def main():
p = build_parser()
opts, args = p.parse_args()
if opts.file:
for fname in args:
tokens = fname.split('.')
symbol = tokens[0]
xc = tokens[1]
name = tokens[2]
if tokens[-1] == 'gz':
import gzip
fopen = gzip.open
else:
fopen = open
source = fopen(fname).read()
from gpaw.setup_data import SetupData
s = SetupData(symbol, xc, name, readxml=False)
s.read_xml(source=source)
basis = get_orbitals_by_energy_shift(opts, s, xc=xc)
basis.write_xml()
else:
for arg in args:
setup = hgh_setups.get(arg)
if setup is None:
setup = hgh_sc_setups.get(arg.split('.')[0])
if setup is None:
raise ValueError('Unknown setup %s' % arg)
print(setup)
basis = get_orbitals_by_energy_shift(opts, HGHSetupData(setup))
basis.write_xml()
def main():
p = build_parser()
opts, args = p.parse_args()
if opts.file:
for fname in args:
tokens = fname.split('.')
symbol = tokens[0]
xc = tokens[1]
name = tokens[2]
if tokens[-1] == 'gz':
import gzip
fopen = gzip.open
else:
fopen = open
source = fopen(fname).read()
from gpaw.setup_data import SetupData
s = SetupData(symbol, xc, name, readxml=False)
s.read_xml(source=source)
basis = get_orbitals_by_energy_shift(opts, s, xc=xc)
basis.write_xml()
else:
for arg in args:
setup = hgh_setups.get(arg)
if setup is None:
setup = hgh_sc_setups.get(arg.split('.')[0])
if setup is None:
raise ValueError('Unknown setup %s' % arg)
print setup
basis = get_orbitals_by_energy_shift(opts, HGHSetupData(setup))
basis.write_xml()
def print_projectors(setup):
"""Print information on the projectors of input nucleus object.
If nucleus is a string, treat this as an element name.
"""
if isinstance(setup, str):
setup = SetupData(setup, 'LDA', 'paw')
n_j = setup.n_j
l_j = setup.l_j
else:
n_j = setup.n_j
l_j = setup.l_j
angular = [
['1'],
['y', 'z', 'x'],
['xy', 'yz', '3z^2-r^2', 'xz', 'x^2-y^2'],
[
'3x^2y-y^3', 'xyz', '5yz^2-yr^2', '5z^3-3zr^2', '5xz^2-xr^2',
'x^2z-y^2z', 'x^3-3xy^2'
],
]
print(' i n l m')
print('--------')
i = 0
for n, l in zip(n_j, l_j):
for m in range(2 * l + 1):
if n == -1:
n = '*'
print('%2s %s %s_%s' % (i, n, 'spdf'[l], angular[l][m]))
i += 1
def create_setup(symbol, xc='LDA', lmax=0,
type='paw', basis=None, setupdata=None,
filter=None, world=None):
if isinstance(xc, str):
xc = XC(xc)
if isinstance(type, str) and ':' in type:
# Parse DFT+U parameters from type-string:
# Examples: "type:l,U" or "type:l,U,scale"
type, lu = type.split(':')
if type == '':
type = 'paw'
l = 'spdf'.find(lu[0])
assert lu[1] == ','
U = lu[2:]
if ',' in U:
U, scale = U.split(',')
else:
scale = True
U = float(U) / units.Hartree
scale = int(scale)
else:
U = None
if setupdata is None:
if type == 'hgh' or type == 'hgh.sc':
lmax = 0
from gpaw.hgh import HGHSetupData, setups, sc_setups
if type == 'hgh.sc':
table = sc_setups
else:
table = setups
parameters = table[symbol]
setupdata = HGHSetupData(parameters)
elif type == 'ah':
from gpaw.ah import AppelbaumHamann
ah = AppelbaumHamann()
ah.build(basis)
return ah
elif type == 'ae':
from gpaw.ae import HydrogenAllElectronSetup
assert symbol == 'H'
ae = HydrogenAllElectronSetup()
ae.build(basis)
return ae
elif type == 'ghost':
from gpaw.lcao.bsse import GhostSetupData
setupdata = GhostSetupData(symbol)
else:
setupdata = SetupData(symbol, xc.get_setup_name(),
type, True,
world=world)
if hasattr(setupdata, 'build'):
setup = LeanSetup(setupdata.build(xc, lmax, basis, filter))
if U is not None:
setup.set_hubbard_u(U, l, scale)
return setup
else:
return setupdata
def number_of_projectors(setup):
"""Returns the number of the bound state projectors.
If setup is a string, treat this as an element name.
"""
if isinstance(setup, str):
setup = SetupData(setup, 'LDA', 'paw')
n_j = setup.n_j
l_j = setup.l_j
else:
n_j = setup.n_j
l_j = setup.l_j
i = 0
for n, l in zip(n_j, l_j):
for m in range(2 * l + 1):
if n != -1:
i += 1
return i
def make_paw_setup(self, tag=None):
aea = self.aea
setup = SetupData(aea.symbol, aea.xc.name, tag, readxml=False)
nj = sum(len(waves) for waves in self.waves_l)
setup.e_kin_jj = np.zeros((nj, nj))
setup.id_j = []
j1 = 0
for l, waves in enumerate(self.waves_l):
ne = 0
for n, f, e, phi_g, phit_g, pt_g in zip(waves.n_n, waves.f_n,
waves.e_n, waves.phi_ng,
waves.phit_ng,
waves.pt_ng):
setup.append(n, l, f, e, waves.rcut, phi_g, phit_g, pt_g)
if n == -1:
ne += 1
id = '%s-%s%d' % (aea.symbol, 'spdf'[l], ne)
else:
id = '%s-%d%s' % (aea.symbol, n, 'spdf'[l])
setup.id_j.append(id)
j2 = j1 + len(waves)
setup.e_kin_jj[j1:j2, j1:j2] = waves.dekin_nn
j1 = j2
setup.nc_g = self.nc_g * sqrt(4 * pi)
setup.nct_g = self.nct_g * sqrt(4 * pi)
setup.e_kinetic_core = self.ekincore
setup.vbar_g = self.v0r_g * sqrt(4 * pi)
setup.vbar_g[1:] /= self.rgd.r_g[1:]
setup.vbar_g[0] = setup.vbar_g[1]
setup.Z = aea.Z
setup.Nc = self.ncore
setup.Nv = self.nvalence
setup.e_kinetic = aea.ekin
setup.e_xc = aea.exc
setup.e_electrostatic = aea.eH + aea.eZ
setup.e_total = aea.exc + aea.ekin + aea.eH + aea.eZ
setup.rgd = self.rgd
setup.rcgauss = 1 / sqrt(self.alpha)
self.calculate_exx_integrals()
setup.ExxC = self.exxcc
setup.X_p = pack2(self.exxcv_ii)
setup.tauc_g = self.rgd.zeros()
setup.tauct_g = self.rgd.zeros()
#print 'no tau!!!!!!!!!!!'
if self.aea.scalar_relativistic:
reltype = 'scalar-relativistic'
else:
reltype = 'non-relativistic'
attrs = [('type', reltype),
('version', 2),
('name', 'gpaw-%s' % version)]
setup.generatorattrs = attrs
setup.l0 = self.l0
setup.e0 = self.e0
setup.r0 = self.r0
setup.nderiv0 = self.nderiv0
return setup
def run(self, core='', rcut=1.0, extra=None,
logderiv=False, vbar=None, exx=False, name=None,
normconserving='', filter=(0.4, 1.75), rcutcomp=None,
write_xml=True, use_restart_file=True,
empty_states=''):
self.name = name
self.core = core
if type(rcut) is float:
rcut_l = [rcut]
else:
rcut_l = rcut
rcutmax = max(rcut_l)
rcutmin = min(rcut_l)
self.rcut_l = rcut_l
if rcutcomp is None:
rcutcomp = rcutmin
self.rcutcomp = rcutcomp
hfilter, xfilter = filter
Z = self.Z
n_j = self.n_j
l_j = self.l_j
f_j = self.f_j
e_j = self.e_j
if vbar is None:
vbar = ('poly', rcutmin * 0.9)
vbar_type, rcutvbar = vbar
normconserving_l = [x in normconserving for x in 'spdf']
# Parse core string:
j = 0
if core.startswith('['):
a, core = core.split(']')
core_symbol = a[1:]
j = len(configurations[core_symbol][1])
while core != '':
assert n_j[j] == int(core[0])
assert l_j[j] == 'spdf'.find(core[1])
if j != self.jcorehole:
assert f_j[j] == 2 * (2 * l_j[j] + 1)
j += 1
core = core[2:]
njcore = j
self.njcore = njcore
lmaxocc = max(l_j[njcore:])
while empty_states != '':
n = int(empty_states[0])
l = 'spdf'.find(empty_states[1])
assert n == 1 + l + l_j.count(l)
n_j.append(n)
l_j.append(l)
f_j.append(0.0)
e_j.append(-0.01)
empty_states = empty_states[2:]
if 2 in l_j[njcore:]:
# We have a bound valence d-state. Add bound s- and
# p-states if not already there:
for l in [0, 1]:
if l not in l_j[njcore:]:
n_j.append(1 + l + l_j.count(l))
l_j.append(l)
f_j.append(0.0)
e_j.append(-0.01)
if l_j[njcore:] == [0] and Z > 2:
# We have only a bound valence s-state and we are not
# hydrogen and not helium. Add bound p-state:
n_j.append(n_j[njcore])
l_j.append(1)
f_j.append(0.0)
e_j.append(-0.01)
nj = len(n_j)
self.Nv = sum(f_j[njcore:])
self.Nc = sum(f_j[:njcore])
# Do all-electron calculation:
AllElectron.run(self, use_restart_file)
# Highest occupied atomic orbital:
self.emax = max(e_j)
N = self.N
r = self.r
dr = self.dr
d2gdr2 = self.d2gdr2
beta = self.beta
dv = r**2 * dr
t = self.text
t()
t('Generating PAW setup')
if core != '':
t('Frozen core:', core)
# So far - no ghost-states:
self.ghost = False
# Calculate the kinetic energy of the core states:
Ekincore = 0.0
j = 0
for f, e, u in zip(f_j[:njcore], e_j[:njcore], self.u_j[:njcore]):
u = np.where(abs(u) < 1e-160, 0, u) # XXX Numeric!
