def __init__(self, name, hybrid=None, xc=None, finegrid=False):
"""Mix standard functionals with exact exchange.
name: str
Name of hybrid functional.
hybrid: float
Fraction of exact exchange.
xc: str or XCFunctional object
Standard DFT functional with scaled down exchange.
finegrid: boolean
Use fine grid for energy functional evaluations?
"""
if name == 'EXX':
assert hybrid is None and xc is None
hybrid = 1.0
xc = XC(XCNull())
elif name == 'PBE0':
assert hybrid is None and xc is None
hybrid = 0.25
xc = XC('HYB_GGA_XC_PBEH')
elif name == 'B3LYP':
assert hybrid is None and xc is None
hybrid = 0.2
xc = XC('HYB_GGA_XC_B3LYP')
if isinstance(xc, str):
xc = XC(xc)
self.hybrid = hybrid
self.xc = xc
self.type = xc.type
self.finegrid = finegrid
XCFunctional.__init__(self, name)
def initialize(self):
self.occupations = self.nlfunc.occupations
self.xc = XC(self.functional)
# Always 1 spin, no matter what calculation nspins is
self.vt_sg = self.nlfunc.finegd.empty(1)
self.e_g = self.nlfunc.finegd.empty() #.ravel()
def vxc(paw, xc=None, coredensity=True):
"""Calculate XC-contribution to eigenvalues."""
ham = paw.hamiltonian
dens = paw.density
wfs = paw.wfs
if xc is None:
xc = ham.xc
elif isinstance(xc, str):
xc = XC(xc)
if dens.nt_sg is None:
dens.interpolate_pseudo_density()
thisisatest = not True
if xc.orbital_dependent:
paw.get_xc_difference(xc)
# Calculate XC-potential:
vxct_sg = ham.finegd.zeros(wfs.nspins)
xc.calculate(dens.finegd, dens.nt_sg, vxct_sg)
vxct_sG = ham.gd.empty(wfs.nspins)
ham.restrict(vxct_sg, vxct_sG)
if thisisatest:
vxct_sG[:] = 1
# ... and PAW corrections:
dvxc_asii = {}
for a, D_sp in dens.D_asp.items():
dvxc_sp = np.zeros_like(D_sp)
xc.calculate_paw_correction(wfs.setups[a], D_sp, dvxc_sp, a=a,
addcoredensity=coredensity)
dvxc_asii[a] = [unpack(dvxc_p) for dvxc_p in dvxc_sp]
if thisisatest:
dvxc_asii[a] = [wfs.setups[a].dO_ii]
vxc_un = np.empty((wfs.kd.mynks, wfs.bd.mynbands))
for u, vxc_n in enumerate(vxc_un):
kpt = wfs.kpt_u[u]
vxct_G = vxct_sG[kpt.s]
for n in range(wfs.bd.mynbands):
psit_G = wfs._get_wave_function_array(u, n, realspace=True)
vxc_n[n] = wfs.gd.integrate((psit_G * psit_G.conj()).real,
vxct_G, global_integral=False)
for a, dvxc_sii in dvxc_asii.items():
P_ni = kpt.P_ani[a]
vxc_n += (np.dot(P_ni, dvxc_sii[kpt.s]) *
P_ni.conj()).sum(1).real
wfs.gd.comm.sum(vxc_un)
vxc_skn = wfs.kd.collect(vxc_un)
if xc.orbital_dependent:
vxc_skn += xc.exx_skn
return vxc_skn * Hartree
def create_setup(symbol, xc='LDA', lmax=0,
type='paw', basis=None, setupdata=None,
filter=None, world=None):
if isinstance(xc, str):
xc = XC(xc)
if isinstance(type, str) and ':' in type:
# Parse DFT+U parameters from type-string:
# Examples: "type:l,U" or "type:l,U,scale"
type, lu = type.split(':')
if type == '':
type = 'paw'
l = 'spdf'.find(lu[0])
assert lu[1] == ','
U = lu[2:]
if ',' in U:
U, scale = U.split(',')
else:
scale = True
U = float(U) / units.Hartree
scale = int(scale)
else:
U = None
if setupdata is None:
if type == 'hgh' or type == 'hgh.sc':
lmax = 0
from gpaw.hgh import HGHSetupData, setups, sc_setups
if type == 'hgh.sc':
table = sc_setups
else:
table = setups
parameters = table[symbol]
setupdata = HGHSetupData(parameters)
elif type == 'ah':
from gpaw.ah import AppelbaumHamann
ah = AppelbaumHamann()
