def __init__(self, calc, xc, ibzq_qc, fd, unit_cells, density_cut, ecut,
tag, timer):
self.calc = calc
self.gd = calc.density.gd
self.xc = xc
self.ibzq_qc = ibzq_qc
self.fd = fd
self.unit_cells = unit_cells
self.density_cut = density_cut
self.ecut = ecut
self.tag = tag
self.timer = timer
self.A_x = -(3 / 4.) * (3 / np.pi)**(1 / 3.)
self.n_g = calc.get_all_electron_density(gridrefinement=1)
self.n_g *= Bohr**3
if xc[-3:] == 'PBE':
nf_g = calc.get_all_electron_density(gridrefinement=2)
nf_g *= Bohr**3
gdf = self.gd.refine()
grad_v = [Gradient(gdf, v, n=1).apply for v in range(3)]
gradnf_vg = gdf.empty(3)
for v in range(3):
grad_v[v](nf_g, gradnf_vg[v])
self.gradn_vg = gradnf_vg[:, ::2, ::2, ::2]
qd = KPointDescriptor(self.ibzq_qc)
self.pd = PWDescriptor(ecut / Hartree, self.gd, complex, qd)
def __init__(self, name=None, calc=None, M=None, spinorbit=None):
self.name = name
self.calc = GPAW(calc, txt=None, communicator=mpi.serial_comm)
self.M = np.array(M, dtype=float)
self.spinorbit = spinorbit
self.gd = self.calc.wfs.gd.new_descriptor()
self.kd = self.calc.wfs.kd
if self.calc.wfs.mode is 'pw':
self.pd = self.calc.wfs.pd
else:
self.pd = PWDescriptor(ecut=None,
gd=self.gd,
kd=self.kd,
dtype=complex)
self.acell_cv = self.gd.cell_cv
self.bcell_cv = 2 * np.pi * self.gd.icell_cv
self.vol = self.gd.volume
self.BZvol = (2 * np.pi)**3 / self.vol
self.nb = self.calc.get_number_of_bands()
self.v_Knm = None
if spinorbit:
if mpi.world.rank == 0:
print('Calculating spinorbit Corrections')
self.nb = 2 * self.calc.get_number_of_bands()
self.e_mK, self.v_Knm = get_spinorbit_eigenvalues(self.calc,
return_wfs=True)
if mpi.world.rank == 0:
print('Done with the spinorbit Corrections')
def initialize(self, density, hamiltonian, wfs, occupations):
self.xc.initialize(density, hamiltonian, wfs, occupations)
self.nspins = wfs.nspins
self.setups = wfs.setups
self.density = density
self.kpt_u = wfs.kpt_u
self.gd = density.gd
self.kd = wfs.kd
self.bd = wfs.bd
if self.bd.comm.size > 1:
raise ValueError('Band parallelization not supported by hybridk')
self.wfs = wfs
self.world = wfs.world
self.fd = logfile(self.fd, self.world.rank)
N = self.gd.N_c.prod()
vol = self.gd.dv * N
if self.alpha is None:
# XXX ?
self.alpha = 6 * vol**(2 / 3.0) / pi**2
if self.ecut is None:
self.ecut = 0.5 * pi**2 / (self.gd.h_cv**2).sum(1).max() * 0.9999
self.bzq_qc = self.kd.get_bz_q_points()
qd = KPointDescriptor(self.bzq_qc)
q0 = self.kd.where_is_q(np.zeros(3), self.bzq_qc)
self.pwd = PWDescriptor(self.ecut, self.gd, complex, kd=qd)
G2_qG = self.pwd.G2_qG
G2_qG[q0][0] = 117.0
self.iG2_qG = [1.0 / G2_G for G2_G in G2_qG]
G2_qG[q0][0] = 0.0
self.iG2_qG[q0][0] = 0.0
self.gamma = (vol / (2 * pi)**2 * sqrt(pi / self.alpha) *
self.kd.nbzkpts)
for q in range(self.kd.nbzkpts):
self.gamma -= np.dot(np.exp(-self.alpha * G2_qG[q]),
self.iG2_qG[q])
self.iG2_qG[q0][0] = self.gamma
self.ghat = LFC(self.gd, [setup.ghat_l for setup in density.setups],
qd,
dtype=complex)
self.log('Value of alpha parameter:', self.alpha)
self.log('Value of gamma parameter:', self.gamma)
self.log('Cutoff energy:', self.ecut, 'Hartree')
self.log('%d x %d x %d k-points' % tuple(self.kd.N_c))
def get_pw_descriptor(q_c, calc, ecut, gammacentered=False):
"""Get the planewave descriptor of q_c."""
qd = KPointDescriptor([q_c])
pd = PWDescriptor(ecut,
calc.wfs.gd,
complex,
qd,
gammacentered=gammacentered)
return pd
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
def calculate(self, q_c, spin='all', A_x=None):
wfs = self.calc.wfs
if spin == 'all':
spins = range(wfs.nspins)
else:
assert spin in range(wfs.nspins)
spins = [spin]
q_c = np.asarray(q_c, dtype=float)
qd = KPointDescriptor([q_c])
pd = PWDescriptor(self.ecut, wfs.gd, complex, qd)
self.print_chi(pd)
if extra_parameters.get('df_dry_run'):
print(' Dry run exit', file=self.fd)
raise SystemExit
nG = pd.ngmax
nw = len(self.omega_w)
mynG = (nG + self.blockcomm.size - 1) // self.blockcomm.size
self.Ga = self.blockcomm.rank * mynG
self.Gb = min(self.Ga + mynG, nG)
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 np.allclose(q_c, 0.0):
chi0_wxvG = np.zeros((len(self.omega_w), 2, 3, nG), complex)
chi0_wvv = np.zeros((len(self.omega_w), 3, 3), complex)
self.chi0_vv = np.zeros((3, 3), complex)
else:
chi0_wxvG = None
chi0_wvv = None
print('Initializing PAW Corrections', file=self.fd)
self.Q_aGii = self.initialize_paw_corrections(pd)
# Do all empty bands:
m1 = self.nocc1
m2 = self.nbands
self._calculate(pd, chi0_wGG, chi0_wxvG, chi0_wvv, self.Q_aGii, m1, m2,
spins)
return pd, chi0_wGG, chi0_wxvG, chi0_wvv
def check(self, i_cG, shift0_c, N_c, q_c, Q_aGii):
I0_G = np.ravel_multi_index(i_cG - shift0_c[:, None], N_c, 'wrap')
qd1 = KPointDescriptor([q_c])
pd1 = PWDescriptor(self.ecut, self.calc.wfs.gd, complex, qd1)
G_I = np.empty(N_c.prod(), int)
G_I[:] = -1
I1_G = pd1.Q_qG[0]
G_I[I1_G] = np.arange(len(I0_G))
G_G = G_I[I0_G]
assert len(I0_G) == len(I1_G)
assert (G_G >= 0).all()
for a, Q_Gii in enumerate(self.initialize_paw_corrections(pd1)):
e = abs(Q_aGii[a] - Q_Gii[G_G]).max()
assert e < 1e-12
def calculate_gamma(self, vol, alpha):
if self.molecule:
return 0.0
N_c = self.kd.N_c
offset_c = (N_c + 1) % 2 * 0.5 / N_c
bzq_qc = monkhorst_pack(N_c) + offset_c
qd = KPointDescriptor(bzq_qc)
pd = PWDescriptor(self.wfs.pd.ecut, self.wfs.gd, kd=qd)
gamma = (vol / (2 * pi)**2 * sqrt(pi / alpha) * self.kd.nbzkpts)
for G2_G in pd.G2_qG:
if G2_G[0] < 1e-7:
G2_G = G2_G[1:]
gamma -= np.dot(np.exp(-alpha * G2_G), G2_G**-1)
return gamma / self.qstride_c.prod()
def calculate_q(self, i, kpt1, kpt2):
wfs = self.calc.wfs
q_c = wfs.kd.bzk_kc[kpt2.K] - wfs.kd.bzk_kc[kpt1.K]
qd = KPointDescriptor([q_c])
pd = PWDescriptor(self.ecut, wfs.gd, wfs.dtype, kd=qd)
Q_G = self.get_fft_indices(kpt1.K, kpt2.K, q_c, pd,
kpt1.shift_c - kpt2.shift_c)
Q_aGii = self.initialize_paw_corrections(pd, soft=True)
for n in range(kpt1.n2 - kpt1.n1):
ut1cc_R = kpt1.ut_nR[n].conj()
C1_aGi = [
np.dot(Q_Gii, P1_ni[n].conj())
for Q_Gii, P1_ni in zip(Q_aGii, kpt1.P_ani)
]
n_mG = self.calculate_pair_densities(ut1cc_R, C1_aGi, kpt2, pd,
Q_G)
e = self.calculate_n(pd, n, n_mG, kpt2)
self.exxvv_sin[kpt1.s, i, n] += e
def calculate_exx(self):
"""Non-selfconsistent calculation."""