k = e - np.sum((u**2 * self.vr * dr)[1:] / r[1:])
Ekincore += f * k
if j == self.jcorehole:
self.Ekincorehole = k
j += 1
# Calculate core density:
if njcore == 0:
nc = np.zeros(N)
else:
uc_j = self.u_j[:njcore]
uc_j = np.where(abs(uc_j) < 1e-160, 0, uc_j) # XXX Numeric!
nc = np.dot(f_j[:njcore], uc_j**2) / (4 * pi)
nc[1:] /= r[1:]**2
nc[0] = nc[1]
self.nc = nc
# Calculate core kinetic energy density
if njcore == 0:
tauc = np.zeros(N)
else:
tauc = self.radial_kinetic_energy_density(f_j[:njcore],
l_j[:njcore],
self.u_j[:njcore])
t('Kinetic energy of the core from tauc =',
np.dot(tauc * r * r, dr) * 4 * pi)
lmax = max(l_j[njcore:])
# Order valence states with respect to angular momentum
# quantum number:
self.n_ln = n_ln = []
self.f_ln = f_ln = []
self.e_ln = e_ln = []
for l in range(lmax + 1):
n_n = []
f_n = []
e_n = []
for j in range(njcore, nj):
if l_j[j] == l:
n_n.append(n_j[j])
f_n.append(f_j[j])
e_n.append(e_j[j])
n_ln.append(n_n)
f_ln.append(f_n)
e_ln.append(e_n)
# Add extra projectors:
if extra is not None:
if len(extra) == 0:
lmaxextra = 0
else:
lmaxextra = max(extra.keys())
if lmaxextra > lmax:
for l in range(lmax, lmaxextra):
n_ln.append([])
f_ln.append([])
e_ln.append([])
lmax = lmaxextra
for l in extra:
nn = -1
for e in extra[l]:
n_ln[l].append(nn)
f_ln[l].append(0.0)
e_ln[l].append(e)
nn -= 1
else:
# Automatic:
# Make sure we have two projectors for each occupied channel:
for l in range(lmaxocc + 1):
if len(n_ln[l]) < 2 and not normconserving_l[l]:
# Only one - add one more:
assert len(n_ln[l]) == 1
n_ln[l].append(-1)
f_ln[l].append(0.0)
e_ln[l].append(1.0 + e_ln[l][0])
if lmaxocc < 2 and lmaxocc == lmax:
# Add extra projector for l = lmax + 1:
n_ln.append([-1])
f_ln.append([0.0])
e_ln.append([0.0])
lmax += 1
self.lmax = lmax
rcut_l.extend([rcutmin] * (lmax + 1 - len(rcut_l)))
t('Cutoffs:')
for rc, s in zip(rcut_l, 'spdf'):
t('rc(%s)=%.3f' % (s, rc))
t('rc(vbar)=%.3f' % rcutvbar)
t('rc(comp)=%.3f' % rcutcomp)
t('rc(nct)=%.3f' % rcutmax)
t()
t('Kinetic energy of the core states: %.6f' % Ekincore)
# Allocate arrays:
self.u_ln = u_ln = [] # phi * r
self.s_ln = s_ln = [] # phi-tilde * r
self.q_ln = q_ln = [] # p-tilde * r
for l in range(lmax + 1):
nn = len(n_ln[l])
u_ln.append(np.zeros((nn, N)))
s_ln.append(np.zeros((nn, N)))
q_ln.append(np.zeros((nn, N)))
# Fill in all-electron wave functions:
for l in range(lmax + 1):
# Collect all-electron wave functions:
u_n = [self.u_j[j] for j in range(njcore, nj) if l_j[j] == l]
for n, u in enumerate(u_n):
u_ln[l][n] = u
# Grid-index corresponding to rcut:
gcut_l = [1 + int(rc * N / (rc + beta)) for rc in rcut_l]
rcutfilter = xfilter * rcutmax
self.rcutfilter = rcutfilter
gcutfilter = 1 + int(rcutfilter * N / (rcutfilter + beta))
gcutmax = 1 + int(rcutmax * N / (rcutmax + beta))
# Outward integration of unbound states stops at 3 * rcut:
gmax = int(3 * rcutmax * N / (3 * rcutmax + beta))
assert gmax > gcutfilter
# Calculate unbound extra states:
c2 = -(r / dr)**2
c10 = -d2gdr2 * r**2
for l, (n_n, e_n, u_n) in enumerate(zip(n_ln, e_ln, u_ln)):
for n, e, u in zip(n_n, e_n, u_n):
if n < 0:
u[:] = 0.0
shoot(u, l, self.vr, e, self.r2dvdr, r, dr, c10, c2,
self.scalarrel, gmax=gmax)
u *= 1.0 / u[gcut_l[l]]
charge = Z - self.Nv - self.Nc
t('Charge: %.1f' % charge)
t('Core electrons: %.1f' % self.Nc)
t('Valence electrons: %.1f' % self.Nv)
# Construct smooth wave functions:
coefs = []
for l, (u_n, s_n) in enumerate(zip(u_ln, s_ln)):
nodeless = True
gc = gcut_l[l]
for u, s in zip(u_n, s_n):
s[:] = u
if normconserving_l[l]:
A = np.zeros((5, 5))
A[:4, 0] = 1.0
A[:4, 1] = r[gc - 2:gc + 2]**2
A[:4, 2] = A[:4, 1]**2
A[:4, 3] = A[:4, 1] * A[:4, 2]
A[:4, 4] = A[:4, 2]**2
A[4, 4] = 1.0
a = u[gc - 2:gc + 3] / r[gc - 2:gc + 3]**(l + 1)
a = np.log(a)
def f(x):
a[4] = x
b = solve(A, a)
r1 = r[:gc]
r2 = r1**2
rl1 = r1**(l + 1)
y = b[0] + r2 * (b[1] + r2 * (b[2] + r2 * (b[3] + r2
* b[4])))
y = np.exp(y)
s[:gc] = rl1 * y
return np.dot(s**2, dr) - 1
x1 = 0.0
x2 = 0.001
f1 = f(x1)
f2 = f(x2)
while abs(f1) > 1e-6:
x0 = (x1 / f1 - x2 / f2) / (1 / f1 - 1 / f2)
f0 = f(x0)
if abs(f1) < abs(f2):
x2, f2 = x1, f1
x1, f1 = x0, f0
else:
A = np.ones((4, 4))
A[:, 0] = 1.0
A[:, 1] = r[gc - 2:gc + 2]**2
A[:, 2] = A[:, 1]**2
A[:, 3] = A[:, 1] * A[:, 2]
a = u[gc - 2:gc + 2] / r[gc - 2:gc + 2]**(l + 1)
if 0:#l < 2 and nodeless:
a = np.log(a)
a = solve(A, a)
r1 = r[:gc]
r2 = r1**2
rl1 = r1**(l + 1)
y = a[0] + r2 * (a[1] + r2 * (a[2] + r2 * (a[3])))
if 0:#l < 2 and nodeless:
y = np.exp(y)
s[:gc] = rl1 * y
coefs.append(a)
if nodeless:
if not np.alltrue(s[1:gc] > 0.0):
raise RuntimeError(
'Error: The %d%s pseudo wave has a node!' %
(n_ln[l][0], 'spdf'[l]))
# Only the first state for each l must be nodeless:
nodeless = False
# Calculate pseudo core density:
gcutnc = 1 + int(rcutmax * N / (rcutmax + beta))
self.nct = nct = nc.copy()
A = np.ones((4, 4))
A[0] = 1.0
A[1] = r[gcutnc - 2:gcutnc + 2]**2
A[2] = A[1]**2
A[3] = A[1] * A[2]
a = nc[gcutnc - 2:gcutnc + 2]
a = solve(np.transpose(A), a)
r2 = r[:gcutnc]**2
nct[:gcutnc] = a[0] + r2 * (a[1] + r2 * (a[2] + r2 * a[3]))
t('Pseudo-core charge: %.6f' % (4 * pi * np.dot(nct, dv)))
# ... and the pseudo core kinetic energy density:
tauct = tauc.copy()
a = tauc[gcutnc - 2:gcutnc + 2]
a = solve(np.transpose(A), a)
tauct[:gcutnc] = a[0] + r2 * (a[1] + r2 * (a[2] + r2 * a[3]))
# ... and the soft valence density:
nt = np.zeros(N)
for f_n, s_n in zip(f_ln, s_ln):
nt += np.dot(f_n, s_n**2) / (4 * pi)
nt[1:] /= r[1:]**2
nt[0] = nt[1]
nt += nct
self.nt = nt
# Calculate the shape function:
x = r / rcutcomp
gaussian = np.zeros(N)
self.gamma = gamma = 10.0
gaussian[:gmax] = np.exp(-gamma * x[:gmax]**2)
gt = 4 * (gamma / rcutcomp**2)**1.5 / sqrt(pi) * gaussian
t('Shape function alpha=%.3f' % (gamma / rcutcomp**2))
norm = np.dot(gt, dv)
#print norm, norm-1
assert abs(norm - 1) < 1e-2
gt /= norm
# Calculate smooth charge density:
Nt = np.dot(nt, dv)
rhot = nt - (Nt + charge / (4 * pi)) * gt
t('Pseudo-electron charge', 4 * pi * Nt)
vHt = np.zeros(N)
hartree(0, rhot * r * dr, self.beta, self.N, vHt)
vHt[1:] /= r[1:]
vHt[0] = vHt[1]
vXCt = np.zeros(N)
extra_xc_data = {}
if self.xc.type != 'GLLB':
Exct = self.xc.calculate_spherical(self.rgd,
nt.reshape((1, -1)),
vXCt.reshape((1, -1)))
else:
Exct = self.xc.get_smooth_xc_potential_and_energy_1d(vXCt)
# Calculate extra-stuff for non-local functionals
self.xc.get_extra_setup_data(extra_xc_data)
vt = vHt + vXCt
