def __init__(self, symbol, xcname='LDA', scalarrel=True, corehole=None,
configuration=None,
nofiles=True, txt='-', gpernode=150,
orbital_free=False, tw_coeff=1.):
AllElectron.__init__(self, symbol, xcname, scalarrel, corehole,
configuration, nofiles, txt, gpernode,
orbital_free, tw_coeff)
def __init__(self,
symbol,
xcname='LDA',
scalarrel=False,
corehole=None,
configuration=None,
nofiles=True,
txt='-',
gpernode=150):
AllElectron.__init__(self, symbol, xcname, scalarrel, corehole,
configuration, nofiles, txt, gpernode)
def write_spherical_ks_potentials(self, txt):
f = open(txt,'w')
for a in self.paw.density.D_asp:
r_g, vKS_g = self.get_spherical_ks_potential(a)
setup = self.paw.density.setups[a]
# Calculate also atomic LDA for reference
g = AllElectron(setup.symbol, xcname='LDA',nofiles=True, scalarrel=True, txt=None)
g.run()
print >>f, r_g[0], vKS_g[0], g.vr[0], 0.0
for r, vKS,vr in zip(r_g[1:],vKS_g[1:], g.vr[1:]):
print >> f, r, vKS,vr, (vKS-vr)/r
f.close()
def get_core_eigenvalues(self, a, scalarrel=True):
"""Return the core eigenvalues by solving the radial schrodinger equation.
Using AllElectron potential class, the spherically averaged Kohn--Sham potential
is obtained around the spesified atom. The eigenstates for this potential are solved,
the the resulting core states returned. Still experimental.
"""
r, v_g = self.get_spherical_ks_potential(a)
# Get xccorr for atom a
setup = self.paw.density.setups[a]
xccorr = setup.xc_correction
symbol = setup.symbol
# Create AllElectron object for eigensolver
atom = AllElectron(symbol, txt=None, scalarrel=scalarrel)
# Calculate initial guess
atom.run()
# Set the potential
atom.vr[:len(v_g)] = v_g
# After the setups cutoff, arbitrary barrier is used
atom.vr[len(v_g):] = 10.0
# Solve the eigenstates
atom.solve()
# The display format is just copy paste from AllElectron class
# TODO: Make it a method in AllElectron class, thus it can be called directly
def t(a):
print(a)
t('Calculated core eigenvalues of atom ' + str(a) + ':' + symbol)
t('state eigenvalue ekin rmax')
t('-----------------------------------------------')
for m, l, f, e, u in zip(atom.n_j, atom.l_j, atom.f_j, atom.e_j,
atom.u_j):
# Find kinetic energy:
k = e - np.sum((
np.where(abs(u) < 1e-160, 0, u)**2 * #XXXNumeric!
atom.vr * atom.dr)[1:] / atom.r[1:])
# Find outermost maximum:
g = atom.N - 4
while u[g - 1] >= u[g]:
g -= 1
x = atom.r[g - 1:g + 2]
y = u[g - 1:g + 2]
A = np.transpose(np.array([x**i for i in range(3)]))
c, b, a = np.linalg.solve(A, y)
assert a < 0.0
rmax = -0.5 * b / a
s = 'spdf'[l]
t('%d%s^%-4.1f: %12.6f %12.6f %12.3f' % (m, s, f, e, k, rmax))
t('-----------------------------------------------')
t('(units: Bohr and Hartree)')
return atom.e_j
def _calculate_bound(self):
from gpaw.atom.all_electron import AllElectron
check_valid_quantum_number(self.Z, self.n, self.l)
config_tuples = config_str_to_config_tuples(
load_electronic_configurations()[chemical_symbols[self.Z]])
subshell_index = [shell[:2] for shell in config_tuples].index(
(self.n, self.l))
with open(os.devnull, "w") as f, contextlib.redirect_stdout(f):
ae = AllElectron(chemical_symbols[self.Z], xcname=self.xc)
ae.run()
# wave = interp1d(ae.r, ae.u_j[subshell_index], kind='cubic', fill_value='extrapolate', bounds_error=False)
return ae.ETotal * units.Hartree, (ae.r, ae.u_j[subshell_index])
def write_spherical_ks_potentials(self, txt):
f = open(txt, 'w')
for a in self.paw.density.D_asp:
r_g, vKS_g = self.get_spherical_ks_potential(a)
setup = self.paw.density.setups[a]
# Calculate also atomic LDA for reference
g = AllElectron(setup.symbol,
xcname='LDA',
nofiles=True,
scalarrel=True,
txt=None)
g.run()
print(r_g[0], vKS_g[0], g.vr[0], 0.0, file=f)
for r, vKS, vr in zip(r_g[1:], vKS_g[1:], g.vr[1:]):
print(r, vKS, vr, (vKS - vr) / r, file=f)
f.close()
def get_core_eigenvalues(self, a, scalarrel=True):
"""Return the core eigenvalues by solving the radial schrodinger equation.
