def main():
"""Work on it."""
N = 1200
beta = 0.4 * 600 / N
rgd = AERadialGridDescriptor(beta / N, 1.0 / N, N)
test_same_sto(rgd)
test_different_sto(rgd)
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.')
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,
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()
generator.run(write_xml=False, use_restart_file=False,
**parameters[generator.symbol])
def initialize(self, ngpts=2000, rcut=50.0,
alpha1=0.01, alpha2=None, ngauss=50,
eps=1.0e-7):
"""Initialize basis sets and radial grid.
ngpts: int
Number of grid points for radial grid.
rcut: float
Cutoff for radial grid.
alpha1: float
Smallest exponent for gaussian.
alpha2: float
Largest exponent for gaussian.
ngauss: int
Number of gaussians.
eps: float
Cutoff for eigenvalues of overlap matrix."""
if alpha2 is None:
alpha2 = 50.0 * self.Z**2
# Use grid with r(0)=0, r(1)=a and r(ngpts)=rcut:
a = 1 / alpha2**0.5 / 20
b = (rcut - a * ngpts) / (rcut * ngpts)
b = 1 / round(1 / b)
self.rgd = AERadialGridDescriptor(a, b, ngpts)
self.log('Grid points: %d (%.5f, %.5f, %.5f, ..., %.3f, %.3f)' %
((self.rgd.N,) + tuple(self.rgd.r_g[[0, 1, 2, -2, -1]])))
# Distribute exponents between alpha1 and alpha2:
alpha_B = alpha1 * (alpha2 / alpha1)**np.linspace(0, 1, ngauss)
self.log('Exponents: %d (%.3f, %.3f, ..., %.3f, %.3f)' %
((ngauss,) + tuple(alpha_B[[0, 1, -2, -1]])))
# Maximum l value:
lmax = max(self.f_lsn.keys())
self.channels = []
nb_l = []
if not self.dirac:
for l in range(lmax + 1):
basis = GaussianBasis(l, alpha_B, self.rgd, eps)
nb_l.append(len(basis))
for s in range(self.nspins):
self.channels.append(Channel(l, s, self.f_lsn[l][s],
basis))
else:
for K in range(1, lmax + 2):
leff = (K**2 - (self.Z / c)**2)**0.5 - 1
basis = GaussianBasis(leff, alpha_B, self.rgd, eps)
nb_l.append(len(basis))
for k, l in [(-K, K - 1), (K, K)]:
if l > lmax:
continue
f_n = self.f_lsn[l][0]
j = abs(k) - 0.5
f_n = (2 * j + 1) / (4 * l + 2) * np.array(f_n)
self.channels.append(DiracChannel(k, f_n, basis))
self.log('Basis functions: %s (%s)' %
(', '.join([str(nb) for nb in nb_l]),
', '.join('spdf'[:lmax + 1])))
self.vr_sg = self.rgd.zeros(self.nspins)
self.vr_sg[:] = -self.Z
class AllElectronAtom:
def __init__(self, symbol, xc='LDA', spinpol=False, dirac=False,
configuration=None,
log=None):
"""All-electron calculation for spherically symmetric atom.
symbol: str (or int)
Chemical symbol (or atomic number).
xc: str
Name of XC-functional.
spinpol: bool
If true, do spin-polarized calculation. Default is spin-paired.
dirac: bool
Solve Dirac equation instead of Schrödinger equation.
configuration: list
Electronic configuration for symbol, format as in
gpaw.atom.configurations
log: stream
Text output."""
if isinstance(symbol, int):
symbol = chemical_symbols[symbol]
self.symbol = symbol
self.Z = atomic_numbers[symbol]
self.nspins = 1 + int(bool(spinpol))
self.dirac = bool(dirac)
if configuration is not None:
self.configuration = copy.deepcopy(configuration)
else:
self.configuration = None
self.scalar_relativistic = False
if isinstance(xc, str):
self.xc = XC(xc)
else:
self.xc = xc
self.fd = log or sys.stdout
self.vr_sg = None # potential * r
self.n_sg = 0.0 # density
self.rgd = None # radial grid descriptor
# Energies:
self.ekin = None
self.eeig = None
self.eH = None
self.eZ = None
self.channels = None
self.initialize_configuration(self.configuration)
self.log('Z: ', self.Z)
self.log('Name: ', atomic_names[self.Z])
self.log('Symbol: ', symbol)
self.log('XC-functional: ', self.xc.name)
self.log('Equation: ', ['Schrödinger', 'Dirac'][self.dirac])
self.method = 'Gaussian basis-set'
def log(self, *args, **kwargs):
print(file=self.fd, *args, **kwargs)
def initialize_configuration(self, configuration=None):
self.f_lsn = {}
if configuration is None:
configuration = configurations[self.symbol][1]
for n, l, f, e in configuration:
if l not in self.f_lsn:
self.f_lsn[l] = [[] for s in range(self.nspins)]
if self.nspins == 1:
self.f_lsn[l][0].append(f)
else:
# Use Hund's rule:
f0 = min(f, 2 * l + 1)
self.f_lsn[l][0].append(f0)
self.f_lsn[l][1].append(f - f0)
if 0:
n = 2 + len(self.f_lsn[2][0])
if self.f_lsn[0][0][n] == 2:
self.f_lsn[0][0][n] = 1
self.f_lsn[2][0][n - 3] += 1
def add(self, n, l, df=+1, s=None):
"""Add (remove) electrons."""
if s is None:
if self.nspins == 1:
s = 0
else:
self.add(n, l, 0.5 * df, 0)
self.add(n, l, 0.5 * df, 1)
return
if l not in self.f_lsn:
self.f_lsn[l] = [[] for x in range(self.nspins)]
f_n = self.f_lsn[l][s]
if len(f_n) < n - l:
f_n.extend([0] * (n - l - len(f_n)))
f_n[n - l - 1] += df
def initialize(self, ngpts=2000, rcut=50.0,
alpha1=0.01, alpha2=None, ngauss=50,
eps=1.0e-7):
"""Initialize basis sets and radial grid.
ngpts: int
Number of grid points for radial grid.
rcut: float
Cutoff for radial grid.
alpha1: float
Smallest exponent for gaussian.
alpha2: float
Largest exponent for gaussian.
ngauss: int
Number of gaussians.
eps: float
Cutoff for eigenvalues of overlap matrix."""
if alpha2 is None:
alpha2 = 50.0 * self.Z**2
# Use grid with r(0)=0, r(1)=a and r(ngpts)=rcut:
a = 1 / alpha2**0.5 / 20
b = (rcut - a * ngpts) / (rcut * ngpts)
b = 1 / round(1 / b)
self.rgd = AERadialGridDescriptor(a, b, ngpts)
self.log('Grid points: %d (%.5f, %.5f, %.5f, ..., %.3f, %.3f)' %
((self.rgd.N,) + tuple(self.rgd.r_g[[0, 1, 2, -2, -1]])))
# Distribute exponents between alpha1 and alpha2:
alpha_B = alpha1 * (alpha2 / alpha1)**np.linspace(0, 1, ngauss)
self.log('Exponents: %d (%.3f, %.3f, ..., %.3f, %.3f)' %
((ngauss,) + tuple(alpha_B[[0, 1, -2, -1]])))
# Maximum l value:
lmax = max(self.f_lsn.keys())
self.channels = []
nb_l = []
if not self.dirac:
for l in range(lmax + 1):
basis = GaussianBasis(l, alpha_B, self.rgd, eps)
nb_l.append(len(basis))
for s in range(self.nspins):
self.channels.append(Channel(l, s, self.f_lsn[l][s],
basis))
else:
for K in range(1, lmax + 2):
leff = (K**2 - (self.Z / c)**2)**0.5 - 1
basis = GaussianBasis(leff, alpha_B, self.rgd, eps)
nb_l.append(len(basis))
for k, l in [(-K, K - 1), (K, K)]:
if l > lmax:
continue
f_n = self.f_lsn[l][0]
j = abs(k) - 0.5
f_n = (2 * j + 1) / (4 * l + 2) * np.array(f_n)
self.channels.append(DiracChannel(k, f_n, basis))
self.log('Basis functions: %s (%s)' %
(', '.join([str(nb) for nb in nb_l]),
', '.join('spdf'[:lmax + 1])))
self.vr_sg = self.rgd.zeros(self.nspins)
self.vr_sg[:] = -self.Z
def solve(self):
"""Diagonalize Schrödinger equation."""
self.eeig = 0.0
for channel in self.channels:
if self.method == 'Gaussian basis-set':
channel.solve(self.vr_sg[channel.s])
else:
channel.solve2(self.vr_sg[channel.s], self.scalar_relativistic,
self.Z)
self.eeig += channel.get_eigenvalue_sum()
def calculate_density(self):
"""Calculate elctron density and kinetic energy."""
self.n_sg = self.rgd.zeros(self.nspins)
for channel in self.channels:
self.n_sg[channel.s] += channel.calculate_density()
def calculate_electrostatic_potential(self):
"""Calculate electrostatic potential and energy."""
n_g = self.n_sg.sum(0)
self.vHr_g = self.rgd.poisson(n_g)
self.eH = 0.5 * self.rgd.integrate(n_g * self.vHr_g, -1)
self.eZ = -self.Z * self.rgd.integrate(n_g, -1)
def calculate_xc_potential(self):
self.vxc_sg = self.rgd.zeros(self.nspins)
self.exc = self.xc.calculate_spherical(self.rgd, self.n_sg,
self.vxc_sg)
def step(self):
self.solve()
self.calculate_density()
self.calculate_electrostatic_potential()
self.calculate_xc_potential()
self.vr_sg = self.vxc_sg * self.rgd.r_g
self.vr_sg += self.vHr_g
self.vr_sg -= self.Z
self.ekin = (self.eeig -
self.rgd.integrate((self.vr_sg * self.n_sg).sum(0), -1))
def run(self, mix=0.4, maxiter=117, dnmax=1e-9):
if self.channels is None:
self.initialize()
if self.dirac:
equation = 'Dirac'
elif self.scalar_relativistic:
equation = 'scalar-relativistic Schrödinger'
else:
equation = 'non-relativistic Schrödinger'
self.log('\nSolving %s equation using %s:' % (equation, self.method))
dn = self.Z
vr_old_sg = None
n_old_sg = None
for iter in range(maxiter):
self.log('.', end='')
self.fd.flush()
if iter > 0:
self.vr_sg *= mix
self.vr_sg += (1 - mix) * vr_old_sg
dn = self.rgd.integrate(abs(self.n_sg - n_old_sg).sum(0))
if dn <= dnmax:
self.log('\nConverged in', iter, 'steps')
break
vr_old_sg = self.vr_sg
n_old_sg = self.n_sg
self.step()
self.summary()
if self.method != 'Gaussian basis-set':
for channel in self.channels:
assert channel.solve2ok
if dn > dnmax:
raise RuntimeError('Did not converge!')
