies(m_m, n_n)
df_mn = pair.get_occupation_differences(self.val_sn[s],
self.con_sn[s])
rho_mnG = get_rho(pd0, pair,
m_m, n_n,
optical_limit=optical_limit,
direction=self.direction,
Q_aGii=Q_aGii,
extend_head=False)
if self.spinors:
if optical_limit:
deps0_mn = -pair.get_transition_energies(m_m, n_n)
rho_mnG[:, :, 0] *= deps0_mn
df_Ksmn[iK, s, ::2, ::2] = df_mn
df_Ksmn[iK, s, ::2, 1::2] = df_mn
df_Ksmn[iK, s, 1::2, ::2] = df_mn
df_Ksmn[iK, s, 1::2, 1::2] = df_mn
vecv0_nm = v_knm[iK][::2][ni:nf, mvi:mvf]
vecc0_nm = v_knm[iKq][::2][ni:nf, mci:mcf]
rho_0mnG = np.dot(vecv0_nm.T.conj(),
np.dot(vecc0_nm.T, rho_mnG))
vecv1_nm = v_knm[iK][1::2][ni:nf, mvi:mvf]
vecc1_nm = v_knm[iKq][1::2][ni:nf, mci:mcf]
rho_1mnG = np.dot(vecv1_nm.T.conj(),
np.dot(vecc1_nm.T, rho_mnG))
rhoex_KsmnG[iK, s] = rho_0mnG + rho_1mnG
if optical_limit:
rhoex_KsmnG[iK, s, :, :, 0] /= deps_ksmn[ik, s]
else:
df_Ksmn[iK, s] = pair.get_occupation_differences(m_m, n_n)
rhoex_KsmnG[iK, s] = rho_mnG
if self.eshift is not None:
deps_ksmn[np.where(df_Ksmn[myKrange] > 1.0e-3)] += self.eshift
deps_ksmn[np.where(df_Ksmn[myKrange] < -1.0e-3)] -= self.eshift
world.sum(df_Ksmn)
world.sum(rhoex_KsmnG)
self.rhoG0_S = np.reshape(rhoex_KsmnG[:, :, :, :, 0], -1)
if hasattr(self, 'H_sS'):
return
# Calculate Hamiltonian
t0 = time()
print('Calculating %s matrix elements at q_c = %s'
% (self.mode, self.q_c), file=self.fd)
H_ksmnKsmn = np.zeros((myKsize, Ns, Nv, Nc, nK, Ns, Nv, Nc), complex)
for ik1, iK1 in enumerate(myKrange):
for s1 in range(Ns):
kptv1 = self.pair.get_k_point(s1, iK1, vi_s[s1], vf_s[s1])
kptc1 = self.pair.get_k_point(s1, ikq_k[iK1], ci_s[s1],
cf_s[s1])
rho1_mnG = rhoex_KsmnG[iK1, s1]
#rhoG0_Ksmn[iK1, s1] = rho1_mnG[:, :, 0]
rho1ccV_mnG = rho1_mnG.conj()[:, :] * v_G
for s2 in range(Ns):
for Q_c in self.qd.bzk_kc:
iK2 = self.kd.find_k_plus_q(Q_c, [kptv1.K])[0]
rho2_mnG = rhoex_KsmnG[iK2, s2]
rho2_mGn = np.swapaxes(rho2_mnG, 1, 2)
H_ksmnKsmn[ik1, s1, :, :, iK2, s2, :, :] += (
np.dot(rho1ccV_mnG, rho2_mGn))
if not self.mode == 'RPA' and s1 == s2:
ikq = ikq_k[iK2]
kptv2 = self.pair.get_k_point(s1, iK2, vi_s[s1],
vf_s[s1])
kptc2 = self.pair.get_k_point(s1, ikq, ci_s[s1],
cf_s[s1])
rho3_mmG, iq = self.get_density_matrix(kptv1,
kptv2)
rho4_nnG, iq = self.get_density_matrix(kptc1,
kptc2)
if self.spinors:
vec0_nm = v_knm[iK1][::2][ni:nf, mvi:mvf]
vec1_nm = v_knm[iK1][1::2][ni:nf, mvi:mvf]
vec2_nm = v_knm[iK2][::2][ni:nf, mvi:mvf]
vec3_nm = v_knm[iK2][1::2][ni:nf, mvi:mvf]
rho_0mnG = np.dot(vec0_nm.T.conj(),
np.dot(vec2_nm.T, rho3_mmG))
rho_1mnG = np.dot(vec1_nm.T.conj(),
np.dot(vec3_nm.T, rho3_mmG))
rho3_mmG = rho_0mnG + rho_1mnG
vec0_nm = v_knm[ikq_k[iK1]][::2][ni:nf, mci:mcf]
vec1_nm = v_knm[ikq_k[iK1]][1::2][ni:nf,mci:mcf]
vec2_nm = v_knm[ikq][::2][ni:nf, mci:mcf]
vec3_nm = v_knm[ikq][1::2][ni:nf, mci:mcf]
rho_0mnG = np.dot(vec0_nm.T.conj(),
np.dot(vec2_nm.T, rho4_nnG))
rho_1mnG = np.dot(vec1_nm.T.conj(),
np.dot(vec3_nm.T, rho4_nnG))
rho4_nnG = rho_0mnG + rho_1mnG
rho3ccW_mmG = np.dot(rho3_mmG.conj(),
self.W_qGG[iq])
W_mmnn = np.dot(rho3ccW_mmG,
np.swapaxes(rho4_nnG, 1, 2))
W_mnmn = np.swapaxes(W_mmnn, 1, 2) * Ns * so
H_ksmnKsmn[ik1, s1, :, :, iK2, s1] -= 0.5 * W_mnmn
if iK1 % (myKsize // 5 + 1) == 0:
dt = time() - t0
tleft = dt * myKsize / (iK1 + 1) - dt
print(' Finished %s pair orbitals in %s - Estimated %s left' %
((iK1 + 1) * Nv * Nc * Ns * world.size,
timedelta(seconds=round(dt)),
timedelta(seconds=round(tleft))), file=self.fd)
#if self.mode == 'BSE':
# del self.Q_qaGii, self.W_qGG, self.pd_q
H_ksmnKsmn /= self.vol
mySsize = myKsize * Nv * Nc * Ns
if myKsize > 0:
iS0 = myKrange[0] * Nv * Nc * Ns
#world.sum(rhoG0_Ksmn)
#self.rhoG0_S = np.reshape(rhoG0_Ksmn, -1)
self.df_S = np.reshape(df_Ksmn, -1)
if not self.td:
self.excludef_S = np.where(np.abs(self.df_S) < 0.001)[0]
# multiply by 2 when spin-paired and no SOC
self.df_S *= 2.0 / nK / Ns / so
self.deps_s = np.reshape(deps_ksmn, -1)
H_sS = np.reshape(H_ksmnKsmn, (mySsize, self.nS))
for iS in range(mySsize):
# Multiply by occupations and adiabatic coupling
H_sS[iS] *= self.df_S[iS0 + iS] * ac
# add bare transition energies
H_sS[iS, iS0 + iS] += self.deps_s[iS]
self.H_sS = H_sS
if self.write_h:
self.par_save('H_SS.ulm', 'H_SS', self.H_sS)
def __init__(self,
calc,
gwfile,
filename=None,
kpts=[0],
bands=None,
structure=None,
d=None,
layer=0,
dW_qw=None,
qqeh=None,
wqeh=None,
txt=sys.stdout,
world=mpi.world,
domega0=0.025,
omega2=10.0,
eta=0.1,
include_q0=True,
metal=False):
"""
Class for calculating quasiparticle energies of van der Waals
heterostructures using the GW approximation for the self-energy.
The quasiparticle energy correction due to increased screening from
surrounding layers is obtained from the QEH model.
