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))
class Interpolator:
def __init__(self, gd1, gd2, dtype=float):
self.pd1 = PWDescriptor(0.0, gd1, dtype)
self.pd2 = PWDescriptor(0.0, gd2, dtype)
def interpolate(self, a_r):
return self.pd1.interpolate(a_r, self.pd2)[0]
def __init__(self, calc, xc, ibzq_qc, fd, unit_cells,
density_cut, ecut, tag):
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.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 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 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 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_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(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.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 __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
class HybridXC(XCFunctional):
orbital_dependent = True
def __init__(self, name, hybrid=None, xc=None, finegrid=False,
alpha=None):
"""Mix standard functionals with exact exchange.
name: str
Name of hybrid functional.
hybrid: float
Fraction of exact exchange.
xc: str or XCFunctional object
Standard DFT functional with scaled down exchange.
finegrid: boolean
Use fine grid for energy functional evaluations?
"""
if name == 'EXX':
assert hybrid is None and xc is None
hybrid = 1.0
xc = XC(XCNull())
elif name == 'PBE0':
assert hybrid is None and xc is None
hybrid = 0.25
xc = XC('HYB_GGA_XC_PBEH')
elif name == 'B3LYP':
assert hybrid is None and xc is None
hybrid = 0.2
xc = XC('HYB_GGA_XC_B3LYP')
if isinstance(xc, str):
xc = XC(xc)
self.hybrid = hybrid
self.xc = xc
self.type = xc.type
self.alpha = alpha
self.exx = 0.0
XCFunctional.__init__(self, name)
def get_setup_name(self):
return 'PBE'
def calculate_radial(self, rgd, n_sLg, Y_L, v_sg,
dndr_sLg=None, rnablaY_Lv=None,
tau_sg=None, dedtau_sg=None):
return self.xc.calculate_radial(rgd, n_sLg, Y_L, v_sg,
dndr_sLg, rnablaY_Lv)
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 set_positions(self, spos_ac):
self.ghat.set_positions(spos_ac)
self.pt.set_positions(spos_ac)
def calculate(self, gd, n_sg, v_sg=None, e_g=None):
# Normal XC contribution:
exc = self.xc.calculate(gd, n_sg, v_sg, e_g)
# Add EXX contribution:
return exc + self.exx
def calculate_exx(self):
"""Non-selfconsistent calculation."""
kd = self.kd
K = self.fullkd.nibzkpts
assert self.nspins == 1
Q = K // world.size
assert Q * world.size == K
parallel = (world.size > self.nspins)
self.exx = 0.0
self.exx_skn = np.zeros((self.nspins, K, self.bd.nbands))
kpt_u = []
for k in range(world.rank * Q, (world.rank + 1) * Q):
k_c = self.fullkd.ibzk_kc[k]
for k1, k1_c in enumerate(kd.bzk_kc):
if abs(k1_c - k_c).max() < 1e-10:
break
# Index of symmetry related point in the irreducible BZ
ik = kd.kibz_k[k1]
kpt = self.kpt_u[ik]
# KPoint from ground-state calculation
phase_cd = np.exp(2j * pi * self.gd.sdisp_cd * k_c[:, np.newaxis])
kpt2 = KPoint0(kpt.weight, kpt.s, k, None, phase_cd)
kpt2.psit_nG = np.empty_like(kpt.psit_nG)
kpt2.f_n = kpt.f_n / kpt.weight / K * 2
for n, psit_G in enumerate(kpt2.psit_nG):
psit_G[:] = kd.transform_wave_function(kpt.psit_nG[n], k1)
kpt2.P_ani = self.pt.dict(len(kpt.psit_nG))
self.pt.integrate(kpt2.psit_nG, kpt2.P_ani, k)
kpt_u.append(kpt2)
for s in range(self.nspins):
kpt1_q = [KPoint(self.fullkd, kpt) for kpt in kpt_u if kpt.s == s]
kpt2_q = kpt1_q[:]
if len(kpt1_q) == 0:
# No s-spins on this CPU:
continue
# Send rank:
srank = self.fullkd.get_rank_and_index(s, (kpt1_q[0].k - 1) % K)[0]
# Receive rank:
rrank = self.fullkd.get_rank_and_index(s, (kpt1_q[-1].k + 1) % K)[0]
# Shift k-points K // 2 times:
for i in range(K // 2 + 1):
if i < K // 2:
if parallel:
kpt = kpt2_q[-1].next()
kpt.start_receiving(rrank)
kpt2_q[0].start_sending(srank)
else:
kpt = kpt2_q[0]
for kpt1, kpt2 in zip(kpt1_q, kpt2_q):
if 2 * i == K:
self.apply(kpt1, kpt2, invert=(kpt1.k > kpt2.k))
else:
self.apply(kpt1, kpt2)
self.apply(kpt1, kpt2, invert=True)
if i < K // 2:
if parallel:
kpt.wait()
kpt2_q[0].wait()
kpt2_q.pop(0)
kpt2_q.append(kpt)
self.exx = world.sum(self.exx)
world.sum(self.exx_skn)
self.exx += self.calculate_paw_correction()
def apply(self, kpt1, kpt2, invert=False):
#print world.rank,kpt1.k,kpt2.k,invert
k1_c = self.fullkd.ibzk_kc[kpt1.k]
k2_c = self.fullkd.ibzk_kc[kpt2.k]
if invert:
k2_c = -k2_c
k12_c = k1_c - k2_c
N_c = self.gd.N_c
eikr_R = np.exp(2j * pi * np.dot(np.indices(N_c).T, k12_c / N_c).T)
for q, k_c in enumerate(self.bzk_kc):
if abs(k_c + k12_c).max() < 1e-9:
q0 = q
break
for q, k_c in enumerate(self.bzk_kc):
if abs(k_c - k12_c).max() < 1e-9:
q00 = q
break
Gpk2_G = self.pwd.G2_qG[q0]
if Gpk2_G[0] == 0:
Gpk2_G = Gpk2_G.copy()
Gpk2_G[0] = 1.0 / self.gamma
N = N_c.prod()
vol = self.gd.dv * N
nspins = self.nspins
same = (kpt1.k == kpt2.k)
for n1, psit1_R in enumerate(kpt1.psit_nG):
f1 = kpt1.f_n[n1]
for n2, psit2_R in enumerate(kpt2.psit_nG):
if same and n2 > n1:
continue
f2 = kpt2.f_n[n2]
nt_R = self.calculate_pair_density(n1, n2, kpt1, kpt2, q0,
invert)
nt_G = self.pwd.fft(nt_R * eikr_R) / N
vt_G = nt_G.copy()
vt_G *= -pi * vol / Gpk2_G
e = np.vdot(nt_G, vt_G).real * nspins * self.hybrid
if same and n1 == n2:
e /= 2
self.exx += e * f1 * f2
self.ekin -= 2 * e * f1 * f2
self.exx_skn[kpt1.s, kpt1.k, n1] += f2 * e
self.exx_skn[kpt2.s, kpt2.k, n2] += f1 * e
calculate_potential = not True
if calculate_potential:
vt_R = self.pwd.ifft(vt_G).conj() * eikr_R * N / vol
if kpt1 is kpt2 and not invert and n1 == n2:
kpt1.vt_nG[n1] = 0.5 * f1 * vt_R
if invert:
kpt1.Htpsit_nG[n1] += \
f2 * nspins * psit2_R.conj() * vt_R
else:
kpt1.Htpsit_nG[n1] += f2 * nspins * psit2_R * vt_R
if kpt1 is not kpt2:
if invert:
kpt2.Htpsit_nG[n2] += (f1 * nspins *
psit1_R.conj() * vt_R)
else:
kpt2.Htpsit_nG[n2] += (f1 * nspins *
psit1_R * vt_R.conj())
def calculate_paw_correction(self):
exx = 0
deg = 2 // self.nspins # spin degeneracy
for a, D_sp in self.density.D_asp.items():
setup = self.setups[a]
for D_p in D_sp:
D_ii = unpack2(D_p)
ni = len(D_ii)
for i1 in range(ni):
for i2 in range(ni):
A = 0.0
for i3 in range(ni):
p13 = packed_index(i1, i3, ni)
for i4 in range(ni):
p24 = packed_index(i2, i4, ni)
A += setup.M_pp[p13, p24] * D_ii[i3, i4]
p12 = packed_index(i1, i2, ni)
exx -= self.hybrid / deg * D_ii[i1, i2] * A
if setup.X_p is not None:
exx -= self.hybrid * np.dot(D_p, setup.X_p)
exx += self.hybrid * setup.ExxC
return exx
def calculate_pair_density(self, n1, n2, kpt1, kpt2, q, invert):
if invert:
nt_G = kpt1.psit_nG[n1].conj() * kpt2.psit_nG[n2].conj()
else:
nt_G = kpt1.psit_nG[n1].conj() * kpt2.psit_nG[n2]
Q_aL = {}
for a, P1_ni in kpt1.P_ani.items():
P1_i = P1_ni[n1]
P2_i = kpt2.P_ani[a][n2]
if invert:
D_ii = np.outer(P1_i.conj(), P2_i.conj())
else:
D_ii = np.outer(P1_i.conj(), P2_i)
D_p = pack(D_ii)
Q_aL[a] = np.dot(D_p, self.setups[a].Delta_pL)
self.ghat.add(nt_G, Q_aL, q)
return nt_G
class HybridXC(HybridXCBase):
orbital_dependent = True
def __init__(self,
name,
hybrid=None,
xc=None,
alpha=None,
gamma_point=1,
method='standard',
bandstructure=False,
logfilename='-',
bands=None,
fcut=1e-10,
molecule=False,
qstride=1,
world=None):
"""Mix standard functionals with exact exchange.
name: str
Name of functional: EXX, PBE0, HSE03, HSE06
hybrid: float
Fraction of exact exchange.
xc: str or XCFunctional object
Standard DFT functional with scaled down exchange.
method: str
Use 'standard' standard formula and 'acdf for
adiabatic-connection dissipation fluctuation formula.
alpha: float
XXX describe
gamma_point: bool
0: Skip k2-k1=0 interactions.
1: Use the alpha method.
2: Integrate the gamma point.
bandstructure: bool
Calculate bandstructure instead of just the total energy.
bands: list of int
List of bands to calculate bandstructure for. Default is
all bands.
molecule: bool
Decouple electrostatic interactions between periodically
repeated images.
fcut: float
Threshold for empty band.
"""
self.alpha = alpha
self.fcut = fcut
self.gamma_point = gamma_point
self.method = method
self.bandstructure = bandstructure
self.bands = bands
self.fd = logfilename
self.write_timing_information = True
HybridXCBase.__init__(self, name, hybrid, xc)
# EXX energies:
self.exx = None # total
self.evv = None # valence-valence (pseudo part)
self.evvacdf = None # valence-valence (pseudo part)
self.devv = None # valence-valence (PAW correction)
self.evc = None # valence-core
self.ecc = None # core-core
self.exx_skn = None # bandstructure
self.qlatest = None
if world is None:
world = mpi.world
self.world = world
self.molecule = molecule
if isinstance(qstride, int):
qstride = [qstride] * 3
self.qstride_c = np.asarray(qstride)
self.timer = Timer()
def log(self, *args, **kwargs):
prnt(file=self.fd, *args, **kwargs)
self.fd.flush()
def calculate_radial(self,
rgd,
n_sLg,
Y_L,
v_sg,
dndr_sLg=None,
rnablaY_Lv=None,
tau_sg=None,
dedtau_sg=None):
return self.xc.calculate_radial(rgd, n_sLg, Y_L, v_sg, dndr_sLg,
rnablaY_Lv)
def calculate_paw_correction(self,
setup,
D_sp,
dEdD_sp=None,
addcoredensity=True,
a=None):
return self.xc.calculate_paw_correction(setup, D_sp, dEdD_sp,
addcoredensity, a)
def initialize(self, dens, ham, wfs, occupations):
assert wfs.bd.comm.size == 1
self.xc.initialize(dens, ham, wfs, occupations)
self.dens = dens
self.wfs = wfs
# Make a k-point descriptor that is not distributed
# (self.kd.comm is serial_comm):
self.kd = wfs.kd.copy()
self.fd = logfile(self.fd, self.world.rank)
wfs.initialize_wave_functions_from_restart_file()
def set_positions(self, spos_ac):
self.spos_ac = spos_ac
def calculate(self, gd, n_sg, v_sg=None, e_g=None):
# Normal XC contribution:
exc = self.xc.calculate(gd, n_sg, v_sg, e_g)
# Add EXX contribution:
return exc + self.exx * self.hybrid
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)
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 indices(self, s, k1, k2):
"""Generator for (K2, q, n1, n2) indices for (k1, k2) pair.
s: int
Spin index.
k1: int
Index of k-point in the IBZ.
k2: int
Index of k-point in the IBZ.
Returns (K, q, n1_n, n2), where K then index of the k-point in
the BZ that k2 is mapped to, q is the index of the q-vector
between K and k1, and n1_n is a list of bands that should be
combined with band n2."""
for K, k in enumerate(self.kd.bz2ibz_k):
if k == k2:
for K, q, n1_n, n2 in self._indices(s, k1, k2, K):
yield K, q, n1_n, n2
def _indices(self, s, k1, k2, K2):
k1_c = self.kd.ibzk_kc[k1]
k2_c = self.kd.bzk_kc[K2]
q_c = k2_c - k1_c
q = abs(self.bzq_qc - q_c).sum(1).argmin()
if abs(self.bzq_qc[q] - q_c).sum() > 1e-7:
return
if self.gamma_point == 0 and q == self.q0:
return
nocc1 = self.nocc_sk[s, k1]
nocc2 = self.nocc_sk[s, k2]
# Is k2 in the IBZ?
is_ibz2 = (self.kd.ibz2bz_k[k2] == K2)
for n2 in range(self.wfs.bd.nbands):
# Find range of n1's (from n1a to n1b-1):
if is_ibz2:
# We get this combination twice, so let's only do half:
if k1 >= k2:
n1a = n2
else:
n1a = n2 + 1
else:
n1a = 0
n1b = self.wfs.bd.nbands
if self.bandstructure:
if n2 >= nocc2:
n1b = min(n1b, nocc1)
else:
if n2 >= nocc2:
break
n1b = min(n1b, nocc1)
if self.bands is not None:
assert self.bandstructure
n1_n = []
for n1 in range(n1a, n1b):
if (n1 in self.bands and n2 < nocc2
or is_ibz2 and n2 in self.bands and n1 < nocc1):
n1_n.append(n1)
n1_n = np.array(n1_n)
else:
n1_n = np.arange(n1a, n1b)
if len(n1_n) == 0:
continue
yield K2, q, n1_n, n2
def apply(self, K2, q, kpt1, kpt2, n1_n, n2):
k20_c = self.kd.ibzk_kc[kpt2.k]
k2_c = self.kd.bzk_kc[K2]
if k2_c.any():
self.timer.start('Initialize plane waves')
eik2r_R = self.wfs.gd.plane_wave(k2_c)
eik20r_R = self.wfs.gd.plane_wave(k20_c)
self.timer.stop('Initialize plane waves')
else:
eik2r_R = 1.0
eik20r_R = 1.0
w1 = self.kd.weight_k[kpt1.k]
w2 = self.kd.weight_k[kpt2.k]
# Is k2 in the 1. BZ?
is_ibz2 = (self.kd.ibz2bz_k[kpt2.k] == K2)
e_n = self.calculate_interaction(n1_n, n2, kpt1, kpt2, q, K2, eik20r_R,
eik2r_R, is_ibz2)
e_n *= 1.0 / self.kd.nbzkpts / self.wfs.nspins * self.qstride_c.prod()
if q == self.q0:
e_n[n1_n == n2] *= 0.5
f1_n = kpt1.f_n[n1_n]
eps1_n = kpt1.eps_n[n1_n]
f2 = kpt2.f_n[n2]
eps2 = kpt2.eps_n[n2]
s_n = np.sign(eps2 - eps1_n)
evv = (f1_n * f2 * e_n).sum()
evvacdf = 0.5 * (f1_n * (1 - s_n) * e_n + f2 * (1 + s_n) * e_n).sum()
self.evv += evv * w1
self.evvacdf += evvacdf * w1
if is_ibz2:
self.evv += evv * w2
self.evvacdf += evvacdf * w2
if self.bandstructure:
x = self.wfs.nspins
self.exx_skn[kpt1.s, kpt1.k, n1_n] += x * f2 * e_n
if is_ibz2:
self.exx_skn[kpt2.s, kpt2.k, n2] += x * np.dot(f1_n, e_n)
def calculate_interaction(self, n1_n, n2, kpt1, kpt2, q, k, eik20r_R,
eik2r_R, is_ibz2):
"""Calculate Coulomb interactions.
