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_paw_exx_corrections(self):
for a, atomdata in enumerate(self.calc.wfs.setups):
V_sii = []
for D_p in self.calc.density.D_asp[a]:
D_ii = unpack2(D_p)
V_ii = pawexxvv(atomdata, D_ii)
V_sii.append(V_ii)
C_ii = unpack(atomdata.X_p)
self.V_asii.append(V_sii)
self.C_aii.append(C_ii)
self.exxcc += atomdata.ExxC
def symmetrize_atomic_density_matrices(self, D_asp):
if len(self.kd.symmetry.op_scc) == 0:
return
a_sa = self.kd.symmetry.a_sa
D_asp.redistribute(self.atom_partition.as_serial())
for s in range(self.nspins):
D_aii = [unpack2(D_asp[a][s]) for a in range(len(D_asp))]
for a, D_ii in enumerate(D_aii):
setup = self.setups[a]
D_asp[a][s] = pack(setup.symmetrize(a, D_aii, a_sa))
D_asp.redistribute(self.atom_partition)
def initialize_paw_exx_corrections(self):
for a, atomdata in enumerate(self.calc.wfs.setups):
V_sii = []
for D_p in self.calc.density.D_asp[a]:
D_ii = unpack2(D_p)
V_ii = pawexxvv(atomdata, D_ii)
V_sii.append(V_ii)
if atomdata.X_p is None:
C_ii = D_ii * 0.0
else:
C_ii = unpack(atomdata.X_p)
self.V_asii.append(V_sii)
self.C_aii.append(C_ii)
self.exxcc += atomdata.ExxC or 0.0
def symmetrize_atomic_density_matrices(self, D_asp):
if len(self.kd.symmetry.op_scc) > 1:
all_D_asp = []
for a, setup in enumerate(self.setups):
D_sp = D_asp.get(a)
if D_sp is None:
ni = setup.ni
D_sp = np.empty((self.ns, ni * (ni + 1) // 2))
self.gd.comm.broadcast(D_sp, self.rank_a[a])
all_D_asp.append(D_sp)
for s in range(self.nspins):
D_aii = [unpack2(D_sp[s]) for D_sp in all_D_asp]
for a, D_sp in D_asp.items():
setup = self.setups[a]
D_sp[s] = pack(setup.symmetrize(a, D_aii, self.kd.symmetry.a_sa))
def symmetrize_atomic_density_matrices(self, D_asp):
if len(self.kd.symmetry.op_scc) > 1:
all_D_asp = []
for a, setup in enumerate(self.setups):
D_sp = D_asp.get(a)
if D_sp is None:
ni = setup.ni
D_sp = np.empty((self.ns, ni * (ni + 1) // 2))
self.gd.comm.broadcast(D_sp, self.rank_a[a])
all_D_asp.append(D_sp)
for s in range(self.nspins):
D_aii = [unpack2(D_sp[s]) for D_sp in all_D_asp]
for a, D_sp in D_asp.items():
setup = self.setups[a]
D_sp[s] = pack(
setup.symmetrize(a, D_aii, self.kd.symmetry.a_sa))
def apply_oper(self, obj, sym, cart_rot, atom_deperm):
from gpaw.utilities import pack, unpack2
a_a = self.symmetry.a_sa[sym]
assert (
a_a == atom_deperm).all(), "mismatched oper order or something?"
# permute the 'a' axis (atoms in the dict)
obj = super().apply_oper(obj, sym, cart_rot, atom_deperm)
# and now the 'p' axis
dH_asp = obj
for a in range(len(dH_asp)):
R_ii = self.symmetry.R_asii[a][sym]
for s in range(self.nspins):
dH_p = dH_asp[a][s]
dH_ii = unpack2(dH_p)
tmp_ii = R_ii @ dH_ii @ R_ii.T
tmp_p = pack(tmp_ii)
dH_asp[a][s][...] = tmp_p
return dH_asp
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 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 atomic_val_val(self, paw, H_nn, u=0):
deg = 2 / self.nspins
kpt = paw.wfs.kpt_u[u]
for a, P_ni in kpt.P_ani.items():
# Add atomic corrections to the valence-valence exchange energy
# --
# > D C D
# -- ii iiii ii
setup = paw.wfs.setups[a]
D_p = paw.density.D_asp[a][kpt.s]
H_p = np.zeros_like(D_p)
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)
H_p[p12] -= 2 / deg * A / ((i1 != i2) + 1)
H_nn += np.dot(P_ni, np.inner(unpack(H_p), P_ni.conj()))
def paw_corrections(self, gridrefinement=2):
Fn_wsg, gd = self.interpolate_pseudo_density(gridrefinement)
# Splines
splines = {}
phi_aj = []
phit_aj = []
for a, id in enumerate(self.setups.id_a):
if id in splines:
phi_j, phit_j = splines[id]
else:
# Load splines:
phi_j, phit_j = self.setups[a].get_partial_waves()[:2]
splines[id] = (phi_j, phit_j)
phi_aj.append(phi_j)
phit_aj.append(phit_j)
# Create localized functions from splines
phi = BasisFunctions(gd, phi_aj, dtype=float)
phit = BasisFunctions(gd, phit_aj, dtype=float)
# phi = BasisFunctions(gd, phi_aj, dtype=complex)
# phit = BasisFunctions(gd, phit_aj, dtype=complex)
spos_ac = self.atoms.get_scaled_positions()
phi.set_positions(spos_ac)
phit.set_positions(spos_ac)
tmp_g = gd.empty(dtype=float)
rho_MM = np.zeros((phi.Mmax, phi.Mmax), dtype=self.dtype)
rho2_MM = np.zeros_like(rho_MM)
for w in range(self.nw):
for s in range(self.nspins):
rho_MM[:] = 0
M1 = 0
for a, setup in enumerate(self.setups):
ni = setup.ni
FD_wsp = self.FD_awsp.get(a)
if FD_wsp is None:
FD_p = np.empty((ni * (ni + 1) // 2), dtype=self.dtype)
else:
FD_p = FD_wsp[w][s]
if gd.comm.size > 1:
gd.comm.broadcast(FD_p, self.rank_a[a])
D_ij = unpack2(FD_p)
# unpack does complex conjugation that we don't want so
# remove conjugation
D_ij = np.triu(D_ij, 1) + np.conj(np.tril(D_ij))
# if FD_wsp is None:
# FD_wsp = np.empty((self.nw, self.nspins,
# ni * (ni + 1) // 2),
# dtype=self.dtype)
# if gd.comm.size > 1:
# gd.comm.broadcast(FD_wsp, self.rank_a[a])
# D_ij = unpack2(FD_wsp[w][s])
# D_ij = np.triu(D_ij, 1) + np.conj(np.tril(D_ij))
M2 = M1 + ni
rho_MM[M1:M2, M1:M2] = D_ij
M1 = M2
# Add real part of AE corrections
tmp_g[:] = 0
rho2_MM[:] = rho_MM.real
# TODO: use ae_valence_density_correction
phi.construct_density(rho2_MM, tmp_g, q=-1)
phit.construct_density(-rho2_MM, tmp_g, q=-1)
# phi.lfc.ae_valence_density_correction(rho2_MM, tmp_g,
# np.zeros(len(phi.M_W),
# np.intc),
# np.zeros(self.na))
# phit.lfc.ae_valence_density_correction(-rho2_MM, tmp_g,
# np.zeros(len(phi.M_W),
# np.intc),
# np.zeros(self.na))
Fn_wsg[w][s] += tmp_g
# Add imag part of AE corrections
tmp_g[:] = 0
rho2_MM[:] = rho_MM.imag
# TODO: use ae_valence_density_correction
phi.construct_density(rho2_MM, tmp_g, q=-1)
phit.construct_density(-rho2_MM, tmp_g, q=-1)
# phi.lfc.ae_valence_density_correction(rho2_MM, tmp_g,
# np.zeros(len(phi.M_W),
# np.intc),
# np.zeros(self.na))
# phit.lfc.ae_valence_density_correction(-rho2_MM, tmp_g,
# np.zeros(len(phi.M_W),
# np.intc),
# np.zeros(self.na))
Fn_wsg[w][s] += 1.0j * tmp_g
return Fn_wsg, gd
def get_M(self, modes, log=None, q=0):
"""Calculate el-ph coupling matrix for given modes(s).
XXX:
kwarg "q=0" is an ugly hack for k-points.
There shuold be loops over q!
Note that modes must be given as a dictionary with mode
frequencies in eV and corresponding mode vectors in units
of 1/sqrt(amu), where amu = 1.6605402e-27 Kg is an atomic mass unit.
In short frequencies and mode vectors must be given in ase units.
::
d d ~
< w | -- v | w' > = < w | -- v | w'>
dP dP
_
\ ~a d . ~a
+ ) < w | p > -- /_\H < p | w' >
/_ i dP ij j
a,ij
_
\ d ~a . ~a
+ ) < w | -- p > /_\H < p | w' >
/_ dP i ij j
a,ij
_
\ ~a . d ~a
+ ) < w | p > /_\H < -- p | w' >
/_ i ij dP j
a,ij
"""
if log is None:
timer = nulltimer
elif log == '-':
timer = StepTimer(name='EPCM')
else:
timer = StepTimer(name='EPCM', out=open(log, 'w'))
modes1 = modes.copy()
#convert to atomic units
amu = 1.6605402e-27 # atomic unit mass [Kg]
me = 9.1093897e-31 # electron mass [Kg]
modes = {}
for k in modes1.keys():
modes[k / Hartree] = modes1[k] / np.sqrt(amu / me)
dvt_Gx, ddH_aspx = self.get_gradient()
from gpaw import restart
atoms, calc = restart('eq.gpw', txt=None)
spos_ac = atoms.get_scaled_positions()
if calc.wfs.S_qMM is None:
calc.initialize(atoms)
calc.initialize_positions(atoms)
wfs = calc.wfs
nao = wfs.setups.nao
bfs = wfs.basis_functions
dtype = wfs.dtype
spin = 0 # XXX
M_lii = {}
timer.write_now('Starting gradient of pseudo part')
for f, mode in modes.items():
mo = []
M_ii = np.zeros((nao, nao), dtype)
for a in self.indices:
mo.append(mode[a])
mode = np.asarray(mo).flatten()
dvtdP_G = np.dot(dvt_Gx, mode)
bfs.calculate_potential_matrix(dvtdP_G, M_ii, q=q)
tri2full(M_ii, 'L')
M_lii[f] = M_ii
timer.write_now('Finished gradient of pseudo part')
P_aqMi = calc.wfs.P_aqMi
# Add the term
# _
# \ ~a d . ~a
# ) < w | p > -- /_\H < p | w' >
# /_ i dP ij j
# a,ij
Ma_lii = {}
for f, mode in modes.items():
Ma_lii[f] = np.zeros_like(M_lii.values()[0])
timer.write_now('Starting gradient of dH^a part')
for f, mode in modes.items():
mo = []
for a in self.indices:
mo.append(mode[a])
mode = np.asarray(mo).flatten()
for a, ddH_spx in ddH_aspx.items():
ddHdP_sp = np.dot(ddH_spx, mode)
ddHdP_ii = unpack2(ddHdP_sp[spin])
Ma_lii[f] += dots(P_aqMi[a][q], ddHdP_ii, P_aqMi[a][q].T)
timer.write_now('Finished gradient of dH^a part')
timer.write_now('Starting gradient of projectors part')
spos_ac = self.atoms.get_scaled_positions() % 1.0
dP_aMix = self.get_dP_aMix(spos_ac, wfs, q, timer)
timer.write_now('Finished gradient of projectors part')
dH_asp = pickle.load(open('v.eq.pckl'))[1]
Mb_lii = {}
for f, mode in modes.items():
Mb_lii[f] = np.zeros_like(M_lii.values()[0])
for f, mode in modes.items():
for a, dP_Mix in dP_aMix.items():
dPdP_Mi = np.dot(dP_Mix, mode[a])
dH_ii = unpack2(dH_asp[a][spin])
dPdP_MM = dots(dPdP_Mi, dH_ii, P_aqMi[a][q].T)
Mb_lii[f] -= dPdP_MM + dPdP_MM.T
# XXX The minus sign here is quite subtle.
# It is related to how the derivative of projector
# functions in GPAW is calculated.
# More thorough explanations, anyone...?
# Units of M_lii are Hartree/(Bohr * sqrt(m_e))
for mode in M_lii.keys():
M_lii[mode] += Ma_lii[mode] + Mb_lii[mode]
# conversion to eV. The prefactor 1 / sqrt(hb^2 / 2 * hb * f)
# has units Bohr * sqrt(me)
M_lii_1 = M_lii.copy()
M_lii = {}
for f in M_lii_1.keys():
M_lii[f * Hartree] = M_lii_1[f] * Hartree / np.sqrt(2 * f)
return M_lii
def update(self, density):
"""Calculate effective potential.