# Construct zero potential:
gc = 1 + int(rcutvbar * N / (rcutvbar + beta))
if vbar_type == 'f':
assert lmax == 2
uf = np.zeros(N)
l = 3
# Solve for all-electron f-state:
eps = 0.0
shoot(uf, l, self.vr, eps, self.r2dvdr, r, dr, c10, c2,
self.scalarrel, gmax=gmax)
uf *= 1.0 / uf[gc]
# Fit smooth pseudo f-state polynomium:
A = np.ones((4, 4))
A[:, 0] = 1.0
A[:, 1] = r[gc - 2:gc + 2]**2
A[:, 2] = A[:, 1]**2
A[:, 3] = A[:, 1] * A[:, 2]
a = uf[gc - 2:gc + 2] / r[gc - 2:gc + 2]**(l + 1)
a0, a1, a2, a3 = solve(A, a)
r1 = r[:gc]
r2 = r1**2
rl1 = r1**(l + 1)
y = a0 + r2 * (a1 + r2 * (a2 + r2 * a3))
sf = uf.copy()
sf[:gc] = rl1 * y
# From 0 to gc, use analytic formula for kinetic energy operator:
r4 = r2**2
r6 = r4 * r2
enumerator = (a0 * l * (l + 1) +
a1 * (l + 2) * (l + 3) * r2 +
a2 * (l + 4) * (l + 5) * r4 +
a3 * (l + 6) * (l + 7) * r6)
denominator = a0 + a1 * r2 + a2 * r4 + a3 * r6
ekin_over_phit = - 0.5 * (enumerator / denominator - l * (l + 1))
ekin_over_phit[1:] /= r2[1:]
vbar = eps - vt
vbar[:gc] -= ekin_over_phit
vbar[0] = vbar[1] # Actually we can collect the terms into
# a single fraction without poles, so as to avoid doing this,
# but this is good enough
# From gc to gmax, use finite-difference formula for kinetic
# energy operator:
vbar[gc:gmax] -= self.kin(l, sf)[gc:gmax] / sf[gc:gmax]
vbar[gmax:] = 0.0
else:
assert vbar_type == 'poly'
A = np.ones((2, 2))
A[0] = 1.0
A[1] = r[gc - 1:gc + 1]**2
a = vt[gc - 1:gc + 1]
a = solve(np.transpose(A), a)
r2 = r**2
vbar = a[0] + r2 * a[1] - vt
vbar[gc:] = 0.0
vt += vbar
# Construct projector functions:
for l, (e_n, s_n, q_n) in enumerate(zip(e_ln, s_ln, q_ln)):
for e, s, q in zip(e_n, s_n, q_n):
q[:] = self.kin(l, s) + (vt - e) * s
q[gcutmax:] = 0.0
filter = Filter(r, dr, gcutfilter, hfilter).filter
vbar = filter(vbar * r)
# Calculate matrix elements:
self.dK_lnn = dK_lnn = []
self.dH_lnn = dH_lnn = []
self.dO_lnn = dO_lnn = []
for l, (e_n, u_n, s_n, q_n) in enumerate(zip(e_ln, u_ln,
s_ln, q_ln)):
A_nn = np.inner(s_n, q_n * dr)
# Do a LU decomposition of A:
nn = len(e_n)
L_nn = np.identity(nn, float)
U_nn = A_nn.copy()
# Keep all bound states normalized
if sum([n > 0 for n in n_ln[l]]) <= 1:
for i in range(nn):
for j in range(i + 1, nn):
L_nn[j, i] = 1.0 * U_nn[j, i] / U_nn[i, i]
U_nn[j, :] -= U_nn[i, :] * L_nn[j, i]
dO_nn = (np.inner(u_n, u_n * dr) -
np.inner(s_n, s_n * dr))
e_nn = np.zeros((nn, nn))
e_nn.ravel()[::nn + 1] = e_n
dH_nn = np.dot(dO_nn, e_nn) - A_nn
q_n[:] = np.dot(inv(np.transpose(U_nn)), q_n)
s_n[:] = np.dot(inv(L_nn), s_n)
u_n[:] = np.dot(inv(L_nn), u_n)
dO_nn = np.dot(np.dot(inv(L_nn), dO_nn),
inv(np.transpose(L_nn)))
dH_nn = np.dot(np.dot(inv(L_nn), dH_nn),
inv(np.transpose(L_nn)))
ku_n = [self.kin(l, u, e) for u, e in zip(u_n, e_n)]
ks_n = [self.kin(l, s) for s in s_n]
dK_nn = 0.5 * (np.inner(u_n, ku_n * dr) -
np.inner(s_n, ks_n * dr))
dK_nn += np.transpose(dK_nn).copy()
dK_lnn.append(dK_nn)
dO_lnn.append(dO_nn)
dH_lnn.append(dH_nn)
for n, q in enumerate(q_n):
q[:] = filter(q, l) * r**(l + 1)
A_nn = np.inner(s_n, q_n * dr)
q_n[:] = np.dot(inv(np.transpose(A_nn)), q_n)
self.vt = vt
self.vbar = vbar
t('state eigenvalue norm')
t('--------------------------------')
for l, (n_n, f_n, e_n) in enumerate(zip(n_ln, f_ln, e_ln)):
for n in range(len(e_n)):
if n_n[n] > 0:
f = '(%d)' % f_n[n]
t('%d%s%-4s: %12.6f %12.6f' % (
n_n[n], 'spdf'[l], f, e_n[n],
np.dot(s_ln[l][n]**2, dr)))
else:
t('*%s : %12.6f' % ('spdf'[l], e_n[n]))
t('--------------------------------')
self.logd = {}
if logderiv:
ni = 300
self.elog = np.linspace(-5.0, 1.0, ni)
# Calculate logarithmic derivatives:
gld = gcutmax + 10
self.rlog = r[gld]
assert gld < gmax
t('Calculating logarithmic derivatives at r=%.3f' % r[gld])
t('(skip with [Ctrl-C])')
try:
u = np.zeros(N)
for l in range(4):
self.logd[l] = (np.empty(ni), np.empty(ni))
if l <= lmax:
dO_nn = dO_lnn[l]
dH_nn = dH_lnn[l]
q_n = q_ln[l]
fae = open(self.symbol + '.ae.ld.' + 'spdf'[l], 'w')
fps = open(self.symbol + '.ps.ld.' + 'spdf'[l], 'w')
for i, e in enumerate(self.elog):
# All-electron logarithmic derivative:
u[:] = 0.0
shoot(u, l, self.vr, e, self.r2dvdr, r, dr, c10, c2,
self.scalarrel, gmax=gld)
dudr = 0.5 * (u[gld + 1] - u[gld - 1]) / dr[gld]
ld = dudr / u[gld] - 1.0 / r[gld]
print >> fae, e, ld
self.logd[l][0][i] = ld
# PAW logarithmic derivative:
s = self.integrate(l, vt, e, gld)
if l <= lmax:
A_nn = dH_nn - e * dO_nn
s_n = [self.integrate(l, vt, e, gld, q)
for q in q_n]
B_nn = np.inner(q_n, s_n * dr)
a_n = np.dot(q_n, s * dr)
B_nn = np.dot(A_nn, B_nn)
B_nn.ravel()[::len(a_n) + 1] += 1.0
c_n = solve(B_nn, np.dot(A_nn, a_n))
s -= np.dot(c_n, s_n)
dsdr = 0.5 * (s[gld + 1] - s[gld - 1]) / dr[gld]
ld = dsdr / s[gld] - 1.0 / r[gld]
print >> fps, e, ld
self.logd[l][1][i] = ld
except KeyboardInterrupt:
pass
self.write(nc,'nc')
self.write(nt, 'nt')
self.write(nct, 'nct')
self.write(vbar, 'vbar')
self.write(vt, 'vt')
self.write(tauc, 'tauc')
self.write(tauct, 'tauct')
for l, (n_n, f_n, u_n, s_n, q_n) in enumerate(zip(n_ln, f_ln,
u_ln, s_ln, q_ln)):
for n, f, u, s, q in zip(n_n, f_n, u_n, s_n, q_n):
if n < 0:
self.write(u, 'ae', n=n, l=l)
self.write(s, 'ps', n=n, l=l)
self.write(q, 'proj', n=n, l=l)
# Test for ghost states:
for h in [0.05]:
self.diagonalize(h)
self.vn_j = vn_j = []
self.vl_j = vl_j = []
self.vf_j = vf_j = []
self.ve_j = ve_j = []
self.vu_j = vu_j = []
self.vs_j = vs_j = []
self.vq_j = vq_j = []
j_ln = [[0 for f in f_n] for f_n in f_ln]
j = 0
for l, n_n in enumerate(n_ln):
for n, nn in enumerate(n_n):
if nn > 0:
vf_j.append(f_ln[l][n])
vn_j.append(nn)
vl_j.append(l)
ve_j.append(e_ln[l][n])
vu_j.append(u_ln[l][n])
vs_j.append(s_ln[l][n])
vq_j.append(q_ln[l][n])
j_ln[l][n] = j
j += 1
for l, n_n in enumerate(n_ln):
for n, nn in enumerate(n_n):
if nn < 0:
vf_j.append(0)
vn_j.append(nn)
vl_j.append(l)
ve_j.append(e_ln[l][n])
vu_j.append(u_ln[l][n])
vs_j.append(s_ln[l][n])
vq_j.append(q_ln[l][n])
j_ln[l][n] = j
j += 1
nj = j
self.dK_jj = np.zeros((nj, nj))
for l, j_n in enumerate(j_ln):
for n1, j1 in enumerate(j_n):
for n2, j2 in enumerate(j_n):
self.dK_jj[j1, j2] = self.dK_lnn[l][n1, n2]
if exx:
X_p = constructX(self)
ExxC = atomic_exact_exchange(self, 'core-core')
else:
X_p = None
ExxC = None
sqrt4pi = sqrt(4 * pi)
setup = SetupData(self.symbol, self.xc.name, self.name,
readxml=False)
def divide_by_r(x_g, l):
r = self.r
#for x_g, l in zip(x_jg, l_j):
p = x_g.copy()
p[1:] /= self.r[1:]
