def init_potential(self):
#initialization of nonlocal part of pseudopotential
# V_NL=|chi_i> V_i <chi_i|
spline_aj = []
for setup in self.wfs.setups:
spline_aj.append(setup.pt_j)
self.lfc = PWLFC(spline_aj, self.pd)
self.lfc.set_positions(self.calc.spos_ac) #set position of atoms
proj_G = []
proj_r = [] #collect chi_i in real space using FFT
for kpt in self.wfs.kpt_u:
proj_G.append(self.lfc.expand(kpt.q))
proj = []
n_i = proj_G[-1].shape[1]
for i in range(n_i):
proj.append(self.pd.ifft(proj_G[-1][:, i].copy(), kpt.q))
proj_r.append(proj)
self.chi = np.array(proj_r) / self.gd.dv
s = 0 # s=0 because we perform spin-paired calculation
V = [] #collect V
for a in range(len(self.wfs.setups)):
dH_ii = unpack(self.ham.dH_asp[a][s])
V.append(dH_ii.diagonal())
V = np.array(V)
self.V = V.ravel()
self.norb = self.V.size # number of orbitals in nonlocal potential
#initialization of local part of pseudopotential
V = self.ham.vbar.pd.zeros()
self.ham.vbar.add(V)
self.Vloc = self.ham.vbar.pd.ifft(V)
def initialize_paw_corrections(self, pd, soft=False):
wfs = self.calc.wfs
q_v = pd.K_qv[0]
optical_limit = np.allclose(q_v, 0)
G_Gv = pd.get_reciprocal_vectors()
if optical_limit:
G_Gv[0] = 1
pos_av = np.dot(self.spos_ac, pd.gd.cell_cv)
# Collect integrals for all species:
Q_xGii = {}
for id, atomdata in wfs.setups.setups.items():
if soft:
ghat = PWLFC([atomdata.ghat_l], pd)
ghat.set_positions(np.zeros((1, 3)))
Q_LG = ghat.expand()
Q_Gii = np.dot(atomdata.Delta_iiL, Q_LG).T
else:
Q_Gii = two_phi_planewave_integrals(G_Gv, atomdata)
ni = atomdata.ni
Q_Gii.shape = (-1, ni, ni)
Q_xGii[id] = Q_Gii
Q_aGii = []
for a, atomdata in enumerate(wfs.setups):
id = wfs.setups.id_a[a]
Q_Gii = Q_xGii[id]
x_G = np.exp(-1j * np.dot(G_Gv, pos_av[a]))
Q_aGii.append(x_G[:, np.newaxis, np.newaxis] * Q_Gii)
if optical_limit:
Q_aGii[a][0] = atomdata.dO_ii
return Q_aGii
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)
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))}
cr_axi[0][0, 0] = 1.9
b = pd.zeros(1, dtype=complex)
br = pdr.zeros(1)
lfc.set_positions(spos_ac)
lfc.add(b, c_axi)
lfcr.set_positions(spos_ac)
lfcr.add(br, cr_axi)
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):
x = [0, 0, 0, 0, 0, 0, 0, 0, 0]
x[i] = 1
s1.append(lfc.stress_tensor_contribution(a_G, {0: x}) - np.eye(3) * e1[i])
x = 1e-6
for dist in [[[x, 0, 0], [0, 0, 0], [0, 0, 0]],
[[0, 0, 0], [0, x, 0], [0, 0, 0]],
def initialize(self):
self.eta /= Hartree
self.ecut /= Hartree
calc = self.calc
self.nspins = self.calc.wfs.nspins
# kpoint init
self.kd = kd = calc.wfs.kd
self.nikpt = kd.nibzkpts
self.ftol /= kd.nbzkpts
# cell init
self.acell_cv = calc.wfs.gd.cell_cv
self.acell_cv, self.bcell_cv, self.vol, self.BZvol = \
get_primitive_cell(self.acell_cv,rpad=self.rpad)
# grid init
gd = calc.wfs.gd.new_descriptor(comm=serial_comm)
self.pbc = gd.pbc_c
self.gd = gd
self.nG0 = np.prod(gd.N_c)
# Number of grid points and volume including zero padding
self.nGrpad = gd.N_c * self.rpad
self.nG0rpad = np.prod(self.nGrpad)
self.d_c = [
Gradient(gd, i, n=4, dtype=complex).apply for i in range(3)
]
# obtain eigenvalues, occupations
nibzkpt = kd.nibzkpts
kweight_k = kd.weight_k
self.eFermi = self.calc.occupations.get_fermi_level()
try:
self.e_skn
self.printtxt('Use eigenvalues from user.')