def refine(self):
self.method = 'finite difference'
self.run(dnmax=1e-6, mix=0.14, maxiter=200)
def summary(self):
self.write_states()
self.write_energies()
def write_states(self):
self.log('\n state occupation eigenvalue <r>')
if self.dirac:
self.log(' nl(j) [Hartree] [eV] [Bohr]')
else:
self.log(' nl [Hartree] [eV] [Bohr]')
self.log('-----------------------------------------------------')
states = []
for ch in self.channels:
for n, f in enumerate(ch.f_n):
states.append((ch.e_n[n], ch, n))
states.sort()
for e, ch, n in states:
name = str(n + ch.l + 1) + ch.name
if self.nspins == 2:
name += '(%s)' % '+-'[ch.s]
n_g = ch.calculate_density(n)
rave = self.rgd.integrate(n_g, 1)
self.log(' %-7s %6.3f %13.6f %13.5f %6.3f' %
(name, ch.f_n[n], e, e * units.Hartree, rave))
def write_energies(self):
self.log('\nEnergies: [Hartree] [eV]')
self.log('--------------------------------------------')
for text, e in [('kinetic ', self.ekin),
('coulomb (e-e)', self.eH),
('coulomb (e-n)', self.eZ),
('xc ', self.exc),
('total ',
self.ekin + self.eH + self.eZ + self.exc)]:
self.log(' %s %+13.6f %+13.5f' % (text, e, units.Hartree * e))
self.calculate_exx()
self.log('\nExact exchange energy: %.6f Hartree, %.5f eV' %
(self.exx, self.exx * units.Hartree))
def get_channel(self, l=None, s=0, k=None):
if self.dirac:
for channel in self.channels:
if channel.k == k:
return channel
else:
for channel in self.channels:
if channel.l == l and channel.s == s:
return channel
raise ValueError
def get_orbital(self, n, l=None, s=0, k=None):
channel = self.get_channel(l, s, k)
return channel.basis.expand(channel.C_nb[n])
def plot_wave_functions(self, rc=4.0):
import matplotlib.pyplot as plt
for ch in self.channels:
for n in range(len(ch.f_n)):
fr_g = ch.basis.expand(ch.C_nb[n]) * self.rgd.r_g
# fr_g = ch.phi_ng[n]
name = str(n + ch.l + 1) + ch.name
lw = 2
if self.nspins == 2:
name += '(%s)' % '+-'[ch.s]
if ch.s == 1:
lw = 1
if self.dirac and ch.k > 0:
lw = 1
ls = ['-', '--', '-.', ':'][ch.l]
n_g = ch.calculate_density(n)
rave = self.rgd.integrate(n_g, 1)
gave = self.rgd.round(rave)
fr_g *= np.sign(fr_g[gave], 0)
plt.plot(self.rgd.r_g, fr_g,
ls=ls, lw=lw, color=colors[n + ch.l], label=name)
plt.legend(loc='best')
plt.xlabel('r [Bohr]')
plt.ylabel('$r\\phi(r)$')
plt.axis(xmax=rc)
plt.show()
def logarithmic_derivative(self, l, energies, rcut):
ch = Channel(l)
gcut = self.rgd.round(rcut)
u_g = self.rgd.empty()
logderivs = []
d0 = 42.0
offset = 0
for e in energies:
dudr = ch.integrate_outwards(u_g, self.rgd, self.vr_sg[0],
gcut, e, self.scalar_relativistic,
self.Z)[0]
d1 = np.arctan(dudr / u_g[gcut]) / pi + offset
if d1 > d0:
offset -= 1
d1 -= 1
logderivs.append(d1)
d0 = d1
return np.array(logderivs)
def calculate_exx(self, s=None):
if s is None:
self.exx = sum(self.calculate_exx(s)
for s in range(self.nspins)) / self.nspins
return self.exx
states = []
lmax = 0
for ch in self.channels:
l = ch.l
for n, phi_g in enumerate(ch.phi_ng):
f = ch.f_n[n]
if f > 0 and ch.s == s:
states.append((l, f * self.nspins / 2.0 / (2 * l + 1),
phi_g))
if l > lmax:
lmax = l
G_LLL = gaunt(lmax)
exx = 0.0
j1 = 0
for l1, f1, phi1_g in states:
f = 1.0
for l2, f2, phi2_g in states[j1:]:
n_g = phi1_g * phi2_g
for l in range((l1 + l2) % 2, l1 + l2 + 1, 2):
G = (G_LLL[l1**2:(l1 + 1)**2,
l2**2:(l2 + 1)**2,
l**2:(l + 1)**2]**2).sum()
vr_g = self.rgd.poisson(n_g, l)
e = f * self.rgd.integrate(vr_g * n_g, -1) / 4 / pi
exx -= e * G * f1 * f2
f = 2.0
j1 += 1
return exx
def startElement(self, name, attrs):
if sys.version_info[0] < 3:
attrs.__contains__ = attrs.has_key
setup = self.setup
if name == 'paw_setup':
setup.version = attrs['version']
assert LooseVersion(setup.version) >= '0.4'
if name == 'atom':
setup.Z = int(attrs['Z'])
setup.Nc = float(attrs['core'])
setup.Nv = int(attrs['valence'])
elif name == 'xc_functional':
if attrs['type'] == 'LDA':
setup.xcname = 'LDA'
else:
setup.xcname = attrs['name']
if attrs['type'] == 'OFDFT':
setup.orbital_free = True
else:
assert attrs['type'] == 'GGA'
elif name == 'ae_energy':
setup.e_total = float(attrs['total'])
setup.e_kinetic = float(attrs['kinetic'])
setup.e_electrostatic = float(attrs['electrostatic'])
setup.e_xc = float(attrs['xc'])
elif name == 'core_energy':
setup.e_kinetic_core = float(attrs['kinetic'])
elif name == 'state':
setup.n_j.append(int(attrs.get('n', -1)))
setup.l_j.append(int(attrs['l']))
setup.f_j.append(float(attrs.get('f', 0)))
setup.eps_j.append(float(attrs['e']))
setup.rcut_j.append(float(attrs.get('rc', -1)))
setup.id_j.append(attrs['id'])
# Compatibility with old setups:
if LooseVersion(setup.version) < '0.6' and setup.f_j[-1] == 0:
setup.n_j[-1] = -1
elif name == 'radial_grid':
if attrs['eq'] == 'r=a*i/(n-i)':
beta = float(attrs['a'])
ng = int(attrs['n'])
setup.rgd = AERadialGridDescriptor(beta / ng, 1.0 / ng, ng)
elif attrs['eq'] == 'r=a*i/(1-b*i)':
a = float(attrs['a'])
b = float(attrs['b'])
N = int(attrs['n'])
setup.rgd = AERadialGridDescriptor(a, b, N)
else:
raise ValueError('Unknown grid:' + attrs['eq'])
elif name == 'shape_function':
if 'rc' in attrs:
assert attrs['type'] == 'gauss'
setup.rcgauss = float(attrs['rc'])
else:
# Old style: XXX
setup.rcgauss = max(setup.rcut_j) / sqrt(float(attrs['alpha']))
elif name in [
'ae_core_density', 'pseudo_core_density',
'localized_potential', 'yukawa_exchange_X_matrix',
'kinetic_energy_differences', 'exact_exchange_X_matrix',
'ae_core_kinetic_energy_density',
'pseudo_core_kinetic_energy_density'
]:
self.data = []
elif name.startswith('GLLB_'):
self.data = []
elif name in ['ae_partial_wave', 'pseudo_partial_wave']:
self.data = []
self.id = attrs['state']
elif name == 'projector_function':
self.id = attrs['state']
self.data = []
elif name == 'exact_exchange':
setup.ExxC = float(attrs['core-core'])
elif name == 'yukawa_exchange':
setup.X_gamma = float(attrs['gamma'])
elif name == 'core_hole_state':
setup.has_corehole = True
setup.fcorehole = float(attrs['removed'])
setup.lcorehole = 'spdf'.find(attrs['state'][1])
setup.core_hole_e = float(attrs['eig'])
setup.core_hole_e_kin = float(attrs['ekin'])
self.data = []
elif name == 'zero_potential':
if 'type' in attrs:
setup.r0 = float(attrs['r0'])
setup.nderiv0 = int(attrs['nderiv'])
if attrs['type'] == 'polynomial':
setup.e0 = None
setup.l0 = None
else:
setup.e0 = float(attrs['e0'])
setup.l0 = 'spdfg'.find(attrs['type'])
self.data = []
elif name == 'generator':
setup.type = attrs['type']
setup.generator_version = int(attrs.get('version', '1'))
else:
self.data = None
def initialize(self, ngpts=2000, rcut=50.0,
alpha1=0.01, alpha2=None, ngauss=50,
eps=1.0e-7):
"""Initialize basis sets and radial grid.
ngpts: int
Number of grid points for radial grid.
rcut: float
Cutoff for radial grid.
alpha1: float
Smallest exponent for gaussian.
alpha2: float
Largest exponent for gaussian.
ngauss: int
Number of gaussians.
eps: float
Cutoff for eigenvalues of overlap matrix."""
if alpha2 is None:
alpha2 = 50.0 * self.Z**2
# Use grid with r(0)=0, r(1)=a and r(ngpts)=rcut:
a = 1 / alpha2**0.5 / 20
b = (rcut - a * ngpts) / (rcut * ngpts)
b = 1 / round(1 / b)
self.rgd = AERadialGridDescriptor(a, b, ngpts)
self.log('Grid points: %d (%.5f, %.5f, %.5f, ..., %.3f, %.3f)' %
((self.rgd.N,) + tuple(self.rgd.r_g[[0, 1, 2, -2, -1]])))
# Distribute exponents between alpha1 and alpha2:
alpha_B = alpha1 * (alpha2 / alpha1)**np.linspace(0, 1, ngauss)
self.log('Exponents: %d (%.3f, %.3f, ..., %.3f, %.3f)' %
((ngauss,) + tuple(alpha_B[[0, 1, -2, -1]])))
# Maximum l value:
lmax = max(self.f_lsn.keys())
self.channels = []
nb_l = []
if not self.dirac:
for l in range(lmax + 1):
basis = GaussianBasis(l, alpha_B, self.rgd, eps)
nb_l.append(len(basis))
for s in range(self.nspins):
self.channels.append(Channel(l, s, self.f_lsn[l][s],
basis))
else:
for K in range(1, lmax + 2):
leff = (K**2 - (self.Z / c)**2)**0.5 - 1
basis = GaussianBasis(leff, alpha_B, self.rgd, eps)
nb_l.append(len(basis))
for k, l in [(-K, K - 1), (K, K)]:
if l > lmax:
continue
f_n = self.f_lsn[l][0]
j = abs(k) - 0.5
f_n = (2 * j + 1) / (4 * l + 2) * np.array(f_n)
self.channels.append(DiracChannel(k, f_n, basis))
self.log('Basis functions: %s (%s)' %
(', '.join([str(nb) for nb in nb_l]),
', '.join('spdf'[:lmax + 1])))
self.vr_sg = self.rgd.zeros(self.nspins)
self.vr_sg[:] = -self.Z
class AllElectronAtom:
def __init__(self, symbol, xc='LDA', spinpol=False, dirac=False,
log=sys.stdout):
"""All-electron calculation for spherically symmetric atom.
symbol: str (or int)
Chemical symbol (or atomic number).
xc: str
Name of XC-functional.
spinpol: bool
If true, do spin-polarized calculation. Default is spin-paired.
dirac: bool
Solve Dirac equation instead of Schrödinger equation.
log: stream
Text output."""
if isinstance(symbol, int):
symbol = chemical_symbols[symbol]
self.symbol = symbol
self.Z = atomic_numbers[symbol]
self.nspins = 1 + int(bool(spinpol))
self.dirac = bool(dirac)
self.scalar_relativistic = False
if isinstance(xc, str):
self.xc = XC(xc)
else:
self.xc = xc
if log is None:
log = devnull
self.fd = log
self.vr_sg = None # potential * r
self.n_sg = 0.0 # density
self.rgd = None # radial grid descriptor
# Energies:
self.ekin = None
self.eeig = None
self.eH = None
self.eZ = None
self.channels = None
self.initialize_configuration()
self.log('Z: ', self.Z)
self.log('Name: ', atomic_names[self.Z])
self.log('Symbol: ', symbol)
self.log('XC-functional: ', self.xc.name)
self.log('Equation: ', ['Schrödinger', 'Dirac'][self.dirac])
self.method = 'Gaussian basis-set'
def log(self, *args, **kwargs):
prnt(file=self.fd, *args, **kwargs)
def initialize_configuration(self):
self.f_lsn = {}
for n, l, f, e in configurations[self.symbol][1]:
if l not in self.f_lsn:
self.f_lsn[l] = [[] for s in range(self.nspins)]
if self.nspins == 1:
self.f_lsn[l][0].append(f)
else:
# Use Hund's rule:
f0 = min(f, 2 * l + 1)
self.f_lsn[l][0].append(f0)
self.f_lsn[l][1].append(f - f0)
def add(self, n, l, df=+1, s=None):
"""Add (remove) electrons."""
if s is None:
if self.nspins == 1:
s = 0
else:
self.add(n, l, 0.5 * df, 0)
self.add(n, l, 0.5 * df, 1)
return
if l not in self.f_lsn:
self.f_lsn[l] = [[] for x in range(self.nspins)]
f_n = self.f_lsn[l][s]
if len(f_n) < n - l:
f_n.extend([0] * (n - l - len(f_n)))
f_n[n - l - 1] += df
def initialize(self, ngpts=2000, rcut=50.0,
alpha1=0.01, alpha2=None, ngauss=50,
eps=1.0e-7):
"""Initialize basis sets and radial grid.
ngpts: int
Number of grid points for radial grid.
rcut: float
Cutoff for radial grid.
alpha1: float
Smallest exponent for gaussian.