# XXXXX go to higher order!!!!!
if l == 0:#l_j[self.jcorehole] == 0:
p[0] = (p[2] +
(p[1] - p[2]) * (r[0] - r[2]) / (r[1] - r[2]))
return p
def divide_all_by_r(x_jg):
return [divide_by_r(x_g, l) for x_g, l in zip(x_jg, vl_j)]
setup.l_j = vl_j
setup.n_j = vn_j
setup.f_j = vf_j
setup.eps_j = ve_j
setup.rcut_j = [rcut_l[l] for l in vl_j]
setup.nc_g = nc * sqrt4pi
setup.nct_g = nct * sqrt4pi
setup.nvt_g = (nt - nct) * sqrt4pi
setup.e_kinetic_core = Ekincore
setup.vbar_g = vbar * sqrt4pi
setup.tauc_g = tauc * sqrt4pi
setup.tauct_g = tauct * sqrt4pi
setup.extra_xc_data = extra_xc_data
setup.Z = Z
setup.Nc = self.Nc
setup.Nv = self.Nv
setup.e_kinetic = self.Ekin
setup.e_xc = self.Exc
setup.e_electrostatic = self.Epot
setup.e_total = self.Epot + self.Exc + self.Ekin
setup.rgd = self.rgd
setup.rcgauss = self.rcutcomp / sqrt(self.gamma)
setup.e_kin_jj = self.dK_jj
setup.ExxC = ExxC
setup.phi_jg = divide_all_by_r(vu_j)
setup.phit_jg = divide_all_by_r(vs_j)
setup.pt_jg = divide_all_by_r(vq_j)
setup.X_p = X_p
if self.jcorehole is not None:
setup.has_corehole = True
setup.lcorehole = l_j[self.jcorehole] # l_j or vl_j ????? XXX
setup.ncorehole = n_j[self.jcorehole]
setup.phicorehole_g = divide_by_r(self.u_j[self.jcorehole],
setup.lcorehole)
setup.core_hole_e = self.e_j[self.jcorehole]
setup.core_hole_e_kin = self.Ekincorehole
setup.fcorehole = self.fcorehole
if self.ghost:
raise RuntimeError('Ghost!')
if self.scalarrel:
reltype = 'scalar-relativistic'
else:
reltype = 'non-relativistic'
attrs = [('type', reltype), ('name', 'gpaw-%s' % version)]
data = 'Frozen core: '+ (self.core or 'none')
setup.generatorattrs = attrs
setup.generatordata = data
self.id_j = []
for l, n in zip(vl_j, vn_j):
if n > 0:
id = '%s-%d%s' % (self.symbol, n, 'spdf'[l])
else:
id = '%s-%s%d' % (self.symbol, 'spdf'[l], -n)
self.id_j.append(id)
setup.id_j = self.id_j
if write_xml:
setup.write_xml()
return setup
def make_paw_setup(self, tag=None):
aea = self.aea
from gpaw.setup_data import SetupData
setup = SetupData(aea.symbol, aea.xc.name, tag, readxml=False)
setup.id_j = []
J = [] # new reordered j and i indices
I = []
# Bound states:
j = 0
i = 0
for l, waves in enumerate(self.waves_l):
for n, f, e, phi_g, phit_g, pt_g in zip(waves.n_n, waves.f_n,
waves.e_n, waves.phi_ng,
waves.phit_ng,
waves.pt_ng):
if n != -1:
setup.append(n, l, f, e, waves.rcut, phi_g, phit_g, pt_g)
id = '%d%s' % (n, 'spdf'[l])
setup.id_j.append(id)
J.append(j)
I.extend(range(i, i + 2 * l + 1))
j += 1
i += 2 * l + 1
# Excited states:
j = 0
i = 0
for l, waves in enumerate(self.waves_l):
ne = 0
for n, f, e, phi_g, phit_g, pt_g in zip(waves.n_n, waves.f_n,
waves.e_n, waves.phi_ng,
waves.phit_ng,
waves.pt_ng):
if n == -1:
setup.append(n, l, f, e, waves.rcut, phi_g, phit_g, pt_g)
ne += 1
id = '%s%d' % ('spdf'[l], ne)
setup.id_j.append(id)
J.append(j)
I.extend(range(i, i + 2 * l + 1))
j += 1
i += 2 * l + 1
nj = sum(len(waves) for waves in self.waves_l)
e_kin_jj = np.zeros((nj, nj))
j1 = 0
for waves in self.waves_l:
j2 = j1 + len(waves)
e_kin_jj[j1:j2, j1:j2] = waves.dekin_nn
j1 = j2
setup.e_kin_jj = e_kin_jj[J][:, J].copy()
setup.nc_g = self.nc_g * sqrt(4 * pi)
setup.nct_g = self.nct_g * sqrt(4 * pi)
setup.e_kinetic_core = self.ekincore
setup.vbar_g = self.v0r_g * sqrt(4 * pi)
setup.vbar_g[1:] /= self.rgd.r_g[1:]
setup.vbar_g[0] = setup.vbar_g[1]
setup.Z = aea.Z
setup.Nc = self.ncore
setup.Nv = self.nvalence
setup.e_kinetic = aea.ekin
setup.e_xc = aea.exc
setup.e_electrostatic = aea.eH + aea.eZ
setup.e_total = aea.exc + aea.ekin + aea.eH + aea.eZ
setup.rgd = self.rgd
setup.rcgauss = 1 / sqrt(self.alpha)
self.calculate_exx_integrals()
setup.ExxC = self.exxcc
setup.X_p = pack2(self.exxcv_ii[I][:, I])
setup.tauc_g = self.tauc_g * (4 * pi)**0.5
setup.tauct_g = self.tauct_g * (4 * pi)**0.5
if self.aea.scalar_relativistic:
reltype = 'scalar-relativistic'
else:
reltype = 'non-relativistic'
attrs = [('type', reltype), ('version', 2),
('name', 'gpaw-%s' % version)]
setup.generatorattrs = attrs
setup.l0 = self.l0
setup.e0 = 0.0
setup.r0 = self.r0
setup.nderiv0 = self.nderiv0
setup.basis = self.basis
if self.core_hole:
n, l, occ = self.core_hole
phi_g = self.aea.channels[l].phi_ng[n - l - 1]
setup.ncorehole = n
setup.lcorehole = l
setup.fcorehole = occ
setup.phicorehole_g = phi_g
setup.has_corehole = True
return setup
def run(self,
core='',
rcut=1.0,
extra=None,
logderiv=False,
vbar=None,
exx=False,
name=None,
normconserving='',
filter=(0.4, 1.75),
rcutcomp=None,
write_xml=True,
use_restart_file=True,
empty_states=''):
self.name = name
self.core = core
if type(rcut) is float:
rcut_l = [rcut]
else:
rcut_l = rcut
rcutmax = max(rcut_l)
rcutmin = min(rcut_l)
self.rcut_l = rcut_l
if rcutcomp is None:
rcutcomp = rcutmin
self.rcutcomp = rcutcomp
hfilter, xfilter = filter
Z = self.Z
n_j = self.n_j
l_j = self.l_j
f_j = self.f_j
e_j = self.e_j
if vbar is None:
vbar = ('poly', rcutmin * 0.9)
vbar_type, rcutvbar = vbar
normconserving_l = [x in normconserving for x in 'spdf']
# Parse core string:
j = 0
if core.startswith('['):
a, core = core.split(']')
core_symbol = a[1:]
j = len(configurations[core_symbol][1])
while core != '':
assert n_j[j] == int(core[0])
assert l_j[j] == 'spdf'.find(core[1])
if j != self.jcorehole:
assert f_j[j] == 2 * (2 * l_j[j] + 1)
j += 1
core = core[2:]
njcore = j
self.njcore = njcore
lmaxocc = max(l_j[njcore:])
while empty_states != '':
n = int(empty_states[0])
l = 'spdf'.find(empty_states[1])
print l_j
assert n == 1 + l + l_j.count(l)
n_j.append(n)
l_j.append(l)
f_j.append(0.0)
e_j.append(-0.01)
empty_states = empty_states[2:]
if 2 in l_j[njcore:]:
# We have a bound valence d-state. Add bound s- and
# p-states if not already there:
for l in [0, 1]:
if l not in l_j[njcore:]:
n_j.append(1 + l + l_j.count(l))
l_j.append(l)
f_j.append(0.0)
e_j.append(-0.01)
if l_j[njcore:] == [0] and Z > 2:
# We have only a bound valence s-state and we are not
# hydrogen and not helium. Add bound p-state:
n_j.append(n_j[njcore])
l_j.append(1)
f_j.append(0.0)
e_j.append(-0.01)
nj = len(n_j)
self.Nv = sum(f_j[njcore:])
self.Nc = sum(f_j[:njcore])
# Do all-electron calculation:
AllElectron.run(self, use_restart_file)
# Highest occupied atomic orbital:
self.emax = max(e_j)
N = self.N
r = self.r
dr = self.dr
d2gdr2 = self.d2gdr2
beta = self.beta
dv = r**2 * dr
t = self.text
t()
t('Generating PAW setup')
if core != '':
t('Frozen core:', core)
# So far - no ghost-states:
self.ghost = False
# Calculate the kinetic energy of the core states:
Ekincore = 0.0
j = 0
for f, e, u in zip(f_j[:njcore], e_j[:njcore], self.u_j[:njcore]):
u = np.where(abs(u) < 1e-160, 0, u) # XXX Numeric!
