def screened_interaction_kernel(self, iq):
"""Calcuate W_GG(w) for a given q.
if static: return W_GG(w=0)
is not static: return W_GG(q,w) - Vc_GG
"""
q = self.ibzq_qc[iq]
w = self.w_w.copy() * Hartree
optical_limit = False
if np.abs(q).sum() < 1e-8:
q = np.array([1e-12, 0,
0]) # arbitrary q, not really need to be calculated
optical_limit = True
hilbert_trans = True
if self.ppa or self.static:
hilbert_trans = False
df = DF(calc=self.calc,
q=q.copy(),
w=w,
nbands=self.nbands,
eshift=None,
optical_limit=optical_limit,
hilbert_trans=hilbert_trans,
xc='RPA',
time_ordered=True,
rpad=self.rpad,
vcut=self.vcut,
G_plus_q=True,
eta=self.eta * Hartree,
ecut=self.ecut.copy() * Hartree,
txt='df.out',
comm=self.dfcomm,
kcommsize=self.kcommsize)
df.initialize()
df.e_skn = self.e_skn.copy()
df.calculate()
dfinv_wGG = df.get_inverse_dielectric_matrix(xc='RPA')
assert df.ecut[0] == self.ecut[0]
if not self.static and not self.ppa:
assert df.eta == self.eta
assert df.Nw == self.Nw
assert df.dw == self.dw
# calculate Coulomb kernel and use truncation in 2D
delta_GG = np.eye(df.npw)
Vq_G = np.diag(
calculate_Kc(q,
df.Gvec_Gc,
self.acell_cv,
self.bcell_cv,
self.pbc,
integrate_gamma=True,
N_k=self.kd.N_c,
vcut=self.vcut))**0.5
if (self.vcut == '2D' and df.optical_limit) or self.numint:
for iG in range(len(df.Gvec_Gc)):
if df.Gvec_Gc[iG, 0] == 0 and df.Gvec_Gc[iG, 1] == 0:
v_q, v0_q = calculate_Kc_q(self.acell_cv,
self.bcell_cv,
self.pbc,
self.kd.N_c,
vcut=self.vcut,
q_qc=np.array([q]),
Gvec_c=df.Gvec_Gc[iG])
Vq_G[iG] = v_q[0]**0.5
self.Kc_GG = np.outer(Vq_G, Vq_G)
if self.ppa:
dfinv1_GG = dfinv_wGG[0] - delta_GG
dfinv2_GG = dfinv_wGG[1] - delta_GG
self.wt_GG = self.E0 * np.sqrt(dfinv2_GG / (dfinv1_GG - dfinv2_GG))
self.R_GG = -self.wt_GG / 2 * dfinv1_GG
del dfinv_wGG
dfinv_wGG = np.array([1j * pi * self.R_GG + delta_GG])
if self.static:
assert len(dfinv_wGG) == 1
W_GG = dfinv_wGG[0] * self.Kc_GG
return df, W_GG
else:
Nw = np.shape(dfinv_wGG)[0]
W_wGG = np.zeros_like(dfinv_wGG)
for iw in range(Nw):
dfinv_wGG[iw] -= delta_GG
W_wGG[iw] = dfinv_wGG[iw] * self.Kc_GG
return df, W_wGG
def initialize(self):
self.printtxt('----------------------------------------')
self.printtxt('Bethe-Salpeter Equation calculation')
self.printtxt('----------------------------------------')
self.printtxt('Started at: %s' % ctime())
self.printtxt('')
BASECHI.initialize(self)
assert self.nspins == 1
calc = self.calc
self.kd = kd = calc.wfs.kd
# frequency points init
self.dw = self.w_w[1] - self.w_w[0]
assert ((self.w_w[1:] - self.w_w[:-1] - self.dw) < 1e-10).all() # make sure its linear w grid
assert self.w_w.max() == self.w_w[-1]
self.dw /= Hartree
self.w_w /= Hartree
self.wmax = self.w_w[-1]
self.Nw = int(self.wmax / self.dw) + 1
# band init
if self.nc is None:
nv = self.nvalence / 2 - 1
self.nv = np.array([nv, nv+1]) # conduction band start / end
self.nc = np.array([nv+1, nv+2]) # valence band start / end
self.printtxt('')
self.printtxt('Number of electrons : %d' % (self.nvalence))
self.printtxt('Valence band included : (band %d to band %d)' %(self.nv[0], self.nv[1]-1))
self.printtxt('Conduction band included : (band %d to band %d)' %(self.nc[0], self.nc[1]-1))
if self.eshift is not None:
self.printtxt('Scissors operator : %2.3f eV' % self.eshift)
self.printtxt('')
# find the pair index and initialized pair energy (e_i - e_j) and occupation(f_i-f_j)
self.e_S = {}
focc_s = {}
self.Sindex_S3 = {}
iS = 0
kq_k = self.kq_k
for k1 in range(self.kd.nbzkpts):
ibzkpt1 = kd.bz2ibz_k[k1]
ibzkpt2 = kd.bz2ibz_k[kq_k[k1]]
for n1 in range(self.nv[0], self.nv[1]):
for m1 in range(self.nc[0], self.nc[1]):
focc = self.f_skn[0][ibzkpt1,n1] - self.f_skn[0][ibzkpt2,m1]
if self.coupling: # Dont use Tamm-Dancoff Approx.