alpha2: float
Largest exponent for gaussian.
ngauss: int
Number of gaussians.
eps: float
Cutoff for eigenvalues of overlap matrix."""
if alpha2 is None:
alpha2 = 50.0 * self.Z**2
# Use grid with r(0)=0, r(1)=a and r(ngpts)=rcut:
a = 1 / alpha2**0.5 / 20
b = (rcut - a * ngpts) / (rcut * ngpts)
b = 1 / round(1 / b)
self.rgd = AERadialGridDescriptor(a, b, ngpts)
self.log('Grid points: %d (%.5f, %.5f, %.5f, ..., %.3f, %.3f)' %
((self.rgd.N,) + tuple(self.rgd.r_g[[0, 1, 2, -2, -1]])))
# Distribute exponents between alpha1 and alpha2:
alpha_B = alpha1 * (alpha2 / alpha1)**np.linspace(0, 1, ngauss)
self.log('Exponents: %d (%.3f, %.3f, ..., %.3f, %.3f)' %
((ngauss,) + tuple(alpha_B[[0, 1, -2, -1]])))
# Maximum l value:
lmax = max(self.f_lsn.keys())
self.channels = []
nb_l = []
if not self.dirac:
for l in range(lmax + 1):
basis = GaussianBasis(l, alpha_B, self.rgd, eps)
nb_l.append(len(basis))
for s in range(self.nspins):
self.channels.append(Channel(l, s, self.f_lsn[l][s],
basis))
else:
for K in range(1, lmax + 2):
leff = (K**2 - (self.Z / c)**2)**0.5 - 1
basis = GaussianBasis(leff, alpha_B, self.rgd, eps)
nb_l.append(len(basis))
for k, l in [(-K, K - 1), (K, K)]:
if l > lmax:
continue
f_n = self.f_lsn[l][0]
j = abs(k) - 0.5
f_n = (2 * j + 1) / (4 * l + 2) * np.array(f_n)
self.channels.append(DiracChannel(k, f_n, basis))
self.log('Basis functions: %s (%s)' %
(', '.join([str(nb) for nb in nb_l]),
', '.join('spdf'[:lmax + 1])))
self.vr_sg = self.rgd.zeros(self.nspins)
self.vr_sg[:] = -self.Z
def solve(self):
"""Diagonalize Schrödinger equation."""
self.eeig = 0.0
for channel in self.channels:
if self.method == 'Gaussian basis-set':
channel.solve(self.vr_sg[channel.s])
else:
channel.solve2(self.vr_sg[channel.s], self.scalar_relativistic)
self.eeig += channel.get_eigenvalue_sum()
def calculate_density(self):
"""Calculate elctron density and kinetic energy."""
self.n_sg = self.rgd.zeros(self.nspins)
for channel in self.channels:
self.n_sg[channel.s] += channel.calculate_density()
def calculate_electrostatic_potential(self):
"""Calculate electrostatic potential and energy."""
n_g = self.n_sg.sum(0)
self.vHr_g = self.rgd.poisson(n_g)
self.eH = 0.5 * self.rgd.integrate(n_g * self.vHr_g, -1)
self.eZ = -self.Z * self.rgd.integrate(n_g, -1)
def calculate_xc_potential(self):
self.vxc_sg = self.rgd.zeros(self.nspins)
self.exc = self.xc.calculate_spherical(self.rgd, self.n_sg, self.vxc_sg)
def step(self):
self.solve()
self.calculate_density()
self.calculate_electrostatic_potential()
self.calculate_xc_potential()
self.vr_sg = self.vxc_sg * self.rgd.r_g
self.vr_sg += self.vHr_g
self.vr_sg -= self.Z
self.ekin = (self.eeig -
self.rgd.integrate((self.vr_sg * self.n_sg).sum(0), -1))
def run(self, mix=0.4, maxiter=117, dnmax=1e-9):
if self.channels is None:
self.initialize()
if self.dirac:
equation = 'Dirac'
elif self.scalar_relativistic:
equation = 'scalar-relativistic Schrödinger'
else:
equation = 'non-relativistic Schrödinger'
self.log('\nSolving %s equation using %s:' % (equation, self.method))
dn = self.Z
for iter in range(maxiter):
self.log('.', end='')
self.fd.flush()
if iter > 0:
self.vr_sg *= mix
self.vr_sg += (1 - mix) * vr_old_sg
dn = self.rgd.integrate(abs(self.n_sg - n_old_sg).sum(0))
if dn <= dnmax:
self.log('\nConverged in', iter, 'steps')
break
vr_old_sg = self.vr_sg
n_old_sg = self.n_sg
self.step()
self.summary()
if dn > dnmax:
raise RuntimeError('Did not converge!')
def refine(self):
self.method = 'finite difference'
self.run(dnmax=1e-6, mix=0.14, maxiter=200)
def summary(self):
self.write_states()
self.write_energies()
def write_states(self):
self.log('\n state occupation eigenvalue <r>')
if self.dirac:
self.log(' nl(j) [Hartree] [eV] [Bohr]')
else:
self.log(' nl [Hartree] [eV] [Bohr]')
self.log('-----------------------------------------------------')
states = []
for ch in self.channels:
for n, f in enumerate(ch.f_n):
states.append((ch.e_n[n], ch, n))
states.sort()
for e, ch, n in states:
name = str(n + ch.l + 1) + ch.name
if self.nspins == 2:
name += '(%s)' % '+-'[ch.s]
n_g = ch.calculate_density(n)
rave = self.rgd.integrate(n_g, 1)
self.log(' %-7s %6.3f %13.6f %13.5f %6.3f' %
(name, ch.f_n[n], e, e * units.Hartree, rave))
def write_energies(self):
self.log('\nEnergies: [Hartree] [eV]')
self.log('--------------------------------------------')
for text, e in [('kinetic ', self.ekin),
('coulomb (e-e)', self.eH),
('coulomb (e-n)', self.eZ),
('xc ', self.exc),
('total ',
self.ekin + self.eH + self.eZ + self.exc)]:
self.log(' %s %+13.6f %+13.5f' % (text, e, units.Hartree * e))
self.calculate_exx()
self.log('\nExact exchange energy: %.6f Hartree, %.5f eV' %
(self.exx, self.exx * units.Hartree))
def get_channel(self, l=None, s=0, k=None):
if self.dirac:
for channel in self.channels:
if channel.k == k:
return channel
else:
for channel in self.channels:
if channel.l == l and channel.s == s:
return channel
raise ValueError
def get_orbital(self, n, l=None, s=0, k=None):
channel = self.get_channel(l, s, k)
return channel.basis.expand(channel.C_nb[n])
def plot_wave_functions(self, rc=4.0):
import matplotlib.pyplot as plt
for ch in self.channels:
for n in range(len(ch.f_n)):
fr_g = ch.basis.expand(ch.C_nb[n]) * self.rgd.r_g
name = str(n + ch.l + 1) + ch.name
lw = 2
if self.nspins == 2:
name += '(%s)' % '+-'[ch.s]
if ch.s == 1:
lw = 1
if self.dirac and ch.k > 0:
lw = 1
ls = ['-', '--', '-.', ':'][ch.l]
n_g = ch.calculate_density(n)
rave = self.rgd.integrate(n_g, 1)
gave = self.rgd.round(rave)
fr_g *= cmp(fr_g[gave], 0)
plt.plot(self.rgd.r_g, fr_g,
ls=ls, lw=lw, color=colors[n + ch.l], label=name)
plt.legend(loc='best')
plt.xlabel('r [Bohr]')
plt.ylabel('$r\\phi(r)$')
plt.axis(xmax=rc)
plt.show()
def logarithmic_derivative(self, l, energies, rcut):
ch = Channel(l)
gcut = self.rgd.round(rcut)
u_g = self.rgd.empty()
logderivs = []
for e in energies:
dudr = ch.integrate_outwards(u_g, self.rgd, self.vr_sg[0],
gcut, e, self.scalar_relativistic)
logderivs.append(dudr / u_g[gcut])
return logderivs
def calculate_exx(self, s=None):
if s is None:
self.exx = sum(self.calculate_exx(s)
for s in range(self.nspins)) / self.nspins
return self.exx
states = []
lmax = 0
for ch in self.channels:
l = ch.l
for n, phi_g in enumerate(ch.phi_ng):
f = ch.f_n[n]
if f > 0 and ch.s == s:
states.append((l, f * self.nspins / 2.0 / (2 * l + 1),
phi_g))
if l > lmax:
lmax = l
G_LLL = make_gaunt(lmax)
exx = 0.0
j1 = 0
for l1, f1, phi1_g in states:
f = 1.0
for l2, f2, phi2_g in states[j1:]:
n_g = phi1_g * phi2_g
for l in range((l1 + l2) % 2, l1 + l2 + 1, 2):
G = (G_LLL[l1**2:(l1 + 1)**2,
l2**2:(l2 + 1)**2,
l**2:(l + 1)**2]**2).sum()
vr_g = self.rgd.poisson(n_g, l)
e = f * self.rgd.integrate(vr_g * n_g, -1) / 4 / pi
exx -= e * G * f1 * f2
f = 2.0
j1 += 1
return exx
def initialize_setup_data(self):
hghdata = self.hghdata
beta = 0.1
N = 450
rgd = AERadialGridDescriptor(beta / N,
1.0 / N,
N,
default_spline_points=100)
# rgd = EquidistantRadialGridDescriptor(0.001, 10000)
self.rgd = rgd
self.Z = hghdata.Z
self.Nc = hghdata.Z - hghdata.Nv
self.Nv = hghdata.Nv
self.rcgauss = np.sqrt(2.0) * hghdata.rloc
threshold = 1e-8
if len(hghdata.c_n) > 0:
vloc_g = create_local_shortrange_potential(rgd.r_g, hghdata.rloc,
hghdata.c_n)
gcutvbar, rcutvbar = self.find_cutoff(rgd.r_g, rgd.dr_g, vloc_g,
threshold)
self.vbar_g = np.sqrt(4.0 * np.pi) * vloc_g[:gcutvbar]
else:
rcutvbar = 0.5
gcutvbar = rgd.ceil(rcutvbar)
self.vbar_g = np.zeros(gcutvbar)
nj = sum([v.nn for v in hghdata.v_l])
if nj == 0:
nj = 1 # Code assumes nj > 0 elsewhere, we fill out with zeroes
if not hghdata.v_l:
# No projectors. But the remaining code assumes that everything
# has projectors! We'll just add the zero function then
hghdata.v_l = [VNonLocal(0, 0.01, [[0.]])]
n_j = []
l_j = []
# j ordering is significant, must be nl rather than ln
for n, l in self.hghdata.nl_iter():
n_j.append(n + 1) # Note: actual n must be positive!
l_j.append(l)
assert nj == len(n_j)
self.nj = nj
self.l_j = l_j
self.l_orb_j = l_j
self.n_j = n_j
self.rcut_j = []
self.pt_jg = []
for n, l in zip(n_j, l_j):
# Note: even pseudopotentials without projectors will get one
# projector, but the coefficients h_ij should be zero so it
# doesn't matter
pt_g = create_hgh_projector(rgd.r_g, l, n, hghdata.v_l[l].r0)
norm = np.sqrt(np.dot(rgd.dr_g, pt_g**2 * rgd.r_g**2))
assert np.abs(1 - norm) < 1e-5, str(1 - norm)
gcut, rcut = self.find_cutoff(rgd.r_g, rgd.dr_g, pt_g, threshold)
if rcut < 0.5:
rcut = 0.5
gcut = rgd.ceil(rcut)
pt_g = pt_g[:gcut].copy()
rcut = max(rcut, 0.5)
self.rcut_j.append(rcut)
self.pt_jg.append(pt_g)
# This is the correct magnitude of the otherwise normalized
# compensation charge
self.Delta0 = -self.Nv / np.sqrt(4.0 * np.pi)
f_ln = self.hghdata.get_occupation_numbers()
f_j = [0] * nj
for j, (n, l) in enumerate(self.hghdata.nl_iter()):
try:
f_j[j] = f_ln[l][n]
except IndexError:
pass
self.f_ln = f_ln
self.f_j = f_j
r_g, lcomp, ghat = self.get_compensation_charge_functions()
assert lcomp == [0] and len(ghat) == 1
renormalized_ghat = self.Nv / (4.0 * np.pi) * ghat[0]
self.Eh_compcharge = get_radial_hartree_energy(r_g, renormalized_ghat)
def initialize_setup_data(self):
hghdata = self.hghdata
beta = 0.1
N = 450
rgd = AERadialGridDescriptor(beta / N, 1.0 / N, N,
default_spline_points=100)
#rgd = EquidistantRadialGridDescriptor(0.001, 10000)
self.rgd = rgd
self.Z = hghdata.Z
self.Nc = hghdata.Z - hghdata.Nv
self.Nv = hghdata.Nv
self.rcgauss = np.sqrt(2.0) * hghdata.rloc
threshold = 1e-8
if len(hghdata.c_n) > 0:
vloc_g = create_local_shortrange_potential(rgd.r_g, hghdata.rloc,
hghdata.c_n)
gcutvbar, rcutvbar = self.find_cutoff(rgd.r_g, rgd.dr_g, vloc_g,
threshold)
self.vbar_g = np.sqrt(4.0 * np.pi) * vloc_g[:gcutvbar]
else:
rcutvbar = 0.5
gcutvbar = rgd.ceil(rcutvbar)
self.vbar_g = np.zeros(gcutvbar)
nj = sum([v.nn for v in hghdata.v_l])
if nj == 0:
nj = 1 # Code assumes nj > 0 elsewhere, we fill out with zeroes
if not hghdata.v_l:
# No projectors. But the remaining code assumes that everything
# has projectors! We'll just add the zero function then
hghdata.v_l = [VNonLocal(0, 0.01, [[0.]])]