Parameters:
calc: str or PAW object
GPAW calculator object or filename of saved calculator object.
gwfile: str
name of gw results file from the monolayer calculation
filename: str
filename for gwqeh output
kpts: list
List of indices of sthe IBZ k-points to calculate the quasi
particle energies for. Set to [0] by default since the QP
correction is generally the same for all k.
bands: tuple
Range of band indices, like (n1, n2+1), to calculate the quasi
particle energies for. Note that the second band index is not
included. Should be the same as used for the GW calculation.
structure: list of str
Heterostructure set up. Each entry should consist of number of
layers + chemical formula.
For example: ['3H-MoS2', graphene', '10H-WS2'] gives 3 layers of
H-MoS2, 1 layer of graphene and 10 layers of H-WS2.
The name of the layers should correspond to building block files:
"<name>-chi.pckl" in the local repository.
d: array of floats
Interlayer distances for neighboring layers in Ang.
Length of array = number of layers - 1
layer: int
index of layer to calculate QP correction for.
dW_qw: 2D array of floats dimension q X w
Change in screened interaction. Should be set to None to calculate
dW directly from buildingblocks.
qqeh: array of floats
q-grid used for dW_qw (only needed if dW is given by hand).
wqeh: array of floats
w-grid used for dW_qw. So far this have to be the same as for the
GWQEH calculation. (only needed if dW is given by hand).
domega0: float
Minimum frequency step (in eV) used in the generation of the non-
linear frequency grid.
omega2: float
Control parameter for the non-linear frequency grid, equal to the
frequency where the grid spacing has doubled in size.
eta: float
Broadening parameter.
include_q0: bool
include q=0 in W or not. if True an integral arround q=0 is
performed, if False the q=0 contribution is set to zero.
metal: bool
If True, the point at q=0 is omitted when averaging the screened
potential close to q=0.
"""
self.gwfile = gwfile
self.inputcalc = calc
# Set low ecut in order to use PairDensity object since only
# G=0 is needed.
self.ecut = 1.
PairDensity.__init__(self,
calc,
ecut=self.ecut,
world=world,
txt=filename + '.txt')
self.filename = filename
self.ecut /= Hartree
self.eta = eta / Hartree
self.domega0 = domega0 / Hartree
self.omega2 = omega2 / Hartree
self.kpts = list(select_kpts(kpts, self.calc))
if bands is None:
bands = [0, self.nocc2]
self.bands = bands
b1, b2 = bands
self.shape = shape = (self.calc.wfs.nspins, len(self.kpts), b2 - b1)
self.eps_sin = np.empty(shape) # KS-eigenvalues
self.f_sin = np.empty(shape) # occupation numbers
self.sigma_sin = np.zeros(shape) # self-energies
self.dsigma_sin = np.zeros(shape) # derivatives of self-energies
self.Z_sin = None # renormalization factors
self.qp_sin = None
self.Qp_sin = None
self.ecutnb = 150 / Hartree
vol = abs(np.linalg.det(self.calc.wfs.gd.cell_cv))
self.vol = vol
self.nbands = min(self.calc.get_number_of_bands(),
int(vol * (self.ecutnb)**1.5 * 2**0.5 / 3 / pi**2))
self.nspins = self.calc.wfs.nspins
kd = self.calc.wfs.kd
self.mysKn1n2 = None # my (s, K, n1, n2) indices
self.distribute_k_points_and_bands(b1, b2, kd.ibz2bz_k[self.kpts])
# Find q-vectors and weights in the IBZ:
assert -1 not in kd.bz2bz_ks
offset_c = 0.5 * ((kd.N_c + 1) % 2) / kd.N_c
bzq_qc = monkhorst_pack(kd.N_c) + offset_c
self.qd = KPointDescriptor(bzq_qc)
self.qd.set_symmetry(self.calc.atoms, kd.symmetry)
# frequency grid
omax = self.find_maximum_frequency()
self.omega_w = frequency_grid(self.domega0, self.omega2, omax)
self.nw = len(self.omega_w)
self.wsize = 2 * self.nw
# Calculate screened potential of Heterostructure
if dW_qw is None:
try:
self.qqeh, self.wqeh, dW_qw = pickle.load(
open(filename + '_dW_qw.pckl', 'rb'))
except:
dW_qw = self.calculate_W_QEH(structure, d, layer)
else:
self.qqeh = qqeh
self.wqeh = None # wqeh
self.dW_qw = self.get_W_on_grid(dW_qw,
include_q0=include_q0,
metal=metal)
assert self.nw == self.dW_qw.shape[1], \
('Frequency grids doesnt match!')
self.htp = HilbertTransform(self.omega_w, self.eta, gw=True)
self.htm = HilbertTransform(self.omega_w, -self.eta, gw=True)
self.complete = False
self.nq = 0
if self.load_state_file():
if self.complete:
print('Self-energy loaded from file', file=self.fd)
class Chi0:
"""Class for calculating non-interacting response functions."""
def __init__(self,
calc,
response='density',
frequencies=None,
domega0=0.1,
omega2=10.0,
omegamax=None,
ecut=50,
gammacentered=False,
hilbert=True,
nbands=None,
timeordered=False,
eta=0.2,
ftol=1e-6,
threshold=1,
real_space_derivatives=False,
intraband=True,
world=mpi.world,
txt='-',
timer=None,
nblocks=1,
gate_voltage=None,
disable_point_group=False,
disable_time_reversal=False,
disable_non_symmorphic=True,
scissor=None,
integrationmode=None,
pbc=None,
rate=0.0,
eshift=0.0):
"""Construct Chi0 object.
Parameters
----------
calc : str
The groundstate calculation file that the linear response
calculation is based on.
response : str
Type of response function. Currently collinear, scalar options
'density', '+-' and '-+' are implemented.
frequencies : ndarray or None
Array of frequencies to evaluate the response function at. If None,
frequencies are determined using the frequency_grid function in
gpaw.response.chi0.
domega0, omega2, omegamax : float
Input parameters for frequency_grid.
ecut : float
Energy cutoff.
gammacentered : bool
Center the grid of plane waves around the gamma point or q-vector
hilbert : bool
Switch for hilbert transform. If True, the full density response
is determined from a hilbert transform of its spectral function.
This is typically much faster, but does not work for imaginary
frequencies.
nbands : int
Maximum band index to include.
timeordered : bool
Switch for calculating the time ordered density response function.
In this case the hilbert transform cannot be used.
eta : float
Artificial broadening of spectra.
ftol : float
Threshold determining whether a band is completely filled
(f > 1 - ftol) or completely empty (f < ftol).
threshold : float
Numerical threshold for the optical limit k dot p perturbation
theory expansion (used in gpaw/response/pair.py).
real_space_derivatives : bool
Switch for calculating nabla matrix elements (in the optical limit)
using a real space finite difference approximation.
intraband : bool
Switch for including the intraband contribution to the density
response function.
world : MPI comm instance
MPI communicator.
txt : str
Output file.
timer : gpaw.utilities.timing.timer instance
nblocks : int
Divide the response function into nblocks. Useful when the response
function is large.
gate_voltage : float
Shift the fermi level by gate_voltage [Hartree].
disable_point_group : bool
Do not use the point group symmetry operators.
disable_time_reversal : bool
Do not use time reversal symmetry.
disable_non_symmorphic : bool
Do no use non symmorphic symmetry operators.
scissor : tuple ([bands], shift [eV])
Use scissor operator on bands.
integrationmode : str
Integrator for the kpoint integration.
If == 'tetrahedron integration' then the kpoint integral is
performed using the linear tetrahedron method.
pbc : list
Periodic directions of the system. Defaults to [True, True, True].
eshift : float
Shift unoccupied bands
Attributes
----------
pair : gpaw.response.pair.PairDensity instance
Class for calculating matrix elements of pairs of wavefunctions.