except:
self.printtxt('Use eigenvalues from the calculator.')
self.e_skn = {}
self.f_skn = {}
for ispin in range(self.nspins):
self.e_skn[ispin] = np.array([
calc.get_eigenvalues(kpt=k, spin=ispin)
for k in range(nibzkpt)
]) / Hartree
self.f_skn[ispin] = np.array([
calc.get_occupation_numbers(kpt=k, spin=ispin) /
kweight_k[k] for k in range(nibzkpt)
]) / kd.nbzkpts
#self.printtxt('Eigenvalues(k=0) are:')
#print >> self.txt, self.e_skn[0][0] * Hartree
self.enoshift_skn = {}
for ispin in range(self.nspins):
self.enoshift_skn[ispin] = self.e_skn[ispin].copy()
if self.eshift is not None:
self.add_discontinuity(self.eshift)
self.printtxt('Shift unoccupied bands by %f eV' % (self.eshift))
# k + q init
if self.q_c is not None:
self.qq_v = np.dot(self.q_c, self.bcell_cv) # summation over c
if self.optical_limit:
kq_k = np.arange(kd.nbzkpts)
self.expqr_g = 1.
else:
r_vg = gd.get_grid_point_coordinates() # (3, nG)
qr_g = gemmdot(self.qq_v, r_vg, beta=0.0)
self.expqr_g = np.exp(-1j * qr_g)
del r_vg, qr_g
kq_k = kd.find_k_plus_q(self.q_c)
self.kq_k = kq_k
# Plane wave init
if self.G_plus_q:
self.npw, self.Gvec_Gc, self.Gindex_G = set_Gvectors(self.acell_cv,
self.bcell_cv,
self.gd.N_c,
self.ecut,
q=self.q_c)
else:
self.npw, self.Gvec_Gc, self.Gindex_G = set_Gvectors(
self.acell_cv, self.bcell_cv, self.gd.N_c, self.ecut)
# band init
if self.nbands is None:
self.nbands = calc.wfs.bd.nbands
self.nvalence = calc.wfs.nvalence
# Projectors init
setups = calc.wfs.setups
self.spos_ac = calc.atoms.get_scaled_positions()
if self.pwmode:
self.pt = PWLFC([setup.pt_j for setup in setups], self.calc.wfs.pd)
self.pt.set_positions(self.spos_ac)
else:
self.pt = LFC(gd, [setup.pt_j for setup in setups],
KPointDescriptor(self.kd.bzk_kc),
dtype=complex,
forces=True)
self.pt.set_positions(self.spos_ac)
# Printing calculation information
self.print_stuff()
return
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)}
c_axi[0][0, 0] = 1.9 - 4.5j
c_axiv = {0: np.zeros((1, 2 * l + 1, 3), complex)}
b1 = gd.zeros(1, dtype=complex)
b2 = pd.zeros(1, dtype=complex)
for lfc, b in [(lfc1, b1), (lfc2, b2)]:
lfc.set_positions(spos_ac)
lfc.add(b, c_axi, 0)
b2 = pd.ifft(b2[0]) * eikr
equal(abs(b2 - b1[0]).max(), 0, 0.001)