n_j = []
l_j = []
# j ordering is significant, must be nl rather than ln
for n, l in self.hghdata.nl_iter():
n_j.append(n + 1) # Note: actual n must be positive!
l_j.append(l)
assert nj == len(n_j)
self.nj = nj
self.l_j = l_j
self.l_orb_j = l_j
self.n_j = n_j
self.rcut_j = []
self.pt_jg = []
for n, l in zip(n_j, l_j):
# Note: even pseudopotentials without projectors will get one
# projector, but the coefficients h_ij should be zero so it
# doesn't matter
pt_g = create_hgh_projector(rgd.r_g, l, n, hghdata.v_l[l].r0)
norm = np.sqrt(np.dot(rgd.dr_g, pt_g**2 * rgd.r_g**2))
assert np.abs(1 - norm) < 1e-5, str(1 - norm)
gcut, rcut = self.find_cutoff(rgd.r_g, rgd.dr_g, pt_g, threshold)
if rcut < 0.5:
rcut = 0.5
gcut = rgd.ceil(rcut)
pt_g = pt_g[:gcut].copy()
rcut = max(rcut, 0.5)
self.rcut_j.append(rcut)
self.pt_jg.append(pt_g)
# This is the correct magnitude of the otherwise normalized
# compensation charge
self.Delta0 = -self.Nv / np.sqrt(4.0 * np.pi)
f_ln = self.hghdata.get_occupation_numbers()
f_j = [0] * nj
for j, (n, l) in enumerate(self.hghdata.nl_iter()):
try:
f_j[j] = f_ln[l][n]
except IndexError:
pass
self.f_ln = f_ln
self.f_j = f_j
class AllElectron:
"""Object for doing an atomic DFT calculation."""
def __init__(self,
symbol,
xcname='LDA',
scalarrel=True,
corehole=None,
configuration=None,
nofiles=True,
txt='-',
gpernode=150,
orbital_free=False,
tw_coeff=1.):
"""Do an atomic DFT calculation.
Example::
a = AllElectron('Fe')
a.run()
"""
if txt is None:
txt = devnull
elif txt == '-':
txt = sys.stdout
elif isinstance(txt, str):
txt = open(txt, 'w')
self.txt = txt
self.symbol = symbol
self.xcname = xcname
self.scalarrel = scalarrel
self.nofiles = nofiles
# Get reference state:
self.Z, nlfe_j = configurations[symbol]
# Collect principal quantum numbers, angular momentum quantum
# numbers, occupation numbers and eigenvalues (j is a combined
# index for n and l):
self.n_j = [n for n, l, f, e in nlfe_j]
self.l_j = [l for n, l, f, e in nlfe_j]
self.f_j = [f for n, l, f, e in nlfe_j]
self.e_j = [e for n, l, f, e in nlfe_j]
if configuration is not None:
j = 0
for conf in configuration.split(','):
if conf[0].isdigit():
n = int(conf[0])
l = 'spdf'.find(conf[1])
if len(conf) == 2:
f = 1.0
else:
f = float(conf[2:])
#try:
assert n == self.n_j[j]
assert l == self.l_j[j]
self.f_j[j] = f
#except IndexError:
# self.n_j.append(n)
# self.l_j.append(l)
# self.f_j.append(f)
# self.e_j.append(self.e_j[-1])
j += 1
else:
j += {'He': 1, 'Ne': 3, 'Ar': 5, 'Kr': 8, 'Xe': 11}[conf]
maxnodes = max([n - l - 1 for n, l in zip(self.n_j, self.l_j)])
self.N = (maxnodes + 1) * gpernode
self.beta = 0.4
self.orbital_free = orbital_free
self.tw_coeff = tw_coeff
if self.orbital_free:
self.n_j = [1]
self.l_j = [0]
self.f_j = [self.Z]
self.e_j = [self.e_j[-1]]
t = self.text
t()
if scalarrel:
t('Scalar-relativistic atomic ', end='')
else:
t('Atomic ', end='')
t('%s calculation for %s (%s, Z=%d)' %
(xcname, symbol, atomic_names[self.Z], self.Z))
if corehole is not None:
self.ncorehole, self.lcorehole, self.fcorehole = corehole
# Find j for core hole and adjust occupation:
for j in range(len(self.f_j)):
if (self.n_j[j] == self.ncorehole
and self.l_j[j] == self.lcorehole):
assert self.f_j[j] == 2 * (2 * self.lcorehole + 1)
self.f_j[j] -= self.fcorehole
self.jcorehole = j
break
coreholestate = '%d%s' % (self.ncorehole, 'spdf'[self.lcorehole])
t('Core hole in %s state (%s occupation: %.1f)' %
(coreholestate, coreholestate, self.f_j[self.jcorehole]))
else:
self.jcorehole = None
self.fcorehole = 0
def text(self, *args, **kwargs):
self.txt.write(
kwargs.get('sep', ' ').join([str(arg) for arg in args]) +
kwargs.get('end', '\n'))
def initialize_wave_functions(self):
r = self.r
dr = self.dr
# Initialize with Slater function:
for l, e, u in zip(self.l_j, self.e_j, self.u_j):
if self.symbol in ['Hf', 'Ta', 'W', 'Re', 'Os', 'Ir', 'Pt', 'Au']:
a = sqrt(-4.0 * e)
else:
a = sqrt(-2.0 * e)
u[:] = r**(1 + l) * np.exp(-a * r)
norm = np.dot(u**2, dr)
u *= 1.0 / sqrt(norm)
def run(self, use_restart_file=True):
# beta g
# r = ------, g = 0, 1, ..., N - 1
# N - g
#
# rN
# g = --------
# beta + r
t = self.text
N = self.N
beta = self.beta
t(N, 'radial gridpoints.')
self.rgd = AERadialGridDescriptor(beta / N, 1.0 / N, N)
g = np.arange(N, dtype=float)
self.r = self.rgd.r_g
self.dr = self.rgd.dr_g
self.d2gdr2 = self.rgd.d2gdr2()
# Number of orbitals:
nj = len(self.n_j)
# Radial wave functions multiplied by radius:
self.u_j = np.zeros((nj, self.N))
# Effective potential multiplied by radius:
self.vr = np.zeros(N)
# Electron density:
self.n = np.zeros(N)
# Always spinpaired nspins=1
self.xc = XC(self.xcname)
# Initialize for non-local functionals
if self.xc.type == 'GLLB':
self.xc.pass_stuff_1d(self)
self.xc.initialize_1d()
n_j = self.n_j
l_j = self.l_j
f_j = self.f_j
e_j = self.e_j
Z = self.Z # nuclear charge
r = self.r # radial coordinate
dr = self.dr # dr/dg
n = self.n # electron density
vr = self.vr # effective potential multiplied by r
vHr = np.zeros(self.N)
self.vXC = np.zeros(self.N)
restartfile = '%s/%s.restart' % (tempdir, self.symbol)
if self.xc.type == 'GLLB' or not use_restart_file:
# Do not start from initial guess when doing
# non local XC!
# This is because we need wavefunctions as well
# on the first iteration.
fd = None
else:
try:
fd = open(restartfile, 'rb')
except IOError:
fd = None
else:
try:
n[:] = pickle.load(fd)
except (ValueError, IndexError):
fd = None
else:
norm = np.dot(n * r**2, dr) * 4 * pi
if abs(norm - sum(f_j)) > 0.01:
fd = None
else:
t('Using old density for initial guess.')
n *= sum(f_j) / norm
if fd is None:
self.initialize_wave_functions()
n[:] = self.calculate_density()
bar = '|------------------------------------------------|'
t(bar)
niter = 0
nitermax = 117
qOK = log(1e-10)
mix = 0.4
# orbital_free needs more iterations and coefficient
if self.orbital_free:
mix = 0.01
nitermax = 2000
e_j[0] /= self.tw_coeff
if Z > 10: #help convergence for third row elements
mix = 0.002
nitermax = 10000
vrold = None
while True:
# calculate hartree potential
hartree(0, n * r * dr, r, vHr)
# add potential from nuclear point charge (v = -Z / r)
vHr -= Z
# calculated exchange correlation potential and energy
self.vXC[:] = 0.0
if self.xc.type == 'GLLB':
# Update the potential to self.vXC an the energy to self.Exc
Exc = self.xc.get_xc_potential_and_energy_1d(self.vXC)
else:
Exc = self.xc.calculate_spherical(self.rgd, n.reshape((1, -1)),
self.vXC.reshape((1, -1)))
# calculate new total Kohn-Sham effective potential and
# admix with old version
vr[:] = (vHr + self.vXC * r)
if self.orbital_free:
vr /= self.tw_coeff
if niter > 0:
vr[:] = mix * vr + (1 - mix) * vrold
vrold = vr.copy()
# solve Kohn-Sham equation and determine the density change
self.solve()
dn = self.calculate_density() - n
n += dn
# estimate error from the square of the density change integrated
q = log(np.sum((r * dn)**2))
# print progress bar
if niter == 0:
q0 = q
b0 = 0
else:
b = int((q0 - q) / (q0 - qOK) * 50)
if b > b0:
self.txt.write(bar[b0:min(b, 50)])
self.txt.flush()
b0 = b
# check if converged and break loop if so
if q < qOK:
self.txt.write(bar[b0:])
self.txt.flush()
break
niter += 1
if niter > nitermax:
raise RuntimeError('Did not converge!')
tau = self.calculate_kinetic_energy_density()
t()
t('Converged in %d iteration%s.' % (niter, 's'[:niter != 1]))
try:
fd = open(restartfile, 'wb')
except IOError:
pass
else:
pickle.dump(n, fd)
try:
os.chmod(restartfile, 0o666)
except OSError:
pass
Ekin = 0
for f, e in zip(f_j, e_j):
Ekin += f * e
e_coulomb = 2 * pi * np.dot(n * r * (vHr - Z), dr)
Ekin += -4 * pi * np.dot(n * vr * r, dr)
if self.orbital_free:
# e and vr are not scaled back
# instead Ekin is scaled for total energy (printed and inside setup)
Ekin *= self.tw_coeff
t()
t('Lambda:{0}'.format(self.tw_coeff))
t('Correct eigenvalue:{0}'.format(e_j[0] * self.tw_coeff))
t()
t()
t('Energy contributions:')
t('-------------------------')
t('Kinetic: %+13.6f' % Ekin)
t('XC: %+13.6f' % Exc)
t('Potential: %+13.6f' % e_coulomb)
t('-------------------------')
t('Total: %+13.6f' % (Ekin + Exc + e_coulomb))
self.ETotal = Ekin + Exc + e_coulomb
t()
t('state eigenvalue ekin rmax')
t('-----------------------------------------------')
for m, l, f, e, u in zip(n_j, l_j, f_j, e_j, self.u_j):
# Find kinetic energy:
k = e - np.sum((
np.where(abs(u) < 1e-160, 0, u)**2 * # XXXNumeric!