self.timer.start('EXX')
self.timer.start('Initialization')
kd = self.kd
wfs = self.wfs
if fftw.FFTPlan is fftw.NumpyFFTPlan:
self.log('NOT USING FFTW !!')
self.log('Spins:', self.wfs.nspins)
W = max(1, self.wfs.kd.comm.size // self.wfs.nspins)
# Are the k-points distributed?
kparallel = (W > 1)
# Find number of occupied bands:
self.nocc_sk = np.zeros((self.wfs.nspins, kd.nibzkpts), int)
for kpt in self.wfs.kpt_u:
for n, f in enumerate(kpt.f_n):
if abs(f) < self.fcut:
self.nocc_sk[kpt.s, kpt.k] = n
break
else:
self.nocc_sk[kpt.s, kpt.k] = self.wfs.bd.nbands
self.wfs.kd.comm.sum(self.nocc_sk)
noccmin = self.nocc_sk.min()
noccmax = self.nocc_sk.max()
self.log('Number of occupied bands (min, max): %d, %d' %
(noccmin, noccmax))
self.log('Number of valence electrons:', self.wfs.setups.nvalence)
if self.bandstructure:
self.log('Calculating eigenvalue shifts.')
# allocate array for eigenvalue shifts:
self.exx_skn = np.zeros(
(self.wfs.nspins, kd.nibzkpts, self.wfs.bd.nbands))
if self.bands is None:
noccmax = self.wfs.bd.nbands
else:
noccmax = max(max(self.bands) + 1, noccmax)
N_c = self.kd.N_c
vol = wfs.gd.dv * wfs.gd.N_c.prod()
if self.alpha is None:
alpha = 6 * vol**(2 / 3.0) / pi**2
else:
alpha = self.alpha
if self.gamma_point == 1:
if alpha == 0.0:
qvol = (2 * np.pi)**3 / vol / N_c.prod()
self.gamma = 4 * np.pi * (3 * qvol /
(4 * np.pi))**(1 / 3.) / qvol
else:
self.gamma = self.calculate_gamma(vol, alpha)
else:
kcell_cv = wfs.gd.cell_cv.copy()
kcell_cv[0] *= N_c[0]
kcell_cv[1] *= N_c[1]
kcell_cv[2] *= N_c[2]
self.gamma = madelung(kcell_cv) * vol * N_c.prod() / (4 * np.pi)
self.log('Value of alpha parameter: %.3f Bohr^2' % alpha)
self.log('Value of gamma parameter: %.3f Bohr^2' % self.gamma)
# Construct all possible q=k2-k1 vectors:
Nq_c = (N_c - 1) // self.qstride_c
i_qc = np.indices(Nq_c * 2 + 1, float).transpose((1, 2, 3, 0)).reshape(
(-1, 3))
self.bzq_qc = (i_qc - Nq_c) / N_c * self.qstride_c
self.q0 = ((Nq_c * 2 + 1).prod() - 1) // 2 # index of q=(0,0,0)
assert not self.bzq_qc[self.q0].any()
# Count number of pairs for each q-vector:
self.npairs_q = np.zeros(len(self.bzq_qc), int)
for s in range(kd.nspins):
for k1 in range(kd.nibzkpts):
for k2 in range(kd.nibzkpts):
for K2, q, n1_n, n2 in self.indices(s, k1, k2):
self.npairs_q[q] += len(n1_n)
self.npairs0 = self.npairs_q.sum() # total number of pairs
self.log('Number of pairs:', self.npairs0)
# Distribute q-vectors to Q processors:
Q = self.world.size // self.wfs.kd.comm.size
myrank = self.world.rank // self.wfs.kd.comm.size
rank = 0
N = 0
myq = []
nq = 0
for q, n in enumerate(self.npairs_q):
if n > 0:
nq += 1
if rank == myrank:
myq.append(q)
N += n
if N >= (rank + 1.0) * self.npairs0 / Q:
rank += 1
assert len(myq) > 0, 'Too few q-vectors for too many processes!'
