def get_C6_coefficient(self,
ecut=100.,
nbands=None,
kcommsize=None,
gauss_legendre=None,
frequency_cut=None,
frequency_scale=None,
direction=2):
self.initialize_calculation(None,
ecut,
nbands,
kcommsize,
gauss_legendre,
frequency_cut,
frequency_scale)
d = direction
d_pro = []
for i in range(3):
if i != d:
d_pro.append(i)
dummy = DF(calc=self.calc,
eta=0.0,
w=self.w * 1j,
ecut=self.ecut,
hilbert_trans=False)
dummy.txt = devnull
dummy.initialize(simple_version=True)
npw = dummy.npw
del dummy
q = [0.,0.,0.]
q[d] = 1.e-5
if self.nbands is None:
nbands = npw
else:
nbands = self.nbands
if self.txt is sys.stdout:
txt = 'response.txt'
else:
txt='response_'+self.txt.name
df = DF(calc=self.calc,
xc=None,
nbands=nbands,
eta=0.0,
q=q,
txt=txt,
vcut=self.vcut,
w=self.w * 1j,
ecut=self.ecut,
comm=world,
optical_limit=True,
G_plus_q=True,
kcommsize=self.kcommsize,
hilbert_trans=False)
print('Calculating RPA response function', file=self.txt)
print('Polarization: %s' % d, file=self.txt)
chi_wGG = df.get_chi(xc='RPA')
chi0_wGG = df.chi0_wGG
Nw_local = len(chi_wGG)
local_a0_w = np.zeros(Nw_local, dtype=complex)
a0_w = np.empty(len(self.w), complex)
local_a_w = np.zeros(Nw_local, dtype=complex)
a_w = np.empty(len(self.w), complex)
Gvec_Gv = np.dot(df.Gvec_Gc + np.array(q), df.bcell_cv)
gd = self.calc.density.gd
n_d = gd.get_size_of_global_array()[d]
d_d = gd.get_grid_spacings()[d]
r_d = np.array([i*d_d for i in range(n_d)])
print('Calculating real space integrals', file=self.txt)
int_G = np.zeros(npw, complex)
for iG in range(npw):
if df.Gvec_Gc[iG, d_pro[0]] == 0 and df.Gvec_Gc[iG, d_pro[1]] == 0:
int_G[iG] = np.sum(r_d * np.exp(1j*Gvec_Gv[iG, d] * r_d))*d_d
int2_GG = np.outer(int_G, int_G.conj())
print('Calculating dynamic polarizability', file=self.txt)
for i in range(Nw_local):
local_a0_w[i] = np.trace(np.dot(chi0_wGG[i], int2_GG))
local_a_w[i] = np.trace(np.dot(chi_wGG[i], int2_GG))
df.wcomm.all_gather(local_a0_w, a0_w)
df.wcomm.all_gather(local_a_w, a_w)
A = df.vol / gd.cell_cv[d,d]
a0_w *= A**2 / df.vol
a_w *= A**2 / df.vol
del df
C06 = np.sum(a0_w**2 * self.gauss_weights
* self.transform) * 3 / (2*np.pi)
C6 = np.sum(a_w**2 * self.gauss_weights
* self.transform) * 3 / (2*np.pi)
print('C06 = %s Ha*Bohr**6' % (C06.real / Ha), file=self.txt)
print('C6 = %s Ha*Bohr**6' % (C6.real / Ha), file=self.txt)
print(file=self.txt)
return C6.real / Ha, C06.real / Ha
def initialize_calculation(self,
w,
ecut,
nbands,
kcommsize,
gauss_legendre,
frequency_cut,
frequency_scale):
if kcommsize is None:
if len(self.calc.wfs.kd.bzk_kc) == 1:
kcommsize = 1
else:
kcommsize = world.size
if w is not None:
assert (gauss_legendre is None and
frequency_cut is None and
frequency_scale is None)
else:
if gauss_legendre is None:
gauss_legendre = 16
self.gauss_points, self.gauss_weights = p_roots(gauss_legendre)
if frequency_scale is None:
frequency_scale = 2.0
if frequency_cut is None:
frequency_cut = 800.