For all n1 in the n1_n list, calculate interaction with n2."""
# number of plane waves:
ng1 = self.wfs.ng_k[kpt1.k]
ng2 = self.wfs.ng_k[kpt2.k]
# Transform to real space and apply symmetry operation:
self.timer.start('IFFT1')
if is_ibz2:
u2_R = self.pd.ifft(kpt2.psit_nG[n2, :ng2], kpt2.k)
else:
psit2_R = self.pd.ifft(kpt2.psit_nG[n2, :ng2], kpt2.k) * eik20r_R
self.timer.start('Symmetry transform')
u2_R = self.kd.transform_wave_function(psit2_R, k) / eik2r_R
self.timer.stop()
self.timer.stop()
# Calculate pair densities:
nt_nG = self.pd2.zeros(len(n1_n), q=q)
for n1, nt_G in zip(n1_n, nt_nG):
self.timer.start('IFFT2')
u1_R = self.pd.ifft(kpt1.psit_nG[n1, :ng1], kpt1.k)
self.timer.stop()
nt_R = u1_R.conj() * u2_R
self.timer.start('FFT')
nt_G[:] = self.pd2.fft(nt_R, q)
self.timer.stop()
s = self.kd.sym_k[k]
time_reversal = self.kd.time_reversal_k[k]
k2_c = self.kd.ibzk_kc[kpt2.k]
self.timer.start('Compensation charges')
Q_anL = {} # coefficients for shape functions
for a, P1_ni in kpt1.P_ani.items():
P1_ni = P1_ni[n1_n]
if is_ibz2:
P2_i = kpt2.P_ani[a][n2]
else:
b = self.kd.symmetry.a_sa[s, a]
S_c = (np.dot(self.spos_ac[a], self.kd.symmetry.op_scc[s]) -
self.spos_ac[b])
assert abs(S_c.round() - S_c).max() < 1e-5
if self.ghat.dtype == complex:
x = np.exp(2j * pi * np.dot(k2_c, S_c))
else:
x = 1.0
P2_i = np.dot(self.wfs.setups[a].R_sii[s],
kpt2.P_ani[b][n2]) * x
if time_reversal:
P2_i = P2_i.conj()
D_np = []
for P1_i in P1_ni:
D_ii = np.outer(P1_i.conj(), P2_i)
D_np.append(pack(D_ii))
Q_anL[a] = np.dot(D_np, self.wfs.setups[a].Delta_pL)
self.timer.start('Expand')
if q != self.qlatest:
self.f_IG = self.ghat.expand(q)
self.qlatest = q
self.timer.stop('Expand')
# Add compensation charges:
self.ghat.add(nt_nG, Q_anL, q, self.f_IG)
self.timer.stop('Compensation charges')
if self.molecule and n2 in n1_n:
nn = (n1_n == n2).nonzero()[0][0]
nt_nG[nn] -= self.ngauss_G
else:
nn = None
iG2_G = self.iG2_qG[q]
# Calculate energies:
e_n = np.empty(len(n1_n))
for n, nt_G in enumerate(nt_nG):
e_n[n] = -4 * pi * np.real(self.pd2.integrate(nt_G, nt_G * iG2_G))
self.npairs += 1
if nn is not None:
e_n[nn] -= 2 * (self.pd2.integrate(nt_nG[nn], self.vgauss_G) +
(self.beta / 2 / pi)**0.5)
if self.write_timing_information:
t = (time() - self.t0) / len(n1_n)
self.log('Time for first pair-density: %10.3f seconds' % t)
self.log('Estimated total time: %10.3f seconds' %
(t * self.npairs0 / self.world.size))
self.write_timing_information = False
return e_n
def calculate_exx_paw_correction(self):
self.timer.start('PAW correction')
self.devv = 0.0
self.evc = 0.0
self.ecc = 0.0
deg = 2 // self.wfs.nspins # spin degeneracy
for a, D_sp in self.dens.D_asp.items():
setup = self.wfs.setups[a]
for D_p in D_sp:
D_ii = unpack2(D_p)
ni = len(D_ii)
for i1 in range(ni):
for i2 in range(ni):
A = 0.0
for i3 in range(ni):
p13 = packed_index(i1, i3, ni)
for i4 in range(ni):
p24 = packed_index(i2, i4, ni)
A += setup.M_pp[p13, p24] * D_ii[i3, i4]
self.devv -= D_ii[i1, i2] * A / deg
self.evc -= np.dot(D_p, setup.X_p)
self.ecc += setup.ExxC
if not self.bandstructure:
self.timer.stop('PAW correction')
return
Q = self.world.size // self.wfs.kd.comm.size
self.exx_skn *= Q
for kpt in self.wfs.kpt_u:
for a, D_sp in self.dens.D_asp.items():
setup = self.wfs.setups[a]
for D_p in D_sp:
D_ii = unpack2(D_p)
ni = len(D_ii)
P_ni = kpt.P_ani[a]
for i1 in range(ni):
for i2 in range(ni):
A = 0.0
for i3 in range(ni):
p13 = packed_index(i1, i3, ni)
for i4 in range(ni):
p24 = packed_index(i2, i4, ni)
A += setup.M_pp[p13, p24] * D_ii[i3, i4]
self.exx_skn[kpt.s, kpt.k] -= \
(A * P_ni[:, i1].conj() * P_ni[:, i2]).real
p12 = packed_index(i1, i2, ni)
self.exx_skn[kpt.s, kpt.k] -= \
(P_ni[:, i1].conj() * setup.X_p[p12] *
P_ni[:, i2]).real / self.wfs.nspins
self.world.sum(self.exx_skn)
self.exx_skn *= self.hybrid / Q
self.timer.stop('PAW correction')
def initialize_gaussian(self):
"""Calculate gaussian compensation charge and its potential.
Used to decouple electrostatic interactions between
periodically repeated images for molecular calculations.
Charge containing one electron::
(beta/pi)^(3/2)*exp(-beta*r^2),
its Fourier transform::
exp(-G^2/(4*beta)),
and its potential::
erf(beta^0.5*r)/r.
"""
gd = self.wfs.gd
# Set exponent of exp-function to -19 on the boundary:
self.beta = 4 * 19 * (gd.icell_cv**2).sum(1).max()
# Calculate gaussian:
G_Gv = self.pd2.get_reciprocal_vectors()
G2_G = self.pd2.G2_qG[0]
C_v = gd.cell_cv.sum(0) / 2 # center of cell
self.ngauss_G = np.exp(-1.0 / (4 * self.beta) * G2_G +
1j * np.dot(G_Gv, C_v)) / gd.dv
# Calculate potential from gaussian:
R_Rv = gd.get_grid_point_coordinates().transpose((1, 2, 3, 0))
r_R = ((R_Rv - C_v)**2).sum(3)**0.5
if (gd.N_c % 2 == 0).all():
r_R[tuple(gd.N_c // 2)] = 1.0 # avoid dividing by zero
v_R = erf(self.beta**0.5 * r_R) / r_R
if (gd.N_c % 2 == 0).all():
v_R[tuple(gd.N_c // 2)] = (4 * self.beta / pi)**0.5
self.vgauss_G = self.pd2.fft(v_R)
# Compare self-interaction to analytic result:
assert abs(0.5 * self.pd2.integrate(self.ngauss_G, self.vgauss_G) -
(self.beta / 2 / pi)**0.5) < 1e-6
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):
class Kernel:
def __init__(self, calc, xc, ibzq_qc, fd, unit_cells,
density_cut, ecut, tag):
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.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 calculate_fhxc(self):
prnt('Calculating %s kernel at %d eV cutoff' %
(self.xc, self.ecut), file=self.fd)
if self.xc[0] == 'r':
self.calculate_rkernel()
else:
assert self.xc[0] == 'A'
self.calculate_local_kernel()
def calculate_rkernel(self):
gd = self.gd
ng_c = gd.N_c
cell_cv = gd.cell_cv
icell_cv = 2 * np.pi * np.linalg.inv(cell_cv)
vol = np.linalg.det(cell_cv)
ns = self.calc.wfs.nspins
n_g = self.n_g # density on rough grid
fx_g = ns * self.get_fxc_g(n_g) # local exchange kernel
qc_g = (-4 * np.pi * ns / fx_g)**0.5 # cutoff functional
flocal_g = qc_g**3 * fx_g / (6 * np.pi**2) # ren. x-kernel for r=r'
Vlocal_g = 2 * qc_g / np.pi # ren. Hartree kernel for r=r'
ng = np.prod(ng_c) # number of grid points
r_vg = gd.get_grid_point_coordinates()
rx_g = r_vg[0].flatten()
ry_g = r_vg[1].flatten()
rz_g = r_vg[2].flatten()
prnt(' %d grid points and %d plane waves at the Gamma point' %
(ng, self.pd.ngmax), file=self.fd)
# Unit cells
R_Rv = []
weight_R = []
nR_v = self.unit_cells
nR = np.prod(nR_v)
for i in range(-nR_v[0] + 1, nR_v[0]):
for j in range(-nR_v[1] + 1, nR_v[1]):
for h in range(-nR_v[2] + 1, nR_v[2]):
R_Rv.append(i * cell_cv[0] +
j * cell_cv[1] +
h * cell_cv[2])
weight_R.append((nR_v[0] - abs(i)) *
(nR_v[1] - abs(j)) *
(nR_v[2] - abs(h)) / float(nR))
if nR > 1:
# with more than one unit cell only the exchange kernel is
# calculated on the grid. The bare Coulomb kernel is added
# in PW basis and Vlocal_g only the exchange part
dv = self.calc.density.gd.dv
gc = (3 * dv / 4 / np.pi)**(1 / 3.)
Vlocal_g -= 2 * np.pi * gc**2 / dv
prnt(' Lattice point sampling: ' +
'(%s x %s x %s)^2 ' % (nR_v[0], nR_v[1], nR_v[2]) +
' Reduced to %s lattice points' % len(R_Rv), file=self.fd)
l_g_size = -(-ng // mpi.world.size)
l_g_range = range(mpi.world.rank * l_g_size,
min((mpi.world.rank+1) * l_g_size, ng))
fhxc_qsGr = {}
for iq in range(len(self.ibzq_qc)):
fhxc_qsGr[iq] = np.zeros((ns, len(self.pd.G2_qG[iq]),
len(l_g_range)), dtype=complex)
inv_error = np.seterr()
np.seterr(invalid='ignore')
np.seterr(divide='ignore')
t0 = time()
# Loop over Lattice points
for i, R_v in enumerate(R_Rv):
# Loop over r'. f_rr and V_rr are functions of r (dim. as r_vg[0])
if i == 1:
prnt(' Finished 1 cell in %s seconds' % int(time() - t0) +
' - estimated %s seconds left' %
int((len(R_Rv) - 1) * (time() - t0)),
file=self.fd)
self.fd.flush()
if len(R_Rv) > 5:
if (i+1) % (len(R_Rv) / 5 + 1) == 0:
prnt(' Finished %s cells in %s seconds'
% (i, int(time() - t0))
+ ' - estimated %s seconds left'
% int((len(R_Rv) - i) * (time() - t0) / i),
file=self.fd)
self.fd.flush()
for g in l_g_range:
rx = rx_g[g] + R_v[0]
ry = ry_g[g] + R_v[1]
rz = rz_g[g] + R_v[2]
# |r-r'-R_i|
rr = ((r_vg[0] - rx)**2 +
(r_vg[1] - ry)**2 +
(r_vg[2] - rz)**2)**0.5
n_av = (n_g + n_g.flatten()[g]) / 2.