k = e - np.sum((u**2 * self.vr * dr)[1:] / r[1:])
Ekincore += f * k
if j == self.jcorehole:
self.Ekincorehole = k
j += 1
# Calculate core density:
if njcore == 0:
nc = np.zeros(N)
else:
uc_j = self.u_j[:njcore]
uc_j = np.where(abs(uc_j) < 1e-160, 0, uc_j) # XXX Numeric!
nc = np.dot(f_j[:njcore], uc_j**2) / (4 * pi)
nc[1:] /= r[1:]**2
nc[0] = nc[1]
self.nc = nc
# Calculate core kinetic energy density
if njcore == 0:
tauc = np.zeros(N)
else:
tauc = self.radial_kinetic_energy_density(f_j[:njcore],
l_j[:njcore],
self.u_j[:njcore])
t('Kinetic energy of the core from tauc =',
np.dot(tauc * r * r, dr) * 4 * pi)
lmax = max(l_j[njcore:])
# Order valence states with respect to angular momentum
# quantum number:
self.n_ln = n_ln = []
self.f_ln = f_ln = []
self.e_ln = e_ln = []
for l in range(lmax + 1):
n_n = []
f_n = []
e_n = []
for j in range(njcore, nj):
if l_j[j] == l:
n_n.append(n_j[j])
f_n.append(f_j[j])
e_n.append(e_j[j])
n_ln.append(n_n)
f_ln.append(f_n)
e_ln.append(e_n)
# Add extra projectors:
if extra is not None:
if len(extra) == 0:
lmaxextra = 0
else:
lmaxextra = max(extra.keys())
if lmaxextra > lmax:
for l in range(lmax, lmaxextra):
n_ln.append([])
f_ln.append([])
e_ln.append([])
lmax = lmaxextra
for l in extra:
nn = -1
for e in extra[l]:
n_ln[l].append(nn)
f_ln[l].append(0.0)
e_ln[l].append(e)
nn -= 1
else:
# Automatic:
# Make sure we have two projectors for each occupied channel:
for l in range(lmaxocc + 1):
if len(n_ln[l]) < 2 and not normconserving_l[l]:
# Only one - add one more:
assert len(n_ln[l]) == 1
n_ln[l].append(-1)
f_ln[l].append(0.0)
e_ln[l].append(1.0 + e_ln[l][0])
if lmaxocc < 2 and lmaxocc == lmax:
# Add extra projector for l = lmax + 1:
n_ln.append([-1])
f_ln.append([0.0])
e_ln.append([0.0])
lmax += 1
self.lmax = lmax
rcut_l.extend([rcutmin] * (lmax + 1 - len(rcut_l)))
t('Cutoffs:')
for rc, s in zip(rcut_l, 'spdf'):
t('rc(%s)=%.3f' % (s, rc))
t('rc(vbar)=%.3f' % rcutvbar)
t('rc(comp)=%.3f' % rcutcomp)
t()
t('Kinetic energy of the core states: %.6f' % Ekincore)
# Allocate arrays:
self.u_ln = u_ln = [] # phi * r
self.s_ln = s_ln = [] # phi-tilde * r
self.q_ln = q_ln = [] # p-tilde * r
for l in range(lmax + 1):
nn = len(n_ln[l])
u_ln.append(np.zeros((nn, N)))
s_ln.append(np.zeros((nn, N)))
q_ln.append(np.zeros((nn, N)))
# Fill in all-electron wave functions:
for l in range(lmax + 1):
# Collect all-electron wave functions:
u_n = [self.u_j[j] for j in range(njcore, nj) if l_j[j] == l]
for n, u in enumerate(u_n):
u_ln[l][n] = u
# Grid-index corresponding to rcut:
gcut_l = [1 + int(rc * N / (rc + beta)) for rc in rcut_l]
rcutfilter = xfilter * rcutmax
self.rcutfilter = rcutfilter
gcutfilter = 1 + int(rcutfilter * N / (rcutfilter + beta))
gcutmax = 1 + int(rcutmax * N / (rcutmax + beta))
# Outward integration of unbound states stops at 3 * rcut:
gmax = int(3 * rcutmax * N / (3 * rcutmax + beta))
assert gmax > gcutfilter
# Calculate unbound extra states:
c2 = -(r / dr)**2
c10 = -d2gdr2 * r**2
for l, (n_n, e_n, u_n) in enumerate(zip(n_ln, e_ln, u_ln)):
for n, e, u in zip(n_n, e_n, u_n):
if n < 0:
u[:] = 0.0
shoot(u,
l,
self.vr,
e,
self.r2dvdr,
r,
dr,
c10,
c2,
self.scalarrel,
gmax=gmax)
u *= 1.0 / u[gcut_l[l]]
charge = Z - self.Nv - self.Nc
t('Charge: %.1f' % charge)
t('Core electrons: %.1f' % self.Nc)
t('Valence electrons: %.1f' % self.Nv)
# Construct smooth wave functions:
coefs = []
for l, (u_n, s_n) in enumerate(zip(u_ln, s_ln)):
nodeless = True
gc = gcut_l[l]
for u, s in zip(u_n, s_n):
s[:] = u
if normconserving_l[l]:
A = np.zeros((5, 5))
A[:4, 0] = 1.0
A[:4, 1] = r[gc - 2:gc + 2]**2
A[:4, 2] = A[:4, 1]**2
A[:4, 3] = A[:4, 1] * A[:4, 2]
A[:4, 4] = A[:4, 2]**2
A[4, 4] = 1.0
a = u[gc - 2:gc + 3] / r[gc - 2:gc + 3]**(l + 1)
a = np.log(a)
def f(x):
a[4] = x
b = solve(A, a)
r1 = r[:gc]
r2 = r1**2
rl1 = r1**(l + 1)
y = b[0] + r2 * (b[1] + r2 * (b[2] + r2 *
(b[3] + r2 * b[4])))
y = np.exp(y)
s[:gc] = rl1 * y
return np.dot(s**2, dr) - 1
x1 = 0.0
x2 = 0.001
f1 = f(x1)
f2 = f(x2)
while abs(f1) > 1e-6:
x0 = (x1 / f1 - x2 / f2) / (1 / f1 - 1 / f2)
f0 = f(x0)
if abs(f1) < abs(f2):
x2, f2 = x1, f1
x1, f1 = x0, f0
else:
A = np.ones((4, 4))
A[:, 0] = 1.0
A[:, 1] = r[gc - 2:gc + 2]**2
A[:, 2] = A[:, 1]**2
A[:, 3] = A[:, 1] * A[:, 2]
a = u[gc - 2:gc + 2] / r[gc - 2:gc + 2]**(l + 1)
if 0: #l < 2 and nodeless:
a = np.log(a)
a = solve(A, a)
r1 = r[:gc]
r2 = r1**2
rl1 = r1**(l + 1)
y = a[0] + r2 * (a[1] + r2 * (a[2] + r2 * (a[3])))
if 0: #l < 2 and nodeless:
y = np.exp(y)
s[:gc] = rl1 * y
coefs.append(a)
if nodeless:
if not np.alltrue(s[1:gc] > 0.0):
raise RuntimeError(
'Error: The %d%s pseudo wave has a node!' %
(n_ln[l][0], 'spdf'[l]))
# Only the first state for each l must be nodeless:
nodeless = False
# Calculate pseudo core density:
gcutnc = 1 + int(rcutmax * N / (rcutmax + beta))
self.nct = nct = nc.copy()
A = np.ones((4, 4))
A[0] = 1.0
A[1] = r[gcutnc - 2:gcutnc + 2]**2
A[2] = A[1]**2
A[3] = A[1] * A[2]
a = nc[gcutnc - 2:gcutnc + 2]
a = solve(np.transpose(A), a)
r2 = r[:gcutnc]**2
nct[:gcutnc] = a[0] + r2 * (a[1] + r2 * (a[2] + r2 * a[3]))
t('Pseudo-core charge: %.6f' % (4 * pi * np.dot(nct, dv)))
# ... and the pseudo core kinetic energy density:
tauct = tauc.copy()
a = tauc[gcutnc - 2:gcutnc + 2]
a = solve(np.transpose(A), a)
tauct[:gcutnc] = a[0] + r2 * (a[1] + r2 * (a[2] + r2 * a[3]))
# ... and the soft valence density:
nt = np.zeros(N)
for f_n, s_n in zip(f_ln, s_ln):
nt += np.dot(f_n, s_n**2) / (4 * pi)
nt[1:] /= r[1:]**2
nt[0] = nt[1]
nt += nct
self.nt = nt
# Calculate the shape function:
x = r / rcutcomp
gaussian = np.zeros(N)
self.gamma = gamma = 10.0
gaussian[:gmax] = np.exp(-gamma * x[:gmax]**2)
gt = 4 * (gamma / rcutcomp**2)**1.5 / sqrt(pi) * gaussian
norm = np.dot(gt, dv)
#print norm, norm-1
assert abs(norm - 1) < 1e-2
gt /= norm
# Calculate smooth charge density:
Nt = np.dot(nt, dv)
rhot = nt - (Nt + charge / (4 * pi)) * gt
t('Pseudo-electron charge', 4 * pi * Nt)
vHt = np.zeros(N)
hartree(0, rhot * r * dr, self.beta, self.N, vHt)
vHt[1:] /= r[1:]
vHt[0] = vHt[1]
vXCt = np.zeros(N)
extra_xc_data = {}
if self.xc.type != 'GLLB':
Exct = self.xc.calculate_spherical(self.rgd, nt.reshape((1, -1)),
vXCt.reshape((1, -1)))
else:
Exct = self.xc.get_smooth_xc_potential_and_energy_1d(vXCt)
# Calculate extra-stuff for non-local functionals
self.xc.get_extra_setup_data(extra_xc_data)
vt = vHt + vXCt