check_ftol = np.abs(focc) > self.ftol
else:
check_ftol = focc > self.ftol
if check_ftol:
if self.gw_skn is None:
self.e_S[iS] = self.e_skn[0][ibzkpt2,m1] - self.e_skn[0][ibzkpt1,n1]
else:
self.e_S[iS] = self.gw_skn[0][ibzkpt2,m1] - self.gw_skn[0][ibzkpt1,n1]
focc_s[iS] = focc
self.Sindex_S3[iS] = (k1, n1, m1)
iS += 1
self.nS = iS
self.focc_S = np.zeros(self.nS)
for iS in range(self.nS):
self.focc_S[iS] = focc_s[iS]
# q points init
self.bzq_qc = kd.get_bz_q_points()
if not self.qsymm:
self.ibzq_qc = self.bzq_qc
else:
(self.ibzq_qc, self.ibzq_q, self.iop_q,
self.timerev_q, self.diff_qc) = kd.get_ibz_q_points(self.bzq_qc,
calc.wfs.symmetry.op_scc)
if np.abs(self.bzq_qc - kd.bzk_kc).sum() < 1e-8:
assert np.abs(self.ibzq_qc - kd.ibzk_kc).sum() < 1e-8
self.nibzq = len(self.ibzq_qc)
# Parallel initialization
# kcomm and wScomm is only to be used when wavefunctions are distributed in parallel.
self.comm = self.Scomm = world
self.kcomm = world
self.wScomm = serial_comm
self.nS, self.nS_local, self.nS_start, self.nS_end = parallel_partition(
self.nS, world.rank, world.size, reshape=False)
self.print_bse()
if calc.input_parameters['mode'] == 'lcao':
calc.initialize_positions()
# Coulomb interaction at q=0 for Hartree coupling
### 2D z direction only !!!!!!!!!!!!!!!!!!!!!!
if self.integrate_coulomb is None:
self.integrate_coulomb = []
if self.vcut is None:
pass
elif self.vcut == '2D':
for iG in range(len(self.Gvec_Gc)):
if self.Gvec_Gc[iG, 0] == 0 and self.Gvec_Gc[iG, 1] == 0:
self.integrate_coulomb.append(iG)
else:
raise NotImplementedError
elif type(self.integrate_coulomb) is int:
self.integrate_coulomb = range(self.integrate_coulomb)
elif self.integrate_coulomb == 'all':
self.integrate_coulomb = range(len(self.Gvec_Gc))
elif type(self.integrate_coulomb) is list:
pass
else:
raise 'Invalid option for integrate_coulomb'
self.printtxt('')
self.printtxt('Calculating bare Coulomb kernel')
if not len(self.integrate_coulomb) == 0:
self.printtxt('Integrating Coulomb kernel at %s reciprocal lattice vector(s)' % len(self.integrate_coulomb))
# Coulomb interaction at problematic G's for exchange coupling
if len(self.integrate_coulomb) != 0:
self.vint_Gq = []
for iG in self.integrate_coulomb:
v_q, v0_q = calculate_Kc_q(self.acell_cv,
self.bcell_cv,
self.pbc,
self.kd.N_c,
vcut=self.vcut,
Gvec_c=self.Gvec_Gc[iG],
q_qc=self.ibzq_qc.copy())
self.vint_Gq.append(v_q)
if self.print_coulomb:
self.printtxt('')
self.printtxt('Average kernel relative to bare kernel - \int v(q)dq / v(q0): ')
self.printtxt(' G: % s' % self.Gvec_Gc[iG])
for iq in range(len(v_q)):
q_s = ' q = [%1.2f, %1.2f, %1.2f]: ' % (self.ibzq_qc[iq,0],
self.ibzq_qc[iq,1],
self.ibzq_qc[iq,2])
v_rel = v_q[iq] / v0_q[iq]
self.printtxt(q_s + '%1.3f' % v_rel)
self.printtxt('')
self.V_qGG = self.full_bare_interaction()
return
def screened_interaction_kernel(self, iq):
"""Calcuate W_GG(w) for a given q.