Using AllElectron potential class, the spherically averaged Kohn--Sham potential
is obtained around the spesified atom. The eigenstates for this potential are solved,
the the resulting core states returned. Still experimental.
"""
r, v_g = self.get_spherical_ks_potential(a)
# Get xccorr for atom a
setup = self.paw.density.setups[a]
xccorr = setup.xc_correction
symbol = setup.symbol
# Create AllElectron object for eigensolver
atom = AllElectron(symbol, txt=None, scalarrel=scalarrel)
# Calculate initial guess
atom.run()
# Set the potential
atom.vr[:len(v_g)] = v_g
# After the setups cutoff, arbitrary barrier is used
atom.vr[len(v_g):] = 10.0
# Solve the eigenstates
atom.solve()
# The display format is just copy paste from AllElectron class
# TODO: Make it a method in AllElectron class, thus it can be called directly
def t(a):
print a
t('Calculated core eigenvalues of atom '+str(a)+':'+symbol)
t('state eigenvalue ekin rmax')
t('-----------------------------------------------')
for m, l, f, e, u in zip(atom.n_j, atom.l_j, atom.f_j, atom.e_j, atom.u_j):
# Find kinetic energy:
k = e - np.sum((np.where(abs(u) < 1e-160, 0, u)**2 * #XXXNumeric!
atom.vr * atom.dr)[1:] / atom.r[1:])
# Find outermost maximum:
g = atom.N - 4
while u[g - 1] >= u[g]:
g -= 1
x = atom.r[g - 1:g + 2]
y = u[g - 1:g + 2]
A = np.transpose(np.array([x**i for i in range(3)]))
c, b, a = np.linalg.solve(A, y)
assert a < 0.0
rmax = -0.5 * b / a
s = 'spdf'[l]
t('%d%s^%-4.1f: %12.6f %12.6f %12.3f' % (m, s, f, e, k, rmax))
t('-----------------------------------------------')
t('(units: Bohr and Hartree)')
return atom.e_j
def _calculate_continuum(self):
from gpaw.atom.all_electron import AllElectron
check_valid_quantum_number(self.Z, self.n, self.l)
config_tuples = config_str_to_config_tuples(
load_electronic_configurations()[chemical_symbols[self.Z]])
subshell_index = [shell[:2] for shell in config_tuples].index(
(self.n, self.l))
with open(os.devnull, "w") as f, contextlib.redirect_stdout(f):
ae = AllElectron(chemical_symbols[self.Z], xcname=self.xc)
ae.f_j[subshell_index] -= 1.