# Construct zero potential:
gc = 1 + int(rcutvbar * N / (rcutvbar + beta))
if vbar_type == 'f':
assert lmax == 2
uf = np.zeros(N)
l = 3
# Solve for all-electron f-state:
eps = 0.0
shoot(uf,
l,
self.vr,
eps,
self.r2dvdr,
r,
dr,
c10,
c2,
self.scalarrel,
gmax=gmax)
uf *= 1.0 / uf[gc]
# Fit smooth pseudo f-state polynomium:
A = np.ones((4, 4))
A[:, 0] = 1.0
A[:, 1] = r[gc - 2:gc + 2]**2
A[:, 2] = A[:, 1]**2
A[:, 3] = A[:, 1] * A[:, 2]
a = uf[gc - 2:gc + 2] / r[gc - 2:gc + 2]**(l + 1)
a0, a1, a2, a3 = solve(A, a)
r1 = r[:gc]
r2 = r1**2
rl1 = r1**(l + 1)
y = a0 + r2 * (a1 + r2 * (a2 + r2 * a3))
sf = uf.copy()
sf[:gc] = rl1 * y
# From 0 to gc, use analytic formula for kinetic energy operator:
r4 = r2**2
r6 = r4 * r2
enumerator = (a0 * l * (l + 1) + a1 * (l + 2) * (l + 3) * r2 + a2 *
(l + 4) * (l + 5) * r4 + a3 * (l + 6) * (l + 7) * r6)
denominator = a0 + a1 * r2 + a2 * r4 + a3 * r6
ekin_over_phit = -0.5 * (enumerator / denominator - l * (l + 1))
ekin_over_phit[1:] /= r2[1:]
vbar = eps - vt
vbar[:gc] -= ekin_over_phit
vbar[0] = vbar[1] # Actually we can collect the terms into
# a single fraction without poles, so as to avoid doing this,
# but this is good enough
# From gc to gmax, use finite-difference formula for kinetic
# energy operator:
vbar[gc:gmax] -= self.kin(l, sf)[gc:gmax] / sf[gc:gmax]
vbar[gmax:] = 0.0
else:
assert vbar_type == 'poly'
A = np.ones((2, 2))
A[0] = 1.0
A[1] = r[gc - 1:gc + 1]**2
a = vt[gc - 1:gc + 1]
a = solve(np.transpose(A), a)
r2 = r**2
vbar = a[0] + r2 * a[1] - vt
vbar[gc:] = 0.0
vt += vbar
# Construct projector functions:
for l, (e_n, s_n, q_n) in enumerate(zip(e_ln, s_ln, q_ln)):
for e, s, q in zip(e_n, s_n, q_n):
q[:] = self.kin(l, s) + (vt - e) * s
q[gcutmax:] = 0.0
filter = Filter(r, dr, gcutfilter, hfilter).filter
vbar = filter(vbar * r)
# Calculate matrix elements:
self.dK_lnn = dK_lnn = []
self.dH_lnn = dH_lnn = []
self.dO_lnn = dO_lnn = []
for l, (e_n, u_n, s_n, q_n) in enumerate(zip(e_ln, u_ln, s_ln, q_ln)):
A_nn = np.inner(s_n, q_n * dr)
# Do a LU decomposition of A:
nn = len(e_n)
L_nn = np.identity(nn, float)
U_nn = A_nn.copy()
# Keep all bound states normalized
if sum([n > 0 for n in n_ln[l]]) <= 1:
for i in range(nn):
for j in range(i + 1, nn):
L_nn[j, i] = 1.0 * U_nn[j, i] / U_nn[i, i]
U_nn[j, :] -= U_nn[i, :] * L_nn[j, i]
dO_nn = (np.inner(u_n, u_n * dr) - np.inner(s_n, s_n * dr))
e_nn = np.zeros((nn, nn))
e_nn.ravel()[::nn + 1] = e_n
dH_nn = np.dot(dO_nn, e_nn) - A_nn
q_n[:] = np.dot(inv(np.transpose(U_nn)), q_n)
s_n[:] = np.dot(inv(L_nn), s_n)
u_n[:] = np.dot(inv(L_nn), u_n)
dO_nn = np.dot(np.dot(inv(L_nn), dO_nn), inv(np.transpose(L_nn)))
dH_nn = np.dot(np.dot(inv(L_nn), dH_nn), inv(np.transpose(L_nn)))
ku_n = [self.kin(l, u, e) for u, e in zip(u_n, e_n)]
ks_n = [self.kin(l, s) for s in s_n]
dK_nn = 0.5 * (np.inner(u_n, ku_n * dr) - np.inner(s_n, ks_n * dr))
dK_nn += np.transpose(dK_nn).copy()
dK_lnn.append(dK_nn)
dO_lnn.append(dO_nn)
dH_lnn.append(dH_nn)
for n, q in enumerate(q_n):
q[:] = filter(q, l) * r**(l + 1)
A_nn = np.inner(s_n, q_n * dr)
q_n[:] = np.dot(inv(np.transpose(A_nn)), q_n)
self.vt = vt
self.vbar = vbar
t('state eigenvalue norm')
t('--------------------------------')
for l, (n_n, f_n, e_n) in enumerate(zip(n_ln, f_ln, e_ln)):
for n in range(len(e_n)):
if n_n[n] > 0:
f = '(%d)' % f_n[n]
t('%d%s%-4s: %12.6f %12.6f' %
(n_n[n], 'spdf'[l], f, e_n[n], np.dot(s_ln[l][n]**2,
dr)))
else:
t('*%s : %12.6f' % ('spdf'[l], e_n[n]))
t('--------------------------------')
self.logd = {}
if logderiv:
ni = 300
self.elog = np.linspace(-5.0, 1.0, ni)
# Calculate logarithmic derivatives:
gld = gcutmax + 10
self.rlog = r[gld]
assert gld < gmax
t('Calculating logarithmic derivatives at r=%.3f' % r[gld])
t('(skip with [Ctrl-C])')
try:
u = np.zeros(N)
for l in range(4):
self.logd[l] = (np.empty(ni), np.empty(ni))
if l <= lmax:
dO_nn = dO_lnn[l]
dH_nn = dH_lnn[l]
q_n = q_ln[l]
fae = open(self.symbol + '.ae.ld.' + 'spdf'[l], 'w')
fps = open(self.symbol + '.ps.ld.' + 'spdf'[l], 'w')
for i, e in enumerate(self.elog):
# All-electron logarithmic derivative:
u[:] = 0.0
shoot(u,
l,
self.vr,
e,
self.r2dvdr,
r,
dr,
c10,
c2,
self.scalarrel,
gmax=gld)
dudr = 0.5 * (u[gld + 1] - u[gld - 1]) / dr[gld]
ld = dudr / u[gld] - 1.0 / r[gld]
print >> fae, e, ld
self.logd[l][0][i] = ld
# PAW logarithmic derivative:
s = self.integrate(l, vt, e, gld)
if l <= lmax:
A_nn = dH_nn - e * dO_nn
s_n = [
self.integrate(l, vt, e, gld, q) for q in q_n
]
B_nn = np.inner(q_n, s_n * dr)
a_n = np.dot(q_n, s * dr)
B_nn = np.dot(A_nn, B_nn)
B_nn.ravel()[::len(a_n) + 1] += 1.0
c_n = solve(B_nn, np.dot(A_nn, a_n))
s -= np.dot(c_n, s_n)
dsdr = 0.5 * (s[gld + 1] - s[gld - 1]) / dr[gld]
ld = dsdr / s[gld] - 1.0 / r[gld]
print >> fps, e, ld
self.logd[l][1][i] = ld
except KeyboardInterrupt:
pass
self.write(nc, 'nc')
self.write(nt, 'nt')
self.write(nct, 'nct')
self.write(vbar, 'vbar')
self.write(vt, 'vt')
self.write(tauc, 'tauc')
self.write(tauct, 'tauct')
for l, (n_n, f_n, u_n, s_n,
q_n) in enumerate(zip(n_ln, f_ln, u_ln, s_ln, q_ln)):
for n, f, u, s, q in zip(n_n, f_n, u_n, s_n, q_n):
if n < 0:
self.write(u, 'ae', n=n, l=l)
self.write(s, 'ps', n=n, l=l)
self.write(q, 'proj', n=n, l=l)
# Test for ghost states:
for h in [0.05]:
self.diagonalize(h)
self.vn_j = vn_j = []
self.vl_j = vl_j = []
self.vf_j = vf_j = []
self.ve_j = ve_j = []
self.vu_j = vu_j = []
self.vs_j = vs_j = []
self.vq_j = vq_j = []
j_ln = [[0 for f in f_n] for f_n in f_ln]
j = 0
for l, n_n in enumerate(n_ln):
for n, nn in enumerate(n_n):
if nn > 0:
vf_j.append(f_ln[l][n])
vn_j.append(nn)
vl_j.append(l)
ve_j.append(e_ln[l][n])
vu_j.append(u_ln[l][n])
vs_j.append(s_ln[l][n])
vq_j.append(q_ln[l][n])
j_ln[l][n] = j
j += 1
for l, n_n in enumerate(n_ln):
for n, nn in enumerate(n_n):
if nn < 0:
vf_j.append(0)
vn_j.append(nn)
vl_j.append(l)
ve_j.append(e_ln[l][n])
vu_j.append(u_ln[l][n])
vs_j.append(s_ln[l][n])
vq_j.append(q_ln[l][n])
j_ln[l][n] = j
j += 1
nj = j
self.dK_jj = np.zeros((nj, nj))
for l, j_n in enumerate(j_ln):
for n1, j1 in enumerate(j_n):
for n2, j2 in enumerate(j_n):
self.dK_jj[j1, j2] = self.dK_lnn[l][n1, n2]
if exx:
X_p = constructX(self)
ExxC = atomic_exact_exchange(self, 'core-core')
else:
X_p = None
ExxC = None
sqrt4pi = sqrt(4 * pi)
setup = SetupData(self.symbol, self.xc.name, self.name, readxml=False)
def divide_by_r(x_g, l):
r = self.r
#for x_g, l in zip(x_jg, l_j):
p = x_g.copy()
p[1:] /= self.r[1:]