The XC-potential and the Hartree potential are evaluated on
the fine grid, and the sum is then restricted to the coarse
grid."""
self.timer.start('Hamiltonian')
if self.vt_sg is None:
self.timer.start('Initialize Hamiltonian')
self.vt_sg = self.finegd.empty(self.ns)
self.vHt_g = self.finegd.zeros()
self.vt_sG = self.gd.empty(self.ns)
self.poisson.initialize()
self.timer.stop('Initialize Hamiltonian')
Ekin, Epot, Ebar, Eext, Exc, W_aL = \
self.update_pseudo_potential(density)
self.timer.start('Atomic')
self.dH_asp = None # XXXX
dH_asp = {}
for a, D_sp in density.D_asp.items():
W_L = W_aL[a]
setup = self.setups[a]
D_p = D_sp[:self.nspins].sum(0)
dH_p = (setup.K_p + setup.M_p + setup.MB_p +
2.0 * np.dot(setup.M_pp, D_p) +
np.dot(setup.Delta_pL, W_L))
Ekin += np.dot(setup.K_p, D_p) + setup.Kc
Ebar += setup.MB + np.dot(setup.MB_p, D_p)
Epot += setup.M + np.dot(D_p,
(setup.M_p + np.dot(setup.M_pp, D_p)))
if self.vext is not None:
vext = self.vext.get_taylor(spos_c=self.spos_ac[a, :])
# Tailor expansion to the zeroth order
Eext += vext[0][0] * (sqrt(4 * pi) * density.Q_aL[a][0] +
setup.Z)
dH_p += vext[0][0] * sqrt(4 * pi) * setup.Delta_pL[:, 0]
if len(vext) > 1:
# Tailor expansion to the first order
Eext += sqrt(4 * pi / 3) * np.dot(vext[1],
density.Q_aL[a][1:4])
# there must be a better way XXXX
Delta_p1 = np.array([
setup.Delta_pL[:, 1], setup.Delta_pL[:, 2],
setup.Delta_pL[:, 3]
])
dH_p += sqrt(4 * pi / 3) * np.dot(vext[1], Delta_p1)
dH_asp[a] = dH_sp = np.zeros_like(D_sp)
if setup.HubU is not None:
assert self.collinear
nspins = len(D_sp)
l_j = setup.l_j
l = setup.Hubl
scale = setup.Hubs
nl = np.where(np.equal(l_j, l))[0]
nn = (2 * np.array(l_j) + 1)[0:nl[0]].sum()
for D_p, H_p in zip(D_sp, dH_asp[a]):
[N_mm, V] = self.aoom(unpack2(D_p), a, l, scale)
N_mm = N_mm / 2 * nspins
Eorb = setup.HubU / 2. * (N_mm -
np.dot(N_mm, N_mm)).trace()
Vorb = setup.HubU * (0.5 * np.eye(2 * l + 1) - N_mm)
Exc += Eorb
if nspins == 1:
# add contribution of other spin manyfold
Exc += Eorb
if len(nl) == 2:
mm = (2 * np.array(l_j) + 1)[0:nl[1]].sum()
V[nn:nn + 2 * l + 1, nn:nn + 2 * l + 1] *= Vorb
V[mm:mm + 2 * l + 1, nn:nn + 2 * l + 1] *= Vorb
V[nn:nn + 2 * l + 1, mm:mm + 2 * l + 1] *= Vorb
V[mm:mm + 2 * l + 1, mm:mm + 2 * l + 1] *= Vorb
else:
V[nn:nn + 2 * l + 1, nn:nn + 2 * l + 1] *= Vorb
Htemp = unpack(H_p)
Htemp += V
H_p[:] = pack2(Htemp)
dH_sp[:self.nspins] += dH_p
if self.ref_dH_asp:
dH_sp += self.ref_dH_asp[a]
# We are not yet done with dH_sp; still need XC correction below
Ddist_asp = self.dh_distributor.distribute(density.D_asp)
dHdist_asp = {}
Exca = 0.0
self.timer.start('XC Correction')
for a, D_sp in Ddist_asp.items():
setup = self.setups[a]
dH_sp = np.zeros_like(D_sp)
Exca += self.xc.calculate_paw_correction(setup, D_sp, dH_sp, a=a)
# XXX Exc are added on the "wrong" distribution; sum only works
# when gd.comm and distribution comm are the same
dHdist_asp[a] = dH_sp
self.timer.stop('XC Correction')
dHdist_asp = self.dh_distributor.collect(dHdist_asp)
# Exca has contributions from all cores so modify it so it is
# parallel in the same way as the other energies.
Exca = self.world.sum(Exca)
if self.gd.comm.rank == 0:
Exc += Exca
assert len(dHdist_asp) == len(self.atom_partition.my_indices)
for a, D_sp in density.D_asp.items():
dH_sp = dH_asp[a]
dH_sp += dHdist_asp[a]
Ekin -= (D_sp * dH_sp).sum() # NCXXX
self.dH_asp = dH_asp
self.timer.stop('Atomic')
# Make corrections due to non-local xc:
#xcfunc = self.xc.xcfunc
self.Enlxc = 0.0 # XXXxcfunc.get_non_local_energy()
Ekin += self.xc.get_kinetic_energy_correction() / self.gd.comm.size
energies = np.array([Ekin, Epot, Ebar, Eext, Exc])
self.timer.start('Communicate energies')
self.gd.comm.sum(energies)
# Make sure that all CPUs have the same energies
self.world.broadcast(energies, 0)
self.timer.stop('Communicate energies')
(self.Ekin0, self.Epot, self.Ebar, self.Eext, self.Exc) = energies
#self.Exc += self.Enlxc
#self.Ekin0 += self.Enlkin
self.timer.stop('Hamiltonian')
def apply_orbital_dependent_hamiltonian(self,
kpt,
psit_nG,
Htpsit_nG=None,
dH_asp=None):
if kpt.f_n is None:
return
deg = 2 // self.nspins # Spin degeneracy
hybrid = self.hybrid
P_ani = kpt.P_ani
setups = self.setups
is_cam = self.is_cam
vt_g = self.finegd.empty()
if self.gd is not self.finegd:
vt_G = self.gd.empty()
if self.rsf == 'Yukawa':
y_vt_g = self.finegd.empty()
# if self.gd is not self.finegd:
# y_vt_G = self.gd.empty()
nocc = int(ceil(kpt.f_n.sum())) // (3 - self.nspins)
if self.excitation is not None:
ex_band = nocc - self.excited - 1
if self.excitation == 'singlet':
ex_weight = -1
elif self.excitation == 'triplet':
ex_weight = +1
else:
ex_weight = 0
if self.unocc or self.excitation is not None:
nbands = len(kpt.f_n)
else:
nbands = nocc
self.nocc_s[kpt.s] = nocc
if Htpsit_nG is not None:
kpt.vt_nG = self.gd.empty(nbands)
kpt.vxx_ani = {}
kpt.vxx_anii = {}
for a, P_ni in P_ani.items():
I = P_ni.shape[1]
kpt.vxx_ani[a] = np.zeros((nbands, I))
kpt.vxx_anii[a] = np.zeros((nbands, I, I))
exx = 0.0
ekin = 0.0
# XXXX nbands can be different numbers on different cpus!
# That means some will execute the loop and others not.
# And deadlocks with augment-grids.
# Determine pseudo-exchange
for n1 in range(nbands):
psit1_G = psit_nG[n1]
f1 = kpt.f_n[n1] / deg
for n2 in range(n1, nbands):
psit2_G = psit_nG[n2]
f2 = kpt.f_n[n2] / deg
if n1 != n2 and f1 == 0 and f1 == f2:
continue # Don't work on double unocc. bands
# Double count factor:
dc = (1 + (n1 != n2)) * deg
nt_G, rhot_g = self.calculate_pair_density(
n1, n2, psit_nG, P_ani)
vt_g[:] = 0.0
# XXXXX This will go wrong because we are solving the
# Poisson equation on the distribution of gd, not finegd
# Or maybe it's fixed now
self.poissonsolver.solve(vt_g,
-rhot_g,
charge=-float(n1 == n2),
eps=1e-12,
zero_initial_phi=True)
vt_g *= hybrid
if self.rsf == 'Yukawa':
y_vt_g[:] = 0.0
self.screened_poissonsolver.solve(y_vt_g,
-rhot_g,
charge=-float(n1 == n2),
eps=1e-12,
zero_initial_phi=True)
if is_cam: # Cam like correction
y_vt_g *= self.cam_beta
else:
y_vt_g *= hybrid
vt_g -= y_vt_g
if self.gd is self.finegd:
vt_G = vt_g
else:
self.restrictor.apply(vt_g, vt_G)
# Integrate the potential on fine and coarse grids
int_fine = self.finegd.integrate(vt_g * rhot_g)
int_coarse = self.gd.integrate(vt_G * nt_G)
if self.gd.comm.rank == 0: # only add to energy on master CPU
exx += 0.5 * dc * f1 * f2 * int_fine
ekin -= dc * f1 * f2 * int_coarse
if Htpsit_nG is not None:
Htpsit_nG[n1] += f2 * vt_G * psit2_G
if n1 == n2:
kpt.vt_nG[n1] = f1 * vt_G
if self.excitation is not None and n1 == ex_band:
Htpsit_nG[nocc:] += f1 * vt_G * psit_nG[nocc:]
else:
if self.excitation is None or n1 != ex_band \
or n2 < nocc:
Htpsit_nG[n2] += f1 * vt_G * psit1_G
else:
Htpsit_nG[n2] += f1 * ex_weight * vt_G * psit1_G
# Update the vxx_uni and vxx_unii vectors of the nuclei,
# used to determine the atomic hamiltonian, and the
# residuals
v_aL = self.ghat.dict()
self.ghat.integrate(vt_g, v_aL)
for a, v_L in v_aL.items():
v_ii = unpack(np.dot(setups[a].Delta_pL, v_L))
v_ni = kpt.vxx_ani[a]
v_nii = kpt.vxx_anii[a]
P_ni = P_ani[a]
v_ni[n1] += f2 * np.dot(v_ii, P_ni[n2])
if n1 != n2:
if self.excitation is None or n1 != ex_band or \
n2 < nocc:
v_ni[n2] += f1 * np.dot(v_ii, P_ni[n1])
else:
v_ni[n2] += f1 * ex_weight * \
np.dot(v_ii, P_ni[n1])
else:
# XXX Check this:
v_nii[n1] = f1 * v_ii
if self.excitation is not None and n1 == ex_band:
for nuoc in range(nocc, nbands):
v_ni[nuoc] += f1 * \
np.dot(v_ii, P_ni[nuoc])
def calculate_vv(ni, D_ii, M_pp, weight, addme=False):
"""Calculate the local corrections depending on Mpp."""
