def get_chi(self, xc='RPA', q_c=[0, 0, 0], direction='x'):
""" Returns v^1/2 chi V^1/2"""
pd, chi0_wGG, chi0_wxvG, chi0_wvv = self.calculate_chi0(q_c)
G_G = pd.G2_qG[0]**0.5
nG = len(G_G)
if pd.kd.gamma:
G_G[0] = 1.0
if isinstance(direction, str):
d_v = {
'x': [1, 0, 0],
'y': [0, 1, 0],
'z': [0, 0, 1]
}[direction]
else:
d_v = direction
d_v = np.asarray(d_v) / np.linalg.norm(d_v)
W = slice(self.w1, self.w2)
chi0_wGG[:, 0] = np.dot(d_v, chi0_wxvG[W, 0])
chi0_wGG[:, :, 0] = np.dot(d_v, chi0_wxvG[W, 1])
chi0_wGG[:, 0, 0] = np.dot(d_v, np.dot(chi0_wvv[W], d_v).T)
G_G /= (4 * pi)**0.5
if self.truncation == 'wigner-seitz':
kernel = WignerSeitzTruncatedCoulomb(pd.gd.cell_cv,
self.chi0.calc.wfs.kd.N_c)
K_G = kernel.get_potential(pd)
K_G *= G_G**2
if pd.kd.gamma:
K_G[0] = 0.0
elif self.truncation == '2D':
K_G = truncated_coulomb(pd)
K_G *= G_G**2
else:
K_G = np.ones(nG)
K_GG = np.zeros((nG, nG), dtype=complex)
for i in range(nG):
K_GG[i, i] = K_G[i]
if xc != 'RPA':
R_av = self.chi0.calc.atoms.positions / Bohr
nt_sG = self.chi0.calc.density.nt_sG
K_GG += calculate_Kxc(pd,
nt_sG,
R_av,
self.chi0.calc.wfs.setups,
self.chi0.calc.density.D_asp,
functional=xc) * G_G * G_G[:, np.newaxis]
chi_wGG = []
for chi0_GG in chi0_wGG:
chi0_GG[:] = chi0_GG / G_G / G_G[:, np.newaxis]
chi_wGG.append(
np.dot(np.linalg.inv(np.eye(nG) - np.dot(chi0_GG, K_GG)),
chi0_GG))
return chi0_wGG, np.array(chi_wGG)
def get_chi(self, xc='RPA', q_c=[0, 0, 0], direction='x'):
""" Returns v^1/2 chi V^1/2"""
pd, chi0_wGG, chi0_wxvG, chi0_wvv = self.calculate_chi0(q_c)
G_G = pd.G2_qG[0]**0.5
nG = len(G_G)
if pd.kd.gamma:
G_G[0] = 1.0
if isinstance(direction, str):
d_v = {'x': [1, 0, 0],
'y': [0, 1, 0],
'z': [0, 0, 1]}[direction]
else:
d_v = direction
d_v = np.asarray(d_v) / np.linalg.norm(d_v)
W = slice(self.w1, self.w2)
chi0_wGG[:, 0] = np.dot(d_v, chi0_wxvG[W, 0])
chi0_wGG[:, :, 0] = np.dot(d_v, chi0_wxvG[W, 1])
chi0_wGG[:, 0, 0] = np.dot(d_v, np.dot(chi0_wvv[W], d_v).T)
G_G /= (4 * pi)**0.5
if self.truncation == 'wigner-seitz':
kernel = WignerSeitzTruncatedCoulomb(pd.gd.cell_cv,
self.chi0.calc.wfs.kd.N_c)
K_G = kernel.get_potential(pd)
K_G *= G_G**2
if pd.kd.gamma:
K_G[0] = 0.0
elif self.truncation == '2D':
K_G = truncated_coulomb(pd)
K_G *= G_G**2
else:
K_G = np.ones(nG)
K_GG = np.zeros((nG, nG), dtype=complex)
for i in range(nG):
K_GG[i, i] = K_G[i]
if xc != 'RPA':
R_av = self.chi0.calc.atoms.positions / Bohr
nt_sG = self.chi0.calc.density.nt_sG
K_GG += calculate_Kxc(pd, nt_sG, R_av, self.chi0.calc.wfs.setups,
self.chi0.calc.density.D_asp,
functional=xc) * G_G * G_G[:, np.newaxis]
chi_wGG = []
for chi0_GG in chi0_wGG:
chi0_GG[:] = chi0_GG / G_G / G_G[:, np.newaxis]
chi_wGG.append(np.dot(np.linalg.inv(np.eye(nG) -
np.dot(chi0_GG, K_GG)),
chi0_GG))
return chi0_wGG, np.array(chi_wGG)
def get_dielectric_matrix(self, xc='RPA', q_c=[0, 0, 0],
direction='x', symmetric=True,
calculate_chi=False):
"""Returns the symmetrized dielectric matrix.
::
\tilde\epsilon_GG' = v^{-1/2}_G \epsilon_GG' v^{1/2}_G',
where::
epsilon_GG' = 1 - v_G * P_GG' and P_GG'
is the polarization.