"""
self.response = response
self.timer = timer or Timer()
self.pair = PairDensity(calc,
ecut,
self.response,
ftol,
threshold,
real_space_derivatives,
world,
txt,
self.timer,
nblocks=nblocks,
gate_voltage=gate_voltage)
self.disable_point_group = disable_point_group
self.disable_time_reversal = disable_time_reversal
self.disable_non_symmorphic = disable_non_symmorphic
self.integrationmode = integrationmode
self.eshift = eshift / Hartree
calc = self.pair.calc
self.calc = calc
if world.rank != 0:
txt = devnull
elif isinstance(txt, str):
txt = open(txt, 'w')
self.fd = txt
self.vol = abs(np.linalg.det(calc.wfs.gd.cell_cv))
self.world = world
if nblocks == 1:
self.blockcomm = self.world.new_communicator([world.rank])
self.kncomm = world
else:
assert world.size % nblocks == 0, world.size
rank1 = world.rank // nblocks * nblocks
rank2 = rank1 + nblocks
self.blockcomm = self.world.new_communicator(range(rank1, rank2))
ranks = range(world.rank % nblocks, world.size, nblocks)
self.kncomm = self.world.new_communicator(ranks)
self.nblocks = nblocks
if world.rank != 0:
txt = devnull
elif isinstance(txt, str):
txt = open(txt, 'w')
self.fd = txt
if ecut is not None:
ecut /= Hartree
self.ecut = ecut
self.gammacentered = gammacentered
self.eta = eta / Hartree
if rate == 'eta':
self.rate = self.eta
else:
self.rate = rate / Hartree
self.domega0 = domega0 / Hartree
self.omega2 = omega2 / Hartree
self.omegamax = None if omegamax is None else omegamax / Hartree
self.nbands = nbands or self.calc.wfs.bd.nbands
self.include_intraband = intraband
omax = self.find_maximum_frequency()
if frequencies is None:
if self.omegamax is None:
self.omegamax = omax
print('Using nonlinear frequency grid from 0 to %.3f eV' %
(self.omegamax * Hartree),
file=self.fd)
self.wd = FrequencyDescriptor(self.domega0, self.omega2,
self.omegamax)
else:
self.wd = ArrayDescriptor(np.asarray(frequencies) / Hartree)
assert not hilbert
self.omega_w = self.wd.get_data()
self.hilbert = hilbert
self.timeordered = bool(timeordered)
if self.eta == 0.0:
assert not hilbert
assert not timeordered
assert not self.omega_w.real.any()
self.nocc1 = self.pair.nocc1 # number of completely filled bands
self.nocc2 = self.pair.nocc2 # number of non-empty bands
self.Q_aGii = None
if pbc is not None:
self.pbc = np.array(pbc)
else:
self.pbc = np.array([True, True, True])
if self.pbc is not None and (~self.pbc).any():
assert np.sum((~self.pbc).astype(int)) == 1, \
print('Only one non-periodic direction supported atm.')
print('Nonperiodic BC\'s: ', (~self.pbc), file=self.fd)
if integrationmode is not None:
print('Using integration method: ' + self.integrationmode,
file=self.fd)
else:
print('Using integration method: PointIntegrator', file=self.fd)
def find_maximum_frequency(self):
"""Determine the maximum electron-hole pair transition energy."""
self.epsmin = 10000.0
self.epsmax = -10000.0
for kpt in self.calc.wfs.kpt_u:
self.epsmin = min(self.epsmin, kpt.eps_n[0])
self.epsmax = max(self.epsmax, kpt.eps_n[self.nbands - 1])
print('Minimum eigenvalue: %10.3f eV' % (self.epsmin * Hartree),
file=self.fd)
print('Maximum eigenvalue: %10.3f eV' % (self.epsmax * Hartree),
file=self.fd)
return self.epsmax - self.epsmin
def calculate(self, q_c, spin='all', A_x=None):
"""Calculate response function.
Parameters
----------
q_c : list or ndarray
Momentum vector.
spin : str or int
If 'all' then include all spins.
If 0 or 1, only include this specific spin.
(not used in transverse reponse functions)
A_x : ndarray
Output array. If None, the output array is created.
Returns
-------
pd : Planewave descriptor
Planewave descriptor for q_c.
chi0_wGG : ndarray
The response function.
chi0_wxvG : ndarray or None
(Only in optical limit) Wings of the density response function.
chi0_wvv : ndarray or None
(Only in optical limit) Head of the density response function.
"""
wfs = self.calc.wfs
if self.response == 'density':
if spin == 'all':
spins = range(wfs.nspins)
else:
assert spin in range(wfs.nspins)
spins = [spin]
else:
if self.response == '+-':
spins = [0]
elif self.response == '-+':
spins = [1]
else:
raise ValueError('Invalid response %s' % self.response)
q_c = np.asarray(q_c, dtype=float)
optical_limit = np.allclose(q_c, 0.0) and self.response == 'density'
pd = self.get_PWDescriptor(q_c, self.gammacentered)
self.print_chi(pd)
if extra_parameters.get('df_dry_run'):
print(' Dry run exit', file=self.fd)
raise SystemExit
nG = pd.ngmax + 2 * optical_limit
nw = len(self.omega_w)
mynG = (nG + self.blockcomm.size - 1) // self.blockcomm.size
self.Ga = min(self.blockcomm.rank * mynG, nG)
self.Gb = min(self.Ga + mynG, nG)
# if self.blockcomm.rank == 0:
# assert self.Gb - self.Ga >= 3
# assert mynG * (self.blockcomm.size - 1) < nG
if A_x is not None:
nx = nw * (self.Gb - self.Ga) * nG
chi0_wGG = A_x[:nx].reshape((nw, self.Gb - self.Ga, nG))
chi0_wGG[:] = 0.0
else:
chi0_wGG = np.zeros((nw, self.Gb - self.Ga, nG), complex)
if optical_limit:
chi0_wxvG = np.zeros((len(self.omega_w), 2, 3, nG), complex)
chi0_wvv = np.zeros((len(self.omega_w), 3, 3), complex)
self.plasmafreq_vv = np.zeros((3, 3), complex)
else:
chi0_wxvG = None
chi0_wvv = None
self.plasmafreq_vv = None
if self.response == 'density':
# Do all empty bands:
m1 = self.nocc1
else:
# Do all bands
m1 = 0
m2 = self.nbands
pd, chi0_wGG, chi0_wxvG, chi0_wvv = self._calculate(
pd, chi0_wGG, chi0_wxvG, chi0_wvv, m1, m2, spins)
return pd, chi0_wGG, chi0_wxvG, chi0_wvv
@timer('Calculate CHI_0')
def _calculate(self,
pd,
chi0_wGG,
chi0_wxvG,
chi0_wvv,
m1,
m2,
spins,
extend_head=True):
"""In-place calculation of the response function.
Parameters
----------
q_c : list or ndarray
Momentum vector..
pd : Planewave descriptor
Planewave descriptor for q_c.
chi0_wGG : ndarray
The response function.
chi0_wxvG : ndarray or None
Wings of the density response function.
chi0_wvv : ndarray or None
Head of the density response function.
m1 : int
Lower band cutoff for band summation
m2 : int
Upper band cutoff for band summation
spins : str or list(ints)
If 'all' then include all spins.
If [0] or [1], only include this specific spin (and flip it,
if calculating the transverse magnetic response).
extend_head : bool
If True: Extend the wings and head of chi in the optical limit to
take into account the non-analytic nature of chi. Effectively
means that chi has dimension (nw, nG + 2, nG + 2) in the optical
limit. This simplifies the code and should only be switched off
for parts of the code that do not support this feature i.e., GW
RPA total energy and RALDA.