ae.run()
vr = interp1d(ae.r,
-ae.vr,
fill_value='extrapolate',
bounds_error=False)
def schroedinger_derivative(y, r, l, e, vr):
(u, up) = y
return np.array([up, (l * (l + 1) / r**2 - 2 * vr(r) / r - e) * u])
r = np.geomspace(1e-7, 200, 1000000)
continuum_waves = {}
for lprime in self.lprimes:
ur = integrate.odeint(schroedinger_derivative, [0.0, 1.],
r,
args=(lprime, self.epsilon, vr))
sqrt_k = 1 / (
2 * self.epsilon / units.Hartree *
(1 + units.alpha**2 * self.epsilon / units.Hartree / 2))**.25
ur = ur[:, 0] / ur[:, 0].max(
) / self.epsilon**.5 * units.Rydberg**0.25 / sqrt_k / np.sqrt(
np.pi)
continuum_waves[lprime] = (
r, ur
) # interp1d(r, ur, kind='cubic', fill_value='extrapolate', bounds_error=False)
return ae.ETotal * units.Hartree, continuum_waves
def __init__(self,
generator,
name=None,
run=True,
gtxt='-',
non_relativistic_guess=False,
xc='PBE'):
if isinstance(generator, str): # treat 'generator' as symbol
generator = Generator(generator,
scalarrel=True,
xcname=xc,
txt=gtxt,
nofiles=True)
generator.N *= 4
self.generator = generator
self.rgd = AERadialGridDescriptor(generator.beta,
generator.N,
default_spline_points=100)
self.name = name
if run:
if non_relativistic_guess:
ae0 = AllElectron(generator.symbol,
scalarrel=False,
nofiles=False,
txt=gtxt,
xcname=xc)
ae0.N = generator.N
ae0.beta = generator.beta
ae0.run()
# Now files will be stored such that they can
# automagically be used by the next run()
generator.run(write_xml=False,
use_restart_file=False,
**parameters[generator.symbol])
def __init__(self, generator, name=None, run=True, gtxt='-',
non_relativistic_guess=False, xc='PBE'):
if isinstance(generator, str): # treat 'generator' as symbol
generator = Generator(generator, scalarrel=True,
xcname=xc, txt=gtxt,
nofiles=True)
generator.N *= 4
self.generator = generator
self.rgd = AERadialGridDescriptor(generator.beta, generator.N,
default_spline_points=100)
self.name = name
if run:
if non_relativistic_guess:
ae0 = AllElectron(generator.symbol, scalarrel=False,
nofiles=False, txt=gtxt, xcname=xc)
ae0.N = generator.N
ae0.beta = generator.beta
ae0.run()
# Now files will be stored such that they can
# automagically be used by the next run()
generator.run(write_xml=False, use_restart_file=False,
**parameters[generator.symbol])
def __init__(self,
generator,
name=None,
run=True,
gtxt='-',
non_relativistic_guess=False,
xc='PBE',
save_setup=False):
if isinstance(generator, str): # treat 'generator' as symbol
generator = Generator(generator,
scalarrel=True,
xcname=xc,
txt=gtxt,
nofiles=True)
generator.N *= 4
self.generator = generator
self.rgd = AERadialGridDescriptor(generator.beta / generator.N,
1.0 / generator.N,
generator.N,
default_spline_points=100)
self.name = name
if run:
if non_relativistic_guess:
ae0 = AllElectron(generator.symbol,
scalarrel=False,
nofiles=False,
txt=gtxt,
xcname=xc)
ae0.N = generator.N
ae0.beta = generator.beta
ae0.run()
# Now files will be stored such that they can
# automagically be used by the next run()
setup = generator.run(write_xml=False,
use_restart_file=False,
name=name,
**parameters[generator.symbol])
if save_setup:
setup.write_xml()
else:
if save_setup:
raise ValueError('cannot save setup here because setup '
'was already generated before basis '
'generation.')
ref2 = 'Gritsenko IntJQuanChem 76, 407 (2000)'
# H**O energy in mHa for closed shell atoms
e_HOMO_cs = { 'He': 851, 'Be': 321, 'Ne': 788,
'Ar': 577, 'Kr': 529, 'Xe': 474,
'Mg' : 281 + 8 }
#e_HOMO_cs = { 'Ne': 788 }
txt=None
print '--- Comparing LB94 with', ref1
print 'and', ref2
print '**** all electron calculations'
print 'atom [refs] -e_homo diff all in mHa'
if rank == 0:
for atom in e_HOMO_cs.keys():
ae = AllElectron(atom, 'LB94', txt=txt)
ae.run()
e_homo = int( ae.e_j[-1] * 10000 + .5 ) / 10.