self.bzq_qc = self.bzq_qc[myq]
try:
self.q0 = myq.index(self.q0)
except ValueError:
self.q0 = None
self.log('%d x %d x %d k-points' % tuple(self.kd.N_c))
self.log('Distributing %d IBZ k-points over %d process(es).' %
(kd.nibzkpts, self.wfs.kd.comm.size))
self.log('Distributing %d q-vectors over %d process(es).' % (nq, Q))
# q-point descriptor for my q-vectors:
qd = KPointDescriptor(self.bzq_qc)
# Plane-wave descriptor for all wave-functions:
self.pd = PWDescriptor(wfs.pd.ecut, wfs.gd, dtype=wfs.pd.dtype, kd=kd)
# Plane-wave descriptor pair-densities:
self.pd2 = PWDescriptor(self.dens.pd2.ecut,
self.dens.gd,
dtype=wfs.dtype,
kd=qd)
self.log('Cutoff energies:')
self.log(' Wave functions: %10.3f eV' %
(self.pd.ecut * Hartree))
self.log(' Density: %10.3f eV' %
(self.pd2.ecut * Hartree))
# Calculate 1/|G+q|^2 with special treatment of |G+q|=0:
G2_qG = self.pd2.G2_qG
if self.q0 is None:
if self.omega is None:
self.iG2_qG = [1.0 / G2_G for G2_G in G2_qG]
else:
self.iG2_qG = [
(1.0 / G2_G * (1 - np.exp(-G2_G / (4 * self.omega**2))))
for G2_G in G2_qG
]
else:
G2_qG[self.q0][0] = 117.0 # avoid division by zero
if self.omega is None:
self.iG2_qG = [1.0 / G2_G for G2_G in G2_qG]
self.iG2_qG[self.q0][0] = self.gamma
else:
self.iG2_qG = [
(1.0 / G2_G * (1 - np.exp(-G2_G / (4 * self.omega**2))))
for G2_G in G2_qG
]
self.iG2_qG[self.q0][0] = 1 / (4 * self.omega**2)
G2_qG[self.q0][0] = 0.0 # restore correct value
# Compensation charges:
self.ghat = PWLFC([setup.ghat_l for setup in wfs.setups], self.pd2)
self.ghat.set_positions(self.spos_ac)
if self.molecule:
self.initialize_gaussian()
self.log('Value of beta parameter: %.3f 1/Bohr^2' % self.beta)
self.timer.stop('Initialization')
# Ready ... set ... go:
self.t0 = time()
self.npairs = 0
self.evv = 0.0
self.evvacdf = 0.0
for s in range(self.wfs.nspins):
kpt1_q = [
KPoint(self.wfs, noccmax).initialize(kpt)
for kpt in self.wfs.kpt_u if kpt.s == s
]
kpt2_q = kpt1_q[:]
if len(kpt1_q) == 0:
# No s-spins on this CPU:
continue
# Send and receive ranks:
srank = self.wfs.kd.get_rank_and_index(s, (kpt1_q[0].k - 1) %
kd.nibzkpts)[0]
rrank = self.wfs.kd.get_rank_and_index(s, (kpt1_q[-1].k + 1) %
kd.nibzkpts)[0]
# Shift k-points kd.nibzkpts - 1 times:
for i in range(kd.nibzkpts):
if i < kd.nibzkpts - 1:
if kparallel:
kpt = kpt2_q[-1].next(self.wfs)
kpt.start_receiving(rrank)
kpt2_q[0].start_sending(srank)
else:
kpt = kpt2_q[0]
self.timer.start('Calculate')
for kpt1, kpt2 in zip(kpt1_q, kpt2_q):
# Loop over all k-points that k2 can be mapped to:
for K2, q, n1_n, n2 in self.indices(s, kpt1.k, kpt2.k):
self.apply(K2, q, kpt1, kpt2, n1_n, n2)
self.timer.stop('Calculate')
if i < kd.nibzkpts - 1:
self.timer.start('Wait')
if kparallel:
kpt.wait()
kpt2_q[0].wait()
self.timer.stop('Wait')
kpt2_q.pop(0)
kpt2_q.append(kpt)
self.evv = self.world.sum(self.evv)
self.evvacdf = self.world.sum(self.evvacdf)
self.calculate_exx_paw_correction()
if self.method == 'standard':
self.exx = self.evv + self.devv + self.evc + self.ecc
elif self.method == 'acdf':
self.exx = self.evvacdf + self.devv + self.evc + self.ecc
else:
1 / 0
self.log('Exact exchange energy:')
for txt, e in [('core-core', self.ecc), ('valence-core', self.evc),
('valence-valence (pseudo, acdf)', self.evvacdf),
('valence-valence (pseudo, standard)', self.evv),
('valence-valence (correction)', self.devv),
('total (%s)' % self.method, self.exx)]:
self.log(' %-36s %14.6f eV' % (txt + ':', e * Hartree))
self.log('Total time: %10.3f seconds' % (time() - self.t0))
self.npairs = self.world.sum(self.npairs)
assert self.npairs == self.npairs0
self.timer.stop('EXX')
self.timer.write(self.fd)
a2[R2] = 1
y = pd2.restrict(a2, pd1)[0][R1] * a2.size / a1.size
equal(x, y, 1e-9)
return x
if world.size == 1:
for size1, size2 in [[(3, 3, 3), (8, 8, 8)], [(4, 4, 4), (9, 9, 9)],
[(2, 4, 4), (5, 9, 9)], [(2, 3, 4), (5, 6, 9)],
[(2, 3, 4), (5, 6, 8)], [(4, 4, 4), (8, 8, 8)],
[(2, 4, 4), (4, 8, 8)], [(2, 4, 2), (4, 8, 4)]]:
print(size1, size2)
gd1 = GridDescriptor(size1, size1)
gd2 = GridDescriptor(size2, size1)
pd1 = PWDescriptor(1, gd1, complex)
pd2 = PWDescriptor(1, gd2, complex)
pd1r = PWDescriptor(1, gd1)
pd2r = PWDescriptor(1, gd2)
for R1, R2 in [[(0, 0, 0), (0, 0, 0)], [(0, 0, 0), (0, 0, 1)]]:
x = test(gd1, gd2, pd1, pd2, R1, R2)
y = test(gd1, gd2, pd1r, pd2r, R1, R2)
equal(x, y, 1e-9)
a1 = np.random.random(size1)
a2 = pd1r.interpolate(a1, pd2r)[0]
c2 = pd1.interpolate(a1 + 0.0j, pd2)[0]
d2 = pd1.interpolate(a1 * 1.0j, pd2)[0]
equal(abs(c2.imag).max(), 0, 1e-14)
equal(abs(d2.real).max(), 0, 1e-14)
equal(gd1.integrate(a1), gd2.integrate(a2), 1e-13)
def initialize(self, density, hamiltonian, wfs, occupations):
self.xc.initialize(density, hamiltonian, wfs, occupations)
self.nspins = wfs.nspins
self.setups = wfs.setups
self.density = density
self.kpt_u = wfs.kpt_u
self.gd = density.gd
self.kd = wfs.kd
self.bd = wfs.bd
N_c = self.gd.N_c
N = self.gd.N_c.prod()
vol = self.gd.dv * N
if self.alpha is None:
self.alpha = 6 * vol**(2 / 3.0) / pi**2
self.gamma = (vol / (2 * pi)**2 * sqrt(pi / self.alpha) *
self.kd.nbzkpts)
ecut = 0.5 * pi**2 / (self.gd.h_cv**2).sum(1).max()
if self.kd.N_c is None:
self.bzk_kc = np.zeros((1, 3))
dfghdfgh
else:
n = self.kd.N_c * 2 - 1
bzk_kc = np.indices(n).transpose((1, 2, 3, 0))
bzk_kc.shape = (-1, 3)
bzk_kc -= self.kd.N_c - 1
self.bzk_kc = bzk_kc.astype(float) / self.kd.N_c
self.pwd = PWDescriptor(ecut, self.gd, self.bzk_kc)
n = 0
for k_c, Gpk2_G in zip(self.bzk_kc[:], self.pwd.G2_qG):
if (k_c > -0.5).all() and (k_c <= 0.5).all(): #XXX???