fx_g = ns * self.get_fxc_g(n_av, index=g)
qc_g = (-4 * np.pi * ns / fx_g)**0.5
x = qc_g * rr
osc_x = np.sin(x) - x*np.cos(x)
f_rr = fx_g * osc_x / (2 * np.pi**2 * rr**3)
if nR > 1: # include only exchange part of the kernel here
V_rr = (sici(x)[0] * 2 / np.pi - 1) / rr
else: # include the full kernel (also hartree part)
V_rr = (sici(x)[0] * 2 / np.pi) / rr
# Terms with r = r'
if (np.abs(R_v) < 0.001).all():
tmp_flat = f_rr.flatten()
tmp_flat[g] = flocal_g.flatten()[g]
f_rr = tmp_flat.reshape(ng_c)
tmp_flat = V_rr.flatten()
tmp_flat[g] = Vlocal_g.flatten()[g]
V_rr = tmp_flat.reshape(ng_c)
del tmp_flat
f_rr[np.where(n_av < self.density_cut)] = 0.0
V_rr[np.where(n_av < self.density_cut)] = 0.0
f_rr *= weight_R[i]
V_rr *= weight_R[i]
# r-r'-R_i
r_r = np.array([r_vg[0] - rx, r_vg[1] - ry, r_vg[2] - rz])
# Fourier transform of r
for iq, q in enumerate(self.ibzq_qc):
q_v = np.dot(q, icell_cv)
e_q = np.exp(-1j * gemmdot(q_v, r_r, beta=0.0))
f_q = self.pd.fft((f_rr + V_rr) * e_q, iq) * vol / ng
fhxc_qsGr[iq][0, :, g - l_g_range[0]] += f_q
if ns == 2:
f_q = self.pd.fft(V_rr * e_q, iq) * vol / ng
fhxc_qsGr[iq][1, :, g - l_g_range[0]] += f_q
mpi.world.barrier()
np.seterr(**inv_error)
for iq, q in enumerate(self.ibzq_qc):
npw = len(self.pd.G2_qG[iq])
fhxc_sGsG = np.zeros((ns * npw, ns * npw), complex)
l_pw_size = -(-npw // mpi.world.size) # parallelize over PW below
l_pw_range = range(mpi.world.rank * l_pw_size,
min((mpi.world.rank + 1) * l_pw_size, npw))
if mpi.world.size > 1:
# redistribute grid and plane waves in fhxc_qsGr[iq]
bg1 = BlacsGrid(mpi.world, 1, mpi.world.size)
bg2 = BlacsGrid(mpi.world, mpi.world.size, 1)
bd1 = bg1.new_descriptor(npw, ng, npw, - (-ng / mpi.world.size))
bd2 = bg2.new_descriptor(npw, ng, -(-npw / mpi.world.size), ng)
fhxc_Glr = np.zeros((len(l_pw_range), ng), dtype=complex)
if ns == 2:
Koff_Glr = np.zeros((len(l_pw_range), ng), dtype=complex)
r = Redistributor(bg1.comm, bd1, bd2)
r.redistribute(fhxc_qsGr[iq][0], fhxc_Glr, npw, ng)
if ns == 2:
r.redistribute(fhxc_qsGr[iq][1], Koff_Glr, npw, ng)
else:
fhxc_Glr = fhxc_qsGr[iq][0]
if ns == 2:
Koff_Glr = fhxc_qsGr[iq][1]
# Fourier transform of r'
for iG in range(len(l_pw_range)):
f_g = fhxc_Glr[iG].reshape(ng_c)
f_G = self.pd.fft(f_g.conj(), iq) * vol / ng
fhxc_sGsG[l_pw_range[0] + iG, :npw] = f_G.conj()
if ns == 2:
v_g = Koff_Glr[iG].reshape(ng_c)
v_G = self.pd.fft(v_g.conj(), iq) * vol / ng
fhxc_sGsG[npw + l_pw_range[0] + iG, :npw] = v_G.conj()
if ns == 2: # f_00 = f_11 and f_01 = f_10
fhxc_sGsG[:npw, npw:] = fhxc_sGsG[npw:, :npw]
fhxc_sGsG[npw:, npw:] = fhxc_sGsG[:npw, :npw]
mpi.world.sum(fhxc_sGsG)
fhxc_sGsG /= vol
if mpi.rank == 0:
w = Writer('fhxc_%s_%s_%s_%s.gpw' %
(self.tag, self.xc, self.ecut, iq))
w.dimension('sG', ns * npw)
w.add('fhxc_sGsG', ('sG', 'sG'), dtype=complex)
if nR > 1: # add Hartree kernel evaluated in PW basis
Gq2_G = self.pd.G2_qG[iq]
if (q == 0).all():
Gq2_G[0] = 1.
vq_G = 4 * np.pi / Gq2_G
fhxc_sGsG += np.tile(np.eye(npw) * vq_G, (ns, ns))
w.fill(fhxc_sGsG)
w.close()
mpi.world.barrier()
prnt(file=self.fd)
def calculate_local_kernel(self):
# Standard ALDA exchange kernel
# Use with care. Results are very difficult to converge
# Sensitive to density_cut
ns = self.calc.wfs.nspins
gd = self.gd
pd = self.pd
cell_cv = gd.cell_cv
icell_cv = 2 * np.pi * np.linalg.inv(cell_cv)
vol = np.linalg.det(cell_cv)
fxc_sg = ns * self.get_fxc_g(ns * self.n_g)
fxc_sg[np.where(self.n_g < self.density_cut)] = 0.0
r_vg = gd.get_grid_point_coordinates()
for iq in range(len(self.ibzq_qc)):
Gvec_Gc = np.dot(pd.G_Qv[pd.Q_qG[iq]], cell_cv / (2 * np.pi))
npw = len(Gvec_Gc)
l_pw_size = -(-npw // mpi.world.size)
l_pw_range = range(mpi.world.rank * l_pw_size,
min((mpi.world.rank + 1) * l_pw_size, npw))
fhxc_sGsG = np.zeros((ns * npw, ns * npw), dtype=complex)
for s in range(ns):
for iG in l_pw_range:
for jG in range(npw):
fxc = fxc_sg[s].copy()
dG_c = Gvec_Gc[iG] - Gvec_Gc[jG]
dG_v = np.dot(dG_c, icell_cv)
dGr_g = gemmdot(dG_v, r_vg, beta=0.0)
ft_fxc = gd.integrate(np.exp(-1j * dGr_g) * fxc)
fhxc_sGsG[s * npw + iG, s * npw + jG] = ft_fxc
mpi.world.sum(fhxc_sGsG)
fhxc_sGsG /= vol
Gq2_G = self.pd.G2_qG[iq]
if (self.ibzq_qc[iq] == 0).all():
Gq2_G[0] = 1.
vq_G = 4 * np.pi / Gq2_G
fhxc_sGsG += np.tile(np.eye(npw) * vq_G, (ns, ns))
if mpi.rank == 0:
w = Writer('fhxc_%s_%s_%s_%s.gpw' %
(self.tag, self.xc, self.ecut, iq))
w.dimension('sG', ns * npw)
w.add('fhxc_sGsG', ('sG', 'sG'), dtype=complex)
w.fill(fhxc_sGsG)
w.close()
mpi.world.barrier()
prnt(file=self.fd)
def get_fxc_g(self, n_g, index=None):
if self.xc[-3:] == 'LDA':
return self.get_lda_g(n_g)
elif self.xc[-3:] == 'PBE':
return self.get_pbe_g(n_g, index=index)
else:
raise '%s kernel not recognized' % self.xc
def get_lda_g(self, n_g):
return (4. / 9.) * self.A_x * n_g**(-2./3.)
def get_pbe_g(self, n_g, index=None):
if index is None:
gradn_vg = self.gradn_vg
else:
gradn_vg = self.calc.density.gd.empty(3)
for v in range(3):
gradn_vg[v] = (self.gradn_vg[v] +
self.gradn_vg[v].flatten()[index]) / 2
kf_g = (3. * np.pi**2 * n_g)**(1 / 3.)
s2_g = np.zeros_like(n_g)
for v in range(3):
axpy(1.0, gradn_vg[v]**2, s2_g)
s2_g /= 4 * kf_g**2 * n_g**2
e_g = self.A_x * n_g**(4 / 3.)
v_g = (4 / 3.) * e_g / n_g
f_g = (1 / 3.) * v_g / n_g
kappa = 0.804
mu = 0.2195149727645171
denom_g = (1 + mu * s2_g / kappa)
F_g = 1. + kappa - kappa / denom_g
Fn_g = -mu / denom_g**2 * 8 * s2_g / (3 * n_g)
Fnn_g = -11 * Fn_g / (3 * n_g) - 2 * Fn_g**2 / kappa
fxc_g = f_g * F_g
fxc_g += 2 * v_g * Fn_g
fxc_g += e_g * Fnn_g
# Contributions from varying the gradient
#Fgrad_vg = np.zeros_like(gradn_vg)
#Fngrad_vg = np.zeros_like(gradn_vg)
#for v in range(3):
# axpy(1.0, mu / den_g**2 * gradn_vg[v] / (2 * kf_g**2 * n_g**2),
# Fgrad_vg[v])
# axpy(-8.0, Fgrad_vg[v] / (3 * n_g), Fngrad_vg[v])
# axpy(-2.0, Fgrad_vg[v] * Fn_g / kappa, Fngrad_vg[v])
#tmp = np.zeros_like(fxc_g)
#tmp1 = np.zeros_like(fxc_g)
#for v in range(3):
#self.grad_v[v](Fgrad_vg[v], tmp)
#axpy(-2.0, tmp * v_g, fxc_g)
#for u in range(3):
#self.grad_v[u](Fgrad_vg[u] * tmp, tmp1)
#axpy(-4.0/kappa, tmp1 * e_g, fxc_g)
#self.grad_v[v](Fngrad_vg[v], tmp)
#axpy(-2.0, tmp * e_g, fxc_g)
#self.laplace(mu / den_g**2 / (2 * kf_g**2 * n_g**2), tmp)
#axpy(1.0, tmp * e_g, fxc_g)
return fxc_g
def get_fxc_libxc_g(self, n_g):
### NOT USED AT THE MOMENT
gd = self.calc.density.gd.refine()
xc = XC('GGA_X_' + self.xc[2:])
#xc = XC('LDA_X')
#sigma = np.zeros_like(n_g).flat[:]
xc.set_grid_descriptor(gd)
sigma_xg, gradn_svg = xc.calculate_sigma(np.array([n_g]))
dedsigma_xg = np.zeros_like(sigma_xg)
e_g = np.zeros_like(n_g)
v_sg = np.array([np.zeros_like(n_g)])
xc.calculate_gga(e_g, np.array([n_g]), v_sg, sigma_xg, dedsigma_xg)
sigma = sigma_xg[0].flat[:]
gradn_vg = gradn_svg[0]
dedsigma_g = dedsigma_xg[0]
libxc = LibXC('GGA_X_' + self.xc[2:])
#libxc = LibXC('LDA_X')
libxc.initialize(1)
libxc_fxc = libxc.xc.calculate_fxc_spinpaired
fxc_g = np.zeros_like(n_g).flat[:]
d2edndsigma_g = np.zeros_like(n_g).flat[:]
d2ed2sigma_g = np.zeros_like(n_g).flat[:]
libxc_fxc(n_g.flat[:], fxc_g, sigma, d2edndsigma_g, d2ed2sigma_g)
fxc_g = fxc_g.reshape(np.shape(n_g))
d2edndsigma_g = d2edndsigma_g.reshape(np.shape(n_g))
d2ed2sigma_g = d2ed2sigma_g.reshape(np.shape(n_g))
tmp = np.zeros_like(fxc_g)
tmp1 = np.zeros_like(fxc_g)
#for v in range(3):
#self.grad_v[v](d2edndsigma_g * gradn_vg[v], tmp)
#axpy(-4.0, tmp, fxc_g)
#for u in range(3):
#for v in range(3):
#self.grad_v[v](d2ed2sigma_g * gradn_vg[u] * gradn_vg[v], tmp)
#self.grad_v[u](tmp, tmp1)
#axpy(4.0, tmp1, fxc_g)
#self.laplace(dedsigma_g, tmp)
#axpy(2.0, tmp, fxc_g)
return fxc_g[::2, ::2, ::2]
def get_numerical_fxc_sg(self, n_sg):
### NOT USED AT THE MOMENT
gd = self.calc.density.gd.refine()
delta = 1.e-4
if self.xc[2:] == 'LDA':
xc = XC('LDA_X')
v1xc_sg = np.zeros_like(n_sg)
v2xc_sg = np.zeros_like(n_sg)
xc.calculate(gd, (1 + delta) * n_sg, v1xc_sg)
xc.calculate(gd, (1 - delta) * n_sg, v2xc_sg)
fxc_sg = (v1xc_sg - v2xc_sg) / (2 * delta * n_sg)
else:
fxc_sg = np.zeros_like(n_sg)
xc = XC('GGA_X_' + self.xc[2:])
vxc_sg = np.zeros_like(n_sg)
xc.calculate(gd, n_sg, vxc_sg)
for s in range(len(n_sg)):
for x in range(len(n_sg[0])):
for y in range(len(n_sg[0, 0])):
for z in range(len(n_sg[0, 0, 0])):
v1xc_sg = np.zeros_like(n_sg)
n1_sg = n_sg.copy()
n1_sg[s, x, y, z] *= (1 + delta)
xc.calculate(gd, n1_sg, v1xc_sg)
num = v1xc_sg[s, x, y, z] - vxc_sg[s, x, y, z]
den = delta * n_sg[s, x, y, z]
fxc_sg[s, x, y, z] = num / den
return fxc_sg[:, ::2, ::2, ::2]
class HybridXC(XCFunctional):
orbital_dependent = True
def __init__(self, name, hybrid=None, xc=None, finegrid=False, alpha=None):
"""Mix standard functionals with exact exchange.
name: str
Name of hybrid functional.
hybrid: float
Fraction of exact exchange.
xc: str or XCFunctional object
Standard DFT functional with scaled down exchange.
finegrid: boolean
Use fine grid for energy functional evaluations?
"""
if name == 'EXX':
assert hybrid is None and xc is None
hybrid = 1.0
xc = XC(XCNull())
elif name == 'PBE0':
assert hybrid is None and xc is None
hybrid = 0.25
xc = XC('HYB_GGA_XC_PBEH')
elif name == 'B3LYP':
assert hybrid is None and xc is None
hybrid = 0.2
xc = XC('HYB_GGA_XC_B3LYP')
if isinstance(xc, str):
xc = XC(xc)
self.hybrid = hybrid
self.xc = xc
self.type = xc.type
self.alpha = alpha
self.exx = 0.0
XCFunctional.__init__(self, name)
def get_setup_name(self):
return 'PBE'
def calculate_radial(self,
rgd,
n_sLg,
Y_L,
v_sg,
dndr_sLg=None,
rnablaY_Lv=None,
tau_sg=None,
dedtau_sg=None):
return self.xc.calculate_radial(rgd, n_sLg, Y_L, v_sg, dndr_sLg,
rnablaY_Lv)
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 set_positions(self, spos_ac):
self.ghat.set_positions(spos_ac)
self.pt.set_positions(spos_ac)
def calculate(self, gd, n_sg, v_sg=None, e_g=None):
# Normal XC contribution:
exc = self.xc.calculate(gd, n_sg, v_sg, e_g)
# Add EXX contribution:
return exc + self.exx
def calculate_exx(self):
"""Non-selfconsistent calculation."""
