def full_static_screened_interaction(self):
"""Calcuate W_GG(q)"""
W_qGG = np.zeros((self.nibzq, self.npw, self.npw), dtype=complex)
t0 = time()
for iq in range(self.nibzq):
q = self.ibzq_qc[iq]
optical_limit = False
if np.abs(q).sum() < 1e-8:
q = self.q_c.copy()
optical_limit = True
df = DF(calc=self.calc,
q=q,
w=(0., ),
optical_limit=optical_limit,
nbands=self.nbands,
hilbert_trans=False,
eta=0.0001,
ecut=self.ecut * Hartree,
xc='RPA',
txt='df.out')
df.initialize()
df.calculate()
if optical_limit:
K_GG = self.V_qGG[iq].copy()
K0 = calculate_Kc(q,
self.Gvec_Gc,
self.acell_cv,
self.bcell_cv,
self.pbc,
vcut=self.vcut)[0, 0]
for iG in range(1, self.npw):
K_GG[0, iG] = self.V_qGG[iq, iG, iG]**0.5 * K0**0.5
K_GG[iG, 0] = self.V_qGG[iq, iG, iG]**0.5 * K0**0.5
K_GG[0, 0] = K0
df_GG = np.eye(self.npw, self.npw) - K_GG * df.chi0_wGG[0]
else:
df_GG = np.eye(self.npw,
self.npw) - self.V_qGG[iq] * df.chi0_wGG[0]
dfinv_GG = np.linalg.inv(df_GG)
if optical_limit:
eps = 1 / dfinv_GG[0, 0]
self.printtxt(
' RPA macroscopic dielectric constant is: %3.3f' %
eps.real)
W_qGG[iq] = dfinv_GG * self.V_qGG[iq]
self.timing(iq, t0, self.nibzq, 'iq')
if rank == 0:
if self.kernel_file is not None:
data = {'W_qGG': W_qGG}
name = self.kernel_file + '.pckl'
pickle.dump(data, open(name, 'w'), -1)
return W_qGG
def full_static_screened_interaction(self):
"""Calcuate W_GG(q)"""
W_qGG = np.zeros((self.nibzq, self.npw, self.npw), dtype=complex)
t0 = time()
for iq in range(self.nibzq):
q = self.ibzq_qc[iq]
optical_limit = False
if np.abs(q).sum() < 1e-8:
q = self.q_c.copy()
optical_limit = True
df = DF(calc=self.calc,
q=q,
w=(0.,),
optical_limit=optical_limit,
nbands=self.nbands,
hilbert_trans=False,
eta=0.0001,
ecut=self.ecut*Hartree,
xc='RPA',
txt='df.out')
df.initialize()
df.calculate()
if optical_limit:
K_GG = self.V_qGG[iq].copy()
q_v = np.dot(q, self.bcell_cv)
K0 = calculate_Kc(q,
self.Gvec_Gc,
self.acell_cv,
self.bcell_cv,
self.pbc,
vcut=self.vcut)[0,0]
for iG in range(1,self.npw):
K_GG[0, iG] = self.V_qGG[iq, iG, iG]**0.5 * K0**0.5
K_GG[iG, 0] = self.V_qGG[iq, iG, iG]**0.5 * K0**0.5
K_GG[0,0] = K0
df_GG = np.eye(self.npw, self.npw) - K_GG*df.chi0_wGG[0]
else:
df_GG = np.eye(self.npw, self.npw) - self.V_qGG[iq]*df.chi0_wGG[0]
dfinv_GG = np.linalg.inv(df_GG)
if optical_limit:
eps = 1/dfinv_GG[0,0]
self.printtxt(' RPA macroscopic dielectric constant is: %3.3f' % eps.real)
W_qGG[iq] = dfinv_GG * self.V_qGG[iq]
self.timing(iq, t0, self.nibzq, 'iq')
if rank == 0:
if self.kernel_file is not None:
data = {'W_qGG': W_qGG}
name = self.kernel_file+'.pckl'
pickle.dump(data, open(name, 'w'), -1)
return W_qGG
def full_bare_interaction(self):
"""Calculate V_GG(q)"""
V_qGG = np.zeros((self.nibzq, self.npw, self.npw), dtype=complex)
for iq in range(self.nibzq):
q = self.ibzq_qc[iq]
Vq_G = np.diag(calculate_Kc(q,
self.Gvec_Gc,
self.acell_cv,
self.bcell_cv,
self.pbc,
integrate_gamma=True,
N_k=self.kd.N_c,
vcut=self.vcut))**0.5
for i, iG in enumerate(self.integrate_coulomb):
Vq_G[iG] = self.vint_Gq[i][iq]**0.5
V_qGG[iq] = np.outer(Vq_G, Vq_G)
return V_qGG
def full_bare_interaction(self):
"""Calculate V_GG(q)"""
V_qGG = np.zeros((self.nibzq, self.npw, self.npw), dtype=complex)
for iq in range(self.nibzq):
q = self.ibzq_qc[iq]
Vq_G = np.diag(
calculate_Kc(q,
self.Gvec_Gc,
self.acell_cv,
self.bcell_cv,
self.pbc,
integrate_gamma=True,
N_k=self.kd.N_c,
vcut=self.vcut))**0.5
for i, iG in enumerate(self.integrate_coulomb):
Vq_G[iG] = self.vint_Gq[i][iq]**0.5
V_qGG[iq] = np.outer(Vq_G, Vq_G)
return V_qGG
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 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