"""
# Parse spins
wfs = self.calc.wfs
if spins == 'all':
spins = range(wfs.nspins)
elif spins == 'pm':
spins = [0]
elif spins == 'mp':
spins = [1]
else:
for spin in spins:
assert spin in range(wfs.nspins)
# Are we calculating the optical limit.
optical_limit = np.allclose(pd.kd.bzk_kc[0], 0.0) and \
self.response == 'density'
# Reset PAW correction in case momentum has change
self.Q_aGii = self.pair.initialize_paw_corrections(pd)
A_wxx = chi0_wGG # Change notation
# Initialize integrator. The integrator class is a general class
# for brillouin zone integration that can integrate user defined
# functions over user defined domains and sum over bands.
if self.integrationmode is None or \
self.integrationmode == 'point integration':
integrator = PointIntegrator(self.pair.calc.wfs.gd.cell_cv,
response=self.response,
comm=self.world,
timer=self.timer,
txt=self.fd,
eshift=self.eshift,
nblocks=self.nblocks)
intnoblock = PointIntegrator(self.pair.calc.wfs.gd.cell_cv,
response=self.response,
comm=self.world,
timer=self.timer,
eshift=self.eshift,
txt=self.fd)
elif self.integrationmode == 'tetrahedron integration':
integrator = TetrahedronIntegrator(self.pair.calc.wfs.gd.cell_cv,
response=self.response,
comm=self.world,
timer=self.timer,
eshift=self.eshift,
txt=self.fd,
nblocks=self.nblocks)
intnoblock = TetrahedronIntegrator(self.pair.calc.wfs.gd.cell_cv,
response=self.response,
comm=self.world,
timer=self.timer,
eshift=self.eshift,
txt=self.fd)
else:
print('Integration mode ' + self.integrationmode +
' not implemented.',
file=self.fd)
raise NotImplementedError
# The integration domain is determined by the following function
# that reduces the integration domain to the irreducible zone
# of the little group of q.
bzk_kv, PWSA = self.get_kpoints(pd,
integrationmode=self.integrationmode)
domain = (bzk_kv, spins)
if self.integrationmode == 'tetrahedron integration':
# If there are non-periodic directions it is possible that the
# integration domain is not compatible with the symmetry operations
# which essentially means that too large domains will be
# integrated. We normalize by vol(BZ) / vol(domain) to make
# sure that to fix this.
domainvol = convex_hull_volume(bzk_kv) * PWSA.how_many_symmetries()
bzvol = (2 * np.pi)**3 / self.vol
factor = bzvol / domainvol
else:
factor = 1
prefactor = (2 * factor * PWSA.how_many_symmetries() /
(wfs.nspins * (2 * np.pi)**3)) # Remember prefactor
if self.integrationmode is None:
if self.calc.wfs.kd.refine_info is not None:
nbzkpts = self.calc.wfs.kd.refine_info.mhnbzkpts
else:
nbzkpts = self.calc.wfs.kd.nbzkpts
prefactor *= len(bzk_kv) / nbzkpts
# The functions that are integrated are defined in the bottom
# of this file and take a number of constant keyword arguments
# which the integrator class accepts through the use of the
# kwargs keyword.
kd = self.calc.wfs.kd
mat_kwargs = {
'kd': kd,
'pd': pd,
'n1': 0,
'm1': m1,
'm2': m2,
'symmetry': PWSA,
'integrationmode': self.integrationmode
}
eig_kwargs = {'kd': kd, 'm1': m1, 'm2': m2, 'n1': 0, 'pd': pd}
if self.response == 'density':
mat_kwargs['n2'] = self.nocc2
eig_kwargs['n2'] = self.nocc2
else:
mat_kwargs['n2'] = self.nbands
eig_kwargs['n2'] = self.nbands
if not extend_head:
mat_kwargs['extend_head'] = False
# Determine what "kind" of integral to make.
extraargs = {} # Initialize extra arguments to integration method.
if self.eta == 0:
# If eta is 0 then we must be working with imaginary frequencies.
# In this case chi is hermitian and it is therefore possible to
# reduce the computational costs by a only computing half of the
# response function.
kind = 'hermitian response function'
elif self.hilbert:
# The spectral function integrator assumes that the form of the
# integrand is a function (a matrix element) multiplied by
# a delta function and should return a function of at user defined
# x's (frequencies). Thus the integrand is tuple of two functions
# and takes an additional argument (x).
kind = 'spectral function'
else:
# Otherwise, we can make no simplifying assumptions of the
# form of the response function and we simply perform a brute
# force calculation of the response function.
kind = 'response function'
extraargs['eta'] = self.eta
extraargs['timeordered'] = self.timeordered
if optical_limit and not extend_head:
wings = True
else:
wings = False
A_wxx /= prefactor
if wings:
chi0_wxvG /= prefactor
chi0_wvv /= prefactor
# Integrate response function
print('Integrating response function.', file=self.fd)
integrator.integrate(
kind=kind, # Kind of integral
domain=domain, # Integration domain
integrand=(
self.get_matrix_element, # Integrand
self.get_eigenvalues), # Integrand
x=self.wd, # Frequency Descriptor
kwargs=(mat_kwargs, eig_kwargs),
# Arguments for integrand functions
out_wxx=A_wxx, # Output array
**extraargs)
# extraargs: Extra arguments to integration method
if wings:
mat_kwargs['extend_head'] = True
mat_kwargs['block'] = False
if self.eta == 0:
extraargs['eta'] = self.eta
# This is horrible but we need to update the wings manually
# in order to make them work with ralda, RPA and GW. This entire
# section can be deleted in the future if the ralda and RPA code is
# made compatible with the head and wing extension that other parts
# of the code is using.
chi0_wxvx = np.zeros(
np.array(chi0_wxvG.shape) + [0, 0, 0, 2],
complex) # Notice the wxv"x" for head extend
intnoblock.integrate(
kind=kind + ' wings', # kind'o int.
domain=domain, # Integration domain
integrand=(
self.get_matrix_element, # Intgrnd
self.get_eigenvalues), # Integrand
x=self.wd, # Frequency Descriptor
kwargs=(mat_kwargs, eig_kwargs),
# Arguments for integrand functions
out_wxx=chi0_wxvx, # Output array
**extraargs)
if self.hilbert:
# The integrator only returns the spectral function and a Hilbert
# transform is performed to return the real part of the density
# response function.
with self.timer('Hilbert transform'):
omega_w = self.wd.get_data() # Get frequencies
# Make Hilbert transform
ht = HilbertTransform(np.array(omega_w),
self.eta,
timeordered=self.timeordered)
ht(A_wxx)
if wings:
ht(chi0_wxvx)
# In the optical limit additional work must be performed
# for the intraband response.
# Only compute the intraband response if there are partially
# unoccupied bands and only if the user has not disabled its
# calculation using the include_intraband keyword.
if optical_limit and self.nocc1 != self.nocc2:
# The intraband response is essentially just the calculation
# of the free space Drude plasma frequency. The calculation is
# similarly to the interband transitions documented above.
mat_kwargs = {
'kd': kd,
'symmetry': PWSA,
'n1': self.nocc1,
'n2': self.nocc2,
'pd': pd
} # Integrand arguments
eig_kwargs = {
'kd': kd,
'n1': self.nocc1,
'n2': self.nocc2,
'pd': pd
} # Integrand arguments
domain = (bzk_kv, spins) # Integration domain
fermi_level = self.pair.fermi_level # Fermi level
# Not so elegant solution but it works
plasmafreq_wvv = np.zeros((1, 3, 3), complex) # Output array
print('Integrating intraband density response.', file=self.fd)
# Depending on which integration method is used we
# have to pass different arguments
extraargs = {}
if self.integrationmode is None:
# Calculate intraband transitions at finite fermi smearing
extraargs['intraband'] = True # Calculate intraband
elif self.integrationmode == 'tetrahedron integration':
# Calculate intraband transitions at T=0
extraargs['x'] = ArrayDescriptor([-fermi_level])
intnoblock.integrate(
kind='spectral function', # Kind of integral
domain=domain, # Integration domain
# Integrands
integrand=(self.get_intraband_response,
self.get_intraband_eigenvalue),
# Integrand arguments
kwargs=(mat_kwargs, eig_kwargs),
out_wxx=plasmafreq_wvv, # Output array
**extraargs) # Extra args for int. method
# Again, not so pretty but that's how it is
plasmafreq_vv = plasmafreq_wvv[0].copy()
if self.include_intraband:
if extend_head:
va = min(self.Ga, 3)
vb = min(self.Gb, 3)
A_wxx[:, :vb - va, :3] += (
plasmafreq_vv[va:vb] /
(self.omega_w[:, np.newaxis, np.newaxis] + 1e-10 +
self.rate * 1j)**2)
elif self.blockcomm.rank == 0:
A_wxx[:, 0,
0] += (plasmafreq_vv[2, 2] /
(self.omega_w + 1e-10 + self.rate * 1j)**2)
# Save the plasmafrequency
try:
self.plasmafreq_vv += 4 * np.pi * plasmafreq_vv * prefactor
except AttributeError:
self.plasmafreq_vv = 4 * np.pi * plasmafreq_vv * prefactor
PWSA.symmetrize_wvv(self.plasmafreq_vv[np.newaxis])
print('Plasma frequency:', file=self.fd)
print((self.plasmafreq_vv**0.5 * Hartree).round(2), file=self.fd)