if k_c.any():
self.gamma -= np.dot(np.exp(-self.alpha * Gpk2_G),
Gpk2_G**-1)
else:
self.gamma -= np.dot(np.exp(-self.alpha * Gpk2_G[1:]),
Gpk2_G[1:]**-1)
n += 1
assert n == self.kd.N_c.prod()
self.ghat = LFC(self.gd, [setup.ghat_l for setup in density.setups],
dtype=complex)
self.ghat.set_k_points(self.bzk_kc)
self.fullkd = KPointDescriptor(self.kd.bzk_kc, nspins=1)
class S:
id_a = []
def set_symmetry(self, s):
pass
self.fullkd.set_symmetry(Atoms(pbc=True), S(), False)
self.fullkd.set_communicator(world)
self.pt = LFC(self.gd, [setup.pt_j for setup in density.setups],
dtype=complex)
self.pt.set_k_points(self.fullkd.ibzk_kc)
self.interpolator = density.interpolator
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 calculate_QEH(self):
print('Calculating QEH self-energy contribution', file=self.fd)
kd = self.calc.wfs.kd
# Reset calculation
self.sigma_sin = np.zeros(self.shape) # self-energies
self.dsigma_sin = np.zeros(self.shape) # derivatives of self-energies
# Get KS eigenvalues and occupation numbers:
b1, b2 = self.bands
nibzk = self.calc.wfs.kd.nibzkpts
for i, k in enumerate(self.kpts):
for s in range(self.nspins):
u = s * nibzk + k
kpt = self.calc.wfs.kpt_u[u]
self.eps_sin[s, i] = kpt.eps_n[b1:b2]
self.f_sin[s, i] = kpt.f_n[b1:b2] / kpt.weight
# My part of the states we want to calculate QP-energies for:
mykpts = [
self.get_k_point(s, K, n1, n2) for s, K, n1, n2 in self.mysKn1n2
]
kplusqdone_u = [set() for kpt in mykpts]
Nq = len((self.qd.ibzk_kc))
for iq, q_c in enumerate(self.qd.ibzk_kc):
self.nq = iq
nq = iq
self.save_state_file()
qcstr = '(' + ', '.join(['%.3f' % x for x in q_c]) + ')'
print('Calculating contribution from IBZ q-point #%d/%d q_c=%s' %
(nq, Nq, qcstr),
file=self.fd)
rcell_cv = 2 * pi * np.linalg.inv(self.calc.wfs.gd.cell_cv).T
q_abs = np.linalg.norm(np.dot(q_c, rcell_cv))
# Screened potential
dW_w = self.dW_qw[nq]
dW_w = dW_w[:, np.newaxis, np.newaxis]
L = abs(self.calc.wfs.gd.cell_cv[2, 2])
dW_w *= L
nw = self.nw
Wpm_w = np.zeros([2 * nw, 1, 1], dtype=complex)
Wpm_w[:nw] = dW_w
Wpm_w[nw:] = Wpm_w[0:nw]
with self.timer('Hilbert transform'):
self.htp(Wpm_w[:nw])
self.htm(Wpm_w[nw:])
qd = KPointDescriptor([q_c])
pd0 = PWDescriptor(self.ecut, self.calc.wfs.gd, complex, qd)
# modify pd0 by hand - only G=0 component is needed
pd0.G_Qv = np.array([1e-17, 1e-17, 1e-17])[np.newaxis, :]
pd0.Q_qG = [np.array([0], dtype='int32')]
pd0.ngmax = 1
G_Gv = pd0.get_reciprocal_vectors()
self.Q_aGii = self.initialize_paw_corrections(pd0)
# Loop over all k-points in the BZ and find those that are related
# to the current IBZ k-point by symmetry
Q1 = self.qd.ibz2bz_k[iq]
Q2s = set()
for s, Q2 in enumerate(self.qd.bz2bz_ks[Q1]):
if Q2 >= 0 and Q2 not in Q2s:
Q2s.add(Q2)
for Q2 in Q2s:
s = self.qd.sym_k[Q2]
self.s = s
U_cc = self.qd.symmetry.op_scc[s]
time_reversal = self.qd.time_reversal_k[Q2]
self.sign = 1 - 2 * time_reversal
Q_c = self.qd.bzk_kc[Q2]
d_c = self.sign * np.dot(U_cc, q_c) - Q_c
assert np.allclose(d_c.round(), d_c)
for u1, kpt1 in enumerate(mykpts):
K2 = kd.find_k_plus_q(Q_c, [kpt1.K])[0]
kpt2 = self.get_k_point(kpt1.s,
K2,
0,
self.nbands,
block=True)
k1 = kd.bz2ibz_k[kpt1.K]
i = self.kpts.index(k1)
N_c = pd0.gd.N_c
i_cG = self.sign * np.dot(
U_cc, np.unravel_index(pd0.Q_qG[0], N_c))
k1_c = kd.bzk_kc[kpt1.K]
k2_c = kd.bzk_kc[K2]
# This is the q that connects K1 and K2 in the 1st BZ
q1_c = kd.bzk_kc[K2] - kd.bzk_kc[kpt1.K]
# G-vector that connects the full Q_c with q1_c
shift1_c = q1_c - self.sign * np.dot(U_cc, q_c)
assert np.allclose(shift1_c.round(), shift1_c)
shift1_c = shift1_c.round().astype(int)
shift_c = kpt1.shift_c - kpt2.shift_c - shift1_c
I_G = np.ravel_multi_index(i_cG + shift_c[:, None], N_c,
'wrap')
pos_av = np.dot(self.spos_ac, pd0.gd.cell_cv)
M_vv = np.dot(
pd0.gd.cell_cv.T,
np.dot(U_cc.T,
np.linalg.inv(pd0.gd.cell_cv).T))
Q_aGii = []
for a, Q_Gii in enumerate(self.Q_aGii):
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[self.s]
Q_Gii = np.dot(
np.dot(U_ii, Q_Gii * x_G[:, None, None]),
U_ii.T).transpose(1, 0, 2)
if self.sign == -1:
Q_Gii = Q_Gii.conj()
Q_aGii.append(Q_Gii)
for n in range(kpt1.n2 - kpt1.n1):
ut1cc_R = kpt1.ut_nR[n].conj()
eps1 = kpt1.eps_n[n]
C1_aGi = [
np.dot(Qa_Gii, P1_ni[n].conj())
for Qa_Gii, P1_ni in zip(Q_aGii, kpt1.P_ani)
]
n_mG = self.calculate_pair_densities(
ut1cc_R, C1_aGi, kpt2, pd0, I_G)
if self.sign == 1:
n_mG = n_mG.conj()
f_m = kpt2.f_n
deps_m = eps1 - kpt2.eps_n
sigma, dsigma = self.calculate_sigma(
n_mG, deps_m, f_m, Wpm_w)
nn = kpt1.n1 + n - self.bands[0]
self.sigma_sin[kpt1.s, i, nn] += sigma
self.dsigma_sin[kpt1.s, i, nn] += dsigma
self.world.sum(self.sigma_sin)
self.world.sum(self.dsigma_sin)
self.complete = True
self.save_state_file()
return self.sigma_sin, self.dsigma_sin
def calculate(self, ecut, nbands=None, spin=False):
"""Calculate RPA correlation energy for one or several cutoffs.
ecut: float or list of floats
Plane-wave cutoff(s).
nbands: int
Number of bands (defaults to number of plane-waves).
spin: bool
Separate spin in response function.