vr * dr)[1:] / r[1:])
# Find outermost maximum:
g = self.N - 4
while u[g - 1] >= u[g]:
g -= 1
x = 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)')
for m, l, u in zip(n_j, l_j, self.u_j):
self.write(u, 'ae', n=m, l=l)
self.write(n, 'n')
self.write(vr, 'vr')
self.write(vHr, 'vHr')
self.write(self.vXC, 'vXC')
self.write(tau, 'tau')
self.Ekin = Ekin
self.e_coulomb = e_coulomb
self.Exc = Exc
def write(self, array, name=None, n=None, l=None):
if self.nofiles:
return
if name:
name = self.symbol + '.' + name
else:
name = self.symbol
if l is not None:
assert n is not None
if n > 0:
# Bound state:
name += '.%d%s' % (n, 'spdf'[l])
else:
name += '.x%d%s' % (-n, 'spdf'[l])
f = open(name, 'w')
for r, a in zip(self.r, array):
print(r, a, file=f)
def calculate_density(self):
"""Return the electron charge density divided by 4 pi"""
n = np.dot(self.f_j,
np.where(abs(self.u_j) < 1e-160, 0, self.u_j)**2) / (4 * pi)
n[1:] /= self.r[1:]**2
n[0] = n[1]
return n
def calculate_kinetic_energy_density(self):
"""Return the kinetic energy density"""
return self.radial_kinetic_energy_density(self.f_j, self.l_j, self.u_j)
def radial_kinetic_energy_density(self, f_j, l_j, u_j):
"""Kinetic energy density from a restricted set of wf's
"""
shape = np.shape(u_j[0])
dudr = np.zeros(shape)
tau = np.zeros(shape)
for f, l, u in zip(f_j, l_j, u_j):
self.rgd.derivative(u, dudr)
# contribution from angular derivatives
if l > 0:
tau += f * l * (l + 1) * np.where(abs(u) < 1e-160, 0, u)**2
# contribution from radial derivatives
dudr = u - self.r * dudr
tau += f * np.where(abs(dudr) < 1e-160, 0, dudr)**2
tau[1:] /= self.r[1:]**4
tau[0] = tau[1]
return 0.5 * tau / (4 * pi)
def calculate_kinetic_energy_density2(self):
"""Return the kinetic energy density
calculation over R(r)=u(r)/r
slower convergence with # of radial grid points for
Ekin of H than radial_kinetic_energy_density
"""
shape = self.u_j.shape[1]
R = np.zeros(shape)
dRdr = np.zeros(shape)
tau = np.zeros(shape)
for f, l, u in zip(self.f_j, self.l_j, self.u_j):
R[1:] = u[1:] / self.r[1:]
if l == 0:
# estimate value at origin by Taylor series to first order
d1 = self.r[1]
d2 = self.r[2]
R[0] = .5 * (R[1] + R[2] + (R[1] - R[2]) * (d1 + d2) /
(d2 - d1))
else:
R[0] = 0
self.rgd.derivative(R, dRdr)
# contribution from radial derivatives
tau += f * np.where(abs(dRdr) < 1e-160, 0, dRdr)**2
# contribution from angular derivatives
if l > 0:
R[1:] = R[1:] / self.r[1:]
if l == 1:
R[0] = R[1]
else:
R[0] = 0
tau += f * l * (l + 1) * np.where(abs(R) < 1e-160, 0, R)**2
return 0.5 * tau / (4 * pi)
def solve(self):
"""Solve the Schrodinger equation
::
2
d u 1 dv du u l(l + 1)
- --- - ---- -- (-- - -) + [-------- + 2M(v - e)] u = 0,
2 2 dr dr r 2
dr 2Mc r
where the relativistic mass::
1
M = 1 - --- (v - e)
2
2c
and the fine-structure constant alpha = 1/c = 1/137.036
is set to zero for non-scalar-relativistic calculations.
On the logaritmic radial grids defined by::
beta g
r = ------, g = 0, 1, ..., N - 1
N - g
rN
g = --------, r = [0; oo[
beta + r
the Schrodinger equation becomes::
2
d u du
--- c + -- c + u c = 0
2 2 dg 1 0
dg
with the vectors c0, c1, and c2 defined by::
2 dg 2
c = -r (--)
2 dr
2 2
d g 2 r dg dv
c = - --- r - ---- -- --
1 2 2 dr dr
dr 2Mc
2 r dv
c = l(l + 1) + 2M(v - e)r + ---- --
0 2 dr
2Mc
"""
r = self.r
dr = self.dr
vr = self.vr
c2 = -(r / dr)**2
c10 = -self.d2gdr2 * r**2 # first part of c1 vector
if self.scalarrel:
self.r2dvdr = np.zeros(self.N)
self.rgd.derivative(vr, self.r2dvdr)
self.r2dvdr *= r
self.r2dvdr -= vr
else:
self.r2dvdr = None
# solve for each quantum state separately
for j, (n, l, e,
u) in enumerate(zip(self.n_j, self.l_j, self.e_j, self.u_j)):
nodes = n - l - 1 # analytically expected number of nodes
delta = -0.2 * e
nn, A = shoot(u, l, vr, e, self.r2dvdr, r, dr, c10, c2,
self.scalarrel)
# adjust eigenenergy until u has the correct number of nodes
while nn != nodes:
diff = np.sign(nn - nodes)
while diff == np.sign(nn - nodes):
e -= diff * delta
nn, A = shoot(u, l, vr, e, self.r2dvdr, r, dr, c10, c2,
self.scalarrel)
delta /= 2
# adjust eigenenergy until u is smooth at the turning point
de = 1.0
while abs(de) > 1e-9:
norm = np.dot(np.where(abs(u) < 1e-160, 0, u)**2, dr)
u *= 1.0 / sqrt(norm)
de = 0.5 * A / norm
x = abs(de / e)
if x > 0.1:
de *= 0.1 / x
e -= de
assert e < 0.0
nn, A = shoot(u, l, vr, e, self.r2dvdr, r, dr, c10, c2,
self.scalarrel)
self.e_j[j] = e
u *= 1.0 / sqrt(np.dot(np.where(abs(u) < 1e-160, 0, u)**2, dr))
def solve_confined(self, j, rc, vconf=None):
"""Solve the Schroedinger equation in a confinement potential.
Solves the Schroedinger equation like the solve method, but with a
number of differences. Before invoking this method, run solve() to
get initial guesses.
Parameters:
j: solves only for the state given by j
rc: solution cutoff. Solution will be zero outside this.
vconf: added to the potential (use this as confinement potential)
Returns: a tuple containing the solution u and its energy e.
Unlike the solve method, this method will not alter any attributes of
this object.
"""
r = self.r
dr = self.dr
vr = self.vr.copy()
if vconf is not None:
vr += vconf * r
c2 = -(r / dr)**2
c10 = -self.d2gdr2 * r**2 # first part of c1 vector
if j is None:
n, l, e, u = 3, 2, -0.15, self.u_j[-1].copy()
else:
n = self.n_j[j]
l = self.l_j[j]
e = self.e_j[j]
u = self.u_j[j].copy()
nn, A = shoot_confined(u,
l,
vr,
e,
self.r2dvdr,
r,
dr,
c10,
c2,
self.scalarrel,
rc=rc,
beta=self.beta)
assert nn == n - l - 1 # run() should have been called already
# adjust eigenenergy until u is smooth at the turning point
de = 1.0
while abs(de) > 1e-9:
norm = np.dot(np.where(abs(u) < 1e-160, 0, u)**2, dr)
u *= 1.0 / sqrt(norm)
de = 0.5 * A / norm
x = abs(de / e)
if x > 0.1:
de *= 0.1 / x
e -= de
assert e < 0.0
nn, A = shoot_confined(u,
l,
vr,
e,
self.r2dvdr,
r,
dr,
c10,
c2,
self.scalarrel,
rc=rc,
beta=self.beta)
u *= 1.0 / sqrt(np.dot(np.where(abs(u) < 1e-160, 0, u)**2, dr))
return u, e
def kin(self, l, u, e=None): # XXX move to Generator
r = self.r[1:]
dr = self.dr[1:]
c0 = 0.5 * l * (l + 1) / r**2
c1 = -0.5 * self.d2gdr2[1:]
c2 = -0.5 * dr**-2
if e is not None and self.scalarrel:
x = 0.5 * alpha**2
Mr = r * (1.0 + x * e) - x * self.vr[1:]
c0 += (
(Mr - r) *
(self.vr[1:] - e * r) + 0.5 * x * self.r2dvdr[1:] / Mr) / r**2
c1 -= 0.5 * x * self.r2dvdr[1:] / (Mr * dr * r)
fp = c2 + 0.5 * c1
fm = c2 - 0.5 * c1
f0 = c0 - 2 * c2
kr = np.zeros(self.N)
kr[1:] = f0 * u[1:] + fm * u[:-1]
kr[1:-1] += fp[:-1] * u[2:]
kr[0] = 0.0
return kr
def r2g(self, r):
"""Convert radius to index of the radial grid."""
return int(r * self.N / (self.beta + r))
def get_confinement_potential(self, alpha, ri, rc):
r"""Create a smooth confinement potential.
Returns a (potential) function which is zero inside the radius ri
and goes to infinity smoothly at rc, after which point it is nan.
The potential is given by::
alpha / rc - ri \
V(r) = -------- exp ( - --------- ) for ri < r < rc
rc - r \ r - ri /
"""
i_ri = self.r2g(ri)
i_rc = self.r2g(rc)
if self.r[i_rc] == rc:
# Avoid division by zero in the odd case that rc coincides
# exactly with a grid point (which actually happens sometimes)
i_rc -= 1
potential = np.zeros(np.shape(self.r))
r = self.r[i_ri + 1:i_rc + 1]
exponent = -(rc - ri) / (r - ri)
denom = rc - r
value = np.exp(exponent) / denom
potential[i_ri + 1:i_rc + 1] = value
potential[i_rc + 1:] = np.inf
return alpha * potential
def run(self, use_restart_file=True):
# beta g
# r = ------, g = 0, 1, ..., N - 1
# N - g
#
# rN
# g = --------
# beta + r
t = self.text
N = self.N
beta = self.beta
t(N, 'radial gridpoints.')
self.rgd = AERadialGridDescriptor(beta / N, 1.0 / N, N)
g = np.arange(N, dtype=float)
self.r = self.rgd.r_g
self.dr = self.rgd.dr_g
self.d2gdr2 = self.rgd.d2gdr2()
# Number of orbitals:
nj = len(self.n_j)
# Radial wave functions multiplied by radius:
self.u_j = np.zeros((nj, self.N))
# Effective potential multiplied by radius:
self.vr = np.zeros(N)
# Electron density:
self.n = np.zeros(N)
# Always spinpaired nspins=1
self.xc = XC(self.xcname)
# Initialize for non-local functionals
if self.xc.type == 'GLLB':
self.xc.pass_stuff_1d(self)
self.xc.initialize_1d()
n_j = self.n_j
l_j = self.l_j
f_j = self.f_j
e_j = self.e_j
Z = self.Z # nuclear charge
r = self.r # radial coordinate
dr = self.dr # dr/dg
n = self.n # electron density
vr = self.vr # effective potential multiplied by r
vHr = np.zeros(self.N)
self.vXC = np.zeros(self.N)
restartfile = '%s/%s.restart' % (tempdir, self.symbol)
if self.xc.type == 'GLLB' or not use_restart_file:
# Do not start from initial guess when doing
# non local XC!
# This is because we need wavefunctions as well
# on the first iteration.
fd = None
else:
try:
fd = open(restartfile, 'rb')
except IOError:
fd = None
else:
try:
n[:] = pickle.load(fd)
except (ValueError, IndexError):
fd = None
else:
norm = np.dot(n * r**2, dr) * 4 * pi
if abs(norm - sum(f_j)) > 0.01:
fd = None
else:
t('Using old density for initial guess.')