ys = 0.5 - 0.5 * self.gauss_points
ys = ys[::-1]
w = (-np.log(1-ys))**frequency_scale
w *= frequency_cut/w[-1]
alpha = (-np.log(1-ys[-1]))**frequency_scale/frequency_cut
transform = (-np.log(1-ys))**(frequency_scale-1) \
/ (1-ys)*frequency_scale/alpha
self.transform = transform
dummy = DF(calc=self.calc,
eta=0.0,
w=w * 1j,
q=[0.,0.,0.0001],
ecut=ecut,
optical_limit=True,
hilbert_trans=False,
kcommsize=kcommsize)
dummy.txt = devnull
dummy.initialize(simple_version=True)
self.npw = dummy.npw
self.ecut = ecut
self.w = w
self.gauss_legendre = gauss_legendre
self.frequency_cut = frequency_cut
self.frequency_scale = frequency_scale
self.kcommsize = kcommsize
self.nbands = nbands
print(file=self.txt)
print('Planewave cutoff : %s eV' % ecut, file=self.txt)
print('Number of Planewaves at Gamma : %s' % self.npw, file=self.txt)
if self.nbands is None:
print('Response function bands :'\
+ ' Equal to number of Planewaves', file=self.txt)
else:
print('Response function bands : %s' \
% self.nbands, file=self.txt)
print('Frequencies', file=self.txt)
if self.gauss_legendre is not None:
print(' Gauss-Legendre integration '\
+ 'with %s frequency points' % len(self.w), file=self.txt)
print(' Frequency cutoff is '\
+ '%s eV and scale (B) is %s' % (self.w[-1],
self.frequency_scale), file=self.txt)
else:
print(' %s specified frequency points' \
% len(self.w), file=self.txt)
print(' Frequency cutoff is %s eV' \
% self.w[-1], file=self.txt)
print(file=self.txt)
print('Parallelization scheme', file=self.txt)
print(' Total CPUs : %d' % dummy.comm.size, file=self.txt)
if dummy.kd.nbzkpts == 1:
print(' Band parsize : %d' % dummy.kcomm.size, file=self.txt)
else:
print(' Kpoint parsize : %d' % dummy.kcomm.size, file=self.txt)
print(' Frequency parsize : %d' % dummy.wScomm.size, file=self.txt)
print('Memory usage estimate', file=self.txt)
print(' chi0_wGG(Q) : %f M / cpu' \
% (dummy.Nw_local * self.npw**2 * 16. / 1024**2), file=self.txt)
print(file=self.txt)
del dummy
def E_q(self,
q,
index=None,
direction=0,
integrated=True):
if abs(np.dot(q, q))**0.5 < 1.e-5:
q = [0.,0.,0.]
q[direction] = 1.e-5
optical_limit = True
else:
optical_limit = False
dummy = DF(calc=self.calc,
eta=0.0,
w=self.w * 1j,
q=q,
ecut=self.ecut,
G_plus_q=True,
optical_limit=optical_limit,
hilbert_trans=False)
dummy.txt = devnull
dummy.initialize(simple_version=True)
npw = dummy.npw
del dummy
if self.nbands is None:
nbands = npw
else:
nbands = self.nbands
if self.txt is sys.stdout:
txt = 'response.txt'
else:
txt='response_'+self.txt.name
df = DF(calc=self.calc,
xc=None,
nbands=nbands,
eta=0.0,
q=q,
txt=txt,
vcut=self.vcut,
w=self.w * 1j,
ecut=self.ecut,
G_plus_q=True,
kcommsize=self.kcommsize,
comm=self.dfcomm,
optical_limit=optical_limit,
hilbert_trans=False)
if index is None:
print('Calculating KS response function at:', file=self.txt)
else:
print('#', index, \
'- Calculating KS response function at:', file=self.txt)
if optical_limit:
print('q = [0 0 0] -', 'Polarization: ', direction, file=self.txt)
else:
print('q = [%1.6f %1.6f %1.6f] -' \
% (q[0],q[1],q[2]), '%s planewaves' % npw, file=self.txt)
e_wGG = df.get_dielectric_matrix(xc='RPA', overwritechi0=True)
df.chi0_wGG = None
Nw_local = len(e_wGG)
local_E_q_w = np.zeros(Nw_local, dtype=complex)
E_q_w = np.empty(len(self.w), complex)
for i in range(Nw_local):
local_E_q_w[i] = (np.log(np.linalg.det(e_wGG[i]))
+ len(e_wGG[0]) - np.trace(e_wGG[i]))
#local_E_q_w[i] = (np.sum(np.log(np.linalg.eigvals(e_wGG[i])))
# + len(e_wGG[0]) - np.trace(e_wGG[i]))
df.wcomm.all_gather(local_E_q_w, E_q_w)
del df
if self.gauss_legendre is not None:
E_q = np.sum(E_q_w * self.gauss_weights * self.transform) \
/ (4*np.pi)
else:
dws = self.w[1:] - self.w[:-1]
E_q = np.dot((E_q_w[:-1] + E_q_w[1:])/2., dws) / (2.*np.pi)
print('E_c(q) = %s eV' % E_q.real, file=self.txt)
print(file=self.txt)
if integrated:
return E_q.real
else:
return E_q_w.real
def get_C6_coefficient(self,
ecut=100.,
nbands=None,
kcommsize=None,
gauss_legendre=None,
frequency_cut=None,
frequency_scale=None,
direction=2):
self.initialize_calculation(None, ecut, nbands, kcommsize,
gauss_legendre, frequency_cut,
frequency_scale)
d = direction
d_pro = []
for i in range(3):
if i != d:
d_pro.append(i)
dummy = DF(calc=self.calc,
eta=0.0,
w=self.w * 1j,
ecut=self.ecut,
hilbert_trans=False)
dummy.txt = devnull
dummy.initialize(simple_version=True)
npw = dummy.npw
del dummy
q = [0., 0., 0.]