(Only needed for beyond RPA methods that inherit this function).
"""
p = functools.partial(print, file=self.fd)
if isinstance(ecut, (float, int)):
ecut = ecut * (1 + 0.5 * np.arange(6))**(-2 / 3)
self.ecut_i = np.asarray(np.sort(ecut)) / Hartree
ecutmax = max(self.ecut_i)
if nbands is None:
p('Response function bands : Equal to number of plane waves')
else:
p('Response function bands : %s' % nbands)
p('Plane wave cutoffs (eV) :', end='')
for e in self.ecut_i:
p(' {0:.3f}'.format(e * Hartree), end='')
p()
if self.truncation is not None:
p('Using %s Coulomb truncation' % self.truncation)
p()
if self.filename and os.path.isfile(self.filename):
self.read()
self.world.barrier()
chi0 = Chi0(self.calc, 1j * Hartree * self.omega_w, eta=0.0,
intraband=False, hilbert=False,
txt='chi0.txt', timer=self.timer, world=self.world,
nblocks=self.nblocks)
self.blockcomm = chi0.blockcomm
wfs = self.calc.wfs
if self.truncation == 'wigner-seitz':
self.wstc = WignerSeitzTruncatedCoulomb(wfs.gd.cell_cv,
wfs.kd.N_c, self.fd)
else:
self.wstc = None
nq = len(self.energy_qi)
nw = len(self.omega_w)
nGmax = max(count_reciprocal_vectors(ecutmax, wfs.gd, q_c)
for q_c in self.ibzq_qc[nq:])
mynGmax = (nGmax + self.nblocks - 1) // self.nblocks
nx = (1 + spin) * nw * mynGmax * nGmax
A1_x = np.empty(nx, complex)
if self.nblocks > 1:
A2_x = np.empty(nx, complex)
else:
A2_x = None
self.timer.start('RPA')
for q_c in self.ibzq_qc[nq:]:
if np.allclose(q_c, 0.0) and self.skip_gamma:
self.energy_qi.append(len(self.ecut_i) * [0.0])
self.write()
p('Not calculating E_c(q) at Gamma')
p()
continue
thisqd = KPointDescriptor([q_c])
pd = PWDescriptor(ecutmax, wfs.gd, complex, thisqd)
nG = pd.ngmax
mynG = (nG + self.nblocks - 1) // self.nblocks
chi0.Ga = self.blockcomm.rank * mynG
chi0.Gb = min(chi0.Ga + mynG, nG)
shape = (1 + spin, nw, chi0.Gb - chi0.Ga, nG)
chi0_swGG = A1_x[:np.prod(shape)].reshape(shape)
chi0_swGG[:] = 0.0
if np.allclose(q_c, 0.0):
chi0_swxvG = np.zeros((1 + spin, nw, 2, 3, nG), complex)
chi0_swvv = np.zeros((1 + spin, nw, 3, 3), complex)
else:
chi0_swxvG = None
chi0_swvv = None
# First not completely filled band:
m1 = chi0.nocc1
p('# %s - %s' % (len(self.energy_qi), ctime().split()[-2]))
p('q = [%1.3f %1.3f %1.3f]' % tuple(q_c))
energy_i = []
for ecut in self.ecut_i:
if ecut == ecutmax:
# Nothing to cut away:
cut_G = None
m2 = nbands or nG
else:
cut_G = np.arange(nG)[pd.G2_qG[0] <= 2 * ecut]
m2 = len(cut_G)
p('E_cut = %d eV / Bands = %d:' % (ecut * Hartree, m2))
self.fd.flush()
energy = self.calculate_q(chi0, pd,
chi0_swGG, chi0_swxvG, chi0_swvv,
m1, m2, cut_G, A2_x)
energy_i.append(energy)
m1 = m2
a = 1 / chi0.kncomm.size
if ecut < ecutmax and a != 1.0:
# Chi0 will be summed again over chicomm, so we divide
# by its size:
chi0_swGG *= a
if chi0_swxvG is not None:
chi0_swxvG *= a
chi0_swvv *= a
self.energy_qi.append(energy_i)
self.write()
p()
e_i = np.dot(self.weight_q, np.array(self.energy_qi))
p('==========================================================')
p()
p('Total correlation energy:')
for e_cut, e in zip(self.ecut_i, e_i):
p('%6.0f: %6.4f eV' % (e_cut * Hartree, e * Hartree))
p()
self.energy_qi = [] # important if another calculation is performed
if len(e_i) > 1:
self.extrapolate(e_i)
p('Calculation completed at: ', ctime())
p()
self.timer.stop('RPA')
self.timer.write(self.fd)
self.fd.flush()
return e_i * Hartree
def __init__(self, gd1, gd2, dtype=float):
self.pd1 = PWDescriptor(0.0, gd1, dtype)
self.pd2 = PWDescriptor(0.0, gd2, dtype)
def __call__(self, pd, calc, functional):
assert functional in self.permitted_functionals
self.functional = functional
add_fxc = self.add_fxc # class methods not within the scope of call
vol = pd.gd.volume
npw = pd.ngmax
if self.RSrep == 'grid':
print("\tFinding all-electron density", file=self.fd)
n_sG, gd = calc.density.get_all_electron_density(atoms=calc.atoms,
gridrefinement=1)
qd = pd.kd
lpd = PWDescriptor(self.ecut,
gd,
complex,
qd,
gammacentered=pd.gammacentered)
print("\tCalculating fxc on real space grid using" +
" all-electron density",
file=self.fd)
fxc_G = np.zeros(np.shape(n_sG[0]))
add_fxc(gd, n_sG, fxc_G)
else:
nt_sG = calc.density.nt_sG
gd, lpd = pd.gd, pd
print("\tCalculating fxc on real space grid using smooth density",
file=self.fd)
fxc_G = np.zeros(np.shape(nt_sG[0]))
add_fxc(gd, nt_sG, fxc_G)
print("\tFourier transforming into reciprocal space", file=self.fd)
nG = gd.N_c
nG0 = nG[0] * nG[1] * nG[2]
tmp_g = np.fft.fftn(fxc_G) * vol / nG0