# XXXXX go to higher order!!!!!
if l == 0: #l_j[self.jcorehole] == 0:
p[0] = (p[2] + (p[1] - p[2]) * (r[0] - r[2]) / (r[1] - r[2]))
return p
def divide_all_by_r(x_jg):
return [divide_by_r(x_g, l) for x_g, l in zip(x_jg, vl_j)]
setup.l_j = vl_j
setup.n_j = vn_j
setup.f_j = vf_j
setup.eps_j = ve_j
setup.rcut_j = [rcut_l[l] for l in vl_j]
setup.nc_g = nc * sqrt4pi
setup.nct_g = nct * sqrt4pi
setup.nvt_g = (nt - nct) * sqrt4pi
setup.e_kinetic_core = Ekincore
setup.vbar_g = vbar * sqrt4pi
setup.tauc_g = tauc * sqrt4pi
setup.tauct_g = tauct * sqrt4pi
setup.extra_xc_data = extra_xc_data
setup.Z = Z
setup.Nc = self.Nc
setup.Nv = self.Nv
setup.e_kinetic = self.Ekin
setup.e_xc = self.Exc
setup.e_electrostatic = self.Epot
setup.e_total = self.Epot + self.Exc + self.Ekin
setup.beta = self.beta
setup.ng = self.N
setup.rcgauss = self.rcutcomp / sqrt(self.gamma)
setup.e_kin_jj = self.dK_jj
setup.ExxC = ExxC
setup.phi_jg = divide_all_by_r(vu_j)
setup.phit_jg = divide_all_by_r(vs_j)
setup.pt_jg = divide_all_by_r(vq_j)
setup.X_p = X_p
if self.jcorehole is not None:
setup.has_corehole = True
setup.lcorehole = l_j[self.jcorehole] # l_j or vl_j ????? XXX
setup.ncorehole = n_j[self.jcorehole]
setup.phicorehole_g = divide_by_r(self.u_j[self.jcorehole],
setup.lcorehole)
setup.core_hole_e = self.e_j[self.jcorehole]
setup.core_hole_e_kin = self.Ekincorehole
setup.fcorehole = self.fcorehole
if self.ghost:
raise RuntimeError('Ghost!')
if self.scalarrel:
reltype = 'scalar-relativistic'
else:
reltype = 'non-relativistic'
attrs = [('type', reltype), ('name', 'gpaw-%s' % version)]
data = 'Frozen core: ' + (self.core or 'none')
setup.generatorattrs = attrs
setup.generatordata = data
self.id_j = []
for l, n in zip(vl_j, vn_j):
if n > 0:
id = '%s-%d%s' % (self.symbol, n, 'spdf'[l])
else:
id = '%s-%s%d' % (self.symbol, 'spdf'[l], -n)
self.id_j.append(id)
setup.id_j = self.id_j
if write_xml:
setup.write_xml()
return setup
def make_paw_setup(self, tag=None):
aea = self.aea
from gpaw.setup_data import SetupData
setup = SetupData(aea.symbol, aea.xc.name, tag, readxml=False)
setup.id_j = []
J = [] # new reordered j and i indices
I = []
# Bound states:
j = 0
i = 0
for l, waves in enumerate(self.waves_l):
for n, f, e, phi_g, phit_g, pt_g in zip(waves.n_n, waves.f_n,
waves.e_n, waves.phi_ng,
waves.phit_ng,
waves.pt_ng):
if n != -1:
setup.append(n, l, f, e, waves.rcut, phi_g, phit_g, pt_g)
id = '%d%s' % (n, 'spdf'[l])
setup.id_j.append(id)
J.append(j)
I.extend(range(i, i + 2 * l + 1))
j += 1
i += 2 * l + 1
# Excited states:
j = 0
i = 0
for l, waves in enumerate(self.waves_l):
ne = 0
for n, f, e, phi_g, phit_g, pt_g in zip(waves.n_n, waves.f_n,
waves.e_n, waves.phi_ng,
waves.phit_ng,
waves.pt_ng):
if n == -1:
setup.append(n, l, f, e, waves.rcut, phi_g, phit_g, pt_g)
ne += 1
id = '%s%d' % ('spdf'[l], ne)
setup.id_j.append(id)
J.append(j)
I.extend(range(i, i + 2 * l + 1))
j += 1
i += 2 * l + 1
nj = sum(len(waves) for waves in self.waves_l)
e_kin_jj = np.zeros((nj, nj))
j1 = 0
for waves in self.waves_l:
j2 = j1 + len(waves)
e_kin_jj[j1:j2, j1:j2] = waves.dekin_nn
j1 = j2
setup.e_kin_jj = e_kin_jj[J][:, J].copy()
setup.nc_g = self.nc_g * sqrt(4 * pi)
setup.nct_g = self.nct_g * sqrt(4 * pi)
setup.e_kinetic_core = self.ekincore
setup.vbar_g = self.v0r_g * sqrt(4 * pi)
setup.vbar_g[1:] /= self.rgd.r_g[1:]
setup.vbar_g[0] = setup.vbar_g[1]
setup.Z = aea.Z
setup.Nc = self.ncore
setup.Nv = self.nvalence
setup.e_kinetic = aea.ekin
setup.e_xc = aea.exc
setup.e_electrostatic = aea.eH + aea.eZ
setup.e_total = aea.exc + aea.ekin + aea.eH + aea.eZ
setup.rgd = self.rgd
setup.rcgauss = 1 / sqrt(self.alpha)
self.calculate_exx_integrals()
setup.ExxC = self.exxcc
setup.X_p = pack2(self.exxcv_ii[I][:, I])
setup.tauc_g = self.tauc_g * (4 * pi)**0.5
setup.tauct_g = self.tauct_g * (4 * pi)**0.5
if self.aea.scalar_relativistic:
reltype = 'scalar-relativistic'
else:
reltype = 'non-relativistic'
attrs = [('type', reltype),
('version', 2),
('name', 'gpaw-%s' % version)]
setup.generatorattrs = attrs
setup.l0 = self.l0
setup.e0 = 0.0
setup.r0 = self.r0
setup.nderiv0 = self.nderiv0
setup.basis = self.basis
if self.core_hole:
n, l, occ = self.core_hole
phi_g = self.aea.channels[l].phi_ng[n - l - 1]
setup.ncorehole = n
setup.lcorehole = l
setup.fcorehole = occ
setup.phicorehole_g = phi_g
setup.has_corehole = True
return setup
def create_setup(symbol,
xc='LDA',
lmax=0,
type='paw',
basis=None,
setupdata=None,
filter=None,
world=None):
if isinstance(xc, basestring):
xc = XC(xc)
if isinstance(type, basestring) and ':' in type:
# Parse DFT+U parameters from type-string:
# Examples: "type:l,U" or "type:l,U,scale"
type, lu = type.split(':')
if type == '':
type = 'paw'
l = 'spdf'.find(lu[0])
assert lu[1] == ','
U = lu[2:]
if ',' in U:
U, scale = U.split(',')
else:
scale = True
U = float(U) / units.Hartree
scale = int(scale)
else:
U = None
if setupdata is None:
if type == 'hgh' or type == 'hgh.sc':
lmax = 0
from gpaw.hgh import HGHSetupData, setups, sc_setups
if type == 'hgh.sc':
table = sc_setups
else:
table = setups
parameters = table[symbol]
setupdata = HGHSetupData(parameters)
elif type == 'ah':
from gpaw.ah import AppelbaumHamann
ah = AppelbaumHamann()
ah.build(basis)
return ah
elif type == 'ae':
from gpaw.ae import HydrogenAllElectronSetup
assert symbol == 'H'
ae = HydrogenAllElectronSetup()
ae.build(basis)
return ae
elif type == 'ghost':
from gpaw.lcao.bsse import GhostSetupData
setupdata = GhostSetupData(symbol)
elif type == 'sg15':
from gpaw.upf import UPFSetupData
upfname = '%s_ONCV_PBE-*.upf' % symbol
upfpath, source = search_for_file(upfname, world=world)
if source is None:
raise IOError('Could not find pseudopotential file %s '
'in any GPAW search path. '
'Please install the SG15 setups using, '
'e.g., "gpaw install-data".' % upfname)
setupdata = UPFSetupData(upfpath)
if xc.name != 'PBE':
raise ValueError('SG15 pseudopotentials support only the PBE '
'functional. This calculation would use '
'the %s functional.' % xc.name)
else:
setupdata = SetupData(symbol,
xc.get_setup_name(),
type,
True,
world=world)
if hasattr(setupdata, 'build'):
setup = LeanSetup(setupdata.build(xc, lmax, basis, filter))