n *= sum(f_j) / norm
if fd is None:
self.initialize_wave_functions()
n[:] = self.calculate_density()
bar = '|------------------------------------------------|'
t(bar)
niter = 0
nitermax = 117
qOK = log(1e-10)
mix = 0.4
# orbital_free needs more iterations and coefficient
if self.orbital_free:
mix = 0.01
nitermax = 2000
e_j[0] /= self.tw_coeff
if Z > 10: #help convergence for third row elements
mix = 0.002
nitermax = 10000
vrold = None
while True:
# calculate hartree potential
hartree(0, n * r * dr, r, vHr)
# add potential from nuclear point charge (v = -Z / r)
vHr -= Z
# calculated exchange correlation potential and energy
self.vXC[:] = 0.0
if self.xc.type == 'GLLB':
# Update the potential to self.vXC an the energy to self.Exc
Exc = self.xc.get_xc_potential_and_energy_1d(self.vXC)
else:
Exc = self.xc.calculate_spherical(self.rgd, n.reshape((1, -1)),
self.vXC.reshape((1, -1)))
# calculate new total Kohn-Sham effective potential and
# admix with old version
vr[:] = (vHr + self.vXC * r)
if self.orbital_free:
vr /= self.tw_coeff
if niter > 0:
vr[:] = mix * vr + (1 - mix) * vrold
vrold = vr.copy()
# solve Kohn-Sham equation and determine the density change
self.solve()
dn = self.calculate_density() - n
n += dn
# estimate error from the square of the density change integrated
q = log(np.sum((r * dn)**2))
# print progress bar
if niter == 0:
q0 = q
b0 = 0
else:
b = int((q0 - q) / (q0 - qOK) * 50)
if b > b0:
self.txt.write(bar[b0:min(b, 50)])
self.txt.flush()
b0 = b
# check if converged and break loop if so
if q < qOK:
self.txt.write(bar[b0:])
self.txt.flush()
break
niter += 1
if niter > nitermax:
raise RuntimeError('Did not converge!')
tau = self.calculate_kinetic_energy_density()
t()
t('Converged in %d iteration%s.' % (niter, 's'[:niter != 1]))
try:
fd = open(restartfile, 'wb')
except IOError:
pass
else:
pickle.dump(n, fd)
try:
os.chmod(restartfile, 0o666)
except OSError:
pass
Ekin = 0
for f, e in zip(f_j, e_j):
Ekin += f * e
e_coulomb = 2 * pi * np.dot(n * r * (vHr - Z), dr)
Ekin += -4 * pi * np.dot(n * vr * r, dr)
if self.orbital_free:
# e and vr are not scaled back
# instead Ekin is scaled for total energy (printed and inside setup)
Ekin *= self.tw_coeff
t()
t('Lambda:{0}'.format(self.tw_coeff))
t('Correct eigenvalue:{0}'.format(e_j[0] * self.tw_coeff))
t()
t()
t('Energy contributions:')
t('-------------------------')
t('Kinetic: %+13.6f' % Ekin)
t('XC: %+13.6f' % Exc)
t('Potential: %+13.6f' % e_coulomb)
t('-------------------------')
t('Total: %+13.6f' % (Ekin + Exc + e_coulomb))
self.ETotal = Ekin + Exc + e_coulomb
t()
t('state eigenvalue ekin rmax')
t('-----------------------------------------------')
for m, l, f, e, u in zip(n_j, l_j, f_j, e_j, self.u_j):
# Find kinetic energy:
k = e - np.sum((
np.where(abs(u) < 1e-160, 0, u)**2 * # XXXNumeric!
vr * dr)[1:] / r[1:])
# Find outermost maximum:
g = self.N - 4
while u[g - 1] >= u[g]:
g -= 1
x = 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)')
for m, l, u in zip(n_j, l_j, self.u_j):
self.write(u, 'ae', n=m, l=l)
self.write(n, 'n')
self.write(vr, 'vr')
self.write(vHr, 'vHr')
self.write(self.vXC, 'vXC')
self.write(tau, 'tau')
self.Ekin = Ekin
self.e_coulomb = e_coulomb
self.Exc = Exc
class AllElectron:
"""Object for doing an atomic DFT calculation."""
def __init__(self, symbol, xcname='LDA', scalarrel=False,
corehole=None, configuration=None, nofiles=True,
txt='-', gpernode=150, orbital_free=False, tf_coeff=1.):
"""Do an atomic DFT calculation.
Example::
a = AllElectron('Fe')
a.run()
"""
if txt is None:
txt = devnull
elif txt == '-':
txt = sys.stdout
elif isinstance(txt, str):
txt = open(txt, 'w')
self.txt = txt
self.symbol = symbol
self.xcname = xcname
self.scalarrel = scalarrel
self.nofiles = nofiles
# Get reference state:
self.Z, nlfe_j = configurations[symbol]
# Collect principal quantum numbers, angular momentum quantum
# numbers, occupation numbers and eigenvalues (j is a combined
# index for n and l):
self.n_j = [n for n, l, f, e in nlfe_j]
self.l_j = [l for n, l, f, e in nlfe_j]
self.f_j = [f for n, l, f, e in nlfe_j]
self.e_j = [e for n, l, f, e in nlfe_j]
if configuration is not None:
j = 0
for conf in configuration.split(','):
if conf[0].isdigit():
n = int(conf[0])
l = 'spdf'.find(conf[1])
if len(conf) == 2:
f = 1.0
else:
f = float(conf[2:])
#try:
assert n == self.n_j[j]
assert l == self.l_j[j]
self.f_j[j] = f
#except IndexError:
# self.n_j.append(n)
# self.l_j.append(l)
# self.f_j.append(f)
# self.e_j.append(self.e_j[-1])
j += 1
else:
j += {'He': 1,
'Ne': 3,
'Ar': 5,
'Kr': 8,
'Xe': 11}[conf]
maxnodes = max([n - l - 1 for n, l in zip(self.n_j, self.l_j)])
self.N = (maxnodes + 1) * gpernode
self.beta = 0.4
self.orbital_free = orbital_free
self.tf_coeff = tf_coeff
if self.orbital_free:
self.n_j = [1]
self.l_j = [0]
self.f_j = [self.Z]
self.e_j = [self.e_j[-1]]
t = self.text
t()
if scalarrel:
t('Scalar-relativistic atomic ', end='')
else:
t('Atomic ', end='')
t('%s calculation for %s (%s, Z=%d)' % (xcname, symbol,
atomic_names[self.Z], self.Z))
if corehole is not None:
self.ncorehole, self.lcorehole, self.fcorehole = corehole
# Find j for core hole and adjust occupation:
for j in range(len(self.f_j)):
if (self.n_j[j] == self.ncorehole and
self.l_j[j] == self.lcorehole):
assert self.f_j[j] == 2 * (2 * self.lcorehole + 1)
self.f_j[j] -= self.fcorehole
self.jcorehole = j
break
coreholestate = '%d%s' % (self.ncorehole, 'spdf'[self.lcorehole])
t('Core hole in %s state (%s occupation: %.1f)' % (
coreholestate, coreholestate, self.f_j[self.jcorehole]))
else:
self.jcorehole = None
self.fcorehole = 0
def text(self, *args, **kwargs):
self.txt.write(kwargs.get('sep', ' ').join([str(arg)
for arg in args]) +
kwargs.get('end', '\n'))
def initialize_wave_functions(self):
r = self.r
dr = self.dr
# Initialize with Slater function:
for l, e, u in zip(self.l_j, self.e_j, self.u_j):
if self.symbol in ['Hf', 'Ta', 'W', 'Re', 'Os',
'Ir', 'Pt', 'Au']:
a = sqrt(-4.0 * e)
else:
a = sqrt(-2.0 * e)
u[:] = r**(1 + l) * np.exp(-a * r)
norm = np.dot(u**2, dr)
u *= 1.0 / sqrt(norm)
def run(self, use_restart_file=True):
# beta g
# r = ------, g = 0, 1, ..., N - 1
# N - g
#
# rN
# g = --------
# beta + r
t = self.text
N = self.N
beta = self.beta
t(N, 'radial gridpoints.')
self.rgd = AERadialGridDescriptor(beta / N, 1.0 / N, N)
g = np.arange(N, dtype=float)
self.r = self.rgd.r_g
self.dr = self.rgd.dr_g
self.d2gdr2 = self.rgd.d2gdr2()
# Number of orbitals:
nj = len(self.n_j)
# Radial wave functions multiplied by radius:
self.u_j = np.zeros((nj, self.N))
# Effective potential multiplied by radius:
self.vr = np.zeros(N)
# Electron density:
self.n = np.zeros(N)
# Always spinpaired nspins=1
self.xc = XC(self.xcname)
# Initialize for non-local functionals
if self.xc.type == 'GLLB':
self.xc.pass_stuff_1d(self)
self.xc.initialize_1d()
n_j = self.n_j
l_j = self.l_j
f_j = self.f_j
e_j = self.e_j
Z = self.Z # nuclear charge
r = self.r # radial coordinate
dr = self.dr # dr/dg
n = self.n # electron density
vr = self.vr # effective potential multiplied by r
vHr = np.zeros(self.N)
self.vXC = np.zeros(self.N)
restartfile = '%s/%s.restart' % (tempdir, self.symbol)
if self.xc.type == 'GLLB' or not use_restart_file:
# Do not start from initial guess when doing
# non local XC!
# This is because we need wavefunctions as well
# on the first iteration.
fd = None
else:
try:
fd = open(restartfile, 'r')
except IOError:
fd = None
else:
try:
n[:] = pickle.load(fd)
except (ValueError, IndexError):
fd = None
else:
norm = np.dot(n * r**2, dr) * 4 * pi
if abs(norm - sum(f_j)) > 0.01:
fd = None
else:
t('Using old density for initial guess.')
n *= sum(f_j) / norm
if fd is None:
self.initialize_wave_functions()
n[:] = self.calculate_density()
bar = '|------------------------------------------------|'
t(bar)
niter = 0
nitermax = 117
qOK = log(1e-10)
mix = 0.4
# orbital_free needs more iterations and coefficient
if self.orbital_free:
#qOK = log(1e-14)
e_j[0] /= self.tf_coeff
mix = 0.01
nitermax = 1000
vrold = None
while True:
# calculate hartree potential
hartree(0, n * r * dr, r, vHr)
# add potential from nuclear point charge (v = -Z / r)
vHr -= Z
# calculated exchange correlation potential and energy
self.vXC[:] = 0.0
if self.xc.type == 'GLLB':
# Update the potential to self.vXC an the energy to self.Exc
Exc = self.xc.get_xc_potential_and_energy_1d(self.vXC)
else:
Exc = self.xc.calculate_spherical(self.rgd,
n.reshape((1, -1)),
self.vXC.reshape((1, -1)))
# calculate new total Kohn-Sham effective potential and
# admix with old version
vr[:] = (vHr + self.vXC * r) / self.tf_coeff
if niter > 0:
vr[:] = mix * vr + (1 - mix) * vrold
vrold = vr.copy()
# solve Kohn-Sham equation and determine the density change
self.solve()
dn = self.calculate_density() - n
n += dn
# estimate error from the square of the density change integrated
q = log(np.sum((r * dn)**2))
# print progress bar
if niter == 0:
q0 = q
b0 = 0
else:
b = int((q0 - q) / (q0 - qOK) * 50)
if b > b0:
self.txt.write(bar[b0:min(b, 50)])
self.txt.flush()
b0 = b
# check if converged and break loop if so
if q < qOK:
self.txt.write(bar[b0:])
self.txt.flush()
break
niter += 1
if niter > nitermax:
raise RuntimeError('Did not converge!')
tau = self.calculate_kinetic_energy_density()
t()
t('Converged in %d iteration%s.' % (niter, 's'[:niter != 1]))
try:
fd = open(restartfile, 'w')
except IOError:
pass
else:
pickle.dump(n, fd)
try:
os.chmod(restartfile, 0666)
except OSError:
pass
Ekin = 0
if self.orbital_free:
e_j[0] *= self.tf_coeff
vr *= self.tf_coeff
for f, e in zip(f_j, e_j):
Ekin += f * e
Epot = 2 * pi * np.dot(n * r * (vHr - Z), dr)
Ekin += -4 * pi * np.dot(n * vr * r, dr)
t()
t('Energy contributions:')
t('-------------------------')
t('Kinetic: %+13.6f' % Ekin)
t('XC: %+13.6f' % Exc)
t('Potential: %+13.6f' % Epot)
t('-------------------------')
t('Total: %+13.6f' % (Ekin + Exc + Epot))
self.ETotal = Ekin + Exc + Epot
t()
t('state eigenvalue ekin rmax')
t('-----------------------------------------------')
for m, l, f, e, u in zip(n_j, l_j, f_j, e_j, self.u_j):
# Find kinetic energy:
k = e - np.sum((np.where(abs(u) < 1e-160, 0, u)**2 * # XXXNumeric!