Kxc_GG = np.zeros((npw, npw), dtype=complex)
for iG, iQ in enumerate(lpd.Q_qG[0]):
iQ_c = (np.unravel_index(iQ, nG) + nG // 2) % nG - nG // 2
for jG, jQ in enumerate(lpd.Q_qG[0]):
jQ_c = (np.unravel_index(jQ, nG) + nG // 2) % nG - nG // 2
ijQ_c = (iQ_c - jQ_c)
if (abs(ijQ_c) < nG // 2).all():
Kxc_GG[iG, jG] = tmp_g[tuple(ijQ_c)]
if self.RSrep == 'gpaw':
print("\tCalculating PAW corrections to the kernel", file=self.fd)
G_Gv = pd.get_reciprocal_vectors()
R_av = calc.atoms.positions / Bohr
setups = calc.wfs.setups
D_asp = calc.density.D_asp
KxcPAW_GG = np.zeros_like(Kxc_GG)
dG_GGv = np.zeros((npw, npw, 3))
for v in range(3):
dG_GGv[:, :, v] = np.subtract.outer(G_Gv[:, v], G_Gv[:, v])
# Distribute computation of PAW correction equally among processes
p_r = self.distribute_correction(setups, self.world.size)
apdone = 0
npdone = 0
pdone = 0
pdonebefore = np.sum(p_r[:self.world.rank])
pdonenow = pdonebefore + p_r[self.world.rank]
for a, setup in enumerate(setups):
# PAW correction is evaluated on a radial grid
Y_nL = setup.xc_correction.Y_nL
rgd = setup.xc_correction.rgd
# Continue if computation has been done already
nn = len(Y_nL)
ng = len(rgd.r_g)
apdone += nn * ng
if pdonebefore >= apdone or pdone >= pdonenow:
npdone += nn * ng
pdone += nn * ng
continue
n_qg = setup.xc_correction.n_qg
nt_qg = setup.xc_correction.nt_qg
nc_g = setup.xc_correction.nc_g
nct_g = setup.xc_correction.nct_g
dv_g = rgd.dv_g
D_sp = D_asp[a]
B_pqL = setup.xc_correction.B_pqL
D_sLq = np.inner(D_sp, B_pqL.T)
nspins = len(D_sp)
f_g = rgd.zeros()
ft_g = rgd.zeros()
n_sLg = np.dot(D_sLq, n_qg)
nt_sLg = np.dot(D_sLq, nt_qg)
# Add core density
n_sLg[:, 0] += np.sqrt(4. * np.pi) / nspins * nc_g
nt_sLg[:, 0] += np.sqrt(4. * np.pi) / nspins * nct_g
coefatoms_GG = np.exp(-1j * np.inner(dG_GGv, R_av[a]))
for n, Y_L in enumerate(Y_nL):
# Continue if computation has been done already
npdone += ng
if pdonebefore >= npdone or pdone >= pdonenow:
pdone += ng
continue
w = weight_n[n]
f_g[:] = 0.
n_sg = np.dot(Y_L, n_sLg)
add_fxc(rgd, n_sg, f_g)
ft_g[:] = 0.
nt_sg = np.dot(Y_L, nt_sLg)
add_fxc(rgd, nt_sg, ft_g)
dG_GG = np.inner(dG_GGv, R_nv[n])
for i in range(len(rgd.r_g)):
# Continue if previous ranks already did computation
pdone += 1
if pdonebefore >= pdone:
continue
# Do computation if needed
if pdone <= pdonenow:
coef_GG = np.exp(-1j * dG_GG * rgd.r_g[i])
KxcPAW_GG += w * coefatoms_GG\
* np.dot(coef_GG, (f_g[i] - ft_g[i])
* dv_g[i])
self.world.sum(KxcPAW_GG)
Kxc_GG += KxcPAW_GG
return Kxc_GG / vol
x = 2.0
rc = 3.5
r = np.linspace(0, rc, 100)
n = 40
a = 8.0
cell_cv = np.array([[a, 0.5, -1], [0, a, 2], [-1, 0, a + 1]])
gd = GridDescriptor((n, n, n), cell_cv, comm=mpi.serial_comm)
a_R = gd.empty()
z = np.linspace(0, n, n, endpoint=False)
a_R[:] = 2 + np.sin(2 * np.pi * z / n)
spos_ac = np.array([(0.15, 0.45, 0.95)])
pd = PWDescriptor(45, gd)
a_G = pd.fft(a_R)
s = Spline(0, rc, 2 * x**1.5 / np.pi * np.exp(-x * r**2))
p = Spline(1, rc, 2 * x**1.5 / np.pi * np.exp(-x * r**2))
d = Spline(2, rc, 2 * x**1.5 / np.pi * np.exp(-x * r**2))
lfc = PWLFC([[s, p, d]], pd)
lfc.set_positions(spos_ac)
b_LG = pd.zeros(9)
lfc.add(b_LG, {0: np.eye(9)})
e1 = pd.integrate(a_G, b_LG)
assert abs(lfc.integrate(a_G)[0] - e1).max() < 1e-11
s1 = []
for i in range(9):
def __init__(self, calc, nbands=None, Fock=False):
self.calc = calc
self.Fock = Fock
self.K = calc.get_ibz_k_points() # reduced Brillioun zone
self.NK = self.K.shape[0]
self.wk = calc.get_k_point_weights(
) # weight of reduced Brillioun zone
if nbands is None:
self.nbands = calc.get_number_of_bands()
else:
self.nbands = nbands
self.nvalence = int(calc.get_number_of_electrons() / 2)
self.EK = [
calc.get_eigenvalues(k)[:self.nbands] for k in range(self.NK)
] # bands energy
self.EK = np.array(self.EK) / Hartree
self.shape = tuple(
calc.get_number_of_grid_points()) # shape of real space grid
self.density = calc.get_pseudo_density(
) * Bohr**3 # density at zero time
# array of u_nk (periodic part of Kohn-Sham orbitals,only reduced Brillion zone)
self.ukn = np.zeros((
self.NK,
self.nbands,
) + self.shape,
dtype=np.complex)
for k in range(self.NK):
kpt = calc.wfs.kpt_u[k]
for n in range(self.nbands):
psit_G = kpt.psit_nG[n]
psit_R = calc.wfs.pd.ifft(psit_G, kpt.q)
self.ukn[k, n] = psit_R
self.icell = 2.0 * np.pi * calc.wfs.gd.icell_cv # inverse cell
self.cell = calc.wfs.gd.cell_cv # cell
self.r = calc.wfs.gd.get_grid_point_coordinates()
for i in range(3):
self.r[i] -= self.cell[i, i] / 2.