kd = self.kd
K = self.fullkd.nibzkpts
assert self.nspins == 1
Q = K // world.size
assert Q * world.size == K
parallel = (world.size > self.nspins)
self.exx = 0.0
self.exx_skn = np.zeros((self.nspins, K, self.bd.nbands))
kpt_u = []
for k in range(world.rank * Q, (world.rank + 1) * Q):
k_c = self.fullkd.ibzk_kc[k]
for k1, k1_c in enumerate(kd.bzk_kc):
if abs(k1_c - k_c).max() < 1e-10:
break
# Index of symmetry related point in the irreducible BZ
ik = kd.kibz_k[k1]
kpt = self.kpt_u[ik]
# KPoint from ground-state calculation
phase_cd = np.exp(2j * pi * self.gd.sdisp_cd * k_c[:, np.newaxis])
kpt2 = KPoint0(kpt.weight, kpt.s, k, None, phase_cd)
kpt2.psit_nG = np.empty_like(kpt.psit_nG)
kpt2.f_n = kpt.f_n / kpt.weight / K * 2
for n, psit_G in enumerate(kpt2.psit_nG):
psit_G[:] = kd.transform_wave_function(kpt.psit_nG[n], k1)
kpt2.P_ani = self.pt.dict(len(kpt.psit_nG))
self.pt.integrate(kpt2.psit_nG, kpt2.P_ani, k)
kpt_u.append(kpt2)
for s in range(self.nspins):
kpt1_q = [KPoint(self.fullkd, kpt) for kpt in kpt_u if kpt.s == s]
kpt2_q = kpt1_q[:]
if len(kpt1_q) == 0:
# No s-spins on this CPU:
continue
# Send rank:
srank = self.fullkd.get_rank_and_index(s, (kpt1_q[0].k - 1) % K)[0]
# Receive rank:
rrank = self.fullkd.get_rank_and_index(s,
(kpt1_q[-1].k + 1) % K)[0]
# Shift k-points K // 2 times:
for i in range(K // 2 + 1):
if i < K // 2:
if parallel:
kpt = kpt2_q[-1].next()
kpt.start_receiving(rrank)
kpt2_q[0].start_sending(srank)
else:
kpt = kpt2_q[0]
for kpt1, kpt2 in zip(kpt1_q, kpt2_q):
if 2 * i == K:
self.apply(kpt1, kpt2, invert=(kpt1.k > kpt2.k))
else:
self.apply(kpt1, kpt2)
self.apply(kpt1, kpt2, invert=True)
if i < K // 2:
if parallel:
kpt.wait()
kpt2_q[0].wait()
kpt2_q.pop(0)
kpt2_q.append(kpt)
self.exx = world.sum(self.exx)
world.sum(self.exx_skn)
self.exx += self.calculate_paw_correction()
def apply(self, kpt1, kpt2, invert=False):
#print world.rank,kpt1.k,kpt2.k,invert
k1_c = self.fullkd.ibzk_kc[kpt1.k]
k2_c = self.fullkd.ibzk_kc[kpt2.k]
if invert:
k2_c = -k2_c
k12_c = k1_c - k2_c
N_c = self.gd.N_c
eikr_R = np.exp(2j * pi * np.dot(np.indices(N_c).T, k12_c / N_c).T)
for q, k_c in enumerate(self.bzk_kc):
if abs(k_c + k12_c).max() < 1e-9:
q0 = q
break
for q, k_c in enumerate(self.bzk_kc):
if abs(k_c - k12_c).max() < 1e-9:
q00 = q
break
Gpk2_G = self.pwd.G2_qG[q0]
if Gpk2_G[0] == 0:
Gpk2_G = Gpk2_G.copy()
Gpk2_G[0] = 1.0 / self.gamma
N = N_c.prod()
vol = self.gd.dv * N
nspins = self.nspins
same = (kpt1.k == kpt2.k)
for n1, psit1_R in enumerate(kpt1.psit_nG):
f1 = kpt1.f_n[n1]
for n2, psit2_R in enumerate(kpt2.psit_nG):
if same and n2 > n1:
continue
f2 = kpt2.f_n[n2]
nt_R = self.calculate_pair_density(n1, n2, kpt1, kpt2, q0,
invert)
nt_G = self.pwd.fft(nt_R * eikr_R) / N
vt_G = nt_G.copy()
vt_G *= -pi * vol / Gpk2_G
e = np.vdot(nt_G, vt_G).real * nspins * self.hybrid
if same and n1 == n2:
e /= 2
self.exx += e * f1 * f2
self.ekin -= 2 * e * f1 * f2
self.exx_skn[kpt1.s, kpt1.k, n1] += f2 * e
self.exx_skn[kpt2.s, kpt2.k, n2] += f1 * e
calculate_potential = not True
if calculate_potential:
vt_R = self.pwd.ifft(vt_G).conj() * eikr_R * N / vol
if kpt1 is kpt2 and not invert and n1 == n2:
kpt1.vt_nG[n1] = 0.5 * f1 * vt_R
if invert:
kpt1.Htpsit_nG[n1] += \
f2 * nspins * psit2_R.conj() * vt_R
else:
kpt1.Htpsit_nG[n1] += f2 * nspins * psit2_R * vt_R
if kpt1 is not kpt2:
if invert:
kpt2.Htpsit_nG[n2] += (f1 * nspins *
psit1_R.conj() * vt_R)
else:
kpt2.Htpsit_nG[n2] += (f1 * nspins * psit1_R *
vt_R.conj())
def calculate_paw_correction(self):
exx = 0
deg = 2 // self.nspins # spin degeneracy
for a, D_sp in self.density.D_asp.items():
setup = self.setups[a]
for D_p in D_sp:
D_ii = unpack2(D_p)
ni = len(D_ii)
for i1 in range(ni):
for i2 in range(ni):
A = 0.0
for i3 in range(ni):
p13 = packed_index(i1, i3, ni)
for i4 in range(ni):
p24 = packed_index(i2, i4, ni)
A += setup.M_pp[p13, p24] * D_ii[i3, i4]
p12 = packed_index(i1, i2, ni)
exx -= self.hybrid / deg * D_ii[i1, i2] * A
if setup.X_p is not None:
exx -= self.hybrid * np.dot(D_p, setup.X_p)
exx += self.hybrid * setup.ExxC
return exx
def calculate_pair_density(self, n1, n2, kpt1, kpt2, q, invert):
if invert:
nt_G = kpt1.psit_nG[n1].conj() * kpt2.psit_nG[n2].conj()
else:
nt_G = kpt1.psit_nG[n1].conj() * kpt2.psit_nG[n2]
Q_aL = {}
for a, P1_ni in kpt1.P_ani.items():
P1_i = P1_ni[n1]
P2_i = kpt2.P_ani[a][n2]
if invert:
D_ii = np.outer(P1_i.conj(), P2_i.conj())
else:
D_ii = np.outer(P1_i.conj(), P2_i)
D_p = pack(D_ii)
Q_aL[a] = np.dot(D_p, self.setups[a].Delta_pL)
self.ghat.add(nt_G, Q_aL, q)
return nt_G
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)
class TDDFT(object):
"""
Time-dependent DFT+Hartree-Fock in Kohn-Sham orbitals basis:
calc: GPAW calculator (setups='sg15')
nbands (int): number of bands in calculation
"""
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()
def get_dipole_matrix(self, direction=[1, 0, 0]):
"""
return two-dimensional numpy complex array of dipole matrix elements(
"""
direction /= np.linalg.norm(direction)
r = np.sum(direction[:, None, None, None] * self.r, axis=0)
dipole = np.zeros((self.NK, self.nbands, self.nbands),
dtype=np.complex)
dipole = operator_matrix_periodic(
dipole, r, self.ukn.conj(),
self.ukn) * self.norm #!!!!!! no direction
return dipole
def get_density(self, wavefunction):
"""
return numpy array of electron density in real space at each k-point of full Brillioun zone
wavefunction: numpy array [N_kpoint X N_band X N_band] of wavefunction in basis of Kohn-Sham orbital
"""
if wavefunction is None:
return self.density
density = np.zeros(self.shape, dtype=np.float)
for k in range(self.NK):
for n in range(self.nbands):
for m in range(self.nbands):
density += 2 * self.wk[k] * self.f[k, n] * np.abs(
wavefunction[k, m, n] * self.ukn[k, m])**2
return density
def get_Hartree_potential(self, wavefunction):
"""
return numpy array of Hartree potential in real space at each k-point of full Brillioun zone
wavefunction: numpy array [N_kpoint X N_band X N_band] of wavefunction in basis of Kohn-Sham orbital
"""
density = self.get_density(wavefunction)
VH = np.zeros(self.shape)
G = self.pdH.get_reciprocal_vectors()
G2 = np.linalg.norm(G, axis=1)**2
G2[G2 == 0] = np.inf
nG = self.pdH.fft(density)
return -4 * np.pi * self.pdH.ifft(nG / G2)
def get_coloumb_potential(self, q):
"""
return coloumb potential in plane wave space V= 4 pi /(|q+G|**2)
q: [qx,qy,qz] vector in units of reciprocal space
"""
G = self.pdF.get_reciprocal_vectors() + np.dot(q, self.icell)
G2 = np.linalg.norm(G, axis=1)**2
G2[G2 == 0] = np.inf
return 4 * np.pi / G2
def get_Hartree_matrix(self, wavefunction=None):
"""
return numpy array [N_kpoint X N_band X N_band] of Hartree potential matrix elements
wavefunction: numpy array [N_kpoint X N_band X N_band] of wavefunction in basis of Kohn-Sham orbital
"""
VH = self.get_Hartree_potential(wavefunction)
VH_matrix = np.zeros((self.NK, self.nbands, self.nbands),
dtype=np.complex)
VH_matrix = operator_matrix_periodic(VH_matrix, VH, self.ukn.conj(),
self.ukn) * self.norm
return VH_matrix
def get_Fock_matrix(self, wavefunction=None):
"""
return numpy array [N_kpoint X N_band X N_band] of Fock potential matrix elements
wavefunction: numpy array [N_kpoint X N_band X N_band] of wavefunction in basis of Kohn-Sham orbital
"""
VF_matrix = np.zeros((self.NK, self.nbands, self.nbands),
dtype=np.complex)
if self.Fock:
if wavefunction is None:
wavefunction = np.zeros((self.NK, self.nbands, self.nbands))
for k in range(self.NK):
wavefunction[k] = np.eye(self.nbands)
K = self.Full_BZ
NK = K.shape[0]
NG = self.pdF.get_reciprocal_vectors().shape[0]
V = np.zeros((self.NK, NK, NG))
for k in range(self.NK):
for q in range(NK):
kq = K[q] - self.K[k]
V[k, q] = self.get_coloumb_potential(kq)
VF_matrix = Fock_matrix(VF_matrix, V, self.M.conj(), self.M,
self.IBZ_map, self.nvalence)
return VF_matrix / self.volume
def get_LDA_exchange_matrix(self, wavefunction=None):
"""
return numpy array [N_kpoint X N_band X N_band] of LDA exchange potential matrix elements
wavefunction: numpy array [N_kpoint X N_band X N_band] of wavefunction in basis of Kohn-Sham orbital
"""
density = self.get_density(wavefunction)
exchange = xc.VLDAx(density)
LDAx_matrix = np.zeros((self.NK, self.nbands, self.nbands),
dtype=np.complex)
LDAx_matrix = operator_matrix_periodic(
LDAx_matrix, exchange, self.ukn.conj(), self.ukn) * self.norm
return LDAx_matrix
def get_LDA_correlation_matrix(self, wavefunction=None):
"""
return numpy array [N_kpoint X N_band X N_band] of LDA correlation potential matrix elements
wavefunction: numpy array [N_kpoint X N_band X N_band] of wavefunction in basis of Kohn-Sham orbital
"""
density = self.get_density(wavefunction)
correlation = xc.VLDAc(density)
LDAc_matrix = np.zeros((self.NK, self.nbands, self.nbands),
dtype=np.complex)
LDAc_matrix = operator_matrix_periodic(
LDAc_matrix, correlation, self.ukn.conj(), self.ukn) * self.norm
return LDAc_matrix
def occupation(self, wavefunction):
return 2 * np.sum(self.wk[:, None, None] * self.f[:, None, :] *
np.abs(wavefunction)**2,
axis=2)
def fast_Hartree_matrix(self, wavefunction):
return np.einsum('kn,knqij->qij', self.occupation(wavefunction),
self.Hartree_elements) - self.VH0
def fast_LDA_correlation_matrix(self, wavefunction):
return np.einsum('kn,knqij->qij', self.occupation(wavefunction),
self.LDAc_elements) - self.VLDAc0
def fast_LDA_exchange_matrix(self, wavefunction):
return np.einsum('kn,knqij->qij', self.occupation(wavefunction),
self.LDAx_elements) - self.VLDAx0
def propagate(self, dt, steps, E, operator, corrections=10):
self.wavefunction = np.zeros((self.NK, self.nbands, self.nbands),
dtype=np.complex)
for k in range(self.NK):
self.wavefunction[k] = np.eye(self.nbands)
H = np.copy(self.Kinetic) + E[0] * self.dipole
operator_macro = np.array(
[operator[k].diagonal() for k in range(self.NK)])
self.macro_dipole = np.zeros(steps, dtype=np.complex)
for t in tqdm(range(steps)):
wavefunction_next = np.copy(self.wavefunction)
error = np.inf
while error > 1e-8:
wavefunction_check = np.copy(wavefunction_next)
H_next = self.Kinetic + E[t] * self.dipole
H_next += self.fast_Hartree_matrix(wavefunction_next)
H_next += self.fast_LDA_correlation_matrix(wavefunction_next)
H_next += self.fast_LDA_exchange_matrix(wavefunction_next)
H_mid = 0.5 * (H + H_next)
for k in range(self.NK):
H_left = np.eye(self.nbands) + 0.5j * dt * H_mid[k]
H_right = np.eye(self.nbands) - 0.5j * dt * H_mid[k]
wavefunction_next[k] = linalg.solve(
H_left, H_right @ self.wavefunction[k])
error = np.abs(np.sum(wavefunction_next - wavefunction_check))
self.wavefunction = np.copy(wavefunction_next)
H = np.copy(H_next)
self.macro_dipole[t] = np.sum(
self.occupation(self.wavefunction) * operator_macro)
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):
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)}
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()
class HybridXC(XCFunctional):
orbital_dependent = True
def __init__(
self,
name,
hybrid=None,
xc=None,
finegrid=False,
alpha=None,
skip_gamma=False,
gygi=False,
acdf=True,
qsym=True,
txt=None,
ecut=None,
):
"""Mix standard functionals with exact exchange.
name: str
Name of hybrid functional.
hybrid: float
Fraction of exact exchange.
xc: str or XCFunctional object
Standard DFT functional with scaled down exchange.
finegrid: boolean
Use fine grid for energy functional evaluations?