dexx = 0
dekin = 0
if not addme:
addsign = -2.0
else:
addsign = 2.0
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 += M_pp[p13, p24] * D_ii[i3, i4]
p12 = packed_index(i1, i2, ni)
if Htpsit_nG is not None:
dH_p[p12] += addsign * weight / \
deg * A / ((i1 != i2) + 1)
dekin += 2 * weight / deg * D_ii[i1, i2] * A
dexx -= weight / deg * D_ii[i1, i2] * A
return (dexx, dekin)
# Apply the atomic corrections to the energy and the Hamiltonian
# matrix
for a, P_ni in P_ani.items():
setup = setups[a]
if Htpsit_nG is not None:
# Add non-trivial corrections the Hamiltonian matrix
h_nn = symmetrize(
np.inner(P_ni[:nbands], kpt.vxx_ani[a][:nbands]))
ekin -= np.dot(kpt.f_n[:nbands], h_nn.diagonal())
dH_p = dH_asp[a][kpt.s]
# Get atomic density and Hamiltonian matrices
D_p = self.density.D_asp[a][kpt.s]
D_ii = unpack2(D_p)
ni = len(D_ii)
# Add atomic corrections to the valence-valence exchange energy
# --
# > D C D
# -- ii iiii ii
(dexx, dekin) = calculate_vv(ni, D_ii, setup.M_pp, hybrid)
ekin += dekin
exx += dexx
if self.rsf is not None:
Mg_pp = setup.calculate_yukawa_interaction(self.omega)
if is_cam:
(dexx, dekin) = calculate_vv(ni,
D_ii,
Mg_pp,
self.cam_beta,
addme=True)
else:
(dexx, dekin) = calculate_vv(ni,
D_ii,
Mg_pp,
hybrid,
addme=True)
ekin -= dekin
exx -= dexx
# Add valence-core exchange energy
# --
# > X D
# -- ii ii
if setup.X_p is not None:
exx -= hybrid * np.dot(D_p, setup.X_p)
if Htpsit_nG is not None:
dH_p -= hybrid * setup.X_p
ekin += hybrid * np.dot(D_p, setup.X_p)
if self.rsf == 'Yukawa' and setup.X_pg is not None:
if is_cam:
thybrid = self.cam_beta # 0th order
else:
thybrid = hybrid
exx += thybrid * np.dot(D_p, setup.X_pg)
if Htpsit_nG is not None:
dH_p += thybrid * setup.X_pg
ekin -= thybrid * np.dot(D_p, setup.X_pg)
elif self.rsf == 'Yukawa' and setup.X_pg is None:
thybrid = exp(-3.62e-2 * self.omega) # educated guess
if is_cam:
thybrid *= self.cam_beta
else:
thybrid *= hybrid
exx += thybrid * np.dot(D_p, setup.X_p)
if Htpsit_nG is not None:
dH_p += thybrid * setup.X_p
ekin -= thybrid * np.dot(D_p, setup.X_p)
# Add core-core exchange energy
if kpt.s == 0:
if self.rsf is None or is_cam:
if is_cam:
exx += self.cam_alpha * setup.ExxC
else:
exx += hybrid * setup.ExxC
self.exx_s[kpt.s] = self.gd.comm.sum(exx)
self.ekin_s[kpt.s] = self.gd.comm.sum(ekin)
def get_M(self, modes, log=None, q=0):
"""Calculate el-ph coupling matrix for given modes(s).
XXX:
kwarg "q=0" is an ugly hack for k-points.
There shuold be loops over q!
Note that modes must be given as a dictionary with mode
frequencies in eV and corresponding mode vectors in units
of 1/sqrt(amu), where amu = 1.6605402e-27 Kg is an atomic mass unit.
In short frequencies and mode vectors must be given in ase units.
::
d d ~
< w | -- v | w' > = < w | -- v | w'>
dP dP
_
\ ~a d . ~a
+ ) < w | p > -- /_\H < p | w' >
/_ i dP ij j
a,ij
_
\ d ~a . ~a
+ ) < w | -- p > /_\H < p | w' >
/_ dP i ij j
a,ij
_
\ ~a . d ~a
+ ) < w | p > /_\H < -- p | w' >
/_ i ij dP j
a,ij
"""
if log is None:
timer = nulltimer
elif log == '-':
timer = StepTimer(name='EPCM')
else:
timer = StepTimer(name='EPCM', out=open(log, 'w'))
modes1 = modes.copy()
#convert to atomic units
amu = 1.6605402e-27 # atomic unit mass [Kg]
me = 9.1093897e-31 # electron mass [Kg]
modes = {}
for k in modes1.keys():
modes[k / Hartree] = modes1[k] / np.sqrt(amu / me)
dvt_Gx, ddH_aspx = self.get_gradient()
from gpaw import restart
atoms, calc = restart('eq.gpw', txt=None)
if calc.wfs.S_qMM is None:
calc.initialize(atoms)
calc.initialize_positions(atoms)
wfs = calc.wfs
nao = wfs.setups.nao
bfs = wfs.basis_functions
dtype = wfs.dtype
spin = 0 # XXX
M_lii = {}
timer.write_now('Starting gradient of pseudo part')
for f, mode in modes.items():
mo = []
M_ii = np.zeros((nao, nao), dtype)
for a in self.indices:
mo.append(mode[a])
mode = np.asarray(mo).flatten()
dvtdP_G = np.dot(dvt_Gx, mode)
bfs.calculate_potential_matrix(dvtdP_G, M_ii, q=q)
tri2full(M_ii, 'L')
M_lii[f] = M_ii
timer.write_now('Finished gradient of pseudo part')
P_aqMi = calc.wfs.P_aqMi
# Add the term
# _
# \ ~a d . ~a
# ) < w | p > -- /_\H < p | w' >
# /_ i dP ij j
# a,ij
Ma_lii = {}
for f, mode in modes.items():
Ma_lii[f] = np.zeros_like(M_lii.values()[0])
timer.write_now('Starting gradient of dH^a part')
for f, mode in modes.items():
mo = []
for a in self.indices:
mo.append(mode[a])
mode = np.asarray(mo).flatten()
for a, ddH_spx in ddH_aspx.items():
ddHdP_sp = np.dot(ddH_spx, mode)
ddHdP_ii = unpack2(ddHdP_sp[spin])
Ma_lii[f] += dots(P_aqMi[a][q], ddHdP_ii, P_aqMi[a][q].T)
timer.write_now('Finished gradient of dH^a part')
timer.write_now('Starting gradient of projectors part')
dP_aMix = self.get_dP_aMix(calc.spos_ac, wfs, q, timer)
timer.write_now('Finished gradient of projectors part')
dH_asp = pickle.load(open('v.eq.pckl', 'rb'))[1]
Mb_lii = {}
for f, mode in modes.items():
Mb_lii[f] = np.zeros_like(M_lii.values()[0])
for f, mode in modes.items():
for a, dP_Mix in dP_aMix.items():
dPdP_Mi = np.dot(dP_Mix, mode[a])
dH_ii = unpack2(dH_asp[a][spin])
dPdP_MM = dots(dPdP_Mi, dH_ii, P_aqMi[a][q].T)
Mb_lii[f] -= dPdP_MM + dPdP_MM.T
# XXX The minus sign here is quite subtle.
# It is related to how the derivative of projector
# functions in GPAW is calculated.
# More thorough explanations, anyone...?
# Units of M_lii are Hartree/(Bohr * sqrt(m_e))
for mode in M_lii.keys():
M_lii[mode] += Ma_lii[mode] + Mb_lii[mode]
# conversion to eV. The prefactor 1 / sqrt(hb^2 / 2 * hb * f)
# has units Bohr * sqrt(me)
M_lii_1 = M_lii.copy()
M_lii = {}
for f in M_lii_1.keys():
M_lii[f * Hartree] = M_lii_1[f] * Hartree / np.sqrt(2 * f)
return M_lii
def with_ae_corrections(self, finegrid=False):
"""Get pair density including the AE corrections"""
nij_g = self.get(finegrid)
# Generate the density matrix
D_ap = {}
# D_aii = {}
for a, P_ni in self.P_ani.items():
Pi_i = P_ni[self.i]
Pj_i = P_ni[self.j]
D_ii = np.outer(Pi_i.conj(), Pj_i)
# Note: D_ii is not symmetric but the products of partial waves are
# so that we can pack
D_ap[a] = pack(D_ii)
# D_aii[a] = D_ii
# Load partial waves if needed
if ((finegrid and (not hasattr(self, 'phi'))) or
((not finegrid) and (not hasattr(self, 'Phi')))):
# Splines
splines = {}
phi_aj = []
phit_aj = []
for a, id in enumerate(self.setups.id_a):
if id in splines:
phi_j, phit_j = splines[id]
else:
# Load splines:
phi_j, phit_j = self.setups[a].get_partial_waves()[:2]
splines[id] = (phi_j, phit_j)
phi_aj.append(phi_j)
phit_aj.append(phit_j)
# Store partial waves as class variables
if finegrid:
gd = self.density.finegd
self.__class__.phi = BasisFunctions(gd, phi_aj)
self.__class__.phit = BasisFunctions(gd, phit_aj)
self.__class__.phi.set_positions(self.spos_ac)
self.__class__.phit.set_positions(self.spos_ac)
else:
gd = self.density.gd
self.__class__.Phi = BasisFunctions(gd, phi_aj)
self.__class__.Phit = BasisFunctions(gd, phit_aj)
self.__class__.Phi.set_positions(self.spos_ac)
self.__class__.Phit.set_positions(self.spos_ac)
# Add AE corrections
if finegrid:
phi = self.phi
phit = self.phit
gd = self.density.finegd
else:
phi = self.Phi
phit = self.Phit
gd = self.density.gd
rho_MM = np.zeros((phi.Mmax, phi.Mmax))
M1 = 0
for a, setup in enumerate(self.setups):
ni = setup.ni
D_p = D_ap.get(a)
if D_p is None:
D_p = np.empty((ni * (ni + 1) // 2))
if gd.comm.size > 1:
gd.comm.broadcast(D_p, self.wfs.rank_a[a])
D_ii = unpack2(D_p)
# D_ii = D_aii.get(a)
# if D_ii is None:
# D_ii = np.empty((ni, ni))
# if gd.comm.size > 1:
# gd.comm.broadcast(D_ii, self.wfs.rank_a[a])
M2 = M1 + ni
rho_MM[M1:M2, M1:M2] = D_ii
M1 = M2
# construct_density assumes symmetric rho_MM and
# takes only the upper half of it
phi.construct_density(rho_MM, nij_g, q=-1)
phit.construct_density(-rho_MM, nij_g, q=-1)
# TODO: use ae_valence_density_correction
# phi.lfc.ae_valence_density_correction(
# rho_MM, nij_g, np.zeros(len(phi.M_W), np.intc), np.zeros(self.na))
# phit.lfc.ae_valence_density_correction(
# -rho_MM, nij_g, np.zeros(len(phit.M_W), np.intc), np.zeros(self.na))
return nij_g
def apply_orbital_dependent_hamiltonian(self,
kpt,
psit_nG,
Htpsit_nG=None,
dH_asp=None):
if kpt.f_n is None:
return
deg = 2 // self.nspins # Spin degeneracy
hybrid = self.hybrid
P_ani = kpt.P_ani
setups = self.setups
vt_g = self.finegd.empty()
if self.gd is not self.finegd:
vt_G = self.gd.empty()
nocc = int(kpt.f_n.sum()) // (3 - self.nspins)
if self.unocc:
nbands = len(kpt.f_n)
else:
nbands = nocc
self.nocc_s[kpt.s] = nocc
if Htpsit_nG is not None:
kpt.vt_nG = self.gd.empty(nbands)
kpt.vxx_ani = {}
kpt.vxx_anii = {}
for a, P_ni in P_ani.items():
I = P_ni.shape[1]
kpt.vxx_ani[a] = np.zeros((nbands, I))
kpt.vxx_anii[a] = np.zeros((nbands, I, I))
exx = 0.0
ekin = 0.0
# Determine pseudo-exchange
for n1 in range(nbands):
psit1_G = psit_nG[n1]
f1 = kpt.f_n[n1] / deg
for n2 in range(n1, nbands):
psit2_G = psit_nG[n2]
f2 = kpt.f_n[n2] / deg
# Double count factor:
dc = (1 + (n1 != n2)) * deg
nt_G, rhot_g = self.calculate_pair_density(
n1, n2, psit_nG, P_ani)
vt_g[:] = 0.0
iter = self.poissonsolver.solve(vt_g,
-rhot_g,
charge=-float(n1 == n2),
eps=1e-12,
zero_initial_phi=True)
vt_g *= hybrid
if self.gd is self.finegd:
vt_G = vt_g
else:
self.restrictor.apply(vt_g, vt_G)