q[d] = 1.e-5
if self.nbands is None:
nbands = npw
else:
nbands = self.nbands
if self.txt is sys.stdout:
txt = 'response.txt'
else:
txt = 'response_' + self.txt.name
df = DF(calc=self.calc,
xc=None,
nbands=nbands,
eta=0.0,
q=q,
txt=txt,
vcut=self.vcut,
w=self.w * 1j,
ecut=self.ecut,
comm=world,
optical_limit=True,
G_plus_q=True,
kcommsize=self.kcommsize,
hilbert_trans=False)
print('Calculating RPA response function', file=self.txt)
print('Polarization: %s' % d, file=self.txt)
chi_wGG = df.get_chi(xc='RPA')
chi0_wGG = df.chi0_wGG
Nw_local = len(chi_wGG)
local_a0_w = np.zeros(Nw_local, dtype=complex)
a0_w = np.empty(len(self.w), complex)
local_a_w = np.zeros(Nw_local, dtype=complex)
a_w = np.empty(len(self.w), complex)
Gvec_Gv = np.dot(df.Gvec_Gc + np.array(q), df.bcell_cv)
gd = self.calc.density.gd
n_d = gd.get_size_of_global_array()[d]
d_d = gd.get_grid_spacings()[d]
r_d = np.array([i * d_d for i in range(n_d)])
print('Calculating real space integrals', file=self.txt)
int_G = np.zeros(npw, complex)
for iG in range(npw):
if df.Gvec_Gc[iG, d_pro[0]] == 0 and df.Gvec_Gc[iG, d_pro[1]] == 0:
int_G[iG] = np.sum(
r_d * np.exp(1j * Gvec_Gv[iG, d] * r_d)) * d_d
int2_GG = np.outer(int_G, int_G.conj())
print('Calculating dynamic polarizability', file=self.txt)
for i in range(Nw_local):
local_a0_w[i] = np.trace(np.dot(chi0_wGG[i], int2_GG))
local_a_w[i] = np.trace(np.dot(chi_wGG[i], int2_GG))
df.wcomm.all_gather(local_a0_w, a0_w)
df.wcomm.all_gather(local_a_w, a_w)
A = df.vol / gd.cell_cv[d, d]
a0_w *= A**2 / df.vol
a_w *= A**2 / df.vol
del df
C06 = np.sum(
a0_w**2 * self.gauss_weights * self.transform) * 3 / (2 * np.pi)
C6 = np.sum(
a_w**2 * self.gauss_weights * self.transform) * 3 / (2 * np.pi)
print('C06 = %s Ha*Bohr**6' % (C06.real / Ha), file=self.txt)
print('C6 = %s Ha*Bohr**6' % (C6.real / Ha), file=self.txt)
print(file=self.txt)
return C6.real / Ha, C06.real / Ha
def initialize_calculation(self, w, ecut, nbands, kcommsize,
gauss_legendre, frequency_cut, frequency_scale):
if kcommsize is None:
if len(self.calc.wfs.kd.bzk_kc) == 1:
kcommsize = 1
else:
kcommsize = world.size
if w is not None:
assert (gauss_legendre is None and frequency_cut is None
and frequency_scale is None)
else:
if gauss_legendre is None:
gauss_legendre = 16
self.gauss_points, self.gauss_weights = p_roots(gauss_legendre)
if frequency_scale is None:
frequency_scale = 2.0
if frequency_cut is None:
frequency_cut = 800.