self.volume = np.abs(np.linalg.det(
calc.wfs.gd.cell_cv)) # volume of cell
self.norm = calc.wfs.gd.dv #
self.Fermi = calc.get_fermi_level() / Hartree #Fermi level
#desriptors at q=gamma for Hartree
self.kdH = KPointDescriptor([[0, 0, 0]])
self.pdH = PWDescriptor(ecut=calc.wfs.pd.ecut,
gd=calc.wfs.gd,
kd=self.kdH,
dtype=complex)
#desriptors at q=gamma for Fock
self.kdF = KPointDescriptor([[0, 0, 0]])
self.pdF = PWDescriptor(ecut=calc.wfs.pd.ecut / 4.,
gd=calc.wfs.gd,
kd=self.kdF,
dtype=complex)
#Fermi-Dirac temperature
self.temperature = calc.occupations.width
#calculate pair-density matrices
if Fock:
self.M = np.zeros((self.nbands, self.nbands, self.NK, self.NK,
self.pdF.get_reciprocal_vectors().shape[0]),
dtype=np.complex)
indexes = [(n, k)
for n, k in product(range(self.nbands), range(self.NK))]
for i1 in range(len(indexes)):
n1, k1 = indexes[i1]
for i2 in range(i1, len(indexes)):
n2, k2 = indexes[i1]
self.M[n1, n2, k1, k2] = self.pdF.fft(
self.ukn[k1, n1].conj() * self.ukn[k2, n2])
self.M[n2, n1, k2, k1] = self.M[n1, n2, k1, k2].conj()
self.M *= calc.wfs.gd.dv
#Fermi-Dirac distribution
self.f = 1 / (1 + np.exp((self.EK - self.Fermi) / self.temperature))
self.Hartree_elements = np.zeros(
(self.NK, self.nbands, self.NK, self.nbands, self.nbands),
dtype=np.complex)
self.LDAx_elements = np.zeros(
(self.NK, self.nbands, self.NK, self.nbands, self.nbands),
dtype=np.complex)
self.LDAc_elements = np.zeros(
(self.NK, self.nbands, self.NK, self.nbands, self.nbands),
dtype=np.complex)
G = self.pdH.get_reciprocal_vectors()
G2 = np.linalg.norm(G, axis=1)**2
G2[G2 == 0] = np.inf
matrix = np.zeros((self.NK, self.nbands, self.nbands),
dtype=np.complex)
for k in tqdm(range(self.NK)):
for n in range(self.nbands):
density = 2 * np.abs(self.ukn[k, n])**2
operator = xc.VLDAx(density)
self.LDAx_elements[k, n] = operator_matrix_periodic(
matrix, operator, self.ukn.conj(), self.ukn) * self.norm
operator = xc.VLDAc(density)
self.LDAc_elements[k, n] = operator_matrix_periodic(
matrix, operator, self.ukn.conj(), self.ukn) * self.norm
density = self.pdH.fft(density)
operator = 4 * np.pi * self.pdH.ifft(density / G2)
self.Hartree_elements[k, n] = operator_matrix_periodic(
matrix, operator, self.ukn.conj(), self.ukn) * self.norm
self.wavefunction = np.zeros((self.NK, self.nbands, self.nbands),
dtype=np.complex)
self.Kinetic = np.zeros((self.NK, self.nbands, self.nbands),
dtype=np.complex)
self.dipole = self.get_dipole_matrix()
for k in range(self.NK):
self.wavefunction[k] = np.eye(self.nbands)
self.Kinetic[k] = np.diag(self.EK[k])
self.VH0 = self.get_Hartree_matrix(self.wavefunction)
self.VLDAc0 = self.get_LDA_correlation_matrix(self.wavefunction)
self.VLDAx0 = self.get_LDA_exchange_matrix(self.wavefunction)
self.Full_BZ = calc.get_bz_k_points()
self.IBZ_map = calc.get_bz_to_ibz_map()
from gpaw.lfc import LocalizedFunctionsCollection as LFC
from gpaw.wavefunctions.pw import PWDescriptor, PWLFC
from gpaw.kpt_descriptor import KPointDescriptor
x = 2.0
rc = 3.5
r = np.linspace(0, rc, 100)
n = 40
a = 8.0
gd = GridDescriptor((n, n, n), (a, a, a), comm=mpi.serial_comm)
spos_ac = np.array([(0.15, 0.45, 0.95)])
pd = PWDescriptor(45, gd, complex)
pdr = PWDescriptor(45, gd)
from gpaw.fftw import FFTPlan
print(FFTPlan)
for l in range(4):
print(l)
s = Spline(l, rc, 2 * x**1.5 / np.pi * np.exp(-x * r**2))
lfc = PWLFC([[s]], pd)
lfcr = PWLFC([[s]], pdr)
c_axi = {0: np.zeros((1, 2 * l + 1), complex)}
c_axi[0][0, 0] = 1.9
cr_axi = {0: np.zeros((1, 2 * l + 1))}
def write(self, calc, ecut=40 * Hartree, spacegroup=1):
#sg = Spacegroup(spacegroup)
#print sg
wfs = calc.wfs
setups = wfs.setups
bd = wfs.bd
kd = wfs.kd
atoms = calc.atoms
natoms = len(atoms)
if wfs.symmetry is None:
op_scc = np.eye(3, dtype=int).reshape((1, 3, 3))
else:
op_scc = wfs.symmetry.op_scc
pwd = PWDescriptor(ecut / Hartree, wfs.gd, kd.ibzk_kc)
N_c = pwd.gd.N_c
i_Qc = np.indices(N_c, np.int32).transpose((1, 2, 3, 0))
i_Qc += N_c // 2
i_Qc %= N_c
i_Qc -= N_c // 2
i_Qc.shape = (-1, 3)
i_Gc = i_Qc[pwd.Q_G]
B_cv = 2.0 * np.pi * wfs.gd.icell_cv
G_Qv = np.dot(i_Gc, B_cv).reshape((-1, 3))
G2_Q = (G_Qv**2).sum(axis=1)
specie_a = np.empty(natoms, np.int32)
nspecies = 0
species = {}
names = []
symbols = []
numbers = []
charges = []
for a, id in enumerate(setups.id_a):
if id not in species:
species[id] = nspecies
nspecies += 1
names.append(setups[a].symbol)
symbols.append(setups[a].symbol)
numbers.append(setups[a].Z)
charges.append(setups[a].Nv)
specie_a[a] = species[id]
dimensions = [('character_string_length', 80),
('max_number_of_coefficients', len(i_Gc)),
('max_number_of_states', bd.nbands),
('number_of_atoms', len(atoms)),
('number_of_atom_species', nspecies),
('number_of_cartesian_directions', 3),
('number_of_components', 1),
('number_of_grid_points_vector1', N_c[0]),
('number_of_grid_points_vector2', N_c[1]),
('number_of_grid_points_vector3', N_c[2]),
('number_of_kpoints', kd.nibzkpts),
('number_of_reduced_dimensions', 3),
('number_of_spinor_components', 1),
('number_of_spins', wfs.nspins),
('number_of_symmetry_operations', len(op_scc)),
('number_of_vectors', 3),
('real_or_complex_coefficients', 2),
('symbol_length', 2)]
for name, size in dimensions:
print('%-34s %d' % (name, size))
self.nc.createDimension(name, size)
var = self.add_variable
var('space_group', (), np.array(spacegroup, dtype=int))
var('primitive_vectors',
('number_of_vectors', 'number_of_cartesian_directions'),
wfs.gd.cell_cv,
units='atomic units')
var('reduced_symmetry_matrices',
('number_of_symmetry_operations', 'number_of_reduced_dimensions',
'number_of_reduced_dimensions'),
op_scc.astype(np.int32),
symmorphic='yes')
var('reduced_symmetry_translations',