::
In RPA: P = chi^0
In TDDFT: P = (1 - chi^0 * f_xc)^{-1} chi^0
The head of the inverse symmetrized dielectric matrix is equal
to the head of the inverse dielectric matrix (inverse dielectric
function)
"""
pd, chi0_wGG, chi0_wxvG, chi0_wvv = self.calculate_chi0(q_c)
G_G = pd.G2_qG[0]**0.5
nG = len(G_G)
if pd.kd.gamma:
G_G[0] = 1.0
if isinstance(direction, str):
d_v = {'x': [1, 0, 0],
'y': [0, 1, 0],
'z': [0, 0, 1]}[direction]
else:
d_v = direction
d_v = np.asarray(d_v) / np.linalg.norm(d_v)
W = slice(self.w1, self.w2)
chi0_wGG[:, 0] = np.dot(d_v, chi0_wxvG[W, 0])
chi0_wGG[:, :, 0] = np.dot(d_v, chi0_wxvG[W, 1])
chi0_wGG[:, 0, 0] = np.dot(d_v, np.dot(chi0_wvv[W], d_v).T)
if self.truncation == 'wigner-seitz':
kernel = WignerSeitzTruncatedCoulomb(pd.gd.cell_cv,
self.chi0.calc.wfs.kd.N_c)
K_G = kernel.get_potential(pd)**0.5
if pd.kd.gamma:
K_G[0] = 0.0
elif self.truncation == '2D':
K_G = truncated_coulomb(pd)
if pd.kd.gamma:
K_G[0] = 0.0
else:
K_G = (4 * pi)**0.5 / G_G
if xc != 'RPA':
R_av = self.chi0.calc.atoms.positions / Bohr
nt_sG = self.chi0.calc.density.nt_sG
Kxc_sGG = calculate_Kxc(pd, nt_sG, R_av,
self.chi0.calc.wfs.setups,
self.chi0.calc.density.D_asp,
functional=xc)
if calculate_chi:
chi_wGG = []
for chi0_GG in chi0_wGG:
if xc == 'RPA':
P_GG = chi0_GG
else:
P_GG = np.dot(np.linalg.inv(np.eye(nG) -
np.dot(chi0_GG, Kxc_sGG[0])),
chi0_GG)
if symmetric:
e_GG = np.eye(nG) - P_GG * K_G * K_G[:, np.newaxis]
else:
K_GG = (K_G**2 * np.ones([nG, nG])).T
e_GG = np.eye(nG) - P_GG * K_GG
if calculate_chi:
K_GG = np.diag(K_G**2)
if xc != 'RPA':
K_GG += Kxc_sGG[0]
chi_wGG.append(np.dot(np.linalg.inv(np.eye(nG) -
np.dot(chi0_GG, K_GG)),
chi0_GG))
chi0_GG[:] = e_GG
# chi0_wGG is now the dielectric matrix
if not calculate_chi:
return chi0_wGG
else:
return pd, chi0_wGG, chi_wGG
def get_dielectric_matrix(self,
xc='RPA',
q_c=[0, 0, 0],
direction='x',
symmetric=True,
calculate_chi=False):
"""Returns the symmetrized dielectric matrix.
::
\tilde\epsilon_GG' = v^{-1/2}_G \epsilon_GG' v^{1/2}_G',
where::
epsilon_GG' = 1 - v_G * P_GG' and P_GG'
is the polarization.
::
In RPA: P = chi^0
In TDDFT: P = (1 - chi^0 * f_xc)^{-1} chi^0
The head of the inverse symmetrized dielectric matrix is equal
to the head of the inverse dielectric matrix (inverse dielectric
function)
"""
pd, chi0_wGG, chi0_wxvG, chi0_wvv = self.calculate_chi0(q_c)
G_G = pd.G2_qG[0]**0.5
nG = len(G_G)
if pd.kd.gamma:
G_G[0] = 1.0
if isinstance(direction, str):
d_v = {
'x': [1, 0, 0],
'y': [0, 1, 0],
'z': [0, 0, 1]
}[direction]
else:
d_v = direction
d_v = np.asarray(d_v) / np.linalg.norm(d_v)
W = slice(self.w1, self.w2)
chi0_wGG[:, 0] = np.dot(d_v, chi0_wxvG[W, 0])
chi0_wGG[:, :, 0] = np.dot(d_v, chi0_wxvG[W, 1])
chi0_wGG[:, 0, 0] = np.dot(d_v, np.dot(chi0_wvv[W], d_v).T)
if self.truncation == 'wigner-seitz':
kernel = WignerSeitzTruncatedCoulomb(pd.gd.cell_cv,
self.chi0.calc.wfs.kd.N_c)
K_G = kernel.get_potential(pd)**0.5
if pd.kd.gamma:
K_G[0] = 0.0
elif self.truncation == '2D':
K_G = truncated_coulomb(pd)
if pd.kd.gamma:
K_G[0] = 0.0
else:
K_G = (4 * pi)**0.5 / G_G
if xc != 'RPA':
R_av = self.chi0.calc.atoms.positions / Bohr
nt_sG = self.chi0.calc.density.nt_sG
Kxc_sGG = calculate_Kxc(pd,
nt_sG,
R_av,
self.chi0.calc.wfs.setups,
self.chi0.calc.density.D_asp,
functional=xc)
if calculate_chi:
chi_wGG = []
for chi0_GG in chi0_wGG:
if xc == 'RPA':
P_GG = chi0_GG
else:
P_GG = np.dot(
np.linalg.inv(np.eye(nG) - np.dot(chi0_GG, Kxc_sGG[0])),
chi0_GG)
if symmetric:
e_GG = np.eye(nG) - P_GG * K_G * K_G[:, np.newaxis]
else:
K_GG = (K_G**2 * np.ones([nG, nG])).T
e_GG = np.eye(nG) - P_GG * K_GG
if calculate_chi:
K_GG = np.diag(K_G**2)
if xc != 'RPA':
K_GG += Kxc_sGG[0]
chi_wGG.append(
np.dot(np.linalg.inv(np.eye(nG) - np.dot(chi0_GG, K_GG)),
chi0_GG))
chi0_GG[:] = e_GG
# chi0_wGG is now the dielectric matrix
if not calculate_chi:
return chi0_wGG
else:
return pd, chi0_wGG, chi_wGG