# Integrate the potential on fine and coarse grids
int_fine = self.finegd.integrate(vt_g * rhot_g)
int_coarse = self.gd.integrate(vt_G * nt_G)
if self.gd.comm.rank == 0: # only add to energy on master CPU
exx += 0.5 * dc * f1 * f2 * int_fine
ekin -= dc * f1 * f2 * int_coarse
if Htpsit_nG is not None:
Htpsit_nG[n1] += f2 * vt_G * psit2_G
if n1 == n2:
kpt.vt_nG[n1] = f1 * vt_G
else:
Htpsit_nG[n2] += f1 * vt_G * psit1_G
# Update the vxx_uni and vxx_unii vectors of the nuclei,
# used to determine the atomic hamiltonian, and the
# residuals
v_aL = self.ghat.dict()
self.ghat.integrate(vt_g, v_aL)
for a, v_L in v_aL.items():
v_ii = unpack(np.dot(setups[a].Delta_pL, v_L))
v_ni = kpt.vxx_ani[a]
v_nii = kpt.vxx_anii[a]
P_ni = P_ani[a]
v_ni[n1] += f2 * np.dot(v_ii, P_ni[n2])
if n1 != n2:
v_ni[n2] += f1 * np.dot(v_ii, P_ni[n1])
else:
# XXX Check this:
v_nii[n1] = f1 * v_ii
# Apply the atomic corrections to the energy and the Hamiltonian matrix
for a, P_ni in P_ani.items():
setup = setups[a]
if Htpsit_nG is not None:
# Add non-trivial corrections the Hamiltonian matrix
h_nn = symmetrize(
np.inner(P_ni[:nbands], kpt.vxx_ani[a][:nbands]))
ekin -= np.dot(kpt.f_n[:nbands], h_nn.diagonal())
dH_p = dH_asp[a][kpt.s]
# Get atomic density and Hamiltonian matrices
D_p = self.density.D_asp[a][kpt.s]
D_ii = unpack2(D_p)
ni = len(D_ii)
# Add atomic corrections to the valence-valence exchange energy
# --
# > D C D
# -- ii iiii 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)
if Htpsit_nG is not None:
dH_p[p12] -= 2 * hybrid / deg * A / ((i1 != i2) + 1)
ekin += 2 * hybrid / deg * D_ii[i1, i2] * A
exx -= hybrid / deg * D_ii[i1, i2] * A
# Add valence-core exchange energy
# --
# > X D
# -- ii ii
if setup.X_p is not None:
exx -= hybrid * np.dot(D_p, setup.X_p)
if Htpsit_nG is not None:
dH_p -= hybrid * setup.X_p
ekin += hybrid * np.dot(D_p, setup.X_p)
# Add core-core exchange energy
if kpt.s == 0:
exx += hybrid * setup.ExxC
self.exx_s[kpt.s] = self.gd.comm.sum(exx)
self.ekin_s[kpt.s] = self.gd.comm.sum(ekin)
def with_ae_corrections(self, finegrid=False):
"""Get pair density including the AE corrections"""
nij_g = self.get(finegrid)
# Generate the density matrix
D_ap = {}
# D_aii = {}
for a, P_ni in self.P_ani.items():
Pi_i = P_ni[self.i]
Pj_i = P_ni[self.j]
D_ii = np.outer(Pi_i.conj(), Pj_i)
# Note: D_ii is not symmetric but the products of partial waves are
# so that we can pack
D_ap[a] = pack(D_ii)
# D_aii[a] = D_ii
# Load partial waves if needed
if ((finegrid and (not hasattr(self, 'phi')))
or ((not finegrid) and (not hasattr(self, 'Phi')))):
# Splines
splines = {}
phi_aj = []
phit_aj = []
for a, id in enumerate(self.setups.id_a):
if id in splines:
phi_j, phit_j = splines[id]
else:
# Load splines:
phi_j, phit_j = self.setups[a].get_partial_waves()[:2]
splines[id] = (phi_j, phit_j)
phi_aj.append(phi_j)
phit_aj.append(phit_j)
# Store partial waves as class variables
if finegrid:
gd = self.density.finegd
self.__class__.phi = BasisFunctions(gd, phi_aj)
self.__class__.phit = BasisFunctions(gd, phit_aj)
self.__class__.phi.set_positions(self.spos_ac)
self.__class__.phit.set_positions(self.spos_ac)
else:
gd = self.density.gd
self.__class__.Phi = BasisFunctions(gd, phi_aj)
self.__class__.Phit = BasisFunctions(gd, phit_aj)
self.__class__.Phi.set_positions(self.spos_ac)
self.__class__.Phit.set_positions(self.spos_ac)
# Add AE corrections
if finegrid:
phi = self.phi
phit = self.phit
gd = self.density.finegd
else:
phi = self.Phi
phit = self.Phit
gd = self.density.gd
rho_MM = np.zeros((phi.Mmax, phi.Mmax))
M1 = 0
for a, setup in enumerate(self.setups):
ni = setup.ni
D_p = D_ap.get(a)
if D_p is None:
D_p = np.empty((ni * (ni + 1) // 2))
if gd.comm.size > 1:
gd.comm.broadcast(D_p, self.wfs.partition.rank_a[a])
D_ii = unpack2(D_p)
# D_ii = D_aii.get(a)
# if D_ii is None:
# D_ii = np.empty((ni, ni))
# if gd.comm.size > 1:
# gd.comm.broadcast(D_ii, self.wfs.atom_partition.rank_a[a])
M2 = M1 + ni
rho_MM[M1:M2, M1:M2] = D_ii
M1 = M2
# construct_density assumes symmetric rho_MM and
# takes only the upper half of it
phi.construct_density(rho_MM, nij_g, q=-1)
phit.construct_density(-rho_MM, nij_g, q=-1)
# TODO: use ae_valence_density_correction
# phi.lfc.ae_valence_density_correction(
# rho_MM, nij_g, np.zeros(len(phi.M_W), np.intc), np.zeros(self.na))
# phit.lfc.ae_valence_density_correction(
# -rho_MM, nij_g, np.zeros(len(phit.M_W), np.intc), np.zeros(self.na))
return nij_g
def calculate_supercell_matrix(self, dump=0, name=None, filter=None,
include_pseudo=True, atoms=None):
"""Calculate matrix elements of the el-ph coupling in the LCAO basis.
This function calculates the matrix elements between LCAOs and local
atomic gradients of the effective potential. The matrix elements are
calculated for the supercell used to obtain finite-difference
approximations to the derivatives of the effective potential wrt to
atomic displacements.
Parameters
----------
dump: int
Dump supercell matrix to pickle file (default: 0).
0: Supercell matrix not saved
1: Supercell matrix saved in a single pickle file.
2: Dump matrix for different gradients in separate files. Useful
for large systems where the total array gets too large for a
single pickle file.
name: string
User specified name of the generated pickle file(s). If not
provided, the string in the ``name`` attribute is used.
filter: str
Fourier filter atomic gradients of the effective potential. The
specified components (``normal`` or ``umklapp``) are removed
(default: None).
include_pseudo: bool
Include the contribution from the psedupotential in the atomic
gradients. If ``False``, only the gradient of the effective
potential is included (default: True).
atoms: Atoms object
Calculate supercell for an ``Atoms`` object different from the one
provided in the ``__init__`` method (WARNING, NOT working!).
"""
assert self.calc_lcao is not None, "Set LCAO calculator"
# Supercell atoms
if atoms is None:
atoms_N = self.atoms * self.N_c
else:
atoms_N = atoms
# Initialize calculator if required and extract useful quantities
calc = self.calc_lcao
if not hasattr(calc.wfs, 'S_qMM'):
calc.initialize(atoms_N)
calc.initialize_positions(atoms_N)
self.set_basis_info()
basis = calc.input_parameters['basis']
# Extract useful objects from the calculator
wfs = calc.wfs
gd = calc.wfs.gd
kd = calc.wfs.kd
kpt_u = wfs.kpt_u
setups = wfs.setups
nao = setups.nao
bfs = wfs.basis_functions
dtype = wfs.dtype
spin = 0 # XXX
# If gamma calculation, overlap with neighboring cell cannot be removed
if kd.gamma:
print "WARNING: Gamma-point calculation."
else:
# Bloch to real-space converter
tb = TightBinding(atoms_N, calc)
self.timer.write_now("Calculating supercell matrix")
self.timer.write_now("Calculating real-space gradients")
# Calculate finite-difference gradients (in Hartree / Bohr)
V1t_xG, dH1_xasp = self.calculate_gradient()
self.timer.write_now("Finished real-space gradients")
# Fourier filter the atomic gradients of the effective potential
if filter is not None:
self.timer.write_now("Fourier filtering gradients")
V1_xG = V1t_xG.copy()
self.fourier_filter(V1t_xG, components=filter)
self.timer.write_now("Finished Fourier filtering")
# For the contribution from the derivative of the projectors
dP_aqvMi = self.calculate_dP_aqvMi(wfs)
# Equilibrium atomic Hamiltonian matrix (projector coefficients)
dH_asp = pickle.load(open(self.name + '.eq.pckl'))[1]
# Check that the grid is the same as in the calculator
assert np.all(V1t_xG.shape[-3:] == (gd.N_c + gd.pbc_c - 1)), \
"Mismatch in grids."
# Calculate < i k | grad H | j k >, i.e. matrix elements in Bloch basis
# List for supercell matrices;
g_xNNMM = []
self.timer.write_now("Calculating gradient of PAW Hamiltonian")
# Do each cartesian component separately
for i, a in enumerate(self.indices):
for v in range(3):
# Corresponding array index
x = 3 * i + v
V1t_G = V1t_xG[x]
self.timer.write_now("%s-gradient of atom %u" %
(['x','y','z'][v], a))
# Array for different k-point components
g_qMM = np.zeros((len(kpt_u), nao, nao), dtype)
# 1) Gradient of effective potential
self.timer.write_now("Starting gradient of effective potential")
for kpt in kpt_u:
# Matrix elements
geff_MM = np.zeros((nao, nao), dtype)
bfs.calculate_potential_matrix(V1t_G, geff_MM, q=kpt.q)
tri2full(geff_MM, 'L')
# Insert in array
g_qMM[kpt.q] += geff_MM
self.timer.write_now("Finished gradient of effective potential")
if include_pseudo:
self.timer.write_now("Starting gradient of pseudo part")
# 2) Gradient of non-local part (projectors)
self.timer.write_now("Starting gradient of dH^a")
P_aqMi = calc.wfs.P_aqMi
# 2a) dH^a part has contributions from all other atoms
for kpt in kpt_u:
# Matrix elements
gp_MM = np.zeros((nao, nao), dtype)
dH1_asp = dH1_xasp[x]
for a_, dH1_sp in dH1_asp.items():
dH1_ii = unpack2(dH1_sp[spin])
gp_MM += np.dot(P_aqMi[a_][kpt.q], np.dot(dH1_ii,
P_aqMi[a_][kpt.q].T.conjugate()))
g_qMM[kpt.q] += gp_MM
self.timer.write_now("Finished gradient of dH^a")
self.timer.write_now("Starting gradient of projectors")
# 2b) dP^a part has only contributions from the same atoms
dP_qvMi = dP_aqvMi[a]
dH_ii = unpack2(dH_asp[a][spin])
for kpt in kpt_u:
#XXX Sort out the sign here; conclusion -> sign = +1 !