('number_of_symmetry_operations', 'number_of_reduced_dimensions'),
np.zeros((len(op_scc), 3), dtype=np.int32))
var('atom_species', ('number_of_atoms', ), specie_a + 1)
var('reduced_atom_positions',
('number_of_atoms', 'number_of_reduced_dimensions'),
atoms.get_scaled_positions())
var('atomic_numbers', ('number_of_atom_species', ),
np.array(numbers, dtype=float))
var('valence_charges', ('number_of_atom_species', ),
np.array(charges, dtype=float))
var('atom_species_names',
('number_of_atom_species', 'character_string_length'), names)
var('chemical_symbols', ('number_of_atom_species', 'symbol_length'),
symbols)
var('pseudopotential_types',
('number_of_atom_species', 'character_string_length'),
['HGH'] * nspecies)
var('fermi_energy', (),
calc.occupations.fermilevel,
units='atomic units')
var('smearing_scheme', ('character_string_length', ), 'fermi-dirac')
var('smearing_width', (), calc.occupations.width, units='atomic units')
var('number_of_states', ('number_of_spins', 'number_of_kpoints'),
np.zeros((wfs.nspins, kd.nibzkpts), np.int32) + bd.nbands,
k_dependent='no')
var('eigenvalues',
('number_of_spins', 'number_of_kpoints', 'max_number_of_states'),
np.array([[
calc.get_eigenvalues(k, s) / Hartree
for k in range(kd.nibzkpts)
] for s in range(wfs.nspins)]),
units='atomic units')
var(
'occupations',
('number_of_spins', 'number_of_kpoints', 'max_number_of_states'),
np.array([[
calc.get_occupation_numbers(k, s) / kd.weight_k[k]
for k in range(kd.nibzkpts)
] for s in range(wfs.nspins)]))
var('reduced_coordinates_of_kpoints',
('number_of_kpoints', 'number_of_reduced_dimensions'), kd.ibzk_kc)
var('kpoint_weights', ('number_of_kpoints', ), kd.weight_k)
var('basis_set', ('character_string_length', ), 'plane_waves')
var('kinetic_energy_cutoff', (), 1.0 * ecut, units='atomic units')
var('number_of_coefficients', ('number_of_kpoints', ),
np.zeros(kd.nibzkpts, np.int32) + len(i_Gc),
k_dependent='no')
var('reduced_coordinates_of_plane_waves',
('max_number_of_coefficients', 'number_of_reduced_dimensions'),
i_Gc[np.argsort(G2_Q)],
k_dependent='no')
var('number_of_electrons', (), np.array(wfs.nvalence, dtype=np.int32))
#var('exchange_functional', ('character_string_length',),
# calc.hamiltonian.xc.name)
#var('correlation_functional', ('character_string_length',),
# calc.hamiltonian.xc.name)
psit_skn1G2 = var(
'coefficients_of_wavefunctions',
('number_of_spins', 'number_of_kpoints', 'max_number_of_states',
'number_of_spinor_components', 'max_number_of_coefficients',
'real_or_complex_coefficients'))
x = atoms.get_volume()**0.5 / N_c.prod()
psit_Gx = np.empty((len(i_Gc), 2))
for s in range(wfs.nspins):
for k in range(kd.nibzkpts):
for n in range(bd.nbands):
psit_G = pwd.fft(calc.get_pseudo_wave_function(
n, k, s))[np.argsort(G2_Q)]
psit_G *= x
psit_Gx[:, 0] = psit_G.real
psit_Gx[:, 1] = psit_G.imag
psit_skn1G2[s, k, n, 0] = psit_Gx
self.nc.close()
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 initialize(self, density, hamiltonian, wfs, occupations):
self.xc.initialize(density, hamiltonian, wfs, occupations)
self.nspins = wfs.nspins
self.setups = wfs.setups
self.density = density
self.kpt_u = wfs.kpt_u
self.wfs = wfs
self.gd = density.gd
self.kd = wfs.kd
self.bd = wfs.bd
N_c = self.gd.N_c
N = self.gd.N_c.prod()
vol = self.gd.dv * N
if self.alpha is None:
# XXX ?
self.alpha = 6 * vol**(2 / 3.0) / pi**2
self.gamma = (vol / (2 * pi)**2 * sqrt(pi / self.alpha) *
self.kd.nbzkpts)
if self.ecut is None:
self.ecut = 0.5 * pi**2 / (self.gd.h_cv**2).sum(1).max() * 0.9999
assert self.kd.N_c is not None
n = self.kd.N_c * 2 - 1
bzk_kc = np.indices(n).transpose((1, 2, 3, 0))
bzk_kc.shape = (-1, 3)
bzk_kc -= self.kd.N_c - 1
self.bzk_kc = bzk_kc.astype(float) / self.kd.N_c
self.bzq_qc = self.kd.get_bz_q_points()
if self.qsym:
op_scc = self.kd.symmetry.op_scc
self.ibzq_qc = self.kd.get_ibz_q_points(self.bzq_qc, op_scc)[0]
self.q_weights = self.kd.q_weights * len(self.bzq_qc)
else:
self.ibzq_qc = self.bzq_qc
self.q_weights = np.ones(len(self.bzq_qc))
self.pwd = PWDescriptor(self.ecut, self.gd, complex)
self.G2_qG = self.pwd.g2(self.bzk_kc)
n = 0
for k_c, Gpk2_G in zip(self.bzk_kc[:], self.G2_qG):
if (k_c > -0.5).all() and (k_c <= 0.5).all(): #XXX???
if k_c.any():
self.gamma -= np.dot(np.exp(-self.alpha * Gpk2_G),
Gpk2_G**-1)
else:
self.gamma -= np.dot(np.exp(-self.alpha * Gpk2_G[1:]),
Gpk2_G[1:]**-1)
n += 1
assert n == self.kd.N_c.prod()
self.pwd = PWDescriptor(self.ecut, self.gd, complex)
self.G2_qG = self.pwd.g2(self.ibzq_qc)
self.ghat = LFC(self.gd, [setup.ghat_l for setup in density.setups],
KPointDescriptor(self.bzq_qc),
dtype=complex)
#self.interpolator = density.interpolator
self.print_initialization(hamiltonian.xc.name)
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)
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)
n_nmvG = pair.get_pair_momentum(pd, kptpair, np.arange(0, nb),
np.arange(0, nb))
if ol:
n2_nmv = np.zeros((nb, nb, 3), complex)
from gpaw.wavefunctions.pw import PWDescriptor, PWLFC
from gpaw.kpt_descriptor import KPointDescriptor
x = 2.0
rc = 3.5
r = np.linspace(0, rc, 100)
n = 40
a = 8.0
gd = GridDescriptor((n, n, n), (a, a, a), comm=mpi.serial_comm)
kpts = np.array([(0.25, 0.25, 0.0)])
kd = KPointDescriptor(kpts)
spos_ac = np.array([(0.15, 0.5, 0.95)])
pd = PWDescriptor(45, gd, complex, kd)
eikr = np.ascontiguousarray(
np.exp(2j * np.pi * np.dot(np.indices(gd.N_c).T, (kpts / gd.N_c).T).T)[0])
from gpaw.fftw import FFTPlan
print(FFTPlan)
for l in range(3):
print(l)
s = Spline(l, rc, 2 * x**1.5 / np.pi * np.exp(-x * r**2))
lfc1 = LFC(gd, [[s]], kd, dtype=complex)
lfc2 = PWLFC([[s]], pd)
c_axi = {0: np.zeros((1, 2 * l + 1), complex)}