# The response function is integrated only over the IBZ. The
# chi calculated above must therefore be extended to include the
# response from the full BZ. This extension can be performed as a
# simple post processing of the response function that makes
# sure that the response function fulfills the symmetries of the little
# group of q. Due to the specific details of the implementation the chi
# calculated above is normalized by the number of symmetries (as seen
# below) and then symmetrized.
A_wxx *= prefactor
tmpA_wxx = self.redistribute(A_wxx)
if extend_head:
PWSA.symmetrize_wxx(tmpA_wxx, optical_limit=optical_limit)
else:
PWSA.symmetrize_wGG(tmpA_wxx)
if wings:
chi0_wxvG += chi0_wxvx[..., 2:]
chi0_wvv += chi0_wxvx[:, 0, :3, :3]
PWSA.symmetrize_wxvG(chi0_wxvG)
PWSA.symmetrize_wvv(chi0_wvv)
self.redistribute(tmpA_wxx, A_wxx)
# If point summation was used then the normalization of the
# response function is not right and we have to make up for this
# fact.
if wings:
chi0_wxvG *= prefactor
chi0_wvv *= prefactor
# In the optical limit, we have extended the wings and the head to
# account for their nonanalytic behaviour which means that the size of
# the chi0_wGG matrix is nw * (nG + 2)**2. Below we extract these
# parameters.
if optical_limit and extend_head:
# The wings are extracted
chi0_wxvG[:, 1, :,
self.Ga:self.Gb] = np.transpose(A_wxx[..., 0:3],
(0, 2, 1))
va = min(self.Ga, 3)
vb = min(self.Gb, 3)
# print(self.world.rank, va, vb, chi0_wxvG[:, 0, va:vb].shape,
# A_wxx[:, va:vb].shape, A_wxx.shape)
chi0_wxvG[:, 0, va:vb] = A_wxx[:, :vb - va]
# Add contributions on different ranks
self.blockcomm.sum(chi0_wxvG)
chi0_wvv[:] = chi0_wxvG[:, 0, :3, :3]
chi0_wxvG = chi0_wxvG[..., 2:] # Jesus, this is complicated
# The head is extracted
# if self.blockcomm.rank == 0:
# chi0_wvv[:] = A_wxx[:, :3, :3]
# self.blockcomm.broadcast(chi0_wvv, 0)
# It is easiest to redistribute over freqs to pick body
tmpA_wxx = self.redistribute(A_wxx)
chi0_wGG = tmpA_wxx[:, 2:, 2:]
chi0_wGG = self.redistribute(chi0_wGG)
elif optical_limit:
# Since chi_wGG is nonanalytic in the head
# and wings we have to take care that
# these are handled correctly. Note that
# it is important that the wings are overwritten first.
chi0_wGG[:, :, 0] = chi0_wxvG[:, 1, 2, self.Ga:self.Gb]
if self.blockcomm.rank == 0:
chi0_wGG[:, 0, :] = chi0_wxvG[:, 0, 2, :]
chi0_wGG[:, 0, 0] = chi0_wvv[:, 2, 2]
else:
chi0_wGG = A_wxx
return pd, chi0_wGG, chi0_wxvG, chi0_wvv
def get_PWDescriptor(self, q_c, gammacentered=False):
"""Get the planewave descriptor of q_c."""
qd = KPointDescriptor([q_c])
pd = PWDescriptor(self.ecut,
self.calc.wfs.gd,
complex,
qd,
gammacentered=gammacentered)
return pd
@timer('Get kpoints')
def get_kpoints(self, pd, integrationmode=None):
"""Get the integration domain."""
# Use symmetries
PWSA = PWSymmetryAnalyzer
PWSA = PWSA(self.calc.wfs.kd,
pd,
timer=self.timer,
txt=self.fd,
disable_point_group=self.disable_point_group,
disable_time_reversal=self.disable_time_reversal,
disable_non_symmorphic=self.disable_non_symmorphic)
if integrationmode is None:
K_gK = PWSA.group_kpoints()
bzk_kc = np.array(
[self.calc.wfs.kd.bzk_kc[K_K[0]] for K_K in K_gK])
elif integrationmode == 'tetrahedron integration':
bzk_kc = PWSA.get_reduced_kd(pbc_c=self.pbc).bzk_kc
if (~self.pbc).any():
bzk_kc = np.append(bzk_kc,
bzk_kc + (~self.pbc).astype(int),
axis=0)
bzk_kv = np.dot(bzk_kc, pd.gd.icell_cv) * 2 * np.pi
return bzk_kv, PWSA
@timer('Get matrix element')
def get_matrix_element(self,
k_v,
s,
n1=None,
n2=None,
m1=None,
m2=None,
pd=None,
kd=None,
symmetry=None,
integrationmode=None,
extend_head=True,
block=True):
"""A function that returns pair-densities.
A pair density is defined as::
<snk| e^(-i (q + G) r) |s'mk+q>,
where s and s' are spins, n and m are band indices, k is
the kpoint and q is the momentum transfer. For dielectric
reponse s'=s, for the transverse magnetic reponse
s' is flipped with respect to s.
Parameters
----------
k_v : ndarray
Kpoint coordinate in cartesian coordinates.
s : int
Spin index.
n1 : int
Lower occupied band index.
n2 : int
Upper occupied band index.
m1 : int
Lower unoccupied band index.
m2 : int
Upper unoccupied band index.
pd : PlanewaveDescriptor instance
kd : KpointDescriptor instance
Calculator kpoint descriptor.
symmetry: gpaw.response.pair.PWSymmetryAnalyzer instance
PWSA object for handling symmetries of the kpoints.
integrationmode : str
The integration mode employed.
extend_head: Bool
Extend the head to include non-analytic behaviour
Return
------
n_nmG : ndarray
Pair densities.
"""
k_c = np.dot(pd.gd.cell_cv, k_v) / (2 * np.pi)
q_c = pd.kd.bzk_kc[0]
optical_limit = np.allclose(q_c, 0.0) and self.response == 'density'
extrapolate_q = False
if self.calc.wfs.kd.refine_info is not None:
K1 = self.pair.find_kpoint(k_c)
label = kd.refine_info.label_k[K1]
if label == 'zero':
return None
elif (kd.refine_info.almostoptical and label == 'mh'):
if not hasattr(self, 'pd0'):
self.pd0 = self.get_PWDescriptor([
0,
] * 3)
pd = self.pd0
extrapolate_q = True
nG = pd.ngmax
weight = np.sqrt(
symmetry.get_kpoint_weight(k_c) / symmetry.how_many_symmetries())
if self.Q_aGii is None:
self.Q_aGii = self.pair.initialize_paw_corrections(pd)
kptpair = self.pair.get_kpoint_pair(pd,
s,
k_c,
n1,
n2,
m1,
m2,
block=block)
m_m = np.arange(m1, m2)
n_n = np.arange(n1, n2)
n_nmG = self.pair.get_pair_density(pd,
kptpair,
n_n,
m_m,
Q_aGii=self.Q_aGii,
block=block)
if integrationmode is None:
n_nmG *= weight
df_nm = kptpair.get_occupation_differences(n_n, m_m)
if not self.response == 'density':
df_nm = np.abs(df_nm)
df_nm[df_nm <= 1e-20] = 0.0
n_nmG *= df_nm[..., np.newaxis]**0.5
if extrapolate_q:
q_v = np.dot(q_c, pd.gd.icell_cv) * (2 * np.pi)
nq_nm = np.dot(n_nmG[:, :, :3], q_v)
n_nmG = n_nmG[:, :, 2:]
n_nmG[:, :, 0] = nq_nm
if not extend_head and optical_limit:
n_nmG = np.copy(n_nmG[:, :, 2:])
optical_limit = False
if extend_head and optical_limit:
return n_nmG.reshape(-1, nG + 2 * optical_limit)
else:
return n_nmG.reshape(-1, nG)
@timer('Get eigenvalues')
def get_eigenvalues(self,
k_v,
s,
n1=None,
n2=None,
m1=None,
m2=None,
kd=None,
pd=None,
wfs=None,
filter=False):
"""A function that can return the eigenvalues.