if static: return W_GG(w=0)
is not static: return W_GG(q,w) - Vc_GG
"""
q = self.ibzq_qc[iq]
w = self.w_w.copy()*Hartree
optical_limit = False
if np.abs(q).sum() < 1e-8:
q = np.array([1e-12, 0, 0]) # arbitrary q, not really need to be calculated
optical_limit = True
hilbert_trans = True
if self.ppa or self.static:
hilbert_trans = False
df = DF(calc=self.calc, q=q.copy(), w=w, nbands=self.nbands, eshift=None,
optical_limit=optical_limit, hilbert_trans=hilbert_trans, xc='RPA', time_ordered=True,
rpad=self.rpad, vcut=self.vcut, G_plus_q=True,
eta=self.eta*Hartree, ecut=self.ecut.copy()*Hartree,
txt='df.out', comm=self.dfcomm, kcommsize=self.kcommsize)
df.initialize()
df.e_skn = self.e_skn.copy()
df.calculate()
dfinv_wGG = df.get_inverse_dielectric_matrix(xc='RPA')
assert df.ecut[0] == self.ecut[0]
if not self.static and not self.ppa:
assert df.eta == self.eta
assert df.Nw == self.Nw
assert df.dw == self.dw
# calculate Coulomb kernel and use truncation in 2D
delta_GG = np.eye(df.npw)
Vq_G = np.diag(calculate_Kc(q,
df.Gvec_Gc,
self.acell_cv,
self.bcell_cv,
self.pbc,
integrate_gamma=True,
N_k=self.kd.N_c,
vcut=self.vcut))**0.5
if (self.vcut == '2D' and df.optical_limit) or self.numint:
for iG in range(len(df.Gvec_Gc)):
if df.Gvec_Gc[iG, 0] == 0 and df.Gvec_Gc[iG, 1] == 0:
v_q, v0_q = calculate_Kc_q(self.acell_cv,
self.bcell_cv,
self.pbc,
self.kd.N_c,
vcut=self.vcut,
q_qc=np.array([q]),
Gvec_c=df.Gvec_Gc[iG])
Vq_G[iG] = v_q[0]**0.5
self.Kc_GG = np.outer(Vq_G, Vq_G)
if self.ppa:
dfinv1_GG = dfinv_wGG[0] - delta_GG
dfinv2_GG = dfinv_wGG[1] - delta_GG
self.wt_GG = self.E0 * np.sqrt(dfinv2_GG / (dfinv1_GG - dfinv2_GG))
self.R_GG = - self.wt_GG / 2 * dfinv1_GG
del dfinv_wGG
dfinv_wGG = np.array([1j*pi*self.R_GG + delta_GG])
if self.static:
assert len(dfinv_wGG) == 1
W_GG = dfinv_wGG[0] * self.Kc_GG
return df, W_GG
else:
Nw = np.shape(dfinv_wGG)[0]
W_wGG = np.zeros_like(dfinv_wGG)
for iw in range(Nw):
dfinv_wGG[iw] -= delta_GG
W_wGG[iw] = dfinv_wGG[iw] * self.Kc_GG
return df, W_wGG
def initialize(self):
self.printtxt('----------------------------------------')
self.printtxt('Bethe-Salpeter Equation calculation')
self.printtxt('----------------------------------------')
self.printtxt('Started at: %s' % ctime())
self.printtxt('')
BASECHI.initialize(self)
assert self.nspins == 1
calc = self.calc
self.kd = kd = calc.wfs.kd
# frequency points init
self.dw = self.w_w[1] - self.w_w[0]
assert ((self.w_w[1:] - self.w_w[:-1] - self.dw) <
1e-10).all() # make sure its linear w grid
assert self.w_w.max() == self.w_w[-1]
self.dw /= Hartree
self.w_w /= Hartree
self.wmax = self.w_w[-1]
self.Nw = int(self.wmax / self.dw) + 1
# band init
if self.nc is None:
nv = self.nvalence / 2 - 1
self.nv = np.array([nv, nv + 1]) # conduction band start / end
self.nc = np.array([nv + 1, nv + 2]) # valence band start / end
self.printtxt('')
self.printtxt('Number of electrons : %d' % (self.nvalence))
self.printtxt('Valence band included : (band %d to band %d)' %
(self.nv[0], self.nv[1] - 1))
self.printtxt('Conduction band included : (band %d to band %d)' %
(self.nc[0], self.nc[1] - 1))
if self.eshift is not None:
self.printtxt('Scissors operator : %2.3f eV' % self.eshift)
self.printtxt('')
# find the pair index and initialized pair energy (e_i - e_j) and occupation(f_i-f_j)
self.e_S = {}
focc_s = {}
self.Sindex_S3 = {}
iS = 0
kq_k = self.kq_k
for k1 in range(self.kd.nbzkpts):
ibzkpt1 = kd.bz2ibz_k[k1]
ibzkpt2 = kd.bz2ibz_k[kq_k[k1]]
for n1 in range(self.nv[0], self.nv[1]):
for m1 in range(self.nc[0], self.nc[1]):
focc = self.f_skn[0][ibzkpt1, n1] - self.f_skn[0][ibzkpt2,
m1]
if self.coupling: # Dont use Tamm-Dancoff Approx.