P1HP_MM = +1 * np.dot(dP_qvMi[kpt.q][v], np.dot(dH_ii,
P_aqMi[a][kpt.q].T.conjugate()))
# Matrix elements
gp_MM = P1HP_MM + P1HP_MM.T.conjugate()
g_qMM[kpt.q] += gp_MM
self.timer.write_now("Finished gradient of projectors")
self.timer.write_now("Finished gradient of pseudo part")
# Extract R_c=(0, 0, 0) block by Fourier transforming
if kd.gamma or kd.N_c is None:
g_MM = g_qMM[0]
else:
# Convert to array
g_MM = tb.bloch_to_real_space(g_qMM, R_c=(0, 0, 0))[0]
# Reshape to global unit cell indices
N = np.prod(self.N_c)
# Number of basis function in the primitive cell
assert (nao % N) == 0, "Alarm ...!"
nao_cell = nao / N
g_NMNM = g_MM.reshape((N, nao_cell, N, nao_cell))
g_NNMM = g_NMNM.swapaxes(1, 2).copy()
self.timer.write_now("Finished supercell matrix")
if dump != 2:
g_xNNMM.append(g_NNMM)
else:
if name is not None:
fname = '%s.supercell_matrix_x_%2.2u.%s.pckl' % (name, x, basis)
else:
fname = self.name + \
'.supercell_matrix_x_%2.2u.%s.pckl' % (x, basis)
if kd.comm.rank == 0:
fd = open(fname, 'w')
M_a = self.basis_info['M_a']
nao_a = self.basis_info['niAO_a']
pickle.dump((g_NNMM, M_a, nao_a), fd, 2)
fd.close()
self.timer.write_now("Finished gradient of PAW Hamiltonian")
if dump != 2:
# Collect gradients in one array
self.g_xNNMM = np.array(g_xNNMM)
# Dump to pickle file using binary mode together with basis info
if dump and kd.comm.rank == 0:
if name is not None:
fname = '%s.supercell_matrix.%s.pckl' % (name, basis)
else:
fname = self.name + '.supercell_matrix.%s.pckl' % basis
fd = open(fname, 'w')
M_a = self.basis_info['M_a']
nao_a = self.basis_info['nao_a']
pickle.dump((self.g_xNNMM, M_a, nao_a), fd, 2)
fd.close()
def update(self, density):
"""Calculate effective potential.
The XC-potential and the Hartree potential are evaluated on
the fine grid, and the sum is then restricted to the coarse
grid."""
self.timer.start('Hamiltonian')
if self.vt_sg is None:
self.timer.start('Initialize Hamiltonian')
self.vt_sg = self.finegd.empty(self.nspins * self.ncomp**2)
self.vHt_g = self.finegd.zeros()
self.vt_sG = self.gd.empty(self.nspins * self.ncomp**2)
self.poisson.initialize()
self.timer.stop('Initialize Hamiltonian')
Ekin, Epot, Ebar, Eext, Exc, W_aL = \
self.update_pseudo_potential(density)
self.timer.start('Atomic')
self.dH_asp = {}
for a, D_sp in density.D_asp.items():
W_L = W_aL[a]
setup = self.setups[a]
D_p = D_sp[:self.nspins].sum(0)
dH_p = (setup.K_p + setup.M_p +
setup.MB_p + 2.0 * np.dot(setup.M_pp, D_p) +
np.dot(setup.Delta_pL, W_L))
Ekin += np.dot(setup.K_p, D_p) + setup.Kc
Ebar += setup.MB + np.dot(setup.MB_p, D_p)
Epot += setup.M + np.dot(D_p, (setup.M_p +
np.dot(setup.M_pp, D_p)))
if self.vext is not None:
vext = self.vext.get_taylor(spos_c=self.spos_ac[a, :])
# Tailor expansion to the zeroth order
Eext += vext[0][0] * (sqrt(4 * pi) * density.Q_aL[a][0]
+ setup.Z)
dH_p += vext[0][0] * sqrt(4 * pi) * setup.Delta_pL[:, 0]
if len(vext) > 1:
# Tailor expansion to the first order
Eext += sqrt(4 * pi / 3) * np.dot(vext[1],
density.Q_aL[a][1:4])
# there must be a better way XXXX
Delta_p1 = np.array([setup.Delta_pL[:, 1],
setup.Delta_pL[:, 2],
setup.Delta_pL[:, 3]])
dH_p += sqrt(4 * pi / 3) * np.dot(vext[1], Delta_p1)
self.dH_asp[a] = dH_sp = np.zeros_like(D_sp)
self.timer.start('XC Correction')
Exc += self.xc.calculate_paw_correction(setup, D_sp, dH_sp, a=a)
self.timer.stop('XC Correction')
if setup.HubU is not None:
assert self.collinear
nspins = len(D_sp)
l_j = setup.l_j
l = setup.Hubl
scale = setup.Hubs
nl = np.where(np.equal(l_j,l))[0]
nn = (2*np.array(l_j)+1)[0:nl[0]].sum()
for D_p, H_p in zip(D_sp, self.dH_asp[a]):
[N_mm,V] =self.aoom(unpack2(D_p),a,l, scale)
N_mm = N_mm / 2 * nspins
Eorb = setup.HubU / 2. * (N_mm - np.dot(N_mm,N_mm)).trace()
Vorb = setup.HubU * (0.5 * np.eye(2*l+1) - N_mm)
Exc += Eorb
if nspins == 1:
# add contribution of other spin manyfold
Exc += Eorb
if len(nl)==2:
mm = (2*np.array(l_j)+1)[0:nl[1]].sum()
V[nn:nn+2*l+1,nn:nn+2*l+1] *= Vorb
V[mm:mm+2*l+1,nn:nn+2*l+1] *= Vorb
V[nn:nn+2*l+1,mm:mm+2*l+1] *= Vorb
V[mm:mm+2*l+1,mm:mm+2*l+1] *= Vorb
else:
V[nn:nn+2*l+1,nn:nn+2*l+1] *= Vorb
Htemp = unpack(H_p)
Htemp += V
H_p[:] = pack2(Htemp)
dH_sp[:self.nspins] += dH_p
Ekin -= (D_sp * dH_sp).sum() # NCXXX
self.timer.stop('Atomic')
# Make corrections due to non-local xc:
#xcfunc = self.xc.xcfunc
self.Enlxc = 0.0 # XXXxcfunc.get_non_local_energy()
Ekin += self.xc.get_kinetic_energy_correction() / self.gd.comm.size
energies = np.array([Ekin, Epot, Ebar, Eext, Exc])
self.timer.start('Communicate energies')
self.gd.comm.sum(energies)
# Make sure that all CPUs have the same energies
self.world.broadcast(energies, 0)
self.timer.stop('Communicate energies')
(self.Ekin0, self.Epot, self.Ebar, self.Eext, self.Exc) = energies
#self.Exc += self.Enlxc
#self.Ekin0 += self.Enlkin
self.timer.stop('Hamiltonian')
def update_corrections(self, dens, W_aL):
self.timer.start('Atomic')
self.dH_asp = None # XXXX
e_kinetic = 0.0
e_coulomb = 0.0
e_zero = 0.0
e_external = 0.0
e_xc = 0.0
D_asp = self.atomdist.to_work(dens.D_asp)
dH_asp = self.setups.empty_atomic_matrix(self.nspins, D_asp.partition)
for a, D_sp in D_asp.items():
W_L = W_aL[a]
setup = self.setups[a]
D_p = D_sp.sum(0)
dH_p = (setup.K_p + setup.M_p + setup.MB_p +
2.0 * np.dot(setup.M_pp, D_p) +
np.dot(setup.Delta_pL, W_L))
e_kinetic += np.dot(setup.K_p, D_p) + setup.Kc
e_zero += setup.MB + np.dot(setup.MB_p, D_p)
e_coulomb += setup.M + np.dot(
D_p, (setup.M_p + np.dot(setup.M_pp, D_p)))
dH_asp[a] = dH_sp = np.zeros_like(D_sp)
if setup.HubU is not None:
nspins = len(D_sp)
l_j = setup.l_j
l = setup.Hubl
scale = setup.Hubs
nl = np.where(np.equal(l_j, l))[0]
nn = (2 * np.array(l_j) + 1)[0:nl[0]].sum()
for D_p, H_p in zip(D_sp, dH_asp[a]):
[N_mm, V] = self.aoom(unpack2(D_p), a, l, scale)
N_mm = N_mm / 2 * nspins
Eorb = setup.HubU / 2. * (N_mm -
np.dot(N_mm, N_mm)).trace()
Vorb = setup.HubU * (0.5 * np.eye(2 * l + 1) - N_mm)
e_xc += Eorb
if nspins == 1:
# add contribution of other spin manyfold
e_xc += Eorb
if len(nl) == 2:
mm = (2 * np.array(l_j) + 1)[0:nl[1]].sum()
V[nn:nn + 2 * l + 1, nn:nn + 2 * l + 1] *= Vorb
V[mm:mm + 2 * l + 1, nn:nn + 2 * l + 1] *= Vorb
V[nn:nn + 2 * l + 1, mm:mm + 2 * l + 1] *= Vorb
V[mm:mm + 2 * l + 1, mm:mm + 2 * l + 1] *= Vorb
else:
V[nn:nn + 2 * l + 1, nn:nn + 2 * l + 1] *= Vorb
Htemp = unpack(H_p)
Htemp += V
H_p[:] = pack2(Htemp)
dH_sp += dH_p
if self.ref_dH_asp:
dH_sp += self.ref_dH_asp[a]
self.timer.start('XC Correction')
for a, D_sp in D_asp.items():
e_xc += self.xc.calculate_paw_correction(self.setups[a],
D_sp,
dH_asp[a],
a=a)
self.timer.stop('XC Correction')
for a, D_sp in D_asp.items():
e_kinetic -= (D_sp * dH_asp[a]).sum() # NCXXX
self.dH_asp = self.atomdist.from_work(dH_asp)
self.timer.stop('Atomic')
# Make corrections due to non-local xc:
self.Enlxc = 0.0 # XXXxcfunc.get_non_local_energy()
e_kinetic += self.xc.get_kinetic_energy_correction() / self.world.size
return np.array([e_kinetic, e_coulomb, e_zero, e_external, e_xc])
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 update(self, density):
"""Calculate effective potential.