A simple function describing the integrand of
the response function which gives an output that
is compatible with the gpaw k-point integration
routines."""
if wfs is None:
wfs = self.calc.wfs
kd = wfs.kd
k_c = np.dot(pd.gd.cell_cv, k_v) / (2 * np.pi)
q_c = pd.kd.bzk_kc[0]
K1 = self.pair.find_kpoint(k_c)
K2 = self.pair.find_kpoint(k_c + q_c)
ik1 = kd.bz2ibz_k[K1]
ik2 = kd.bz2ibz_k[K2]
kpt1 = wfs.kpt_u[s * wfs.kd.nibzkpts + ik1]
if self.response in ['+-', '-+']:
s2 = 1 - s
else:
s2 = s
kpt2 = wfs.kpt_u[s2 * wfs.kd.nibzkpts + ik2]
deps_nm = np.subtract(kpt1.eps_n[n1:n2][:, np.newaxis],
kpt2.eps_n[m1:m2])
if filter:
fermi_level = self.pair.fermi_level
deps_nm[kpt1.eps_n[n1:n2] > fermi_level, :] = np.nan
deps_nm[:, kpt2.eps_n[m1:m2] < fermi_level] = np.nan
return deps_nm.reshape(-1)
def get_intraband_response(self,
k_v,
s,
n1=None,
n2=None,
kd=None,
symmetry=None,
pd=None,
integrationmode=None):
k_c = np.dot(pd.gd.cell_cv, k_v) / (2 * np.pi)
kpt1 = self.pair.get_k_point(s, k_c, n1, n2)
n_n = range(n1, n2)
vel_nv = self.pair.intraband_pair_density(kpt1, n_n)
if self.integrationmode is None:
f_n = kpt1.f_n
width = self.calc.occupations.width
if width > 1e-15:
dfde_n = -1. / width * (f_n - f_n**2.0)
else:
dfde_n = np.zeros_like(f_n)
vel_nv *= np.sqrt(-dfde_n[:, np.newaxis])
weight = np.sqrt(
symmetry.get_kpoint_weight(k_c) /
symmetry.how_many_symmetries())
vel_nv *= weight
return vel_nv
@timer('Intraband eigenvalue')
def get_intraband_eigenvalue(self,
k_v,
s,
n1=None,
n2=None,
kd=None,
pd=None):
"""A function that can return the eigenvalues.
A simple function describing the integrand of
the response function which gives an output that
is compatible with the gpaw k-point integration
routines."""
wfs = self.calc.wfs
kd = wfs.kd
k_c = np.dot(pd.gd.cell_cv, k_v) / (2 * np.pi)
K1 = self.pair.find_kpoint(k_c)
ik = kd.bz2ibz_k[K1]
kpt1 = wfs.kpt_u[s * wfs.kd.nibzkpts + ik]
return kpt1.eps_n[n1:n2]
@timer('redist')
def redistribute(self, in_wGG, out_x=None):
"""Redistribute array.
Switch between two kinds of parallel distributions:
1) parallel over G-vectors (second dimension of in_wGG)
2) parallel over frequency (first dimension of in_wGG)
Returns new array using the memory in the 1-d array out_x.
"""
comm = self.blockcomm
if comm.size == 1:
return in_wGG
nw = len(self.omega_w)
nG = in_wGG.shape[2]
mynw = (nw + comm.size - 1) // comm.size
mynG = (nG + comm.size - 1) // comm.size
bg1 = BlacsGrid(comm, comm.size, 1)
bg2 = BlacsGrid(comm, 1, comm.size)
md1 = BlacsDescriptor(bg1, nw, nG**2, mynw, nG**2)
md2 = BlacsDescriptor(bg2, nw, nG**2, nw, mynG * nG)
if len(in_wGG) == nw:
mdin = md2
mdout = md1
else:
mdin = md1
mdout = md2
r = Redistributor(comm, mdin, mdout)
outshape = (mdout.shape[0], mdout.shape[1] // nG, nG)
if out_x is None:
out_wGG = np.empty(outshape, complex)
else:
out_wGG = out_x[:np.product(outshape)].reshape(outshape)
r.redistribute(in_wGG.reshape(mdin.shape),
out_wGG.reshape(mdout.shape))
return out_wGG
@timer('dist freq')
def distribute_frequencies(self, chi0_wGG):
"""Distribute frequencies to all cores."""
world = self.world
comm = self.blockcomm
if world.size == 1:
return chi0_wGG
nw = len(self.omega_w)
nG = chi0_wGG.shape[2]
mynw = (nw + world.size - 1) // world.size
mynG = (nG + comm.size - 1) // comm.size
wa = min(world.rank * mynw, nw)
wb = min(wa + mynw, nw)
if self.blockcomm.size == 1:
return chi0_wGG[wa:wb].copy()
if self.kncomm.rank == 0:
bg1 = BlacsGrid(comm, 1, comm.size)
in_wGG = chi0_wGG.reshape((nw, -1))
else:
bg1 = DryRunBlacsGrid(mpi.serial_comm, 1, 1)
in_wGG = np.zeros((0, 0), complex)
md1 = BlacsDescriptor(bg1, nw, nG**2, nw, mynG * nG)
bg2 = BlacsGrid(world, world.size, 1)
md2 = BlacsDescriptor(bg2, nw, nG**2, mynw, nG**2)
r = Redistributor(world, md1, md2)
shape = (wb - wa, nG, nG)
out_wGG = np.empty(shape, complex)
r.redistribute(in_wGG, out_wGG.reshape((wb - wa, nG**2)))
return out_wGG
def print_chi(self, pd):
calc = self.calc
gd = calc.wfs.gd
if extra_parameters.get('df_dry_run'):
from gpaw.mpi import DryRunCommunicator
size = extra_parameters['df_dry_run']
world = DryRunCommunicator(size)
else:
world = self.world
q_c = pd.kd.bzk_kc[0]
nw = len(self.omega_w)
ecut = self.ecut * Hartree
ns = calc.wfs.nspins
nbands = self.nbands
nk = calc.wfs.kd.nbzkpts
nik = calc.wfs.kd.nibzkpts
ngmax = pd.ngmax
eta = self.eta * Hartree
wsize = world.size
knsize = self.kncomm.size
nocc = self.nocc1
npocc = self.nocc2
ngridpoints = gd.N_c[0] * gd.N_c[1] * gd.N_c[2]
nstat = (ns * npocc + world.size - 1) // world.size
occsize = nstat * ngridpoints * 16. / 1024**2
bsize = self.blockcomm.size
chisize = nw * pd.ngmax**2 * 16. / 1024**2 / bsize
p = partial(print, file=self.fd)
p('%s' % ctime())
p('Called response.chi0.calculate with')
p(' q_c: [%f, %f, %f]' % (q_c[0], q_c[1], q_c[2]))
p(' Number of frequency points: %d' % nw)
p(' Planewave cutoff: %f' % ecut)
p(' Number of spins: %d' % ns)
p(' Number of bands: %d' % nbands)
p(' Number of kpoints: %d' % nk)
p(' Number of irredicible kpoints: %d' % nik)
p(' Number of planewaves: %d' % ngmax)
p(' Broadening (eta): %f' % eta)
p(' world.size: %d' % wsize)
p(' kncomm.size: %d' % knsize)
p(' blockcomm.size: %d' % bsize)
p(' Number of completely occupied states: %d' % nocc)
p(' Number of partially occupied states: %d' % npocc)
p()
p(' Memory estimate of potentially large arrays:')
p(' chi0_wGG: %f M / cpu' % chisize)
p(' Occupied states: %f M / cpu' % occsize)
p(' Memory usage before allocation: %f M / cpu' %
(maxrss() / 1024**2))
p()
def read_gpaw(input_gpw,
nb_max=None,
spin_factor=2,
output_file='out.hdf5',
calculate_overlap=True,
calculate_momentum=True):
""" Read .gpw file and create a hdf5 as output.