check_ftol = np.abs(focc) > self.ftol
else:
check_ftol = focc > self.ftol
if check_ftol:
if self.gw_skn is None:
self.e_S[iS] = self.e_skn[0][
ibzkpt2, m1] - self.e_skn[0][ibzkpt1, n1]
else:
self.e_S[iS] = self.gw_skn[0][
ibzkpt2, m1] - self.gw_skn[0][ibzkpt1, n1]
focc_s[iS] = focc
self.Sindex_S3[iS] = (k1, n1, m1)
iS += 1
self.nS = iS
self.focc_S = np.zeros(self.nS)
for iS in range(self.nS):
self.focc_S[iS] = focc_s[iS]
# q points init
self.bzq_qc = kd.get_bz_q_points()
if not self.qsymm:
self.ibzq_qc = self.bzq_qc
else:
(self.ibzq_qc, self.ibzq_q, self.iop_q, self.timerev_q,
self.diff_qc) = kd.get_ibz_q_points(self.bzq_qc,
calc.wfs.kd.symmetry.op_scc)
if np.abs(self.bzq_qc - kd.bzk_kc).sum() < 1e-8:
assert np.abs(self.ibzq_qc - kd.ibzk_kc).sum() < 1e-8
self.nibzq = len(self.ibzq_qc)
# Parallel initialization
# kcomm and wScomm is only to be used when wavefunctions are distributed in parallel.
self.comm = self.Scomm = world
self.kcomm = world
self.wScomm = serial_comm
self.nS, self.nS_local, self.nS_start, self.nS_end = parallel_partition(
self.nS, world.rank, world.size, reshape=False)
self.print_bse()
if calc.input_parameters['mode'] == 'lcao':
calc.initialize_positions()
# Coulomb interaction at q=0 for Hartree coupling
### 2D z direction only !!!!!!!!!!!!!!!!!!!!!!
if self.integrate_coulomb is None:
self.integrate_coulomb = []
if self.vcut is None:
pass
elif self.vcut == '2D':
for iG in range(len(self.Gvec_Gc)):
if self.Gvec_Gc[iG, 0] == 0 and self.Gvec_Gc[iG, 1] == 0:
self.integrate_coulomb.append(iG)
else:
raise NotImplementedError
elif type(self.integrate_coulomb) is int:
self.integrate_coulomb = range(self.integrate_coulomb)
elif self.integrate_coulomb == 'all':
self.integrate_coulomb = range(len(self.Gvec_Gc))
elif type(self.integrate_coulomb) is list:
pass
else:
raise 'Invalid option for integrate_coulomb'
self.printtxt('')
self.printtxt('Calculating bare Coulomb kernel')
if not len(self.integrate_coulomb) == 0:
self.printtxt(
'Integrating Coulomb kernel at %s reciprocal lattice vector(s)'
% len(self.integrate_coulomb))
# Coulomb interaction at problematic G's for exchange coupling
if len(self.integrate_coulomb) != 0:
self.vint_Gq = []
for iG in self.integrate_coulomb:
v_q, v0_q = calculate_Kc_q(self.acell_cv,
self.bcell_cv,
self.pbc,
self.kd.N_c,
vcut=self.vcut,
Gvec_c=self.Gvec_Gc[iG],
q_qc=self.ibzq_qc.copy())
self.vint_Gq.append(v_q)
if self.print_coulomb:
self.printtxt('')
self.printtxt(
'Average kernel relative to bare kernel - \int v(q)dq / v(q0): '
)
self.printtxt(' G: % s' % self.Gvec_Gc[iG])
for iq in range(len(v_q)):
q_s = ' q = [%1.2f, %1.2f, %1.2f]: ' % (
self.ibzq_qc[iq, 0], self.ibzq_qc[iq, 1],
self.ibzq_qc[iq, 2])
v_rel = v_q[iq] / v0_q[iq]
self.printtxt(q_s + '%1.3f' % v_rel)
self.printtxt('')
self.V_qGG = self.full_bare_interaction()