The XC-potential and the Hartree potential are evaluated on
the fine grid, and the sum is then restricted to the coarse
grid."""
self.timer.start('Hamiltonian')
if self.vt_sg is None:
self.timer.start('Initialize Hamiltonian')
self.vt_sg = self.finegd.empty(self.nspins)
self.vHt_g = self.finegd.zeros()
self.vt_sG = self.gd.empty(self.nspins)
self.poisson.initialize()
self.timer.stop('Initialize Hamiltonian')
self.timer.start('vbar')
Ebar = self.finegd.integrate(self.vbar_g, density.nt_g,
global_integral=False)
vt_g = self.vt_sg[0]
vt_g[:] = self.vbar_g
self.timer.stop('vbar')
Eext = 0.0
if self.vext_g is not None:
vt_g += self.vext_g.get_potential(self.finegd)
Eext = self.finegd.integrate(vt_g, density.nt_g,
global_integral=False) - Ebar
if self.nspins == 2:
self.vt_sg[1] = vt_g
self.timer.start('XC 3D grid')
Exc = self.xc.calculate(self.finegd, density.nt_sg, self.vt_sg)
Exc /= self.gd.comm.size
self.timer.stop('XC 3D grid')
self.timer.start('Poisson')
# npoisson is the number of iterations:
self.npoisson = self.poisson.solve(self.vHt_g, density.rhot_g,
charge=-density.charge)
self.timer.stop('Poisson')
self.timer.start('Hartree integrate/restrict')
Epot = 0.5 * self.finegd.integrate(self.vHt_g, density.rhot_g,
global_integral=False)
Ekin = 0.0
for vt_g, vt_G, nt_G in zip(self.vt_sg, self.vt_sG, density.nt_sG):
vt_g += self.vHt_g
self.restrict(vt_g, vt_G)
Ekin -= self.gd.integrate(vt_G, nt_G - density.nct_G,
global_integral=False)
self.timer.stop('Hartree integrate/restrict')
# Calculate atomic hamiltonians:
self.timer.start('Atomic')
W_aL = {}
for a in density.D_asp:
W_aL[a] = np.empty((self.setups[a].lmax + 1)**2)
density.ghat.integrate(self.vHt_g, W_aL)
self.dH_asp = {}
for a, D_sp in density.D_asp.items():
W_L = W_aL[a]
setup = self.setups[a]
D_p = D_sp.sum(0)
dH_p = (setup.K_p + setup.M_p +
setup.MB_p + 2.0 * np.dot(setup.M_pp, D_p) +
np.dot(setup.Delta_pL, W_L))
Ekin += np.dot(setup.K_p, D_p) + setup.Kc
Ebar += setup.MB + np.dot(setup.MB_p, D_p)
Epot += setup.M + np.dot(D_p, (setup.M_p +
np.dot(setup.M_pp, D_p)))
if self.vext_g is not None:
vext = self.vext_g.get_taylor(spos_c=self.spos_ac[a, :])
# Tailor expansion to the zeroth order
Eext += vext[0][0] * (sqrt(4 * pi) * density.Q_aL[a][0]
+ setup.Z)
dH_p += vext[0][0] * sqrt(4 * pi) * setup.Delta_pL[:, 0]
if len(vext) > 1:
# Tailor expansion to the first order
Eext += sqrt(4 * pi / 3) * np.dot(vext[1],
density.Q_aL[a][1:4])
# there must be a better way XXXX
Delta_p1 = np.array([setup.Delta_pL[:, 1],
setup.Delta_pL[:, 2],
setup.Delta_pL[:, 3]])
dH_p += sqrt(4 * pi / 3) * np.dot(vext[1], Delta_p1)
self.dH_asp[a] = dH_sp = np.zeros_like(D_sp)
self.timer.start('XC Correction')
Exc += setup.xc_correction.calculate(self.xc, D_sp, dH_sp, a)
self.timer.stop('XC Correction')
if setup.HubU is not None:
nspins = len(D_sp)
l_j = setup.l_j
l = setup.Hubl
nl = np.where(np.equal(l_j,l))[0]
nn = (2*np.array(l_j)+1)[0:nl[0]].sum()
for D_p, H_p in zip(D_sp, self.dH_asp[a]):
[N_mm,V] =self.aoom(unpack2(D_p),a,l)
N_mm = N_mm / 2 * nspins
Eorb = setup.HubU / 2. * (N_mm - np.dot(N_mm,N_mm)).trace()
Vorb = setup.HubU * (0.5 * np.eye(2*l+1) - N_mm)
Exc += Eorb
if nspins == 1:
# add contribution of other spin manyfold
Exc += Eorb
if len(nl)==2:
mm = (2*np.array(l_j)+1)[0:nl[1]].sum()
V[nn:nn+2*l+1,nn:nn+2*l+1] *= Vorb
V[mm:mm+2*l+1,nn:nn+2*l+1] *= Vorb
V[nn:nn+2*l+1,mm:mm+2*l+1] *= Vorb
V[mm:mm+2*l+1,mm:mm+2*l+1] *= Vorb
else:
V[nn:nn+2*l+1,nn:nn+2*l+1] *= Vorb
Htemp = unpack(H_p)
Htemp += V
H_p[:] = pack2(Htemp)
dH_sp += dH_p
Ekin -= (D_sp * dH_sp).sum()
self.timer.stop('Atomic')
# Make corrections due to non-local xc:
#xcfunc = self.xc.xcfunc
self.Enlxc = 0.0#XXXxcfunc.get_non_local_energy()
Ekin += self.xc.get_kinetic_energy_correction() / self.gd.comm.size
energies = np.array([Ekin, Epot, Ebar, Eext, Exc])
self.timer.start('Communicate energies')
self.gd.comm.sum(energies)
self.timer.stop('Communicate energies')
(self.Ekin0, self.Epot, self.Ebar, self.Eext, self.Exc) = energies
#self.Exc += self.Enlxc
#self.Ekin0 += self.Enlkin
self.timer.stop('Hamiltonian')
def apply_orbital_dependent_hamiltonian(self, kpt, psit_nG,
Htpsit_nG=None, dH_asp=None):
if kpt.f_n is None:
return
deg = 2 // self.nspins # Spin degeneracy
hybrid = self.hybrid
P_ani = kpt.P_ani
setups = self.setups
vt_g = self.finegd.empty()
if self.gd is not self.finegd:
vt_G = self.gd.empty()
nocc = int(kpt.f_n.sum()) // (3 - self.nspins)
if self.unocc:
nbands = len(kpt.f_n)
else:
nbands = nocc
self.nocc_s[kpt.s] = nocc
if Htpsit_nG is not None:
kpt.vt_nG = self.gd.empty(nbands)
kpt.vxx_ani = {}
kpt.vxx_anii = {}
for a, P_ni in P_ani.items():
I = P_ni.shape[1]
kpt.vxx_ani[a] = np.zeros((nbands, I))
kpt.vxx_anii[a] = np.zeros((nbands, I, I))
exx = 0.0
ekin = 0.0
# Determine pseudo-exchange
for n1 in range(nbands):
psit1_G = psit_nG[n1]
f1 = kpt.f_n[n1] / deg
for n2 in range(n1, nbands):
psit2_G = psit_nG[n2]
f2 = kpt.f_n[n2] / deg
# Double count factor:
dc = (1 + (n1 != n2)) * deg
nt_G, rhot_g = self.calculate_pair_density(n1, n2, psit_nG,
P_ani)
vt_g[:] = 0.0
iter = self.poissonsolver.solve(vt_g, -rhot_g,
charge=-float(n1 == n2),
eps=1e-12,
zero_initial_phi=True)
vt_g *= hybrid
if self.gd is self.finegd:
vt_G = vt_g
else:
self.restrictor.apply(vt_g, vt_G)
# Integrate the potential on fine and coarse grids
int_fine = self.finegd.integrate(vt_g * rhot_g)
int_coarse = self.gd.integrate(vt_G * nt_G)
if self.gd.comm.rank == 0: # only add to energy on master CPU
exx += 0.5 * dc * f1 * f2 * int_fine
ekin -= dc * f1 * f2 * int_coarse
if Htpsit_nG is not None:
Htpsit_nG[n1] += f2 * vt_G * psit2_G
if n1 == n2:
kpt.vt_nG[n1] = f1 * vt_G
else:
Htpsit_nG[n2] += f1 * vt_G * psit1_G
# Update the vxx_uni and vxx_unii vectors of the nuclei,
# used to determine the atomic hamiltonian, and the
# residuals
v_aL = self.ghat.dict()
self.ghat.integrate(vt_g, v_aL)
for a, v_L in v_aL.items():
v_ii = unpack(np.dot(setups[a].Delta_pL, v_L))
v_ni = kpt.vxx_ani[a]
v_nii = kpt.vxx_anii[a]
P_ni = P_ani[a]
v_ni[n1] += f2 * np.dot(v_ii, P_ni[n2])
if n1 != n2:
v_ni[n2] += f1 * np.dot(v_ii, P_ni[n1])
else:
# XXX Check this:
v_nii[n1] = f1 * v_ii
# Apply the atomic corrections to the energy and the Hamiltonian matrix
for a, P_ni in P_ani.items():
setup = setups[a]
if Htpsit_nG is not None:
# Add non-trivial corrections the Hamiltonian matrix
h_nn = symmetrize(np.inner(P_ni[:nbands],
kpt.vxx_ani[a][:nbands]))
ekin -= np.dot(kpt.f_n[:nbands], h_nn.diagonal())
dH_p = dH_asp[a][kpt.s]
# Get atomic density and Hamiltonian matrices
D_p = self.density.D_asp[a][kpt.s]
D_ii = unpack2(D_p)
ni = len(D_ii)
# Add atomic corrections to the valence-valence exchange energy
# --
# > D C D
# -- ii iiii 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)
if Htpsit_nG is not None:
dH_p[p12] -= 2 * hybrid / deg * A / ((i1 != i2) + 1)
ekin += 2 * hybrid / deg * D_ii[i1, i2] * A
exx -= hybrid / deg * D_ii[i1, i2] * A
# Add valence-core exchange energy
# --
# > X D
# -- ii ii
if setup.X_p is not None:
exx -= hybrid * np.dot(D_p, setup.X_p)
if Htpsit_nG is not None:
dH_p -= hybrid * setup.X_p
ekin += hybrid * np.dot(D_p, setup.X_p)
# Add core-core exchange energy
if kpt.s == 0:
exx += hybrid * setup.ExxC
self.exx_s[kpt.s] = self.gd.comm.sum(exx)
self.ekin_s[kpt.s] = self.gd.comm.sum(ekin)
def update(self, density):
"""Calculate effective potential.
The XC-potential and the Hartree potential are evaluated on
the fine grid, and the sum is then restricted to the coarse
grid."""