if U is not None:
setup.set_hubbard_u(U, l, scale)
return setup
else:
return setupdata
def main():
parser = OptionParser(usage='%prog [OPTION...] [SYMBOL...]',
description=description)
parser.add_option('--xc',
metavar='FUNCTIONAL',
default='PBE',
help='generate basis sets for FUNCTIONAL[=%default]')
parser.add_option('--from',
metavar='SYMBOL',
dest='_from',
help='generate starting from SYMBOL if generating '
'for all elements')
opts, symbols = parser.parse_args()
if len(symbols) == 0:
symbols = sorted(parameters.keys())
othersymbols = []
for symbol in parameters_extra:
name = parameters_extra[symbol]['name']
code = '%s.%s' % (symbol, name)
othersymbols.append(code)
trouble = set(['Os.8', 'Ta.5', 'V.5', 'W.6', 'Ir.9'])
othersymbols = [
symbol for symbol in othersymbols if symbol not in trouble
]
symbols.extend(sorted(othersymbols))
if opts._from:
index = symbols.index(opts._from)
symbols = symbols[index:]
specifications = []
for sym in symbols:
try:
s = SetupData(sym, opts.xc)
except RuntimeError as e:
if str(e).startswith('Could not find'):
#print 'No %s' % sym
continue
else:
raise
# One could include basis functions also for the ``virtual'' states
# (marked with negative n)
jvalues = []
jextra = []
for j in range(len(s.f_j)):
if s.eps_j[j] < 0:
jvalues.append(j)
if s.f_j[j] == 0.0 and s.n_j[j] > 0:
jextra.append(j)
if len(jextra) > 0:
specifications.append(BasisSpecification(s, jvalues, jextra))
#print sym, jvalues
# XXX check whether automatic settings coincide with those of official
# setups distribution
#bm = BasisMaker(sym, ''
if world.rank == 0:
print('Generating basis sets for: %s' %
' '.join(spec.setup.symbol for spec in specifications))
sys.stdout.flush()
world.barrier()
for i, spec in enumerate(specifications):
if i % world.size != world.rank:
continue
if world.size > 1:
print(world.rank, spec)
else:
print(spec)
gtxt = None
# XXX figure out how to accept Ag.11
tokens = spec.setup.symbol.split('.')
sym = tokens[0]
if len(tokens) == 1:
p = parameters
name = 'pvalence'
elif len(tokens) == 2:
p = parameters_extra
name = '%s.pvalence' % tokens[1]
else:
raise ValueError('Strange setup specification')
type = 'dz' # XXXXXXXXX
bm = BasisMaker(sym,
'%s.%s' % (name, type),
run=False,
gtxt=gtxt,
xc=opts.xc)
bm.generator.run(write_xml=False, use_restart_file=False, **p[sym])
basis = bm.generate(2, 0, txt=None, jvalues=spec.jvalues)
basis.write_xml()
def read_GPAW_all(name='OUTPUT.gpw',
fermi=None,
orbs='sp',
pbc=(1, 1),
imaginary=False,
cut_min=-15.0,
cut_max=5.0,
cut_at=-1,
lower_atoms=[],
lower_coefs=[]):
'''
read_GPAW_all(name = 'OUTPUT.gpw', fermi = None, orbs = 'sp', pbc=(1,1), imaginary = False, cut_min=-15.0, cut_max=5.0, cut_at=-1, lower_atoms=[], lower_coefs=[]):
This procedure nead to import ASE and GPAW
read eigen energies, coffecients, Fermi Level and geometry from the GPAW *.gpw file.
If fermi = None then Fermi comes from the GPAW calculation
orbs - only 'sp' works can read only sp structure of valence orbitals (hydrogens_has to be at the end !!!!)
pbc (1,1) - means 3 times 3 cell around the original, (0,0) cluster, (0.5,0.5) 2x2 cell etc.
imaginary = False (other options for future k-points dependency
cut_min = -15.0, cut_max = 5.0 - cut off states(=mol orbitals) bellow cut_min and above cut_max; energy in eV
cut_at = -1 .. all atoms; eg. cut_at = 15 --> only first fifteen atoms for the current calculations (mostly the 1st layer is the important one)
lower_atotms=[], lower_coefs=[] ... do nothing; lower_atoms=[0,1,2,3], lower_coefs=[0.5,0.5,0.5,0.5] lower coefficients (=hoppings) for the first four atoms by 0.5
'''
initial_check(orbs=orbs,
pbc=pbc,
imaginary=imaginary,
cut_min=cut_min,
cut_max=cut_max,
cut_at=cut_at,
lower_atoms=lower_atoms,
lower_coefs=lower_coefs)
# obtaining the geometry :
from ase import Atoms
from gpaw import GPAW
calc = GPAW(name)
slab = calc.get_atoms()
Ratin = get_GPAW_geom(geom=slab)
# getting eigen-energies
n_bands = calc.get_number_of_bands()
eig = calc.get_eigenvalues(kpt=0, spin=0, broadcast=True)
at_num = slab.get_atomic_numbers()
eig = to_fermi(eig, fermi, orig_fermi=calc.get_fermi_level())
eig = cut_eigenenergies(eig)
print("eigen-energies read")
# obtaining the LCAO coefficients (automatically removed unwanted states - molecular orbitals - and atoms)
coef = np.zeros((n_max_ - n_min_, num_at_, Ynum_))
if (orbs == 'spd'):
print(
"!!! WARNING: d-orbitals should be in principle working, but coefficients can be wrong, according to my experiences !!!"
)
print(
"DEBUG: going to crazy procedure, which finds, where the d-orbs starts"
)
print(
"from gpaw.utilities.dos import print_projectors; print_projectors('X')"
)
print("this prints you where the d-orb should start")
from gpaw.setup_data import SetupData
chem_sym = slab.get_chemical_symbols()
d_orb = np.zeros((num_at_))
for i in range(num_at_):
if at_num[i] > 2:
setup = SetupData(chem_sym[i], 'LDA', 'paw')
l_j = setup.l_j
tmp = l_j[:l_j.index(2)]
a = [1, 3]
oo = 0
for j in range(len(tmp)):
oo += a[tmp[j]]
d_orb[i] = oo
for i in range(n_min_, n_max_):
h = 0
for j in range(num_at_):
ii = i - n_min_
coef[ii, j, 0] = calc.wfs.kpt_u[0].C_nM[i, h]
if (at_num[j] > 2):
coef[ii, j, 1] = calc.wfs.kpt_u[0].C_nM[i, h + 1]
coef[ii, j, 2] = calc.wfs.kpt_u[0].C_nM[i, h + 2]
coef[ii, j, 3] = calc.wfs.kpt_u[0].C_nM[i, h + 3]
if ((orbs == 'spd') and (d_orb[j] > 1)):
coef[ii, j, 4] = calc.wfs.kpt_u[0].C_nM[i, h + d_orb[j]]
coef[ii, j, 5] = calc.wfs.kpt_u[0].C_nM[i,
h + d_orb[j] + 1]
coef[ii, j, 6] = calc.wfs.kpt_u[0].C_nM[i,
h + d_orb[j] + 2]
coef[ii, j, 7] = calc.wfs.kpt_u[0].C_nM[i,
h + d_orb[j] + 3]
coef[ii, j, 8] = calc.wfs.kpt_u[0].C_nM[i,
h + d_orb[j] + 4]
h += calc.wfs.setups[j].nao
#from gpaw.utilities.dos import print_projectors; print_projectors('Cu')
#print "DEBUG: Cu coeffs:"
#for i in range(n_min,n_max):
# for j in range(15):
# print j, calc.wfs.kpt_u[0].C_nM[i,j]
# print "DEBUG: coef[sth,0,:]" , coef[i-n_min,0,:]
# lowering tunneling for predefined atoms
# lowering over atoms and applying PBC
coeffs = handle_coef(coef)
print("All coefficients read")
return eig.copy(), coeffs.copy(), Ratin.copy()