ys = 0.5 - 0.5 * self.gauss_points
ys = ys[::-1]
w = (-np.log(1 - ys))**frequency_scale
w *= frequency_cut / w[-1]
alpha = (-np.log(1 - ys[-1]))**frequency_scale / frequency_cut
transform = (-np.log(1-ys))**(frequency_scale-1) \
/ (1-ys)*frequency_scale/alpha
self.transform = transform
dummy = DF(calc=self.calc,
eta=0.0,
w=w * 1j,
q=[0., 0., 0.0001],
ecut=ecut,
optical_limit=True,
hilbert_trans=False,
kcommsize=kcommsize)
dummy.txt = devnull
dummy.initialize(simple_version=True)
self.npw = dummy.npw
self.ecut = ecut
self.w = w
self.gauss_legendre = gauss_legendre
self.frequency_cut = frequency_cut
self.frequency_scale = frequency_scale
self.kcommsize = kcommsize
self.nbands = nbands
print(file=self.txt)
print('Planewave cutoff : %s eV' % ecut, file=self.txt)
print('Number of Planewaves at Gamma : %s' % self.npw, file=self.txt)
if self.nbands is None:
print('Response function bands :'\
+ ' Equal to number of Planewaves', file=self.txt)
else:
print('Response function bands : %s' \
% self.nbands, file=self.txt)
print('Frequencies', file=self.txt)
if self.gauss_legendre is not None:
print(' Gauss-Legendre integration '\
+ 'with %s frequency points' % len(self.w), file=self.txt)
print(' Frequency cutoff is '\
+ '%s eV and scale (B) is %s' % (self.w[-1],
self.frequency_scale), file=self.txt)
else:
print(' %s specified frequency points' \
% len(self.w), file=self.txt)
print(' Frequency cutoff is %s eV' \
% self.w[-1], file=self.txt)
print(file=self.txt)
print('Parallelization scheme', file=self.txt)
print(' Total CPUs : %d' % dummy.comm.size, file=self.txt)
if dummy.kd.nbzkpts == 1:
print(' Band parsize : %d' % dummy.kcomm.size,
file=self.txt)
else:
print(' Kpoint parsize : %d' % dummy.kcomm.size,
file=self.txt)
print(' Frequency parsize : %d' % dummy.wScomm.size, file=self.txt)
print('Memory usage estimate', file=self.txt)
print(' chi0_wGG(Q) : %f M / cpu' \
% (dummy.Nw_local * self.npw**2 * 16. / 1024**2), file=self.txt)
print(file=self.txt)
del dummy
def E_q(self, q, index=None, direction=0, integrated=True):
if abs(np.dot(q, q))**0.5 < 1.e-5:
q = [0., 0., 0.]
q[direction] = 1.e-5
optical_limit = True
else:
optical_limit = False
dummy = DF(calc=self.calc,
eta=0.0,
w=self.w * 1j,
q=q,
ecut=self.ecut,
G_plus_q=True,
optical_limit=optical_limit,
hilbert_trans=False)
dummy.txt = devnull
dummy.initialize(simple_version=True)
npw = dummy.npw
del dummy
if self.nbands is None:
nbands = npw
else:
nbands = self.nbands
if self.txt is sys.stdout:
txt = 'response.txt'
else:
txt = 'response_' + self.txt.name
df = DF(calc=self.calc,
xc=None,
nbands=nbands,
eta=0.0,
q=q,
txt=txt,
vcut=self.vcut,
w=self.w * 1j,
ecut=self.ecut,
G_plus_q=True,
kcommsize=self.kcommsize,
comm=self.dfcomm,
optical_limit=optical_limit,
hilbert_trans=False)
if index is None:
print('Calculating KS response function at:', file=self.txt)
else:
print('#', index, \
'- Calculating KS response function at:', file=self.txt)
if optical_limit:
print('q = [0 0 0] -', 'Polarization: ', direction, file=self.txt)
else:
print('q = [%1.6f %1.6f %1.6f] -' \
% (q[0],q[1],q[2]), '%s planewaves' % npw, file=self.txt)
e_wGG = df.get_dielectric_matrix(xc='RPA', overwritechi0=True)
df.chi0_wGG = None
Nw_local = len(e_wGG)
local_E_q_w = np.zeros(Nw_local, dtype=complex)
E_q_w = np.empty(len(self.w), complex)
for i in range(Nw_local):
local_E_q_w[i] = (np.log(np.linalg.det(e_wGG[i])) + len(e_wGG[0]) -
np.trace(e_wGG[i]))
#local_E_q_w[i] = (np.sum(np.log(np.linalg.eigvals(e_wGG[i])))
# + len(e_wGG[0]) - np.trace(e_wGG[i]))
df.wcomm.all_gather(local_E_q_w, E_q_w)
del df
if self.gauss_legendre is not None:
E_q = np.sum(E_q_w * self.gauss_weights * self.transform) \
/ (4*np.pi)
else:
dws = self.w[1:] - self.w[:-1]
E_q = np.dot((E_q_w[:-1] + E_q_w[1:]) / 2., dws) / (2. * np.pi)
print('E_c(q) = %s eV' % E_q.real, file=self.txt)
print(file=self.txt)
if integrated:
return E_q.real
else:
return E_q_w.real