"""
if name == "EXX":
assert hybrid is None and xc is None
hybrid = 1.0
xc = XC(XCNull())
elif name == "PBE0":
assert hybrid is None and xc is None
hybrid = 0.25
xc = XC("HYB_GGA_XC_PBEH")
elif name == "B3LYP":
assert hybrid is None and xc is None
hybrid = 0.2
xc = XC("HYB_GGA_XC_B3LYP")
if isinstance(xc, str):
xc = XC(xc)
self.hybrid = hybrid
self.xc = xc
self.type = xc.type
self.alpha = alpha
self.qsym = qsym
self.skip_gamma = skip_gamma
self.gygi = gygi
self.acdf = acdf
self.exx = None
self.ecut = ecut
if txt is None:
if rank == 0:
# self.txt = devnull
self.txt = sys.stdout
else:
sys.stdout = devnull
self.txt = devnull
else:
assert type(txt) is str
from ase.parallel import paropen
self.txt = paropen(txt, "w")
XCFunctional.__init__(self, name)
def get_setup_name(self):
return "PBE"
def calculate_radial(self, rgd, n_sLg, Y_L, v_sg, dndr_sLg=None, rnablaY_Lv=None, tau_sg=None, dedtau_sg=None):
return self.xc.calculate_radial(rgd, n_sLg, Y_L, v_sg, dndr_sLg, rnablaY_Lv)
def calculate_paw_correction(self, setup, D_sp, dEdD_sp=None, addcoredensity=True, a=None):
return self.xc.calculate_paw_correction(setup, D_sp, dEdD_sp, addcoredensity, a)
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 set_positions(self, spos_ac):
self.ghat.set_positions(spos_ac)
self.spos_ac = spos_ac
def calculate(self, gd, n_sg, v_sg=None, e_g=None):
# Normal XC contribution:
exc = self.xc.calculate(gd, n_sg, v_sg, e_g)
# Add EXX contribution:
return exc + self.exx
def calculate_exx(self):
"""Non-selfconsistent calculation."""
kd = self.kd
K = len(kd.bzk_kc)
W = world.size // self.nspins
parallel = W > 1
self.exx = 0.0
self.exx_kq = np.zeros((K, len(self.ibzq_qc)), float)
for s in range(self.nspins):
ibz_kpts = [KPoint(kd, kpt) for kpt in self.kpt_u if kpt.s == s]
for ik, kpt in enumerate(kd.bzk_kc):
print >>self.txt, "K %s %s ..." % (ik, kpt)
for iq, q in enumerate(self.ibzq_qc):
kpq = kd.find_k_plus_q(q, kpts_k=[ik])
self.apply(ibz_kpts[kd.bz2ibz_k[ik]], ibz_kpts[kd.bz2ibz_k[kpq[0]]], ik, kpq[0], iq)
self.exx = world.sum(self.exx)
self.exx += self.calculate_exx_paw_correction()
exx_q = np.sum(self.exx_kq, 0)
print >>self.txt
print >>self.txt, "------------------------------------------------------"
print >>self.txt
print >>self.txt, "Contributions: q w E_q (eV)"
for q in range(len(exx_q)):
print >>self.txt, "[%1.3f %1.3f %1.3f] %1.3f %s" % (
self.ibzq_qc[q][0],
self.ibzq_qc[q][1],
self.ibzq_qc[q][2],
self.q_weights[q] / len(self.bzq_qc),
exx_q[q] / self.q_weights[q] * len(self.bzq_qc) * Ha,
)
print >>self.txt, "E_EXX = %s eV" % (self.exx * Ha)
print >>self.txt
print >>self.txt, "Calculation completed at: ", ctime()
print >>self.txt
print >>self.txt, "------------------------------------------------------"
print >>self.txt
def apply(self, kpt1, kpt2, ik1, ik2, iq):
k1_c = self.kd.bzk_kc[ik1]
k2_c = self.kd.bzk_kc[ik2]
q = self.ibzq_qc[iq]
if self.qsym:
for i, q in enumerate(self.bzq_qc):
if abs(q - self.ibzq_qc[iq]).max() < 1e-9:
bzq_index = i
break
else:
bzq_index = iq
N_c = self.gd.N_c
eikr_R = np.exp(-2j * pi * np.dot(np.indices(N_c).T, q / N_c).T)
Gamma = abs(q).max() < 1e-9
if Gamma and self.skip_gamma:
return
Gpk2_G = self.G2_qG[iq]
if Gamma:
Gpk2_G = Gpk2_G.copy()
Gpk2_G[0] = 1.0 / self.gamma
N = N_c.prod()
vol = self.gd.dv * N
nspins = self.nspins
fcut = 1e-10
for n1, psit1_R in enumerate(kpt1.psit_nG):
f1 = kpt1.f_n[n1]
for n2, psit2_R in enumerate(kpt2.psit_nG):
if self.acdf:
if self.gygi and Gamma:
# print n2, kpt2.f_n[n2]/kpt2.weight
f2 = self.q_weights[iq] * kpt2.weight
else:
f2 = self.q_weights[iq] * kpt2.weight * (1 - np.sign(kpt2.eps_n[n2] - kpt1.eps_n[n1]))
else:
f2 = kpt2.f_n[n2] * self.q_weights[iq]
if abs(f1) < fcut or abs(f2) < fcut:
continue
nt_R = self.calculate_pair_density(n1, n2, kpt1, kpt2, ik1, ik2, bzq_index)
nt_G = self.pwd.fft(nt_R * eikr_R) / N
vt_G = nt_G.copy()
vt_G *= -pi * vol / Gpk2_G
e = np.vdot(nt_G, vt_G).real * nspins * self.hybrid
self.exx += f1 * f2 * e
self.exx_kq[ik1, iq] += f1 * f2 * e
def calculate_pair_density(self, n1, n2, kpt1, kpt2, ik1, ik2, bzq_index):
psit1_G = self.kd.transform_wave_function(kpt1.psit_nG[n1], ik1)
psit2_G = self.kd.transform_wave_function(kpt2.psit_nG[n2], ik2)
nt_G = psit1_G.conj() * psit2_G
s1 = self.kd.sym_k[ik1]
s2 = self.kd.sym_k[ik2]
t1 = self.kd.time_reversal_k[ik1]
t2 = self.kd.time_reversal_k[ik2]
k1_c = self.kd.ibzk_kc[kpt1.k]
k2_c = self.kd.ibzk_kc[kpt2.k]
Q_aL = {}
for a in kpt1.P_ani.keys():
b1 = self.kd.symmetry.a_sa[s1, a]
b2 = self.kd.symmetry.a_sa[s2, a]
S1_c = np.dot(self.spos_ac[a], self.kd.symmetry.op_scc[s1]) - self.spos_ac[b1]
S2_c = np.dot(self.spos_ac[a], self.kd.symmetry.op_scc[s2]) - self.spos_ac[b2]
assert abs(S1_c.round() - S1_c).max() < 1e-13
assert abs(S2_c.round() - S2_c).max() < 1e-13
x1 = np.exp(2j * pi * np.dot(k1_c, S1_c))
x2 = np.exp(2j * pi * np.dot(k2_c, S2_c))
P1_i = np.dot(self.setups[a].R_sii[s1], kpt1.P_ani[b1][n1]) * x1
P2_i = np.dot(self.setups[a].R_sii[s2], kpt2.P_ani[b2][n2]) * x2
if t1:
P1_i = P1_i.conj()
if t2:
P2_i = P2_i.conj()
D_ii = np.outer(P1_i.conj(), P2_i)
D_p = pack(D_ii)
Q_aL[a] = np.dot(D_p, self.setups[a].Delta_pL)
self.ghat.add(nt_G, Q_aL, bzq_index)
return nt_G
def calculate_exx_paw_correction(self):
exx = 0
deg = 2 // self.nspins # spin degeneracy
for a, D_sp in self.density.D_asp.items():
setup = self.setups[a]
for D_p in D_sp:
D_ii = unpack2(D_p)
ni = len(D_ii)
for i1 in range(ni):
for i2 in range(ni):
A = 0.0
for i3 in range(ni):
p13 = packed_index(i1, i3, ni)
for i4 in range(ni):
p24 = packed_index(i2, i4, ni)
A += setup.M_pp[p13, p24] * D_ii[i3, i4]
p12 = packed_index(i1, i2, ni)
exx -= self.hybrid / deg * D_ii[i1, i2] * A
if setup.X_p is not None:
exx -= self.hybrid * np.dot(D_p, setup.X_p)
exx += self.hybrid * setup.ExxC
return exx
def print_initialization(self, xc):
print >>self.txt, "------------------------------------------------------"
print >>self.txt, "Non-self-consistent HF correlation energy"
print >>self.txt, "------------------------------------------------------"
print >>self.txt, "Started at: ", ctime()
print >>self.txt
print >>self.txt, "Ground state XC functional : %s" % xc
print >>self.txt, "Valence electrons : %s" % self.setups.nvalence
print >>self.txt, "Number of Spins : %s" % self.nspins
print >>self.txt, "Plane wave cutoff energy : %4.1f eV" % (self.ecut * Ha)
print >>self.txt, "Gamma q-point excluded : %s" % self.skip_gamma
if not self.skip_gamma:
print >>self.txt, "Alpha parameter : %s" % self.alpha
print >>self.txt, "Gamma parameter : %3.3f" % self.gamma
print >>self.txt, "ACDF method : %s" % self.acdf
print >>self.txt, "Number of k-points : %s" % len(self.kd.bzk_kc)
print >>self.txt, "Number of Irreducible k-points : %s" % len(self.kd.ibzk_kc)
print >>self.txt, "Number of q-points : %s" % len(self.bzq_qc)
if not self.qsym:
print >>self.txt, "q-point symmetry : %s" % self.qsym
else:
print >>self.txt, "Number of Irreducible q-points : %s" % len(self.ibzq_qc)
print >>self.txt
for q, weight in zip(self.ibzq_qc, self.q_weights):
print >>self.txt, "q: [%1.3f %1.3f %1.3f] - weight: %1.3f" % (q[0], q[1], q[2], weight / len(self.bzq_qc))
print >>self.txt
print >>self.txt, "------------------------------------------------------"
print >>self.txt, "------------------------------------------------------"
print >>self.txt
print >>self.txt, "Looping over k-points in the full Brillouin zone"
print >>self.txt
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)
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 __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()
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)
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),
np.arange(0, nb))
momentum[i, :, :, :] = n_nmvG[..., 0][:nb, :nb, :]
np.save(output_directory + case + ".gpaw.momentum.npy", momentum)
hdf5 = h5py.File(output_directory.rstrip('/') + '.hdf5', 'w')
dset_energy = hdf5.create_dataset("energy", data=energy)
class TDDFT(object):
"""
Time-dependent DFT+Hartree-Fock in Kohn-Sham orbitals basis:
calc: GPAW calculator (setups='sg15')
nbands (int): number of bands in calculation
"""
def __init__(self,calc,nbands=None):
self.calc=calc
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.kd=KPointDescriptor([[0,0,0]])
self.pd=PWDescriptor(ecut=calc.wfs.pd.ecut,gd=calc.wfs.gd,kd=self.kd,dtype=complex)
#Fermi-Dirac temperature
self.temperature=calc.occupations.width
#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.pd.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=self.norm*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.pd.fft(density)
operator=4*np.pi*self.pd.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)
for k in range(self.NK):
self.wavefunction[k]=np.eye(self.nbands)
self.Kinetic[k]=np.diag(self.EK[k])
self.VH0=np.einsum('kn,knqij->qij',self.occupation(self.wavefunction),self.Hartree_elements)
self.VLDAc0=np.einsum('kn,knqij->qij',self.occupation(self.wavefunction),self.LDAc_elements)
self.VLDAx0=np.einsum('kn,knqij->qij',self.occupation(self.wavefunction),self.LDAx_elements)
self.Full_BZ=calc.get_bz_k_points()
self.IBZ_map=calc.get_bz_to_ibz_map()
def get_transition_matrix(self,direction):
direction/=np.linalg.norm(direction)
self.dipole=np.zeros((self.NK,self.nbands,self.nbands),dtype=np.complex)
for k in range(self.NK):
kpt = self.calc.wfs.kpt_u[k]
G=self.calc.wfs.pd.get_reciprocal_vectors(q=k,add_q=True)
G=np.sum(G*direction[None,:],axis=1)
for n in range(self.nvalence):
for m in range(self.nvalence,self.nbands):
wfn=kpt.psit_nG[n];wfm=kpt.psit_nG[m]
self.dipole[k,n,m]=self.calc.wfs.pd.integrate(wfm,G*wfn)/(self.EK[k,n]-self.EK[k,m])
self.dipole[k,m,n]=self.dipole[k,n,m].conj()
return self.dipole
def occupation(self,wavefunction):
return 2*np.sum(self.wk[:,None,None]*self.f[:,None,:]*np.abs(wavefunction)**2,axis=2)
def fast_Hartree_matrix(self,wavefunction):
return np.einsum('kn,knqij->qij',self.occupation(wavefunction),self.Hartree_elements)-self.VH0
def fast_LDA_correlation_matrix(self,wavefunction):
return np.einsum('kn,knqij->qij',self.occupation(wavefunction),self.LDAc_elements)-self.VLDAc0
def fast_LDA_exchange_matrix(self,wavefunction):
return np.einsum('kn,knqij->qij',self.occupation(wavefunction),self.LDAx_elements)-self.VLDAx0
def propagate(self,dt,steps,E,direction,corrections=10):
dipole=self.get_transition_matrix(direction)
self.time_occupation=np.zeros((steps,self.nbands),dtype=np.complex)
self.polarization=np.zeros(steps,dtype=np.complex)
self.time_occupation[0]=np.sum(self.occupation(self.wavefunction),axis=0)
for k in range(self.NK):
operator=np.linalg.multi_dot([self.wavefunction[k].T.conj(),dipole[k],self.wavefunction[k]])
self.polarization[0]+=self.wk[k]*np.sum(operator.diagonal())
for t in tqdm(range(1,steps)):
H = self.Kinetic+E[t]*self.dipole
H+= self.fast_Hartree_matrix(self.wavefunction)
H+= self.fast_LDA_correlation_matrix(self.wavefunction)
H+= self.fast_LDA_exchange_matrix(self.wavefunction)
for k in range(self.NK):
H_left = np.eye(self.nbands)+0.5j*dt*H[k]
H_right= np.eye(self.nbands)-0.5j*dt*H[k]
self.wavefunction[k]=linalg.solve(H_left, [email protected][k])
operator=np.linalg.multi_dot([self.wavefunction[k].T.conj(),dipole[k],self.wavefunction[k]])
self.polarization[t]+=self.wk[k]*np.sum(operator.diagonal())
self.time_occupation[t]=np.sum(self.occupation(self.wavefunction),axis=0)
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)
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))}
class HybridXC(XCFunctional):
orbital_dependent = True
def __init__(self,
name,
hybrid=None,
xc=None,
finegrid=False,
alpha=None,
skip_gamma=False,
gygi=False,
acdf=True,
qsym=True,
txt=None,
ecut=None):
"""Mix standard functionals with exact exchange.
name: str
Name of hybrid functional.
hybrid: float
Fraction of exact exchange.
xc: str or XCFunctional object
Standard DFT functional with scaled down exchange.
finegrid: boolean
Use fine grid for energy functional evaluations?