vr * dr)[1:] / r[1:])
# Find outermost maximum:
g = self.N - 4
while u[g - 1] >= u[g]:
g -= 1
x = 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)')
for m, l, u in zip(n_j, l_j, self.u_j):
self.write(u, 'ae', n=m, l=l)
self.write(n, 'n')
self.write(vr, 'vr')
self.write(vHr, 'vHr')
self.write(self.vXC, 'vXC')
self.write(tau, 'tau')
self.Ekin = Ekin
self.Epot = Epot
self.Exc = Exc
def write(self, array, name=None, n=None, l=None):
if self.nofiles:
return
if name:
name = self.symbol + '.' + name
else:
name = self.symbol
if l is not None:
assert n is not None
if n > 0:
# Bound state:
name += '.%d%s' % (n, 'spdf'[l])
else:
name += '.x%d%s' % (-n, 'spdf'[l])
f = open(name, 'w')
for r, a in zip(self.r, array):
print(r, a, file=f)
def calculate_density(self):
"""Return the electron charge density divided by 4 pi"""
n = np.dot(self.f_j,
np.where(abs(self.u_j) < 1e-160, 0,
self.u_j)**2) / (4 * pi)
n[1:] /= self.r[1:]**2
n[0] = n[1]
return n
def calculate_kinetic_energy_density(self):
"""Return the kinetic energy density"""
return self.radial_kinetic_energy_density(self.f_j, self.l_j, self.u_j)
def radial_kinetic_energy_density(self, f_j, l_j, u_j):
"""Kinetic energy density from a restricted set of wf's
"""
shape = np.shape(u_j[0])
dudr = np.zeros(shape)
tau = np.zeros(shape)
for f, l, u in zip(f_j, l_j, u_j):
self.rgd.derivative(u, dudr)
# contribution from angular derivatives
if l > 0:
tau += f * l * (l + 1) * np.where(abs(u) < 1e-160, 0, u)**2
# contribution from radial derivatives
dudr = u - self.r * dudr
tau += f * np.where(abs(dudr) < 1e-160, 0, dudr)**2
tau[1:] /= self.r[1:]**4
tau[0] = tau[1]
return 0.5 * tau / (4 * pi)
def calculate_kinetic_energy_density2(self):
"""Return the kinetic energy density
calculation over R(r)=u(r)/r
slower convergence with # of radial grid points for
Ekin of H than radial_kinetic_energy_density
"""
shape = self.u_j.shape[1]
R = np.zeros(shape)
dRdr = np.zeros(shape)
tau = np.zeros(shape)
for f, l, u in zip(self.f_j, self.l_j, self.u_j):
R[1:] = u[1:] / self.r[1:]
if l == 0:
# estimate value at origin by Taylor series to first order
d1 = self.r[1]
d2 = self.r[2]
R[0] = .5 * (R[1] + R[2] + (R[1] - R[2]) *
(d1 + d2) / (d2 - d1))
else:
R[0] = 0
self.rgd.derivative(R, dRdr)
# contribution from radial derivatives
tau += f * np.where(abs(dRdr) < 1e-160, 0, dRdr)**2
# contribution from angular derivatives
if l > 0:
R[1:] = R[1:] / self.r[1:]
if l == 1:
R[0] = R[1]
else:
R[0] = 0
tau += f * l * (l + 1) * np.where(abs(R) < 1e-160, 0, R)**2
return 0.5 * tau / (4 * pi)
def solve(self):
"""Solve the Schrodinger equation
::
2
d u 1 dv du u l(l + 1)
- --- - ---- -- (-- - -) + [-------- + 2M(v - e)] u = 0,
2 2 dr dr r 2
dr 2Mc r
where the relativistic mass::
1
M = 1 - --- (v - e)
2
2c
and the fine-structure constant alpha = 1/c = 1/137.036
is set to zero for non-scalar-relativistic calculations.
On the logaritmic radial grids defined by::
beta g
r = ------, g = 0, 1, ..., N - 1
N - g
rN
g = --------, r = [0; oo[
beta + r
the Schrodinger equation becomes::
2
d u du
--- c + -- c + u c = 0
2 2 dg 1 0
dg
with the vectors c0, c1, and c2 defined by::
2 dg 2
c = -r (--)
2 dr
2 2
d g 2 r dg dv
c = - --- r - ---- -- --
1 2 2 dr dr
dr 2Mc
2 r dv
c = l(l + 1) + 2M(v - e)r + ---- --
0 2 dr
2Mc
"""
r = self.r
dr = self.dr
vr = self.vr
c2 = -(r / dr)**2
c10 = -self.d2gdr2 * r**2 # first part of c1 vector
if self.scalarrel:
self.r2dvdr = np.zeros(self.N)
self.rgd.derivative(vr, self.r2dvdr)
self.r2dvdr *= r
self.r2dvdr -= vr
else:
self.r2dvdr = None
# solve for each quantum state separately
for j, (n, l, e, u) in enumerate(zip(self.n_j, self.l_j,
self.e_j, self.u_j)):
nodes = n - l - 1 # analytically expected number of nodes
delta = -0.2 * e
nn, A = shoot(u, l, vr, e, self.r2dvdr, r, dr, c10, c2,
self.scalarrel)
# adjust eigenenergy until u has the correct number of nodes
while nn != nodes:
diff = cmp(nn, nodes)
while diff == cmp(nn, nodes):
e -= diff * delta
nn, A = shoot(u, l, vr, e, self.r2dvdr, r, dr, c10, c2,
self.scalarrel)
delta /= 2
# adjust eigenenergy until u is smooth at the turning point
de = 1.0
while abs(de) > 1e-9:
norm = np.dot(np.where(abs(u) < 1e-160, 0, u)**2, dr)
u *= 1.0 / sqrt(norm)
de = 0.5 * A / norm
x = abs(de / e)
if x > 0.1:
de *= 0.1 / x
e -= de
assert e < 0.0
nn, A = shoot(u, l, vr, e, self.r2dvdr, r, dr, c10, c2,
self.scalarrel)
self.e_j[j] = e
u *= 1.0 / sqrt(np.dot(np.where(abs(u) < 1e-160, 0, u)**2, dr))
def solve_confined(self, j, rc, vconf=None):
"""Solve the Schroedinger equation in a confinement potential.
Solves the Schroedinger equation like the solve method, but with a
number of differences. Before invoking this method, run solve() to
get initial guesses.
Parameters:
j: solves only for the state given by j
rc: solution cutoff. Solution will be zero outside this.
vconf: added to the potential (use this as confinement potential)
Returns: a tuple containing the solution u and its energy e.
Unlike the solve method, this method will not alter any attributes of
this object.
"""
r = self.r
dr = self.dr
vr = self.vr.copy()
if vconf is not None:
vr += vconf * r
c2 = -(r / dr)**2
c10 = -self.d2gdr2 * r**2 # first part of c1 vector
if j is None:
n, l, e, u = 3, 2, -0.15, self.u_j[-1].copy()
else:
n = self.n_j[j]
l = self.l_j[j]
e = self.e_j[j]
u = self.u_j[j].copy()
nn, A = shoot_confined(u, l, vr, e, self.r2dvdr, r, dr, c10, c2,
self.scalarrel, rc=rc, beta=self.beta)
assert nn == n - l - 1 # run() should have been called already
# adjust eigenenergy until u is smooth at the turning point
de = 1.0
while abs(de) > 1e-9:
norm = np.dot(np.where(abs(u) < 1e-160, 0, u)**2, dr)
u *= 1.0 / sqrt(norm)
de = 0.5 * A / norm
x = abs(de / e)
if x > 0.1:
de *= 0.1 / x
e -= de
assert e < 0.0
nn, A = shoot_confined(u, l, vr, e, self.r2dvdr, r, dr, c10, c2,
self.scalarrel, rc=rc, beta=self.beta)
u *= 1.0 / sqrt(np.dot(np.where(abs(u) < 1e-160, 0, u)**2, dr))
return u, e
def kin(self, l, u, e=None): # XXX move to Generator
r = self.r[1:]
dr = self.dr[1:]
c0 = 0.5 * l * (l + 1) / r**2
c1 = -0.5 * self.d2gdr2[1:]
c2 = -0.5 * dr**-2
if e is not None and self.scalarrel:
x = 0.5 * alpha**2
Mr = r * (1.0 + x * e) - x * self.vr[1:]
c0 += ((Mr - r) * (self.vr[1:] - e * r) +
0.5 * x * self.r2dvdr[1:] / Mr) / r**2
c1 -= 0.5 * x * self.r2dvdr[1:] / (Mr * dr * r)
fp = c2 + 0.5 * c1
fm = c2 - 0.5 * c1
f0 = c0 - 2 * c2
kr = np.zeros(self.N)
kr[1:] = f0 * u[1:] + fm * u[:-1]
kr[1:-1] += fp[:-1] * u[2:]
kr[0] = 0.0
return kr
def r2g(self, r):
"""Convert radius to index of the radial grid."""
return int(r * self.N / (self.beta + r))
def get_confinement_potential(self, alpha, ri, rc):
"""Create a smooth confinement potential.
Returns a (potential) function which is zero inside the radius ri
and goes to infinity smoothly at rc, after which point it is nan.
The potential is given by::
alpha / rc - ri \
V(r) = -------- exp ( - --------- ) for ri < r < rc
rc - r \ r - ri /
"""
i_ri = self.r2g(ri)
i_rc = self.r2g(rc)
if self.r[i_rc] == rc:
# Avoid division by zero in the odd case that rc coincides
# exactly with a grid point (which actually happens sometimes)
i_rc -= 1
potential = np.zeros(np.shape(self.r))
r = self.r[i_ri + 1:i_rc + 1]
exponent = - (rc - ri) / (r - ri)
denom = rc - r
value = np.exp(exponent) / denom
potential[i_ri + 1:i_rc + 1] = value
potential[i_rc + 1:] = np.inf
return alpha * potential
def run(self, use_restart_file=True):
# beta g
# r = ------, g = 0, 1, ..., N - 1
# N - g
#
# rN
# g = --------
# beta + r
t = self.text
N = self.N
beta = self.beta
t(N, 'radial gridpoints.')
self.rgd = AERadialGridDescriptor(beta / N, 1.0 / N, N)
g = np.arange(N, dtype=float)
self.r = self.rgd.r_g
self.dr = self.rgd.dr_g
self.d2gdr2 = self.rgd.d2gdr2()
# Number of orbitals:
nj = len(self.n_j)
# Radial wave functions multiplied by radius:
self.u_j = np.zeros((nj, self.N))
# Effective potential multiplied by radius:
self.vr = np.zeros(N)
# Electron density:
self.n = np.zeros(N)
# Always spinpaired nspins=1
self.xc = XC(self.xcname)
# Initialize for non-local functionals
if self.xc.type == 'GLLB':
self.xc.pass_stuff_1d(self)
self.xc.initialize_1d()
n_j = self.n_j
l_j = self.l_j
f_j = self.f_j
e_j = self.e_j
Z = self.Z # nuclear charge
r = self.r # radial coordinate
dr = self.dr # dr/dg
n = self.n # electron density
vr = self.vr # effective potential multiplied by r
vHr = np.zeros(self.N)
self.vXC = np.zeros(self.N)
restartfile = '%s/%s.restart' % (tempdir, self.symbol)
if self.xc.type == 'GLLB' or not use_restart_file:
# Do not start from initial guess when doing
# non local XC!
# This is because we need wavefunctions as well
# on the first iteration.
fd = None
else:
try:
fd = open(restartfile, 'r')
except IOError:
fd = None
else:
try:
n[:] = pickle.load(fd)
except (ValueError, IndexError):
fd = None
else:
norm = np.dot(n * r**2, dr) * 4 * pi
if abs(norm - sum(f_j)) > 0.01:
fd = None
else:
t('Using old density for initial guess.')