Partially adapted from gpaw.wannier90.write_overlaps.
input_gpw: location of .gpw input file
nb_max: maximum band
spin_factor: electrons per band (only default value supported!)
"""
nn = 1
au = AtomicUnits()
atoms, calc = restart(input_gpw, txt=None)
# Generate full Brillouin zone if necessary
if calc.parameters['symmetry'] != 'off':
calc.set(symmetry='off')
calc.get_potential_energy()
calc.write(input_gpw.replace('.gpw', '_FBZ.gpw'), mode='all')
calc.get_potential_energy()
#Optional parameters:
nb = calc.parameters['convergence']['bands']
if nb_max is not None:
nb = min(nb, nb_max)
nk_size = calc.parameters['kpts']['size']
nk = calc.wfs.kd.nbzkpts
kpts = calc.get_bz_k_points()
wfs = calc.wfs
nvalence = calc.setups.nvalence // spin_factor
lattice = atoms.get_cell() / au.AA
reciprocal_lattice = (2 * np.pi * au.AA) * atoms.get_reciprocal_cell()
bands = range(nb)
direction = np.eye(3, dtype=np.intp)
klist1d = np.zeros((nk, 3))
klist3d = np.zeros((nk_size), dtype=np.intp)
energy = np.zeros((nk, nb))
for i in range(nk):
klist1d[i, :] = calc.wfs.kd.bzk_kc[i]
for i in range(nk):
ix, iy, iz = [int(q) for q in np.rint(nk_size * kpts[i, :])]
klist3d[ix, iy, iz] = i
nn_table = nearest_neighbor_table(klist3d, nn)
energy_fermi = calc.get_fermi_level()
for i in range(nk):
energy[i, :] = (calc.get_eigenvalues(kpt=i, spin=0) -
energy_fermi)[:nb] / au.eV
if calculate_overlap:
overlap = np.zeros((nk, 3, 2 * nn, nb, nb), dtype=np.complex)
icell_cv = (2 * np.pi) * np.linalg.inv(calc.wfs.gd.cell_cv).T
r_grid = calc.wfs.gd.get_grid_point_coordinates()
n_grid = np.prod(np.shape(r_grid)[1:]) * (False + 1)
u_kng = []
for i in range(nk):
u_kng.append(
np.array([wfs.get_wave_function_array(n, i, 0)
for n in bands]))
d0_aii = []
for i in calc.wfs.kpt_u[0].p_ani.keys():
d0_ii = calc.wfs.setups[i].d0_ii
d0_aii.append(d0_ii)
p_kani = []
for i in range(nk):
p_kani.append(calc.wfs.kpt_u[0 * nk + i].p_ani)
for ik1 in range(nk):
u1_ng = u_kng[ik1]
for i in range(3):
for j in range(-nn, nn):
ik2 = nn_table[ik1, i, j]
if j < 0:
g_vector = (kpts[ik1] + 1.0 * j * direction[i, :] /
nk_size) - kpts[ik2]
if j >= 0:
g_vector = (
kpts[ik1] + 1.0 *
(j + 1) * direction[i, :] / nk_size) - kpts[ik2]
bg_c = kpts[ik2] - kpts[ik1] + g_vector
bg_v = np.dot(bg_c, icell_cv)
u2_ng = u_kng[ik2] * np.exp(
-1j * np.inner(r_grid.T, bg_v).T)
overlap[ik1, i, j, :, :] = get_overlap(
calc, bands, np.reshape(u1_ng, (len(u1_ng), n_grid)),
np.reshape(u2_ng, (len(u2_ng), n_grid)), p_kani[ik1],
p_kani[ik2], d0_aii, bg_v)[:nb, :nb]
if calculate_momentum:
pair = PairDensity(calc=calc)
momentum = np.zeros((nk, nb, nb, 3), dtype=np.complex)
delta_q_vector = [0.0, 0.0, 0.0]
delta_q_descriptor = KPointDescriptor([delta_q_vector])
plane_wave_descriptor = PWDescriptor(pair.ecut, calc.wfs.gd, complex,
delta_q_descriptor)
for i in range(nk):
kpoint_pair = pair.get_kpoint_pair(plane_wave_descriptor,
s=0,
K=i,
n1=0,
n2=nb,
m1=0,
m2=nb)
kpoint_momentum = pair.get_pair_momentum(plane_wave_descriptor,
kpoint_pair,
np.arange(0, nb),
np.arange(0, nb))
momentum[i, :, :, :] = kpoint_momentum[..., 0]
hdf5 = h5py.File(output_file, 'w')
hdf5.create_dataset("energy", data=energy)
hdf5.create_dataset("klist1d", data=klist1d)
hdf5.create_dataset("klist3d", data=klist3d)
hdf5.create_dataset("lattice_vectors", data=lattice.T)
hdf5.create_dataset("reciprocal_vectors", data=reciprocal_lattice.T)
hdf5.create_dataset("valence_bands", data=nvalence)
hdf5.create_dataset("size", data=nk_size)
hdf5.create_dataset("spin_factor", data=spin_factor)
if calculate_momentum:
hdf5.create_dataset("momentum", data=momentum)
if calculate_overlap:
hdf5.create_dataset("overlap", data=overlap)
hdf5.create_dataset("neighbour_table", data=nn_table)
def __init__(self,
calc,
response='density',
frequencies=None,
domega0=0.1,
omega2=10.0,
omegamax=None,
ecut=50,
gammacentered=False,
hilbert=True,
nbands=None,
timeordered=False,
eta=0.2,
ftol=1e-6,
threshold=1,
real_space_derivatives=False,
intraband=True,
world=mpi.world,
txt='-',
timer=None,
nblocks=1,
gate_voltage=None,
disable_point_group=False,
disable_time_reversal=False,
disable_non_symmorphic=True,
scissor=None,
integrationmode=None,
pbc=None,
rate=0.0,
eshift=0.0):
"""Construct Chi0 object.
Parameters
----------
calc : str
The groundstate calculation file that the linear response
calculation is based on.
response : str
Type of response function. Currently collinear, scalar options
'density', '+-' and '-+' are implemented.
frequencies : ndarray or None
Array of frequencies to evaluate the response function at. If None,
frequencies are determined using the frequency_grid function in
gpaw.response.chi0.
domega0, omega2, omegamax : float
Input parameters for frequency_grid.
ecut : float
Energy cutoff.
gammacentered : bool
Center the grid of plane waves around the gamma point or q-vector
hilbert : bool
Switch for hilbert transform. If True, the full density response
is determined from a hilbert transform of its spectral function.
This is typically much faster, but does not work for imaginary
frequencies.
nbands : int
Maximum band index to include.
timeordered : bool
Switch for calculating the time ordered density response function.
In this case the hilbert transform cannot be used.
eta : float
Artificial broadening of spectra.
ftol : float
Threshold determining whether a band is completely filled
(f > 1 - ftol) or completely empty (f < ftol).
threshold : float
Numerical threshold for the optical limit k dot p perturbation
theory expansion (used in gpaw/response/pair.py).
real_space_derivatives : bool
Switch for calculating nabla matrix elements (in the optical limit)
using a real space finite difference approximation.
intraband : bool
Switch for including the intraband contribution to the density
response function.
world : MPI comm instance
MPI communicator.
txt : str
Output file.
timer : gpaw.utilities.timing.timer instance
nblocks : int
Divide the response function into nblocks. Useful when the response
function is large.
gate_voltage : float
Shift the fermi level by gate_voltage [Hartree].
disable_point_group : bool
Do not use the point group symmetry operators.
disable_time_reversal : bool
Do not use time reversal symmetry.
disable_non_symmorphic : bool
Do no use non symmorphic symmetry operators.
scissor : tuple ([bands], shift [eV])
Use scissor operator on bands.
integrationmode : str
Integrator for the kpoint integration.