self.timer.start("Hamiltonian")
if self.vt_sg is None:
self.timer.start("Initialize Hamiltonian")
self.vt_sg = self.finegd.empty(self.ns)
self.vHt_g = self.finegd.zeros()
self.vt_sG = self.gd.empty(self.ns)
self.poisson.initialize()
self.timer.stop("Initialize Hamiltonian")
Ekin, Epot, Ebar, Eext, Exc, W_aL = self.update_pseudo_potential(density)
self.timer.start("Atomic")
self.dH_asp = None # XXXX
dH_asp = {}
for a, D_sp in density.D_asp.items():
W_L = W_aL[a]
setup = self.setups[a]
D_p = D_sp[: self.nspins].sum(0)
dH_p = setup.K_p + setup.M_p + setup.MB_p + 2.0 * np.dot(setup.M_pp, D_p) + np.dot(setup.Delta_pL, W_L)
Ekin += np.dot(setup.K_p, D_p) + setup.Kc
Ebar += setup.MB + np.dot(setup.MB_p, D_p)
Epot += setup.M + np.dot(D_p, (setup.M_p + np.dot(setup.M_pp, D_p)))
if self.vext is not None:
vext = self.vext.get_taylor(spos_c=self.spos_ac[a, :])
# Tailor expansion to the zeroth order
Eext += vext[0][0] * (sqrt(4 * pi) * density.Q_aL[a][0] + setup.Z)
dH_p += vext[0][0] * sqrt(4 * pi) * setup.Delta_pL[:, 0]
if len(vext) > 1:
# Tailor expansion to the first order
Eext += sqrt(4 * pi / 3) * np.dot(vext[1], density.Q_aL[a][1:4])
# there must be a better way XXXX
Delta_p1 = np.array([setup.Delta_pL[:, 1], setup.Delta_pL[:, 2], setup.Delta_pL[:, 3]])
dH_p += sqrt(4 * pi / 3) * np.dot(vext[1], Delta_p1)
dH_asp[a] = dH_sp = np.zeros_like(D_sp)
if setup.HubU is not None:
assert self.collinear
nspins = len(D_sp)
l_j = setup.l_j
l = setup.Hubl
scale = setup.Hubs
nl = np.where(np.equal(l_j, l))[0]
nn = (2 * np.array(l_j) + 1)[0 : nl[0]].sum()
for D_p, H_p in zip(D_sp, dH_asp[a]):
[N_mm, V] = self.aoom(unpack2(D_p), a, l, scale)
N_mm = N_mm / 2 * nspins
Eorb = setup.HubU / 2.0 * (N_mm - np.dot(N_mm, N_mm)).trace()
Vorb = setup.HubU * (0.5 * np.eye(2 * l + 1) - N_mm)
Exc += Eorb
if nspins == 1:
# add contribution of other spin manyfold
Exc += Eorb
if len(nl) == 2:
mm = (2 * np.array(l_j) + 1)[0 : nl[1]].sum()
V[nn : nn + 2 * l + 1, nn : nn + 2 * l + 1] *= Vorb
V[mm : mm + 2 * l + 1, nn : nn + 2 * l + 1] *= Vorb
V[nn : nn + 2 * l + 1, mm : mm + 2 * l + 1] *= Vorb
V[mm : mm + 2 * l + 1, mm : mm + 2 * l + 1] *= Vorb
else:
V[nn : nn + 2 * l + 1, nn : nn + 2 * l + 1] *= Vorb
Htemp = unpack(H_p)
Htemp += V
H_p[:] = pack2(Htemp)
dH_sp[: self.nspins] += dH_p
if self.ref_dH_asp:
dH_sp += self.ref_dH_asp[a]
# We are not yet done with dH_sp; still need XC correction below
Ddist_asp = self.dh_distributor.distribute(density.D_asp)
dHdist_asp = {}
Exca = 0.0
self.timer.start("XC Correction")
for a, D_sp in Ddist_asp.items():
setup = self.setups[a]
dH_sp = np.zeros_like(D_sp)
Exca += self.xc.calculate_paw_correction(setup, D_sp, dH_sp, a=a)
# XXX Exc are added on the "wrong" distribution; sum only works
# when gd.comm and distribution comm are the same
dHdist_asp[a] = dH_sp
self.timer.stop("XC Correction")
dHdist_asp = self.dh_distributor.collect(dHdist_asp)
# Exca has contributions from all cores so modify it so it is
# parallel in the same way as the other energies.
Exca = self.world.sum(Exca)
if self.gd.comm.rank == 0:
Exc += Exca
assert len(dHdist_asp) == len(self.atom_partition.my_indices)
for a, D_sp in density.D_asp.items():
dH_sp = dH_asp[a]
dH_sp += dHdist_asp[a]
Ekin -= (D_sp * dH_sp).sum() # NCXXX
self.dH_asp = dH_asp
self.timer.stop("Atomic")
# Make corrections due to non-local xc:
# xcfunc = self.xc.xcfunc
self.Enlxc = 0.0 # XXXxcfunc.get_non_local_energy()
Ekin += self.xc.get_kinetic_energy_correction() / self.gd.comm.size
energies = np.array([Ekin, Epot, Ebar, Eext, Exc])
self.timer.start("Communicate energies")
self.gd.comm.sum(energies)
# Make sure that all CPUs have the same energies
self.world.broadcast(energies, 0)
self.timer.stop("Communicate energies")
(self.Ekin0, self.Epot, self.Ebar, self.Eext, self.Exc) = energies
# self.Exc += self.Enlxc
# self.Ekin0 += self.Enlkin
self.timer.stop("Hamiltonian")
def new_get_all_electron_density(self, atoms, gridrefinement=2):
"""Return real all-electron density array."""
# Refinement of coarse grid, for representation of the AE-density
if gridrefinement == 1:
gd = self.gd
n_sg = self.nt_sG.copy()
elif gridrefinement == 2:
gd = self.finegd
if self.nt_sg is None:
self.interpolate()
n_sg = self.nt_sg.copy()
elif gridrefinement == 4:
# Extra fine grid
gd = self.finegd.refine()
# Interpolation function for the density:
interpolator = Transformer(self.finegd, gd, 3)
# Transfer the pseudo-density to the fine grid:
n_sg = gd.empty(self.nspins)
if self.nt_sg is None:
self.interpolate()
for s in range(self.nspins):
interpolator.apply(self.nt_sg[s], n_sg[s])
else:
raise NotImplementedError
# Add corrections to pseudo-density to get the AE-density
splines = {}
phi_aj = []
phit_aj = []
nc_a = []
nct_a = []
for a, id in enumerate(self.setups.id_a):
if id in splines:
phi_j, phit_j, nc, nct = splines[id]
else:
# Load splines:
phi_j, phit_j, nc, nct = self.setups[a].get_partial_waves()[:4]
splines[id] = (phi_j, phit_j, nc, nct)
phi_aj.append(phi_j)
phit_aj.append(phit_j)
nc_a.append([nc])
nct_a.append([nct])
# Create localized functions from splines
phi = BasisFunctions(gd, phi_aj)
phit = BasisFunctions(gd, phit_aj)
nc = LFC(gd, nc_a)
nct = LFC(gd, nct_a)
spos_ac = atoms.get_scaled_positions() % 1.0
phi.set_positions(spos_ac)
phit.set_positions(spos_ac)
nc.set_positions(spos_ac)
nct.set_positions(spos_ac)
I_sa = np.zeros((self.nspins, len(atoms)))
a_W = np.empty(len(phi.M_W), np.int32)
W = 0
for a in phi.atom_indices:
nw = len(phi.sphere_a[a].M_w)
a_W[W:W + nw] = a
W += nw
rho_MM = np.zeros((phi.Mmax, phi.Mmax))
for s, I_a in enumerate(I_sa):
M1 = 0
for a, setup in enumerate(self.setups):
ni = setup.ni
D_sp = self.D_asp.get(a)
if D_sp is None:
D_sp = np.empty((self.nspins, ni * (ni + 1) // 2))
else:
I_a[a] = ((setup.Nct - setup.Nc) / self.nspins -
sqrt(4 * pi) *
np.dot(D_sp[s], setup.Delta_pL[:, 0]))
if gd.comm.size > 1:
gd.comm.broadcast(D_sp, self.rank_a[a])
M2 = M1 + ni
rho_MM[M1:M2, M1:M2] = unpack2(D_sp[s])
M1 = M2
phi.lfc.ae_valence_density_correction(rho_MM, n_sg[s], a_W, I_a)
phit.lfc.ae_valence_density_correction(-rho_MM, n_sg[s], a_W, I_a)
a_W = np.empty(len(nc.M_W), np.int32)
W = 0
for a in nc.atom_indices:
nw = len(nc.sphere_a[a].M_w)
a_W[W:W + nw] = a
W += nw
scale = 1.0 / self.nspins
for s, I_a in enumerate(I_sa):
nc.lfc.ae_core_density_correction(scale, n_sg[s], a_W, I_a)
nct.lfc.ae_core_density_correction(-scale, n_sg[s], a_W, I_a)
gd.comm.sum(I_a)
N_c = gd.N_c
g_ac = np.around(N_c * spos_ac).astype(int) % N_c - gd.beg_c
for I, g_c in zip(I_a, g_ac):
if (g_c >= 0).all() and (g_c < gd.n_c).all():
n_sg[s][tuple(g_c)] -= I / gd.dv
return n_sg, gd
def calculate_supercell_matrix(self,
dump=0,
name=None,
filter=None,
include_pseudo=True,
atoms=None):
"""Calculate matrix elements of the el-ph coupling in the LCAO basis.
This function calculates the matrix elements between LCAOs and local
atomic gradients of the effective potential. The matrix elements are
calculated for the supercell used to obtain finite-difference
approximations to the derivatives of the effective potential wrt to
atomic displacements.
Parameters
----------
dump: int
Dump supercell matrix to pickle file (default: 0).
0: Supercell matrix not saved
1: Supercell matrix saved in a single pickle file.
2: Dump matrix for different gradients in separate files. Useful
for large systems where the total array gets too large for a
single pickle file.
name: string
User specified name of the generated pickle file(s). If not
provided, the string in the ``name`` attribute is used.
filter: str
Fourier filter atomic gradients of the effective potential. The
specified components (``normal`` or ``umklapp``) are removed
(default: None).
include_pseudo: bool
Include the contribution from the psedupotential in the atomic
gradients. If ``False``, only the gradient of the effective
potential is included (default: True).
atoms: Atoms object
Calculate supercell for an ``Atoms`` object different from the one
provided in the ``__init__`` method (WARNING, NOT working!).
"""
assert self.calc_lcao is not None, "Set LCAO calculator"
# Supercell atoms
if atoms is None:
atoms_N = self.atoms * self.N_c
else:
atoms_N = atoms
# Initialize calculator if required and extract useful quantities
calc = self.calc_lcao
if not hasattr(calc.wfs, 'S_qMM'):
calc.initialize(atoms_N)
calc.initialize_positions(atoms_N)
self.set_basis_info()
basis = calc.input_parameters['basis']
# Extract useful objects from the calculator
wfs = calc.wfs
gd = calc.wfs.gd
kd = calc.wfs.kd
kpt_u = wfs.kpt_u
setups = wfs.setups
nao = setups.nao
bfs = wfs.basis_functions
dtype = wfs.dtype
spin = 0 # XXX
# If gamma calculation, overlap with neighboring cell cannot be removed
if kd.gamma:
print("WARNING: Gamma-point calculation.")
else:
# Bloch to real-space converter
tb = TightBinding(atoms_N, calc)
self.timer.write_now("Calculating supercell matrix")
self.timer.write_now("Calculating real-space gradients")
# Calculate finite-difference gradients (in Hartree / Bohr)
V1t_xG, dH1_xasp = self.calculate_gradient()
self.timer.write_now("Finished real-space gradients")
# Fourier filter the atomic gradients of the effective potential
if filter is not None:
self.timer.write_now("Fourier filtering gradients")
V1_xG = V1t_xG.copy()
self.fourier_filter(V1t_xG, components=filter)
self.timer.write_now("Finished Fourier filtering")
# For the contribution from the derivative of the projectors
dP_aqvMi = self.calculate_dP_aqvMi(wfs)
# Equilibrium atomic Hamiltonian matrix (projector coefficients)
dH_asp = pickle.load(open(self.name + '.eq.pckl'))[1]
# Check that the grid is the same as in the calculator
assert np.all(V1t_xG.shape[-3:] == (gd.N_c + gd.pbc_c - 1)), \
"Mismatch in grids."