n *= sum(f_j) / norm
if fd is None:
self.initialize_wave_functions()
n[:] = self.calculate_density()
bar = '|------------------------------------------------|'
t(bar)
niter = 0
nitermax = 117
qOK = log(1e-10)
mix = 0.4
# orbital_free needs more iterations and coefficient
if self.orbital_free:
#qOK = log(1e-14)
e_j[0] /= self.tf_coeff
mix = 0.01
nitermax = 1000
vrold = None
while True:
# calculate hartree potential
hartree(0, n * r * dr, r, vHr)
# add potential from nuclear point charge (v = -Z / r)
vHr -= Z
# calculated exchange correlation potential and energy
self.vXC[:] = 0.0
if self.xc.type == 'GLLB':
# Update the potential to self.vXC an the energy to self.Exc
Exc = self.xc.get_xc_potential_and_energy_1d(self.vXC)
else:
Exc = self.xc.calculate_spherical(self.rgd,
n.reshape((1, -1)),
self.vXC.reshape((1, -1)))
# calculate new total Kohn-Sham effective potential and
# admix with old version
vr[:] = (vHr + self.vXC * r) / self.tf_coeff
if niter > 0:
vr[:] = mix * vr + (1 - mix) * vrold
vrold = vr.copy()
# solve Kohn-Sham equation and determine the density change
self.solve()
dn = self.calculate_density() - n
n += dn
# estimate error from the square of the density change integrated
q = log(np.sum((r * dn)**2))
# print progress bar
if niter == 0:
q0 = q
b0 = 0
else:
b = int((q0 - q) / (q0 - qOK) * 50)
if b > b0:
self.txt.write(bar[b0:min(b, 50)])
self.txt.flush()
b0 = b
# check if converged and break loop if so
if q < qOK:
self.txt.write(bar[b0:])
self.txt.flush()
break
niter += 1
if niter > nitermax:
raise RuntimeError('Did not converge!')
tau = self.calculate_kinetic_energy_density()
t()
t('Converged in %d iteration%s.' % (niter, 's'[:niter != 1]))
try:
fd = open(restartfile, 'w')
except IOError:
pass
else:
pickle.dump(n, fd)
try:
os.chmod(restartfile, 0666)
except OSError:
pass
Ekin = 0
if self.orbital_free:
e_j[0] *= self.tf_coeff
vr *= self.tf_coeff
for f, e in zip(f_j, e_j):
Ekin += f * e
Epot = 2 * pi * np.dot(n * r * (vHr - Z), dr)
Ekin += -4 * pi * np.dot(n * vr * r, dr)
t()
t('Energy contributions:')
t('-------------------------')
t('Kinetic: %+13.6f' % Ekin)
t('XC: %+13.6f' % Exc)
t('Potential: %+13.6f' % Epot)
t('-------------------------')
t('Total: %+13.6f' % (Ekin + Exc + Epot))
self.ETotal = Ekin + Exc + Epot
t()
t('state eigenvalue ekin rmax')
t('-----------------------------------------------')
for m, l, f, e, u in zip(n_j, l_j, f_j, e_j, self.u_j):
# Find kinetic energy:
k = e - np.sum((np.where(abs(u) < 1e-160, 0, u)**2 * # XXXNumeric!
vr * dr)[1:] / r[1:])
# Find outermost maximum:
g = self.N - 4
while u[g - 1] >= u[g]:
g -= 1
x = 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)')
for m, l, u in zip(n_j, l_j, self.u_j):
self.write(u, 'ae', n=m, l=l)
self.write(n, 'n')
self.write(vr, 'vr')
self.write(vHr, 'vHr')
self.write(self.vXC, 'vXC')
self.write(tau, 'tau')
self.Ekin = Ekin
self.Epot = Epot
self.Exc = Exc
def __init__(self, data, xc, lmax=0, basis=None, filter=None):
self.type = data.name
self.HubU = None
if not data.is_compatible(xc):
raise ValueError('Cannot use %s setup with %s functional' %
(data.setupname, xc.get_setup_name()))
self.symbol = data.symbol
self.data = data
self.Nc = data.Nc
self.Nv = data.Nv
self.Z = data.Z
l_j = self.l_j = data.l_j
self.l_orb_j = data.l_orb_j
n_j = self.n_j = data.n_j
self.f_j = data.f_j
self.eps_j = data.eps_j
nj = self.nj = len(l_j)
rcut_j = self.rcut_j = data.rcut_j
self.ExxC = data.ExxC
self.X_p = data.X_p
self.orbital_free = data.orbital_free
pt_jg = data.pt_jg
phit_jg = data.phit_jg
phi_jg = data.phi_jg
self.fingerprint = data.fingerprint
self.filename = data.filename
rgd = self.rgd = data.rgd
r_g = rgd.r_g
dr_g = rgd.dr_g
self.lmax = lmax
rcutmax = max(rcut_j)
rcut2 = 2 * rcutmax
gcut2 = rgd.ceil(rcut2)
self.gcut2 = gcut2
self.gcutmin = rgd.ceil(min(rcut_j))
if data.generator_version < 2:
# Find Fourier-filter cutoff radius:
gcutfilter = data.get_max_projector_cutoff()
elif filter:
rc = rcutmax
filter(rgd, rc, data.vbar_g)
for l, pt_g in zip(l_j, pt_jg):
filter(rgd, rc, pt_g, l)
for l in range(max(l_j) + 1):
J = [j for j, lj in enumerate(l_j) if lj == l]
A_nn = [[
rgd.integrate(phit_jg[j1] * pt_jg[j2]) / 4 / pi for j1 in J
] for j2 in J]
B_nn = np.linalg.inv(A_nn)
pt_ng = np.dot(B_nn, [pt_jg[j] for j in J])
for n, j in enumerate(J):
pt_jg[j] = pt_ng[n]
gcutfilter = data.get_max_projector_cutoff()
else:
rcutfilter = max(rcut_j)
gcutfilter = rgd.ceil(rcutfilter)
self.rcutfilter = rcutfilter = r_g[gcutfilter]
assert (data.vbar_g[gcutfilter:] == 0).all()
ni = 0
i = 0
j = 0
jlL_i = []
for l, n in zip(l_j, n_j):
for m in range(2 * l + 1):
jlL_i.append((j, l, l**2 + m))
i += 1
j += 1
ni = i
self.ni = ni
_np = ni * (ni + 1) // 2
self.nq = nq = nj * (nj + 1) // 2
lcut = max(l_j)
if 2 * lcut < lmax:
lcut = (lmax + 1) // 2
self.lcut = lcut
self.B_ii = self.calculate_projector_overlaps(pt_jg)
self.fcorehole = data.fcorehole
self.lcorehole = data.lcorehole
if data.phicorehole_g is not None:
if self.lcorehole == 0:
self.calculate_oscillator_strengths(phi_jg)
else:
self.A_ci = None
# Construct splines:
self.vbar = rgd.spline(data.vbar_g, rcutfilter)
rcore, nc_g, nct_g, nct = self.construct_core_densities(data)
self.rcore = rcore
self.nct = nct
# Construct splines for core kinetic energy density:
tauct_g = data.tauct_g
self.tauct = rgd.spline(tauct_g, self.rcore)
self.pt_j = self.create_projectors(rcutfilter)
if basis is None:
basis = self.create_basis_functions(phit_jg, rcut2, gcut2)
phit_j = basis.tosplines()
self.phit_j = phit_j
self.basis = basis
self.nao = 0
for phit in self.phit_j:
l = phit.get_angular_momentum_number()
self.nao += 2 * l + 1
rgd2 = self.rgd2 = AERadialGridDescriptor(rgd.a, rgd.b, gcut2)
r_g = rgd2.r_g
dr_g = rgd2.dr_g
phi_jg = np.array([phi_g[:gcut2].copy() for phi_g in phi_jg])
phit_jg = np.array([phit_g[:gcut2].copy() for phit_g in phit_jg])
self.nc_g = nc_g = nc_g[:gcut2].copy()
self.nct_g = nct_g = nct_g[:gcut2].copy()
vbar_g = data.vbar_g[:gcut2].copy()
extra_xc_data = dict(data.extra_xc_data)
# Cut down the GLLB related extra data
for key, item in extra_xc_data.items():
if len(item) == rgd.N:
extra_xc_data[key] = item[:gcut2].copy()
self.extra_xc_data = extra_xc_data
self.phicorehole_g = data.phicorehole_g
if self.phicorehole_g is not None:
self.phicorehole_g = self.phicorehole_g[:gcut2].copy()
T_Lqp = self.calculate_T_Lqp(lcut, nq, _np, nj, jlL_i)
(g_lg, n_qg, nt_qg, Delta_lq, self.Lmax, self.Delta_pL, Delta0,
self.N0_p) = self.get_compensation_charges(phi_jg, phit_jg, _np,
T_Lqp)
self.Delta0 = Delta0
self.g_lg = g_lg
# Solves the radial poisson equation for density n_g
def H(n_g, l):
return rgd2.poisson(n_g, l) * r_g * dr_g
wnc_g = H(nc_g, l=0)
wnct_g = H(nct_g, l=0)
self.wg_lg = wg_lg = [H(g_lg[l], l) for l in range(lmax + 1)]
wn_lqg = [
np.array([H(n_qg[q], l) for q in range(nq)])
for l in range(2 * lcut + 1)
]
wnt_lqg = [
np.array([H(nt_qg[q], l) for q in range(nq)])
for l in range(2 * lcut + 1)
]
rdr_g = r_g * dr_g
dv_g = r_g * rdr_g
A = 0.5 * np.dot(nc_g, wnc_g)
A -= sqrt(4 * pi) * self.Z * np.dot(rdr_g, nc_g)
mct_g = nct_g + Delta0 * g_lg[0]
wmct_g = wnct_g + Delta0 * wg_lg[0]
A -= 0.5 * np.dot(mct_g, wmct_g)
self.M = A
self.MB = -np.dot(dv_g * nct_g, vbar_g)
AB_q = -np.dot(nt_qg, dv_g * vbar_g)
self.MB_p = np.dot(AB_q, T_Lqp[0])
# Correction for average electrostatic potential:
#
# dEH = dEH0 + dot(D_p, dEH_p)
#
self.dEH0 = sqrt(4 * pi) * (wnc_g - wmct_g -
sqrt(4 * pi) * self.Z * r_g * dr_g).sum()
dEh_q = (wn_lqg[0].sum(1) - wnt_lqg[0].sum(1) -
Delta_lq[0] * wg_lg[0].sum())
self.dEH_p = np.dot(dEh_q, T_Lqp[0]) * sqrt(4 * pi)
M_p, M_pp = self.calculate_coulomb_corrections(lcut, n_qg, wn_lqg,
lmax, Delta_lq, wnt_lqg,
g_lg, wg_lg, nt_qg, _np,
T_Lqp, nc_g, wnc_g,
rdr_g, mct_g, wmct_g)
self.M_p = M_p
self.M_pp = M_pp
if xc.type == 'GLLB':
if 'core_f' in self.extra_xc_data:
self.wnt_lqg = wnt_lqg
self.wn_lqg = wn_lqg
self.fc_j = self.extra_xc_data['core_f']
self.lc_j = self.extra_xc_data['core_l']
self.njcore = len(self.lc_j)
if self.njcore > 0:
self.uc_jg = self.extra_xc_data['core_states'].reshape(
(self.njcore, -1))
self.uc_jg = self.uc_jg[:, :gcut2]
self.phi_jg = phi_jg
self.Kc = data.e_kinetic_core - data.e_kinetic
self.M -= data.e_electrostatic
self.E = data.e_total
Delta0_ii = unpack(self.Delta_pL[:, 0].copy())
self.dO_ii = data.get_overlap_correction(Delta0_ii)
self.dC_ii = self.get_inverse_overlap_coefficients(
self.B_ii, self.dO_ii)
self.Delta_iiL = np.zeros((ni, ni, self.Lmax))
for L in range(self.Lmax):
self.Delta_iiL[:, :, L] = unpack(self.Delta_pL[:, L].copy())
self.Nct = data.get_smooth_core_density_integral(Delta0)
self.K_p = data.get_linear_kinetic_correction(T_Lqp[0])
r = 0.02 * rcut2 * np.arange(51, dtype=float)
alpha = data.rcgauss**-2
self.ghat_l = data.get_ghat(lmax, alpha, r, rcut2)
self.rcgauss = data.rcgauss
self.xc_correction = data.get_xc_correction(rgd2, xc, gcut2, lcut)
self.nabla_iiv = self.get_derivative_integrals(rgd2, phi_jg, phit_jg)
self.rnabla_iiv = self.get_magnetic_integrals(rgd2, phi_jg, phit_jg)
try:
from gpaw.lrtddft2.rxnabla import get_magnetic_integrals_new
self.rxnabla_iiv = get_magnetic_integrals_new(
self, rgd2, phi_jg, phit_jg)
except NotImplementedError:
self.rxnabla_iiv = None