If == 'tetrahedron integration' then the kpoint integral is
performed using the linear tetrahedron method.
pbc : list
Periodic directions of the system. Defaults to [True, True, True].
eshift : float
Shift unoccupied bands
Attributes
----------
pair : gpaw.response.pair.PairDensity instance
Class for calculating matrix elements of pairs of wavefunctions.
"""
self.response = response
self.timer = timer or Timer()
self.pair = PairDensity(calc,
ecut,
self.response,
ftol,
threshold,
real_space_derivatives,
world,
txt,
self.timer,
nblocks=nblocks,
gate_voltage=gate_voltage)
self.disable_point_group = disable_point_group
self.disable_time_reversal = disable_time_reversal
self.disable_non_symmorphic = disable_non_symmorphic
self.integrationmode = integrationmode
self.eshift = eshift / Hartree
calc = self.pair.calc
self.calc = calc
if world.rank != 0:
txt = devnull
elif isinstance(txt, str):
txt = open(txt, 'w')
self.fd = txt
self.vol = abs(np.linalg.det(calc.wfs.gd.cell_cv))
self.world = world
if nblocks == 1:
self.blockcomm = self.world.new_communicator([world.rank])
self.kncomm = world
else:
assert world.size % nblocks == 0, world.size
rank1 = world.rank // nblocks * nblocks
rank2 = rank1 + nblocks
self.blockcomm = self.world.new_communicator(range(rank1, rank2))
ranks = range(world.rank % nblocks, world.size, nblocks)
self.kncomm = self.world.new_communicator(ranks)
self.nblocks = nblocks
if world.rank != 0:
txt = devnull
elif isinstance(txt, str):
txt = open(txt, 'w')
self.fd = txt
if ecut is not None:
ecut /= Hartree
self.ecut = ecut
self.gammacentered = gammacentered
self.eta = eta / Hartree
if rate == 'eta':
self.rate = self.eta
else:
self.rate = rate / Hartree
self.domega0 = domega0 / Hartree
self.omega2 = omega2 / Hartree
self.omegamax = None if omegamax is None else omegamax / Hartree
self.nbands = nbands or self.calc.wfs.bd.nbands
self.include_intraband = intraband
omax = self.find_maximum_frequency()
if frequencies is None:
if self.omegamax is None:
self.omegamax = omax
print('Using nonlinear frequency grid from 0 to %.3f eV' %
(self.omegamax * Hartree),
file=self.fd)
self.wd = FrequencyDescriptor(self.domega0, self.omega2,
self.omegamax)
else:
self.wd = ArrayDescriptor(np.asarray(frequencies) / Hartree)
assert not hilbert
self.omega_w = self.wd.get_data()
self.hilbert = hilbert
self.timeordered = bool(timeordered)
if self.eta == 0.0:
assert not hilbert
assert not timeordered
assert not self.omega_w.real.any()
self.nocc1 = self.pair.nocc1 # number of completely filled bands
self.nocc2 = self.pair.nocc2 # number of non-empty bands
self.Q_aGii = None
if pbc is not None:
self.pbc = np.array(pbc)
else:
self.pbc = np.array([True, True, True])
if self.pbc is not None and (~self.pbc).any():
assert np.sum((~self.pbc).astype(int)) == 1, \
print('Only one non-periodic direction supported atm.')
print('Nonperiodic BC\'s: ', (~self.pbc), file=self.fd)
if integrationmode is not None:
print('Using integration method: ' + self.integrationmode,
file=self.fd)
else:
print('Using integration method: PointIntegrator', file=self.fd)
from gpaw.response.pair import PairDensity
from gpaw.response.math_func import two_phi_nabla_planewave_integrals
np.set_printoptions(precision=1)
nb = 6
a = Atoms('H', cell=(3 * np.eye(3)), pbc=True)
calc = GPAW(mode=PW(600), kpts=[[0, 0, 0], [0.25, 0, 0]])
a.calc = calc
a.get_potential_energy()
calc.diagonalize_full_hamiltonian(nbands=nb, expert=True)
calc.write('a.gpw', 'all')
pair = PairDensity('a.gpw', ecut=100)
# Check continuity eq.
for q_c in [[0, 0, 0], [1. / 4, 0, 0]]:
ol = np.allclose(q_c, 0.0)
qd = KPointDescriptor([q_c])
pd = PWDescriptor(pair.ecut, calc.wfs.gd, complex, qd)
kptpair = pair.get_kpoint_pair(pd, 0, [0, 0, 0], 0, nb, 0, nb)
deps_nm = kptpair.get_transition_energies(np.arange(0, nb),
np.arange(0, nb))
n_nmG = pair.get_pair_density(pd,
kptpair,
np.arange(0, nb),
np.arange(0, nb),
optical_limit=ol)
def __init__(self, calc, filename='gw',
kpts=None, bands=None, nbands=None, ppa=False,
wstc=False,
ecut=150.0, eta=0.1, E0=1.0 * Hartree,
domega0=0.025, omega2=10.0,
nblocks=1, savew=False,
world=mpi.world):
if world.rank != 0:
txt = devnull
else:
txt = open(filename + '.txt', 'w')
p = functools.partial(print, file=txt)
p(' ___ _ _ _ ')
p(' | || | | |')
p(' | | || | | |')
p(' |__ ||_____|')
p(' |___|')
p()
PairDensity.__init__(self, calc, ecut, world=world, nblocks=nblocks,
txt=txt)
self.filename = filename
self.savew = savew
ecut /= Hartree
self.ppa = ppa
self.wstc = wstc
self.eta = eta / Hartree
self.E0 = E0 / Hartree
self.domega0 = domega0 / Hartree
self.omega2 = omega2 / Hartree
self.kpts = select_kpts(kpts, self.calc)
if bands is None:
bands = [0, self.nocc2]
self.bands = bands
b1, b2 = bands
self.shape = shape = (self.calc.wfs.nspins, len(self.kpts), b2 - b1)
self.eps_sin = np.empty(shape) # KS-eigenvalues
self.f_sin = np.empty(shape) # occupation numbers
self.sigma_sin = np.zeros(shape) # self-energies
self.dsigma_sin = np.zeros(shape) # derivatives of self-energies
self.vxc_sin = None # KS XC-contributions
self.exx_sin = None # exact exchange contributions
self.Z_sin = None # renormalization factors
if nbands is None:
nbands = int(self.vol * ecut**1.5 * 2**0.5 / 3 / pi**2)
self.nbands = nbands
p()
p('Quasi particle states:')
if kpts is None:
p('All k-points in IBZ')
else:
kptstxt = ', '.join(['{0:d}'.format(k) for k in self.kpts])
p('k-points (IBZ indices): [' + kptstxt + ']')
p('Band range: ({0:d}, {1:d})'.format(b1, b2))
p()
p('Computational parameters:')
p('Plane wave cut-off: {0:g} eV'.format(self.ecut * Hartree))
p('Number of bands: {0:d}'.format(self.nbands))
p('Broadening: {0:g} eV'.format(self.eta * Hartree))
kd = self.calc.wfs.kd
self.mysKn1n2 = None # my (s, K, n1, n2) indices
self.distribute_k_points_and_bands(b1, b2, kd.ibz2bz_k[self.kpts])
# Find q-vectors and weights in the IBZ:
assert -1 not in kd.bz2bz_ks
offset_c = 0.5 * ((kd.N_c + 1) % 2) / kd.N_c
bzq_qc = monkhorst_pack(kd.N_c) + offset_c
self.qd = KPointDescriptor(bzq_qc)
self.qd.set_symmetry(self.calc.atoms, kd.symmetry)
assert self.calc.wfs.nspins == 1