# Calculate < i k | grad H | j k >, i.e. matrix elements in Bloch basis
# List for supercell matrices;
g_xNNMM = []
self.timer.write_now("Calculating gradient of PAW Hamiltonian")
# Do each cartesian component separately
for i, a in enumerate(self.indices):
for v in range(3):
# Corresponding array index
x = 3 * i + v
V1t_G = V1t_xG[x]
self.timer.write_now("%s-gradient of atom %u" %
(['x', 'y', 'z'][v], a))
# Array for different k-point components
g_qMM = np.zeros((len(kpt_u), nao, nao), dtype)
# 1) Gradient of effective potential
self.timer.write_now(
"Starting gradient of effective potential")
for kpt in kpt_u:
# Matrix elements
geff_MM = np.zeros((nao, nao), dtype)
bfs.calculate_potential_matrix(V1t_G, geff_MM, q=kpt.q)
tri2full(geff_MM, 'L')
# Insert in array
g_qMM[kpt.q] += geff_MM
self.timer.write_now(
"Finished gradient of effective potential")
if include_pseudo:
self.timer.write_now("Starting gradient of pseudo part")
# 2) Gradient of non-local part (projectors)
self.timer.write_now("Starting gradient of dH^a")
P_aqMi = calc.wfs.P_aqMi
# 2a) dH^a part has contributions from all other atoms
for kpt in kpt_u:
# Matrix elements
gp_MM = np.zeros((nao, nao), dtype)
dH1_asp = dH1_xasp[x]
for a_, dH1_sp in dH1_asp.items():
dH1_ii = unpack2(dH1_sp[spin])
gp_MM += np.dot(
P_aqMi[a_][kpt.q],
np.dot(dH1_ii,
P_aqMi[a_][kpt.q].T.conjugate()))
g_qMM[kpt.q] += gp_MM
self.timer.write_now("Finished gradient of dH^a")
self.timer.write_now("Starting gradient of projectors")
# 2b) dP^a part has only contributions from the same atoms
dP_qvMi = dP_aqvMi[a]
dH_ii = unpack2(dH_asp[a][spin])
for kpt in kpt_u:
#XXX Sort out the sign here; conclusion -> sign = +1 !
P1HP_MM = +1 * np.dot(
dP_qvMi[kpt.q][v],
np.dot(dH_ii, P_aqMi[a][kpt.q].T.conjugate()))
# Matrix elements
gp_MM = P1HP_MM + P1HP_MM.T.conjugate()
g_qMM[kpt.q] += gp_MM
self.timer.write_now("Finished gradient of projectors")
self.timer.write_now("Finished gradient of pseudo part")
# Extract R_c=(0, 0, 0) block by Fourier transforming
if kd.gamma or kd.N_c is None:
g_MM = g_qMM[0]
else:
# Convert to array
g_MM = tb.bloch_to_real_space(g_qMM, R_c=(0, 0, 0))[0]
# Reshape to global unit cell indices
N = np.prod(self.N_c)
# Number of basis function in the primitive cell
assert (nao % N) == 0, "Alarm ...!"
nao_cell = nao / N
g_NMNM = g_MM.reshape((N, nao_cell, N, nao_cell))
g_NNMM = g_NMNM.swapaxes(1, 2).copy()
self.timer.write_now("Finished supercell matrix")
if dump != 2:
g_xNNMM.append(g_NNMM)
else:
if name is not None:
fname = '%s.supercell_matrix_x_%2.2u.%s.pckl' % (
name, x, basis)
else:
fname = self.name + \
'.supercell_matrix_x_%2.2u.%s.pckl' % (x, basis)
if kd.comm.rank == 0:
fd = open(fname, 'w')
M_a = self.basis_info['M_a']
nao_a = self.basis_info['nao_a']
pickle.dump((g_NNMM, M_a, nao_a), fd, 2)
fd.close()
self.timer.write_now("Finished gradient of PAW Hamiltonian")
if dump != 2:
# Collect gradients in one array
self.g_xNNMM = np.array(g_xNNMM)
# Dump to pickle file using binary mode together with basis info
if dump and kd.comm.rank == 0:
if name is not None:
fname = '%s.supercell_matrix.%s.pckl' % (name, basis)
else:
fname = self.name + '.supercell_matrix.%s.pckl' % basis
fd = open(fname, 'w')
M_a = self.basis_info['M_a']
nao_a = self.basis_info['nao_a']
pickle.dump((self.g_xNNMM, M_a, nao_a), fd, 2)
fd.close()
def get_all_electron_density(self,
atoms=None,
gridrefinement=2,
spos_ac=None,
skip_core=False):
"""Return real all-electron density array.
Usage: Either get_all_electron_density(atoms) or
get_all_electron_density(spos_ac=spos_ac)
skip_core=True theoretically returns the
all-electron valence density (use with
care; will not in general integrate
to valence)
"""
if spos_ac is None:
spos_ac = atoms.get_scaled_positions() % 1.0
# Refinement of coarse grid, for representation of the AE-density
# XXXXXXXXXXXX think about distribution depending on gridrefinement!
if gridrefinement == 1:
gd = self.redistributor.aux_gd
n_sg = self.nt_sG.copy()
# This will get the density with the same distribution
# as finegd:
n_sg = self.redistributor.distribute(n_sg)
elif gridrefinement == 2:
gd = self.finegd
if self.nt_sg is None:
self.interpolate_pseudo_density()
n_sg = self.nt_sg.copy()
elif gridrefinement == 4:
# Extra fine grid
gd = self.finegd.refine()
# Interpolation function for the density:
interpolator = Transformer(self.finegd, gd, 3) # XXX grids!
# Transfer the pseudo-density to the fine grid:
n_sg = gd.empty(self.nspins)
if self.nt_sg is None:
self.interpolate_pseudo_density()
for s in range(self.nspins):
interpolator.apply(self.nt_sg[s], n_sg[s])
else:
raise NotImplementedError
# Add corrections to pseudo-density to get the AE-density
splines = {}
phi_aj = []
phit_aj = []
nc_a = []
nct_a = []
for a, id in enumerate(self.setups.id_a):
if id in splines:
phi_j, phit_j, nc, nct = splines[id]
else:
# Load splines:
phi_j, phit_j, nc, nct = self.setups[a].get_partial_waves()[:4]
splines[id] = (phi_j, phit_j, nc, nct)
phi_aj.append(phi_j)
phit_aj.append(phit_j)
nc_a.append([nc])
nct_a.append([nct])
# Create localized functions from splines
phi = BasisFunctions(gd, phi_aj)
phit = BasisFunctions(gd, phit_aj)
nc = LFC(gd, nc_a)
nct = LFC(gd, nct_a)
phi.set_positions(spos_ac)
phit.set_positions(spos_ac)
nc.set_positions(spos_ac)
nct.set_positions(spos_ac)
I_sa = np.zeros((self.nspins, len(spos_ac)))
a_W = np.empty(len(phi.M_W), np.intc)
W = 0
for a in phi.atom_indices:
nw = len(phi.sphere_a[a].M_w)
a_W[W:W + nw] = a
W += nw
x_W = phi.create_displacement_arrays()[0]
D_asp = self.D_asp # XXX really?
rho_MM = np.zeros((phi.Mmax, phi.Mmax))
for s, I_a in enumerate(I_sa):
M1 = 0
for a, setup in enumerate(self.setups):
ni = setup.ni
D_sp = D_asp.get(a)
if D_sp is None:
D_sp = np.empty((self.nspins, ni * (ni + 1) // 2))
else:
I_a[a] = (
(setup.Nct) / self.nspins -
sqrt(4 * pi) * np.dot(D_sp[s], setup.Delta_pL[:, 0]))
if not skip_core:
I_a[a] -= setup.Nc / self.nspins
if gd.comm.size > 1:
gd.comm.broadcast(D_sp, D_asp.partition.rank_a[a])
M2 = M1 + ni
rho_MM[M1:M2, M1:M2] = unpack2(D_sp[s])
M1 = M2
assert np.all(n_sg[s].shape == phi.gd.n_c)
phi.lfc.ae_valence_density_correction(rho_MM, n_sg[s], a_W, I_a,
x_W)
phit.lfc.ae_valence_density_correction(-rho_MM, n_sg[s], a_W, I_a,
x_W)
a_W = np.empty(len(nc.M_W), np.intc)
W = 0
for a in nc.atom_indices:
nw = len(nc.sphere_a[a].M_w)
a_W[W:W + nw] = a
W += nw
scale = 1.0 / self.nspins
for s, I_a in enumerate(I_sa):
if not skip_core:
nc.lfc.ae_core_density_correction(scale, n_sg[s], a_W, I_a)
nct.lfc.ae_core_density_correction(-scale, n_sg[s], a_W, I_a)
gd.comm.sum(I_a)
N_c = gd.N_c
g_ac = np.around(N_c * spos_ac).astype(int) % N_c - gd.beg_c
if not skip_core:
for I, g_c in zip(I_a, g_ac):
if (g_c >= 0).all() and (g_c < gd.n_c).all():
n_sg[s][tuple(g_c)] -= I / gd.dv
return n_sg, gd
def paw_corrections(self, gridrefinement=2):
Fn_wsg, gd = self.interpolate_pseudo_density(gridrefinement)
# Splines
splines = {}
phi_aj = []
phit_aj = []
for a, id in enumerate(self.setups.id_a):
if id in splines:
phi_j, phit_j = splines[id]
else:
# Load splines:
phi_j, phit_j = self.setups[a].get_partial_waves()[:2]
splines[id] = (phi_j, phit_j)
phi_aj.append(phi_j)
phit_aj.append(phit_j)
# Create localized functions from splines
phi = BasisFunctions(gd, phi_aj, dtype=float)
phit = BasisFunctions(gd, phit_aj, dtype=float)
# phi = BasisFunctions(gd, phi_aj, dtype=complex)
# phit = BasisFunctions(gd, phit_aj, dtype=complex)
spos_ac = self.atoms.get_scaled_positions()
phi.set_positions(spos_ac)
phit.set_positions(spos_ac)
tmp_g = gd.empty(dtype=float)
rho_MM = np.zeros((phi.Mmax, phi.Mmax), dtype=self.dtype)
rho2_MM = np.zeros_like(rho_MM)
for w in range(self.nw):
for s in range(self.nspins):
rho_MM[:] = 0
M1 = 0
for a, setup in enumerate(self.setups):
ni = setup.ni
FD_wsp = self.FD_awsp.get(a)
if FD_wsp is None:
FD_p = np.empty((ni * (ni + 1) // 2), dtype=self.dtype)
else:
FD_p = FD_wsp[w][s]
if gd.comm.size > 1:
gd.comm.broadcast(FD_p, self.rank_a[a])
D_ij = unpack2(FD_p)
# unpack does complex conjugation that we don't want so
# remove conjugation
D_ij = np.triu(D_ij, 1) + np.conj(np.tril(D_ij))
# if FD_wsp is None:
# FD_wsp = np.empty((self.nw, self.nspins,
# ni * (ni + 1) // 2),
# dtype=self.dtype)
# if gd.comm.size > 1:
# gd.comm.broadcast(FD_wsp, self.rank_a[a])
# D_ij = unpack2(FD_wsp[w][s])
# D_ij = np.triu(D_ij, 1) + np.conj(np.tril(D_ij))
M2 = M1 + ni
rho_MM[M1:M2, M1:M2] = D_ij
M1 = M2
# Add real part of AE corrections
tmp_g[:] = 0
rho2_MM[:] = rho_MM.real
# TODO: use ae_valence_density_correction
phi.construct_density(rho2_MM, tmp_g, q=-1)
phit.construct_density(-rho2_MM, tmp_g, q=-1)
# phi.lfc.ae_valence_density_correction(rho2_MM, tmp_g,
# np.zeros(len(phi.M_W),
# np.intc),
# np.zeros(self.na))
# phit.lfc.ae_valence_density_correction(-rho2_MM, tmp_g,
# np.zeros(len(phi.M_W),
# np.intc),
# np.zeros(self.na))
Fn_wsg[w][s] += tmp_g
# Add imag part of AE corrections
tmp_g[:] = 0
rho2_MM[:] = rho_MM.imag
# TODO: use ae_valence_density_correction
phi.construct_density(rho2_MM, tmp_g, q=-1)
phit.construct_density(-rho2_MM, tmp_g, q=-1)
# phi.lfc.ae_valence_density_correction(rho2_MM, tmp_g,
# np.zeros(len(phi.M_W),
# np.intc),
# np.zeros(self.na))
# phit.lfc.ae_valence_density_correction(-rho2_MM, tmp_g,
# np.zeros(len(phi.M_W),
# np.intc),
# np.zeros(self.na))
Fn_wsg[w][s] += 1.0j * tmp_g
return Fn_wsg, gd