diff = e_HOMO_cs[atom] + e_homo
print '%2s %8g %6.1f %4.1g' % (atom, e_HOMO_cs[atom], -e_homo, diff)
assert abs(diff) < 6
barrier()
setup_paths.insert(0, '.')
setups = {}
print '**** 3D calculations'
print 'atom [refs] -e_homo diff all in mHa'
for atom in e_HOMO_cs.keys():
e_ref = e_HOMO_cs[atom]
from gpaw.atom.all_electron import AllElectron
a = AllElectron("C")
a.run()
from gpaw.test import equal
data = []
def out(a,b,c,d,e,f):
data.append( (a,b,c,d,e,f) )
ETotal = {'Be': -14.572+0.012, 'Ne': -128.548 -0.029, 'Mg': -199.612 - 0.005 }
EX = {'Be': -2.666 - 0.010, 'Ne': -12.107 -0.122, 'Mg': -15.992 -0.092 }
EHOMO = {'Be': -0.309 + 0.008, 'Ne': -0.851 + 0.098, 'Mg': -0.253 + 0.006}
eignum = {'Be': 0, 'Ne':3, 'Mg':0 }
for xcname in ['GLLB','GLLBSC']:
atoms = ['Be','Ne','Mg']
for atom in atoms:
# Test AllElectron GLLB
GLLB = AllElectron(atom, xcname = xcname, scalarrel = False, gpernode = 600)
GLLB.run()
out("Total energy", xcname+"1D", atom, ETotal[atom] , GLLB.ETotal,"Ha")
out("Exchange energy", xcname+"1D", atom, EX[atom], GLLB.Exc,"Ha")
out("H**O Eigenvalue", xcname+"1D", atom, EHOMO[atom], GLLB.e_j[-1],"Ha")
if xcname == 'GLLB':
equal(GLLB.ETotal, ETotal[atom], tolerance=1e-2)
equal(GLLB.Exc, EX[atom], tolerance=1e-2)
equal(GLLB.e_j[-1], EHOMO[atom], tolerance=1e-2)
print " Quanity Method Symbol Ref[1] GPAW Unit "
for a,b,c,d,e,f in data:
print "%20s %10s %10s %10.3f %10.3f %5s" % (a,b,c,d,e,f)
print """References:
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
from gpaw import *
from ase import *
from gpaw.atom.all_electron import AllElectron
# Calculate Helium atom using 3D-code
he = Atoms(positions=[(0,0,0)], symbols='He')
he.center(vacuum=3.0)
calc = GPAW(h=0.17)
he.set_calculator(calc)
he.get_potential_energy()
# Get the all-electron potential around the nucleus
vKS_sLg = calc.nuclei[0].calculate_all_electron_potential(calc.hamiltonian.vHt_g)
# Calculate Helium atom using 1D-code
he_atom =AllElectron('He')
he_atom.run()
# Get the KS-potential
vKS_atom = he_atom.vr / he_atom.r
vKS_atom[0] = vKS_atom[1]
# Get the spherical symmetric part and multiply with Y_00
vKS = vKS_sLg[0][0] / sqrt(4*pi)
# Compare
avg_diff = 0.0
for i, v in enumerate(vKS):
avg_diff += abs(vKS_atom[i]-v)
avg_diff /= len(vKS)
from gpaw.atom.all_electron import AllElectron
def check(name, atomE, atomeig, total, H**O):
#print name, " ", atomE,"/", total, " | ", atomeig,"/",H**O," |"
print "|", name, " |%12.4f/%12.4f | %12.4f/%12.4f |" % (atomE, total,
atomeig, H**O)
assert abs(atomE - total) < 8e-3
assert abs(atomeig - H**O) < 1e-3
A = AllElectron('He', 'KLI', False)
A.run()
HeE = A.Ekin + A.Epot + A.Exc
Heeig = A.e_j[0]
A = AllElectron('Be', 'KLI', False)
A.run()
BeE = A.Ekin + A.Epot + A.Exc
Beeig = A.e_j[1]
A = AllElectron('Ne', 'KLI', False)
A.run()
NeE = A.Ekin + A.Epot + A.Exc
Neeig = A.e_j[2]
A = AllElectron('Mg', 'KLI', False)
A.run()
MgE = A.Ekin + A.Epot + A.Exc
ref2 = 'Gritsenko IntJQuanChem 76, 407 (2000)'
# H**O energy in mHa for closed shell atoms
e_HOMO_cs = { 'He': 851, 'Be': 321, 'Ne': 788,
'Ar': 577, 'Kr': 529, 'Xe': 474,
'Mg' : 281 + 8 }
#e_HOMO_cs = { 'Ne': 788 }
txt=None
print('--- Comparing LB94 with', ref1)
print('and', ref2)
print('**** all electron calculations')
print('atom [refs] -e_homo diff all in mHa')
if rank == 0:
for atom in e_HOMO_cs.keys():
ae = AllElectron(atom, 'LB94', txt=txt)
ae.run()
e_homo = int( ae.e_j[-1] * 10000 + .5 ) / 10.