"""
if name == 'EXX':
assert hybrid is None and xc is None
hybrid = 1.0
xc = XC(XCNull())
elif name == 'PBE0':
assert hybrid is None and xc is None
hybrid = 0.25
xc = XC('HYB_GGA_XC_PBEH')
elif name == 'B3LYP':
assert hybrid is None and xc is None
hybrid = 0.2
xc = XC('HYB_GGA_XC_B3LYP')
if isinstance(xc, str):
xc = XC(xc)
self.hybrid = hybrid
self.xc = xc
self.type = xc.type
self.alpha = alpha
self.qsym = qsym
self.skip_gamma = skip_gamma
self.gygi = gygi
self.acdf = acdf
self.exx = None
self.ecut = ecut
if txt is None:
if rank == 0:
#self.txt = devnull
self.txt = sys.stdout
else:
sys.stdout = devnull
self.txt = devnull
else:
assert type(txt) is str
from ase.parallel import paropen
self.txt = paropen(txt, 'w')
XCFunctional.__init__(self, name)
def get_setup_name(self):
return 'PBE'
def calculate_radial(self,
rgd,
n_sLg,
Y_L,
v_sg,
dndr_sLg=None,
rnablaY_Lv=None,
tau_sg=None,
dedtau_sg=None):
return self.xc.calculate_radial(rgd, n_sLg, Y_L, v_sg, dndr_sLg,
rnablaY_Lv)
def calculate_paw_correction(self,
setup,
D_sp,
dEdD_sp=None,
addcoredensity=True,
a=None):
return self.xc.calculate_paw_correction(setup, D_sp, dEdD_sp,
addcoredensity, a)
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 set_positions(self, spos_ac):
self.ghat.set_positions(spos_ac)
self.spos_ac = spos_ac
def calculate(self, gd, n_sg, v_sg=None, e_g=None):
# Normal XC contribution:
exc = self.xc.calculate(gd, n_sg, v_sg, e_g)
# Add EXX contribution:
return exc + self.exx
def calculate_exx(self):
"""Non-selfconsistent calculation."""
kd = self.kd
K = len(kd.bzk_kc)
W = world.size // self.nspins
parallel = (W > 1)
self.exx = 0.0
self.exx_kq = np.zeros((K, len(self.ibzq_qc)), float)
for s in range(self.nspins):
ibz_kpts = [KPoint(kd, kpt) for kpt in self.kpt_u if kpt.s == s]
for ik, kpt in enumerate(kd.bzk_kc):
print('K %s %s ...' % (ik, kpt), file=self.txt)
for iq, q in enumerate(self.ibzq_qc):
kpq = kd.find_k_plus_q(q, kpts_k=[ik])
self.apply(ibz_kpts[kd.bz2ibz_k[ik]],
ibz_kpts[kd.bz2ibz_k[kpq[0]]], ik, kpq[0], iq)
self.exx = world.sum(self.exx)
self.exx += self.calculate_exx_paw_correction()
exx_q = np.sum(self.exx_kq, 0)
print(file=self.txt)
print('------------------------------------------------------',
file=self.txt)
print(file=self.txt)
print('Contributions: q w E_q (eV)', file=self.txt)
for q in range(len(exx_q)):
print('[%1.3f %1.3f %1.3f] %1.3f %s' % \
(self.ibzq_qc[q][0], self.ibzq_qc[q][1], self.ibzq_qc[q][2],
self.q_weights[q]/len(self.bzq_qc),
exx_q[q]/self.q_weights[q]*len(self.bzq_qc)*Ha), file=self.txt)
print('E_EXX = %s eV' % (self.exx * Ha), file=self.txt)
print(file=self.txt)
print('Calculation completed at: ', ctime(), file=self.txt)
print(file=self.txt)
print('------------------------------------------------------',
file=self.txt)
print(file=self.txt)
def apply(self, kpt1, kpt2, ik1, ik2, iq):
k1_c = self.kd.bzk_kc[ik1]
k2_c = self.kd.bzk_kc[ik2]
q = self.ibzq_qc[iq]
if self.qsym:
for i, q in enumerate(self.bzq_qc):
if abs(q - self.ibzq_qc[iq]).max() < 1e-9:
bzq_index = i
break
else:
bzq_index = iq
N_c = self.gd.N_c
eikr_R = np.exp(-2j * pi * np.dot(np.indices(N_c).T, q / N_c).T)
Gamma = abs(q).max() < 1e-9
if Gamma and self.skip_gamma:
return
Gpk2_G = self.G2_qG[iq]
if Gamma:
Gpk2_G = Gpk2_G.copy()
Gpk2_G[0] = 1.0 / self.gamma
N = N_c.prod()
vol = self.gd.dv * N
nspins = self.nspins
fcut = 1e-10
for n1, psit1_R in enumerate(kpt1.psit_nG):
f1 = kpt1.f_n[n1]
for n2, psit2_R in enumerate(kpt2.psit_nG):
if self.acdf:
if self.gygi and Gamma:
#print n2, kpt2.f_n[n2]/kpt2.weight
f2 = (self.q_weights[iq] * kpt2.weight)
else:
f2 = (self.q_weights[iq] * kpt2.weight *
(1 - np.sign(kpt2.eps_n[n2] - kpt1.eps_n[n1])))
else:
f2 = kpt2.f_n[n2] * self.q_weights[iq]
if abs(f1) < fcut or abs(f2) < fcut:
continue
nt_R = self.calculate_pair_density(n1, n2, kpt1, kpt2, ik1,
ik2, bzq_index)
nt_G = self.pwd.fft(nt_R * eikr_R) / N
vt_G = nt_G.copy()
vt_G *= -pi * vol / Gpk2_G
e = np.vdot(nt_G, vt_G).real * nspins * self.hybrid
self.exx += f1 * f2 * e
self.exx_kq[ik1, iq] += f1 * f2 * e
def calculate_pair_density(self, n1, n2, kpt1, kpt2, ik1, ik2, bzq_index):
psit1_G = self.kd.transform_wave_function(kpt1.psit_nG[n1], ik1)
psit2_G = self.kd.transform_wave_function(kpt2.psit_nG[n2], ik2)
nt_G = psit1_G.conj() * psit2_G
s1 = self.kd.sym_k[ik1]
s2 = self.kd.sym_k[ik2]
t1 = self.kd.time_reversal_k[ik1]
t2 = self.kd.time_reversal_k[ik2]
k1_c = self.kd.ibzk_kc[kpt1.k]
k2_c = self.kd.ibzk_kc[kpt2.k]
Q_aL = {}
for a in kpt1.P_ani.keys():
b1 = self.kd.symmetry.a_sa[s1, a]
b2 = self.kd.symmetry.a_sa[s2, a]
S1_c = (np.dot(self.spos_ac[a], self.kd.symmetry.op_scc[s1]) -
self.spos_ac[b1])
S2_c = (np.dot(self.spos_ac[a], self.kd.symmetry.op_scc[s2]) -
self.spos_ac[b2])
assert abs(S1_c.round() - S1_c).max() < 1e-13
assert abs(S2_c.round() - S2_c).max() < 1e-13
x1 = np.exp(2j * pi * np.dot(k1_c, S1_c))
x2 = np.exp(2j * pi * np.dot(k2_c, S2_c))
P1_i = np.dot(self.setups[a].R_sii[s1], kpt1.P_ani[b1][n1]) * x1
P2_i = np.dot(self.setups[a].R_sii[s2], kpt2.P_ani[b2][n2]) * x2
if t1:
P1_i = P1_i.conj()
if t2:
P2_i = P2_i.conj()
D_ii = np.outer(P1_i.conj(), P2_i)
D_p = pack(D_ii)
Q_aL[a] = np.dot(D_p, self.setups[a].Delta_pL)
self.ghat.add(nt_G, Q_aL, bzq_index)
return nt_G
def calculate_exx_paw_correction(self):
exx = 0
deg = 2 // self.nspins # spin degeneracy
for a, D_sp in self.density.D_asp.items():
setup = self.setups[a]
for D_p in D_sp:
D_ii = unpack2(D_p)
ni = len(D_ii)
for i1 in range(ni):
for i2 in range(ni):
A = 0.0
for i3 in range(ni):
p13 = packed_index(i1, i3, ni)
for i4 in range(ni):
p24 = packed_index(i2, i4, ni)
A += setup.M_pp[p13, p24] * D_ii[i3, i4]
p12 = packed_index(i1, i2, ni)
exx -= self.hybrid / deg * D_ii[i1, i2] * A
if setup.X_p is not None:
exx -= self.hybrid * np.dot(D_p, setup.X_p)
exx += self.hybrid * setup.ExxC
return exx
def print_initialization(self, xc):
print('------------------------------------------------------',
file=self.txt)
print('Non-self-consistent HF correlation energy', file=self.txt)
print('------------------------------------------------------',
file=self.txt)
print('Started at: ', ctime(), file=self.txt)
print(file=self.txt)
print('Ground state XC functional : %s' % xc, file=self.txt)
print('Valence electrons : %s' % self.setups.nvalence,
file=self.txt)
print('Number of Spins : %s' % self.nspins,
file=self.txt)
print('Plane wave cutoff energy : %4.1f eV' % (self.ecut * Ha),
file=self.txt)
print('Gamma q-point excluded : %s' % self.skip_gamma,
file=self.txt)
if not self.skip_gamma:
print('Alpha parameter : %s' % self.alpha,
file=self.txt)
print('Gamma parameter : %3.3f' % self.gamma,
file=self.txt)
print('ACDF method : %s' % self.acdf,
file=self.txt)
print('Number of k-points : %s' % len(self.kd.bzk_kc),
file=self.txt)
print('Number of Irreducible k-points : %s' % len(self.kd.ibzk_kc),
file=self.txt)
print('Number of q-points : %s' % len(self.bzq_qc),
file=self.txt)
if not self.qsym:
print('q-point symmetry : %s' % self.qsym,
file=self.txt)
else:
print('Number of Irreducible q-points : %s' % len(self.ibzq_qc),
file=self.txt)
print(file=self.txt)
for q, weight in zip(self.ibzq_qc, self.q_weights):
print('q: [%1.3f %1.3f %1.3f] - weight: %1.3f' % \
(q[0],q[1],q[2], weight/len(self.bzq_qc)), file=self.txt)
print(file=self.txt)
print('------------------------------------------------------',
file=self.txt)
print('------------------------------------------------------',
file=self.txt)
print(file=self.txt)
print('Looping over k-points in the full Brillouin zone',
file=self.txt)
print(file=self.txt)
class HybridXC(HybridXCBase):
orbital_dependent = True
def __init__(self, name, hybrid=None, xc=None,
alpha=None,
gamma_point=1,
method='standard',
bandstructure=False,
logfilename='-', bands=None,
fcut=1e-10,
molecule=False,
qstride=1,
world=None):
"""Mix standard functionals with exact exchange.
name: str
Name of functional: EXX, PBE0, HSE03, HSE06
hybrid: float
Fraction of exact exchange.
xc: str or XCFunctional object
Standard DFT functional with scaled down exchange.
method: str
Use 'standard' standard formula and 'acdf for
adiabatic-connection dissipation fluctuation formula.
alpha: float
XXX describe
gamma_point: bool
0: Skip k2-k1=0 interactions.
1: Use the alpha method.
2: Integrate the gamma point.
bandstructure: bool
Calculate bandstructure instead of just the total energy.
bands: list of int
List of bands to calculate bandstructure for. Default is
all bands.
molecule: bool
Decouple electrostatic interactions between periodically
repeated images.
fcut: float
Threshold for empty band.
"""
self.alpha = alpha
self.fcut = fcut
self.gamma_point = gamma_point
self.method = method
self.bandstructure = bandstructure
self.bands = bands
self.fd = logfilename
self.write_timing_information = True
HybridXCBase.__init__(self, name, hybrid, xc)
# EXX energies:
self.exx = None # total
self.evv = None # valence-valence (pseudo part)
self.evvacdf = None # valence-valence (pseudo part)
self.devv = None # valence-valence (PAW correction)
self.evc = None # valence-core
self.ecc = None # core-core
self.exx_skn = None # bandstructure
self.qlatest = None
if world is None:
world = mpi.world
self.world = world
self.molecule = molecule
if isinstance(qstride, int):
qstride = [qstride] * 3
self.qstride_c = np.asarray(qstride)
self.timer = Timer()
def log(self, *args, **kwargs):
prnt(file=self.fd, *args, **kwargs)
self.fd.flush()
def calculate_radial(self, rgd, n_sLg, Y_L, v_sg,
dndr_sLg=None, rnablaY_Lv=None,
tau_sg=None, dedtau_sg=None):
return self.xc.calculate_radial(rgd, n_sLg, Y_L, v_sg,
dndr_sLg, rnablaY_Lv)
def calculate_paw_correction(self, setup, D_sp, dEdD_sp=None,
addcoredensity=True, a=None):
return self.xc.calculate_paw_correction(setup, D_sp, dEdD_sp,
addcoredensity, a)
def initialize(self, dens, ham, wfs, occupations):
assert wfs.bd.comm.size == 1
self.xc.initialize(dens, ham, wfs, occupations)
self.dens = dens
self.wfs = wfs
# Make a k-point descriptor that is not distributed
# (self.kd.comm is serial_comm):
self.kd = wfs.kd.copy()
self.fd = logfile(self.fd, self.world.rank)
wfs.initialize_wave_functions_from_restart_file()
def set_positions(self, spos_ac):
self.spos_ac = spos_ac
def calculate(self, gd, n_sg, v_sg=None, e_g=None):
# Normal XC contribution:
exc = self.xc.calculate(gd, n_sg, v_sg, e_g)
# Add EXX contribution:
return exc + self.exx * self.hybrid
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)
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 indices(self, s, k1, k2):
"""Generator for (K2, q, n1, n2) indices for (k1, k2) pair.
s: int
Spin index.
k1: int
Index of k-point in the IBZ.
k2: int
Index of k-point in the IBZ.
Returns (K, q, n1_n, n2), where K then index of the k-point in
the BZ that k2 is mapped to, q is the index of the q-vector
between K and k1, and n1_n is a list of bands that should be
combined with band n2."""
for K, k in enumerate(self.kd.bz2ibz_k):
if k == k2:
for K, q, n1_n, n2 in self._indices(s, k1, k2, K):
yield K, q, n1_n, n2
def _indices(self, s, k1, k2, K2):
k1_c = self.kd.ibzk_kc[k1]
k2_c = self.kd.bzk_kc[K2]
q_c = k2_c - k1_c
q = abs(self.bzq_qc - q_c).sum(1).argmin()
if abs(self.bzq_qc[q] - q_c).sum() > 1e-7:
return
if self.gamma_point == 0 and q == self.q0:
return
nocc1 = self.nocc_sk[s, k1]
nocc2 = self.nocc_sk[s, k2]
# Is k2 in the IBZ?
is_ibz2 = (self.kd.ibz2bz_k[k2] == K2)
for n2 in range(self.wfs.bd.nbands):
# Find range of n1's (from n1a to n1b-1):
if is_ibz2:
# We get this combination twice, so let's only do half:
if k1 >= k2:
n1a = n2
else:
n1a = n2 + 1
else:
n1a = 0
n1b = self.wfs.bd.nbands
if self.bandstructure:
if n2 >= nocc2:
n1b = min(n1b, nocc1)
else:
if n2 >= nocc2:
break
n1b = min(n1b, nocc1)
if self.bands is not None:
assert self.bandstructure
n1_n = []
for n1 in range(n1a, n1b):
if (n1 in self.bands and n2 < nocc2 or
is_ibz2 and n2 in self.bands and n1 < nocc1):
n1_n.append(n1)
n1_n = np.array(n1_n)
else:
n1_n = np.arange(n1a, n1b)
if len(n1_n) == 0:
continue
yield K2, q, n1_n, n2
def apply(self, K2, q, kpt1, kpt2, n1_n, n2):
k20_c = self.kd.ibzk_kc[kpt2.k]
k2_c = self.kd.bzk_kc[K2]
if k2_c.any():
self.timer.start('Initialize plane waves')
eik2r_R = self.wfs.gd.plane_wave(k2_c)
eik20r_R = self.wfs.gd.plane_wave(k20_c)
self.timer.stop('Initialize plane waves')
else:
eik2r_R = 1.0
eik20r_R = 1.0
w1 = self.kd.weight_k[kpt1.k]
w2 = self.kd.weight_k[kpt2.k]
# Is k2 in the 1. BZ?
is_ibz2 = (self.kd.ibz2bz_k[kpt2.k] == K2)
e_n = self.calculate_interaction(n1_n, n2, kpt1, kpt2, q, K2,
eik20r_R, eik2r_R,
is_ibz2)
e_n *= 1.0 / self.kd.nbzkpts / self.wfs.nspins * self.qstride_c.prod()
if q == self.q0:
e_n[n1_n == n2] *= 0.5
f1_n = kpt1.f_n[n1_n]
eps1_n = kpt1.eps_n[n1_n]
f2 = kpt2.f_n[n2]
eps2 = kpt2.eps_n[n2]
s_n = np.sign(eps2 - eps1_n)
evv = (f1_n * f2 * e_n).sum()
evvacdf = 0.5 * (f1_n * (1 - s_n) * e_n +
f2 * (1 + s_n) * e_n).sum()
self.evv += evv * w1
self.evvacdf += evvacdf * w1
if is_ibz2:
self.evv += evv * w2
self.evvacdf += evvacdf * w2
if self.bandstructure:
x = self.wfs.nspins
self.exx_skn[kpt1.s, kpt1.k, n1_n] += x * f2 * e_n
if is_ibz2:
self.exx_skn[kpt2.s, kpt2.k, n2] += x * np.dot(f1_n, e_n)
def calculate_interaction(self, n1_n, n2, kpt1, kpt2, q, k,
eik20r_R, eik2r_R, is_ibz2):
"""Calculate Coulomb interactions.
For all n1 in the n1_n list, calculate interaction with n2."""
# number of plane waves:
ng1 = self.wfs.ng_k[kpt1.k]
ng2 = self.wfs.ng_k[kpt2.k]
# Transform to real space and apply symmetry operation:
self.timer.start('IFFT1')
if is_ibz2:
u2_R = self.pd.ifft(kpt2.psit_nG[n2, :ng2], kpt2.k)
else:
psit2_R = self.pd.ifft(kpt2.psit_nG[n2, :ng2], kpt2.k) * eik20r_R
self.timer.start('Symmetry transform')
u2_R = self.kd.transform_wave_function(psit2_R, k) / eik2r_R
self.timer.stop()
self.timer.stop()
# Calculate pair densities:
nt_nG = self.pd2.zeros(len(n1_n), q=q)
for n1, nt_G in zip(n1_n, nt_nG):
self.timer.start('IFFT2')
u1_R = self.pd.ifft(kpt1.psit_nG[n1, :ng1], kpt1.k)
self.timer.stop()
nt_R = u1_R.conj() * u2_R
self.timer.start('FFT')
nt_G[:] = self.pd2.fft(nt_R, q)
self.timer.stop()
s = self.kd.sym_k[k]
time_reversal = self.kd.time_reversal_k[k]
k2_c = self.kd.ibzk_kc[kpt2.k]
self.timer.start('Compensation charges')
Q_anL = {} # coefficients for shape functions
for a, P1_ni in kpt1.P_ani.items():
P1_ni = P1_ni[n1_n]
if is_ibz2:
P2_i = kpt2.P_ani[a][n2]
else:
b = self.kd.symmetry.a_sa[s, a]
S_c = (np.dot(self.spos_ac[a], self.kd.symmetry.op_scc[s]) -
self.spos_ac[b])
assert abs(S_c.round() - S_c).max() < 1e-5
if self.ghat.dtype == complex:
x = np.exp(2j * pi * np.dot(k2_c, S_c))
else:
x = 1.0
P2_i = np.dot(self.wfs.setups[a].R_sii[s],
kpt2.P_ani[b][n2]) * x
if time_reversal:
P2_i = P2_i.conj()
D_np = []
for P1_i in P1_ni:
D_ii = np.outer(P1_i.conj(), P2_i)
D_np.append(pack(D_ii))
Q_anL[a] = np.dot(D_np, self.wfs.setups[a].Delta_pL)
self.timer.start('Expand')
if q != self.qlatest:
self.f_IG = self.ghat.expand(q)
self.qlatest = q
self.timer.stop('Expand')
# Add compensation charges:
self.ghat.add(nt_nG, Q_anL, q, self.f_IG)
self.timer.stop('Compensation charges')
if self.molecule and n2 in n1_n:
nn = (n1_n == n2).nonzero()[0][0]
nt_nG[nn] -= self.ngauss_G
else:
nn = None
iG2_G = self.iG2_qG[q]
# Calculate energies:
e_n = np.empty(len(n1_n))
for n, nt_G in enumerate(nt_nG):
e_n[n] = -4 * pi * np.real(self.pd2.integrate(nt_G, nt_G * iG2_G))
self.npairs += 1
if nn is not None:
e_n[nn] -= 2 * (self.pd2.integrate(nt_nG[nn], self.vgauss_G) +
(self.beta / 2 / pi)**0.5)
if self.write_timing_information:
t = (time() - self.t0) / len(n1_n)
self.log('Time for first pair-density: %10.3f seconds' % t)
self.log('Estimated total time: %10.3f seconds' %
(t * self.npairs0 / self.world.size))
self.write_timing_information = False
return e_n
def calculate_exx_paw_correction(self):
self.timer.start('PAW correction')
self.devv = 0.0
self.evc = 0.0
self.ecc = 0.0
deg = 2 // self.wfs.nspins # spin degeneracy
for a, D_sp in self.dens.D_asp.items():
setup = self.wfs.setups[a]
for D_p in D_sp:
D_ii = unpack2(D_p)
ni = len(D_ii)
for i1 in range(ni):
for i2 in range(ni):
A = 0.0
for i3 in range(ni):
p13 = packed_index(i1, i3, ni)
for i4 in range(ni):
p24 = packed_index(i2, i4, ni)
A += setup.M_pp[p13, p24] * D_ii[i3, i4]
self.devv -= D_ii[i1, i2] * A / deg
self.evc -= np.dot(D_p, setup.X_p)
self.ecc += setup.ExxC
if not self.bandstructure:
self.timer.stop('PAW correction')
return
Q = self.world.size // self.wfs.kd.comm.size
self.exx_skn *= Q
for kpt in self.wfs.kpt_u:
for a, D_sp in self.dens.D_asp.items():
setup = self.wfs.setups[a]
for D_p in D_sp:
D_ii = unpack2(D_p)
ni = len(D_ii)
P_ni = kpt.P_ani[a]
for i1 in range(ni):
for i2 in range(ni):
A = 0.0
for i3 in range(ni):
p13 = packed_index(i1, i3, ni)
for i4 in range(ni):
p24 = packed_index(i2, i4, ni)
A += setup.M_pp[p13, p24] * D_ii[i3, i4]
self.exx_skn[kpt.s, kpt.k] -= \
(A * P_ni[:, i1].conj() * P_ni[:, i2]).real
p12 = packed_index(i1, i2, ni)
self.exx_skn[kpt.s, kpt.k] -= \
(P_ni[:, i1].conj() * setup.X_p[p12] *
P_ni[:, i2]).real / self.wfs.nspins
self.world.sum(self.exx_skn)
self.exx_skn *= self.hybrid / Q
self.timer.stop('PAW correction')
def initialize_gaussian(self):
"""Calculate gaussian compensation charge and its potential.
Used to decouple electrostatic interactions between
periodically repeated images for molecular calculations.
Charge containing one electron::
(beta/pi)^(3/2)*exp(-beta*r^2),
its Fourier transform::
exp(-G^2/(4*beta)),
and its potential::
erf(beta^0.5*r)/r.
"""
gd = self.wfs.gd
# Set exponent of exp-function to -19 on the boundary:
self.beta = 4 * 19 * (gd.icell_cv**2).sum(1).max()
# Calculate gaussian:
G_Gv = self.pd2.get_reciprocal_vectors()
G2_G = self.pd2.G2_qG[0]
C_v = gd.cell_cv.sum(0) / 2 # center of cell
self.ngauss_G = np.exp(-1.0 / (4 * self.beta) * G2_G +
1j * np.dot(G_Gv, C_v)) / gd.dv
# Calculate potential from gaussian:
R_Rv = gd.get_grid_point_coordinates().transpose((1, 2, 3, 0))
r_R = ((R_Rv - C_v)**2).sum(3)**0.5
if (gd.N_c % 2 == 0).all():
r_R[tuple(gd.N_c // 2)] = 1.0 # avoid dividing by zero
v_R = erf(self.beta**0.5 * r_R) / r_R
if (gd.N_c % 2 == 0).all():
v_R[tuple(gd.N_c // 2)] = (4 * self.beta / pi)**0.5
self.vgauss_G = self.pd2.fft(v_R)
# Compare self-interaction to analytic result:
assert abs(0.5 * self.pd2.integrate(self.ngauss_G, self.vgauss_G) -
(self.beta / 2 / pi)**0.5) < 1e-6
class HybridXC(HybridXCBase):
orbital_dependent = True
def __init__(self,
name,
hybrid=None,
xc=None,
gygi=False,
alpha=None,
skip_gamma=False,
ecut=None,
etotflag=False,
acdf=False,
coredensity=True,
logfilename='-',
bands=None,
core_valence=True):
"""Mix standard functionals with exact exchange.
bands: list or None
List of bands to calculate energy for. Default is None
meaning do all bands.
"""
self.alpha = alpha
self.skip_gamma = skip_gamma
self.gygi = gygi
self.exx = 0.0
self.etotflag = etotflag
self.ecut = ecut
self.fd = logfilename
self.write_timing_information = True
self.bands = bands
self.acdf = acdf # adiabatic-connection dissipation fluctuation for RPA correlation energy
self.coredensity = coredensity
self.core_valence = core_valence
if self.acdf:
self.exxacdf = 0.0
self.etotflag = True
print('etotflag is True')
HybridXCBase.__init__(self, name, hybrid, xc)
def log(self, *args, **kwargs):
prnt(file=self.fd, *args, **kwargs)
self.fd.flush()
def calculate_radial(self,
rgd,
n_sLg,
Y_L,
v_sg,
dndr_sLg=None,
rnablaY_Lv=None,
tau_sg=None,
dedtau_sg=None):
return self.xc.calculate_radial(rgd, n_sLg, Y_L, v_sg, dndr_sLg,
rnablaY_Lv)
def calculate_paw_correction(self,
setup,
D_sp,
dEdD_sp=None,
addcoredensity=True,
a=None):
addcoredensity = self.coredensity # XXX overwrites input
return self.xc.calculate_paw_correction(setup, D_sp, dEdD_sp,
addcoredensity, a)
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 set_positions(self, spos_ac):
self.ghat.set_positions(spos_ac)
self.spos_ac = spos_ac
def calculate(self, gd, n_sg, v_sg=None, e_g=None):
# Normal XC contribution:
exc = self.xc.calculate(gd, n_sg, v_sg, e_g)
# Add EXX contribution:
return exc + self.exx
def calculate_exx(self):
"""Non-selfconsistent calculation."""