diff = e_HOMO_cs[atom] + e_homo
print('%2s %8g %6.1f %4.1g' % (atom, e_HOMO_cs[atom], -e_homo, diff))
assert abs(diff) < 6
barrier()
setup_paths.insert(0, '.')
setups = {}
print('**** 3D calculations')
print('atom [refs] -e_homo diff all in mHa')
for atom in e_HOMO_cs.keys():
e_ref = e_HOMO_cs[atom]
def __init__(self, symbol, xcname='LDA', scalarrel=False, corehole=None,
configuration=None,
nofiles=True, txt='-', gpernode=150):
AllElectron.__init__(self, symbol, xcname, scalarrel, corehole,
configuration, nofiles, txt, gpernode)
# creates: paw_note.pdf
import os
from distutils.version import LooseVersion
import matplotlib
import matplotlib.pyplot as plt
from gpaw.atom.all_electron import AllElectron
ae = AllElectron('Pt')
ae.run()
fig = plt.figure(figsize=(7, 4), dpi=80)
fig.subplots_adjust(left=0.05, bottom=0.11, right=0.85, top=0.95)
for n, l, u in zip(ae.n_j, ae.l_j, ae.u_j):
plt.plot(ae.r, u, label='%i%s' % (n, 'spdf'[l]))
rcut = 2.5
lim = [0, 3.5, -2, 3]
plt.plot([rcut, rcut], lim[2:], 'k--', label='_nolegend_')
plt.axis(lim)
# The pad keyword to legend was deprecated in MPL v. 0.98.4
if LooseVersion(matplotlib.__version__) < '0.98.4':
kwpad = {'pad': 0.05}
else:
kwpad = {'borderpad': 0.05, 'labelspacing': 0.01}
plt.legend(loc=(1.02, 0.03), markerscale=1, **kwpad)
plt.xlabel(r'$r$ [Bohr]')
from gpaw.atom.all_electron import AllElectron
def check(name, atomE, atomeig, total, H**O):
#print name, " ", atomE,"/", total, " | ", atomeig,"/",H**O," |"
print "|",name, " |%12.4f/%12.4f | %12.4f/%12.4f |" % (atomE,total,atomeig,H**O)
assert abs(atomE-total)<8e-3
assert abs(atomeig-H**O)<1e-3
A = AllElectron('He', 'KLI', False)
A.run()
HeE = A.Ekin+A.Epot+A.Exc
Heeig = A.e_j[0]
A = AllElectron('Be', 'KLI', False)
A.run()
BeE = A.Ekin+A.Epot+A.Exc
Beeig = A.e_j[1]
A = AllElectron('Ne', 'KLI', False)
A.run()
NeE = A.Ekin+A.Epot+A.Exc
Neeig = A.e_j[2]
A = AllElectron('Mg', 'KLI', False)
A.run()
MgE = A.Ekin+A.Epot+A.Exc
Mgeig = A.e_j[3]
ETotal = {
'Be': -14.572 + 0.012,
'Ne': -128.548 - 0.029,
'Mg': -199.612 - 0.005
}
EX = {'Be': -2.666 - 0.010, 'Ne': -12.107 - 0.122, 'Mg': -15.992 - 0.092}
EHOMO = {'Be': -0.309 + 0.008, 'Ne': -0.851 + 0.098, 'Mg': -0.253 + 0.006}
eignum = {'Be': 0, 'Ne': 3, 'Mg': 0}
for xcname in ['GLLB', 'GLLBSC']:
atoms = ['Be', 'Ne', 'Mg']
for atom in atoms:
# Test AllElectron GLLB
GLLB = AllElectron(atom, xcname=xcname, scalarrel=False, gpernode=600)
GLLB.run()
out("Total energy", xcname + "1D", atom, ETotal[atom], GLLB.ETotal,
"Ha")
out("Exchange energy", xcname + "1D", atom, EX[atom], GLLB.Exc, "Ha")
out("H**O Eigenvalue", xcname + "1D", atom, EHOMO[atom], GLLB.e_j[-1],
"Ha")
if xcname == 'GLLB':
equal(GLLB.ETotal, ETotal[atom], tolerance=1e-2)
equal(GLLB.Exc, EX[atom], tolerance=1e-2)
equal(GLLB.e_j[-1], EHOMO[atom], tolerance=1e-2)
print(
" Quanity Method Symbol Ref[1] GPAW Unit "
)
def main():
parser = build_parser()
opt, args = parser.parse_args()
import sys
from gpaw.atom.generator import Generator
from gpaw.atom.configurations import parameters, tf_parameters
from gpaw.atom.all_electron import AllElectron
from gpaw import ConvergenceError
if args:
atoms = args
else:
atoms = parameters.keys()
bad_density_warning = """\
Problem with initial electron density guess! Try to run the program
with the '-nw' option (non-scalar-relativistic calculation + write
density) and then try again without the '-n' option (this will
generate a good initial guess for the density)."""
for symbol in atoms:
scalarrel = not opt.non_scalar_relativistic
corehole = None
if opt.core_hole is not None:
state, occ = opt.core_hole.split(',')
# Translate corestate string ('1s') to n and l:
ncorehole = int(state[0])
lcorehole = 'spdf'.find(state[1])
fcorehole = float(occ)
corehole = (ncorehole, lcorehole, fcorehole)
if opt.all_electron_only:
a = AllElectron(symbol, opt.xcfunctional, scalarrel, corehole,
opt.configuration, not opt.write_files, '-',
opt.points_per_node,
opt.orbital_free, opt.tw_coefficient)
try:
a.run()
except ConvergenceError:
print(bad_density_warning, file=sys.stderr)
continue
g = Generator(symbol, opt.xcfunctional, scalarrel, corehole,
opt.configuration, not opt.write_files, '-',
opt.points_per_node, orbital_free=opt.orbital_free,
tw_coeff=opt.tw_coefficient)
if opt.orbital_free:
p = tf_parameters.get(symbol, {'rcut': 0.9})
else:
p = parameters.get(symbol, {})
if opt.core is not None:
p['core'] = opt.core
if opt.radius is not None:
p['rcut'] = [float(x) for x in opt.radius.split(',')]
if opt.extra_projectors is not None:
extra = {}
if opt.extra_projectors != '':
for l, x in enumerate(opt.extra_projectors.split(';')):
if x != '':
extra[l] = [float(y) for y in x.split(',')]
p['extra'] = extra
if opt.normconserving is not None:
p['normconserving'] = opt.normconserving
if opt.filter is not None:
p['filter'] = [float(x) for x in opt.filter.split(',')]
if opt.compensation_charge_radius is not None:
p['rcutcomp'] = opt.compensation_charge_radius
if opt.zero_potential is not None:
vbar = opt.zero_potential.split(',')
p['vbar'] = (vbar[0], float(vbar[1]))
if opt.empty_states is not None:
p['empty_states'] = opt.empty_states
try:
g.run(logderiv=opt.logarithmic_derivatives,
exx=opt.exact_exchange, name=opt.name,
use_restart_file=opt.use_restart_file,
**p)
except ConvergenceError:
print(bad_density_warning, file=sys.stderr)
except RuntimeError as m:
if len(m.__str__()) == 0:
raise
print(m)
if opt.plot:
from gpaw.atom.analyse_setup import analyse
analyse(g, show=True)
def main():
parser = build_parser()
opt, args = parser.parse_args()
import sys
from gpaw.atom.generator import Generator
from gpaw.atom.configurations import parameters, tf_parameters
from gpaw.atom.all_electron import AllElectron
from gpaw import ConvergenceError
if args:
atoms = args
else:
atoms = parameters.keys()
bad_density_warning = """\
Problem with initial electron density guess! Try to run the program
with the '-nw' option (non-scalar-relativistic calculation + write
density) and then try again without the '-n' option (this will
generate a good initial guess for the density)."""