kd = self.kd
K = kd.nibzkpts
W = self.world.size // self.nspins
parallel = (W > 1)
self.log("%d CPU's used for %d IBZ k-points" % (W, K))
self.log('Spins:', self.nspins)
if self.etotflag and not self.gygi:
self.nbandstmp = 0
for s in range(self.nspins):
kpt1_k = [KPoint(kd, kpt) for kpt in self.kpt_u if kpt.s == s]
for kpt1 in kpt1_k:
for n1 in range(self.bd.nbands):
f_n = kpt1.f_n[n1]
if np.abs(f_n) < 1e-10:
self.nbandstmp = max(self.nbandstmp, n1)
break
else:
self.nbandstmp = self.bd.nbands
tmp = np.zeros(kd.comm.size, dtype=int)
kd.comm.all_gather(np.array([self.nbandstmp]), tmp)
self.nbands = tmp.max()
else:
self.nbands = self.bd.nbands
B = self.nbands
self.log('Number of bands calculated:', B)
self.log('Number of valence electrons:', self.setups.nvalence)
E = B - self.setups.nvalence / 2.0 # empty bands
self.npairs = (K * kd.nbzkpts - 0.5 * K**2) * (B**2 - E**2)
self.log('Approximate number of pairs:', self.npairs)
if not self.etotflag:
self.exx_skn = np.zeros((self.nspins, K, B))
self.debug_skn = np.zeros((self.nspins, K, B))
for s in range(self.nspins):
kpt1_q = [KPoint(kd, kpt) for kpt in self.kpt_u if kpt.s == s]
kpt2_q = kpt1_q[:]
if len(kpt1_q) == 0:
# No s-spins on this CPU:
continue
# Send rank:
srank = kd.get_rank_and_index(s, (kpt1_q[0].k - 1) % K)[0]
# Receive rank:
rrank = kd.get_rank_and_index(s, (kpt1_q[-1].k + 1) % K)[0]
# Shift k-points K - 1 times:
for i in range(K):
if i < K - 1:
if parallel:
kpt = kpt2_q[-1].next()
kpt.start_receiving(rrank)
kpt2_q[0].start_sending(srank)
else:
kpt = kpt2_q[0]
for kpt1, kpt2 in zip(kpt1_q, kpt2_q):
for k, ik in enumerate(kd.bz2ibz_k):
if ik == kpt2.k:
self.apply(kpt1, kpt2, k)
if i < K - 1:
if parallel:
kpt.wait()
kpt2_q[0].wait()
kpt2_q.pop(0)
kpt2_q.append(kpt)
if self.etotflag:
if self.acdf:
self.exxacdf = self.world.sum(self.exxacdf[0])
self.exx = self.exxacdf
else:
self.exx = self.world.sum(self.exx)
self.exx += self.calculate_exx_paw_correction()
else:
for kpt in self.kpt_u:
for a, D_sp in self.density.D_asp.items():
setup = self.setups[a]
for D_p in D_sp:
D_ii = unpack2(D_p)
ni = len(D_ii)
P_ni = kpt.P_ani[a]
for i1 in range(ni):
for i2 in range(ni):
A = 0.0
for i3 in range(ni):
p13 = packed_index(i1, i3, ni)
for i4 in range(ni):
p24 = packed_index(i2, i4, ni)
A += setup.M_pp[p13, p24] * D_ii[i3,
i4]
self.exx_skn[kpt.s, kpt.k] -= \
(self.hybrid * A *
P_ni[:, i1].conj() * P_ni[:, i2]).real
p12 = packed_index(i1, i2, ni)
if self.core_valence:
if setup.X_p is not None:
self.exx_skn[kpt.s, kpt.k] -= self.hybrid * \
(P_ni[:, i1].conj() * setup.X_p[p12] *
P_ni[:, i2]).real / self.nspins
self.world.sum(self.exx_skn)
self.exx = 0.0
for kpt in self.kpt_u:
self.exx += 0.5 * np.dot(kpt.f_n, self.exx_skn[kpt.s, kpt.k])
self.exx = self.world.sum(self.exx)
for a, D_sp in self.density.D_asp.items():
setup = self.setups[a]
if self.coredensity:
self.exx += self.hybrid * setup.ExxC
if self.core_valence:
self.exx -= self.hybrid * 0.5 * np.dot(
D_sp.sum(0), setup.X_p)
self.world.sum(self.debug_skn)
assert (self.debug_skn == self.kd.nbzkpts * B).all()
def apply(self, kpt1, kpt2, k):
k1_c = self.kd.ibzk_kc[kpt1.k]
k20_c = self.kd.ibzk_kc[kpt2.k]
k2_c = self.kd.bzk_kc[k]
q_c = k2_c - k1_c
N_c = self.gd.N_c
q = self.kd.where_is_q(q_c, self.bzq_qc)
q_c = self.bzq_qc[q]
eik1r_R = np.exp(2j * pi * np.dot(np.indices(N_c).T, k1_c / N_c).T)
eik2r_R = np.exp(2j * pi * np.dot(np.indices(N_c).T, k20_c / N_c).T)
eiqr_R = np.exp(2j * pi * np.dot(np.indices(N_c).T, q_c / N_c).T)
same = abs(k1_c - k2_c).max() < 1e-9
iG2_G = self.iG2_qG[q]
N = N_c.prod()
vol = self.gd.dv * N
nspins = self.nspins
fcut = 1e-10
is_ibz2 = abs(k2_c - self.kd.ibzk_kc[kpt2.k]).max() < 1e-9
for n1 in range(self.nbands):
f1 = kpt1.f_n[n1]
e1 = kpt1.eps_n[n1]
for n2 in range(self.nbands):
if same:
assert is_ibz2
if n2 > n1:
continue
elif is_ibz2:
if kpt1.k > kpt2.k:
if n2 > n1:
continue
else:
if n2 >= n1:
continue
f2 = kpt2.f_n[n2]
e2 = kpt2.eps_n[n2]
x = 1.0
if same and n1 == n2:
x = 0.5
if not self.etotflag:
self.debug_skn[kpt1.s, kpt1.k, n1] += x
if is_ibz2:
self.debug_skn[kpt2.s, kpt2.k, n2] += x
if self.etotflag and not self.gygi:
if abs(f1) < fcut or abs(f2) < fcut:
continue
else:
if abs(f1) < fcut and abs(f2) < fcut:
continue
if self.bands is not None:
if not (n1 in self.bands or is_ibz2 and n2 in self.bands):
continue
if self.skip_gamma and same:
continue
t0 = time()
nt_R = self.calculate_pair_density(n1, n2, kpt1, kpt2, q, k,
eik1r_R, eik2r_R, eiqr_R,
is_ibz2)
nt_G = self.pwd.fft(nt_R, q) / N
vt_G = nt_G.copy()
vt_G *= -pi * vol * iG2_G
e = np.vdot(nt_G, vt_G).real * nspins * self.hybrid * x
if self.etotflag:
if self.acdf:
if self.gygi and same:
self.exxacdf += f2 * e * kpt1.weight
else:
self.exxacdf += 0.5 * (
f1 * (1 - np.sign(e2 - e1)) * e + f2 *
(1 - np.sign(e1 - e2)) * e) * kpt1.weight
else:
self.exx += f2 * e * kpt1.weight[
0] * f1 * self.kd.nbzkpts * nspins / 2
else:
self.exx_skn[kpt1.s, kpt1.k, n1] += 2 * f2 * e
if is_ibz2:
if self.etotflag:
if self.acdf:
if self.gygi and same:
self.exxacdf += f1 * e * kpt2.weight
else:
self.exxacdf += 0.5 * (
f1 * (1 - np.sign(e2 - e1)) * e + f2 *
(1 - np.sign(e1 - e2)) * e) * kpt2.weight
else:
self.exx += f1 * e * kpt2.weight[
0] * f2 * self.kd.nbzkpts * nspins / 2
else:
self.exx_skn[kpt2.s, kpt2.k, n2] += 2 * f1 * e
if self.write_timing_information:
t = time() - t0
self.log('Time for first pair-density:', t, 'seconds')
self.log('Estimated total time',
t * self.npairs / self.world.size, 'seconds')
self.write_timing_information = False
def calculate_exx_paw_correction(self):
exx = 0
deg = 2 // self.nspins # spin degeneracy
for a, D_sp in self.density.D_asp.items():
setup = self.setups[a]
for D_p in D_sp:
D_ii = unpack2(D_p)
ni = len(D_ii)
for i1 in range(ni):
for i2 in range(ni):
A = 0.0
for i3 in range(ni):
p13 = packed_index(i1, i3, ni)
for i4 in range(ni):
p24 = packed_index(i2, i4, ni)
A += setup.M_pp[p13, p24] * D_ii[i3, i4]
exx -= self.hybrid / deg * D_ii[i1, i2] * A
if self.core_valence:
if setup.X_p is not None:
exx -= self.hybrid * np.dot(D_p, setup.X_p)
if self.coredensity:
exx += self.hybrid * setup.ExxC
return exx
def calculate_pair_density(self, n1, n2, kpt1, kpt2, q, k, eik1r_R,
eik2r_R, eiqr_R, ibz2):
if isinstance(self.wfs, PWWaveFunctions):
psit1_R = self.wfs.pd.ifft(kpt1.psit_nG[n1]) * eik1r_R
psit2_R = self.wfs.pd.ifft(kpt2.psit_nG[n2]) * eik2r_R
else:
psit1_R = kpt1.psit_nG[n1]
psit2_R = kpt2.psit_nG[n2]
if ibz2:
psit2_R = psit2_R
else:
psit2_R = np.asarray(self.kd.transform_wave_function(psit2_R, k),
complex)
nt_R = psit1_R.conj() * psit2_R
s = self.kd.sym_k[k]
time_reversal = self.kd.time_reversal_k[k]
k2_c = self.kd.ibzk_kc[kpt2.k]
Q_aL = {}
for a, P1_ni in kpt1.P_ani.items():
P1_i = P1_ni[n1]
b = self.kd.symmetry.a_sa[s, a]
S_c = (np.dot(self.spos_ac[a], self.kd.symmetry.op_scc[s]) -
self.spos_ac[b])
assert abs(S_c.round() - S_c).max() < 1e-13
x = np.exp(2j * pi * np.dot(k2_c, S_c))
P2_i = np.dot(self.setups[a].R_sii[s], kpt2.P_ani[b][n2]) * x
if time_reversal:
P2_i = P2_i.conj()
if ibz2:
P2_i = kpt2.P_ani[a][n2]
D_ii = np.outer(P1_i.conj(), P2_i)
D_p = pack(D_ii)
Q_aL[a] = np.dot(D_p, self.setups[a].Delta_pL)
self.ghat.add(nt_R, Q_aL, q)
return nt_R / eiqr_R
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)
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(gd1.integrate(a1), gd2.integrate(a2), 1e-13)
equal(abs(c2 - a2).max(), 0, 1e-14)
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 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)
class Unfold:
"""This Class is used to Unfold the Bands of a supercell (SC) calculations
into a the primitive cell (PC). As a convention (when possible) capital
letters variables are related to the SC while lowercase ones to the
PC """
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 get_K_index(self, K):
"""Find the index of a given K."""
K = np.array([K])
bzKG = to1bz(K, self.acell_cv)[0]
iK = self.kd.where_is_q(bzKG, self.kd.bzk_kc)
return iK
def get_g(self, iK):
"""Not all the G vectors are relevant for the bands unfolding,
but only the ones that match the PC reciprocal vectors.
This function finds the relevant ones."""
G_Gv_temp = self.pd.get_reciprocal_vectors(q=iK, add_q=False)
G_Gc_temp = np.dot(G_Gv_temp, np.linalg.inv(self.bcell_cv))
iG_list = []
g_list = []
for iG, G in enumerate(G_Gc_temp):
a = np.dot(G, np.linalg.inv(self.M).T)
check = np.abs(a) % 1 < 1e-5
check2 = np.abs((np.abs(a[np.where(~check)]) % 1) - 1) < 1e-5
if all(check) or all(check2):
iG_list.append(iG)
g_list.append(G)
return np.array(iG_list), np.array(g_list)
def get_G_index(self, iK, G, G_list):
"""Find the index of a given G."""
G_list -= G
sumG = np.sum(abs(G_list), axis=1)
iG = np.where(sumG < 1e-5)[0]
return iG
def get_eigenvalues(self, iK):
"""Get the list of eigenvalues for a given iK."""
if not self.spinorbit:
e_m = self.calc.get_eigenvalues(kpt=iK, spin=0) / Hartree
else:
e_m = self.e_mK[:, iK] / Hartree
return np.array(e_m)
def get_pw_wavefunctions_k(self, iK):
"""Get the list of Fourier coefficients of the WaveFunction for a
given iK. For spinors the number of bands is doubled and a spin
dimension is added."""
psi_mgrid = get_rs_wavefunctions_k(self.calc, iK, self.spinorbit,
self.v_Knm)
if not self.spinorbit:
psi_list_mG = []
for i in range(len(psi_mgrid)):
psi_list_mG.append(self.pd.fft(psi_mgrid[i], iK))
psi_mG = np.array(psi_list_mG)
return psi_mG
else:
u0_list_mG = []
u1_list_mG = []
for i in range(psi_mgrid.shape[0]):
u0_list_mG.append(self.pd.fft(psi_mgrid[i, 0], iK))
u1_list_mG.append(self.pd.fft(psi_mgrid[i, 1], iK))
u0_mG = np.array(u0_list_mG)
u1_mG = np.array(u1_list_mG)
u_mG = np.zeros((len(u0_mG), 2, u0_mG.shape[1]), complex)
u_mG[:, 0] = u0_mG
u_mG[:, 1] = u1_mG
return u_mG
def get_spectral_weights_k(self, k_t):
"""Returns the spectral weights for a given k in the PC:
P_mK(k_t) = \sum_n |<Km|k_t n>|**2
which can be shown to be equivalent to:
P_mK(k_t) = \sum_g |C_Km(g+k_t-K)|**2
"""
K_c, G_t = find_K_from_k(k_t, self.M)
iK = self.get_K_index(K_c)
iG_list, g_list = self.get_g(iK)
gG_t_list = g_list + G_t
G_Gv = self.pd.get_reciprocal_vectors(q=iK, add_q=False)
G_Gc = np.dot(G_Gv, np.linalg.inv(self.bcell_cv))
igG_t_list = []
for g in gG_t_list:
igG_t_list.append(self.get_G_index(iK, g.copy(), G_Gc.copy()))
C_mG = self.get_pw_wavefunctions_k(iK)
P_m = []
if not self.spinorbit:
for m in range(self.nb):
P = 0.
norm = np.sum(np.linalg.norm(C_mG[m, :])**2)
for iG in igG_t_list:
P += np.linalg.norm(C_mG[m, iG])**2
P_m.append(P / norm)
else:
for m in range(self.nb):
P = 0.
norm = np.sum(
np.linalg.norm(C_mG[m, 0, :])**2 +
np.linalg.norm(C_mG[m, 1, :])**2)
for iG in igG_t_list:
P += (np.linalg.norm(C_mG[m, 0, iG])**2 +
np.linalg.norm(C_mG[m, 1, iG])**2)
P_m.append(P / norm)
return np.array(P_m)
def get_spectral_weights(self, kpoints, filename=None):
"""Collect the spectral weights for the k points in the kpoints list.
This function is parallelized over k's."""
Nk = len(kpoints)
Nb = self.nb
world = mpi.world
if filename is None:
try:
e_mK, P_mK = pickle.load(
open('weights_' + self.name + '.pckl', 'rb'))
except IOError:
e_Km = []
P_Km = []
if world.rank == 0:
print('Getting EigenValues and Weights')
e_Km = np.zeros((Nk, Nb))
P_Km = np.zeros((Nk, Nb))
myk = range(0, Nk)[world.rank::world.size]
for ik in myk:
k = kpoints[ik]
print('kpoint: %s' % k)
K_c, G_c = find_K_from_k(k, self.M)
iK = self.get_K_index(K_c)
e_Km[ik] = self.get_eigenvalues(iK)
P_Km[ik] = self.get_spectral_weights_k(k)
world.barrier()
world.sum(e_Km)
world.sum(P_Km)
e_mK = np.array(e_Km).T
P_mK = np.array(P_Km).T
if world.rank == 0:
pickle.dump((e_mK, P_mK),
open('weights_' + self.name + '.pckl', 'wb'))
else:
e_mK, P_mK = pickle.load(open(filename, 'rb'))
return e_mK, P_mK
def spectral_function(self,
kpts,
x,
X,
points_name,
width=0.002,
npts=10000,
filename=None):
"""Returns the spectral function for all the ks in kpoints:
eta / pi
A_k(e) = \sum_m P_mK(k) x ---------------------
(e - e_mk)**2 + eta**2
at each k-points defined on npts energy points in the range
[emin, emax]. The width keyword is FWHM = 2 * eta."""
Nk = len(kpts)
A_ke = np.zeros((Nk, npts), float)
world = mpi.world
e_mK, P_mK = self.get_spectral_weights(kpts, filename)
if world.rank == 0:
print('Calculating the Spectral Function')
emin = np.min(e_mK) - 5 * width
emax = np.max(e_mK) + 5 * width
e = np.linspace(emin, emax, npts)
for ik in range(Nk):
for ie in range(len(e_mK[:, ik])):
e0 = e_mK[ie, ik]
D = (width / 2 / np.pi) / ((e - e0)**2 + (width / 2)**2)
A_ke[ik] += P_mK[ie, ik] * D
if world.rank == 0:
pickle.dump((e * Hartree, A_ke, x, X, points_name),
open('sf_' + self.name + '.pckl', 'wb'))
print('Spectral Function calculation completed!')
return
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)
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()