for symbol in atoms:
scalarrel = not opt.non_scalar_relativistic
corehole = None
if opt.core_hole is not None:
state, occ = opt.core_hole.split(',')
# Translate corestate string ('1s') to n and l:
ncorehole = int(state[0])
lcorehole = 'spdf'.find(state[1])
fcorehole = float(occ)
corehole = (ncorehole, lcorehole, fcorehole)
if opt.all_electron_only:
a = AllElectron(symbol, opt.xcfunctional, scalarrel, corehole,
opt.configuration, not opt.write_files, '-',
opt.points_per_node,
opt.orbital_free, opt.tf_coefficient)
try:
a.run()
except ConvergenceError:
print(bad_density_warning, file=sys.stderr)
continue
g = Generator(symbol, opt.xcfunctional, scalarrel, corehole,
opt.configuration, not opt.write_files, '-',
opt.points_per_node, orbital_free=opt.orbital_free,
tf_coeff=opt.tf_coefficient)
if opt.orbital_free:
p = tf_parameters.get(symbol, {'rcut': 0.9})
else:
p = parameters.get(symbol, {})
if opt.core is not None:
p['core'] = opt.core
if opt.radius is not None:
p['rcut'] = [float(x) for x in opt.radius.split(',')]
if opt.extra_projectors is not None:
extra = {}
if opt.extra_projectors != '':
for l, x in enumerate(opt.extra_projectors.split(';')):
if x != '':
extra[l] = [float(y) for y in x.split(',')]
p['extra'] = extra
if opt.normconserving is not None:
p['normconserving'] = opt.normconserving
if opt.filter is not None:
p['filter'] = [float(x) for x in opt.filter.split(',')]
if opt.compensation_charge_radius is not None:
p['rcutcomp'] = opt.compensation_charge_radius
if opt.zero_potential is not None:
vbar = opt.zero_potential.split(',')
p['vbar'] = (vbar[0], float(vbar[1]))
if opt.empty_states is not None:
p['empty_states'] = opt.empty_states
try:
g.run(logderiv=opt.logarithmic_derivatives,
exx=opt.exact_exchange, name=opt.name,
use_restart_file=opt.use_restart_file,
**p)
except ConvergenceError:
print(bad_density_warning, file=sys.stderr)
except RuntimeError, m:
if len(m.__str__()) == 0:
raise
print(m)
if opt.plot:
from gpaw.atom.analyse_setup import analyse
analyse(g, show=True)
#!/usr/bin/env python
# coding: utf-8
# In[1]:
from gpaw.atom.all_electron import AllElectron
import numpy as np
import matplotlib.pyplot as plt
# In[2]:
ti = AllElectron('Ti', xcname='LDA', scalarrel=True)
ti.run()
# In[4]:
fig = plt.figure(figsize=(10, 7))
for i in range(len(ti.n_j)):
plt.plot(ti.rgd.r_g,
ti.u_j[i, :],
label='n=%i, l=%i' % (ti.n_j[i], ti.l_j[i]))
plt.legend()
plt.xlim(0, 5)
plt.show()
# In[5]:
rgd = ti.rgd
phi, c0 = rgd.pseudize(ti.u_j[6], gc=rgd.ceil(3.0), l=0)
# In[6]:
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