ah.build(basis)
return ah
elif type == 'ae':
from gpaw.ae import HydrogenAllElectronSetup
assert symbol == 'H'
ae = HydrogenAllElectronSetup()
ae.build(basis)
return ae
elif type == 'ghost':
from gpaw.lcao.bsse import GhostSetupData
setupdata = GhostSetupData(symbol)
else:
setupdata = SetupData(symbol, xc.get_setup_name(),
type, True,
world=world)
if hasattr(setupdata, 'build'):
setup = LeanSetup(setupdata.build(xc, lmax, basis, filter))
if U is not None:
setup.set_hubbard_u(U, l, scale)
return setup
else:
return setupdata
def get_xc_difference(self, xc):
if isinstance(xc, str):
xc = XC(xc)
xc.initialize(self.density, self.hamiltonian, self.wfs,
self.occupations)
xc.set_positions(self.atoms.get_scaled_positions() % 1.0)
if xc.orbital_dependent:
self.converge_wave_functions()
return self.hamiltonian.get_xc_difference(xc, self.density) * Hartree
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)
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.gd = 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])
def linearize_to_xc(self, newxc):
"""Linearize Hamiltonian to difference XC functional.
Used in real time TDDFT to perform calculations with various kernels.
"""
if isinstance(newxc, str):
newxc = XC(newxc)
self.log('Linearizing xc-hamiltonian to ' + str(newxc))
newxc.initialize(self.density, self.hamiltonian, self.wfs,
self.occupations)
self.hamiltonian.linearize_to_xc(newxc, self.density)
def _calculate_fxc(self, gd, n_sG):
if self.functional == 'ALDA_x':
n_G = np.sum(n_sG, axis=0)
fx_G = -1. / 3. * (3. / np.pi)**(1. / 3.) * n_G**(-2. / 3.)
return fx_G
else:
fxc_sG = np.zeros_like(n_sG)
xc = XC(self.functional[1:])
xc.calculate_fxc(gd, n_sG, fxc_sG)
return fxc_sG[0]
def linearize_to_xc(self, newxc):
"""Linearize Hamiltonian to difference XC functional.
Used in real time TDDFT to perform calculations with various kernels.
"""
if isinstance(newxc, str):
newxc = XC(newxc)
self.txt.write('Linearizing xc-hamiltonian to ' + str(newxc))
newxc.initialize(self.density, self.hamiltonian, self.wfs,
self.occupations)
self.hamiltonian.linearize_to_xc(newxc, self.density)
def _calculate_pol_fxc(self, gd, n_sG, m_G):
""" Calculate polarized fxc """
assert np.shape(m_G) == np.shape(n_sG[0])
if self.functional == 'ALDA_x':
fx_G = - (6. / np.pi)**(1. / 3.) \
* (n_sG[0]**(1. / 3.) - n_sG[1]**(1. / 3.)) / m_G
return fx_G
else:
v_sG = np.zeros(np.shape(n_sG))
xc = XC(self.functional[1:])
xc.calculate(gd, n_sG, v_sg=v_sG)
return (v_sG[0] - v_sG[1]) / m_G
def forced_update(self):
"""Recalc yourself."""
if not self.force_ApmB:
Om = OmegaMatrix
name = 'LrTDDFT'
if self.xc:
xc = XC(self.xc)
if hasattr(xc, 'hybrid') and xc.hybrid > 0.0:
Om = ApmB
name = 'LrTDDFThyb'
else:
Om = ApmB
name = 'LrTDDFThyb'
self.kss = KSSingles(calculator=self.calculator,
nspins=self.nspins,
eps=self.eps,
istart=self.istart,
jend=self.jend,
energy_range=self.energy_range,
txt=self.txt)
self.Om = Om(self.calculator, self.kss,
self.xc, self.derivative_level, self.numscale,
finegrid=self.finegrid, eh_comm=self.eh_comm,
txt=self.txt)
self.name = name
def paired():
xc = XC('vdW-DF')
n = 0.3 * np.ones((1, N, N, N))
n += 0.01 * np.cos(np.arange(N) * 2 * pi / N)
v = 0.0 * n
E = xc.calculate(gd, n, v)
n2 = 1.0 * n
i = 1
n2[0, i, i, i] += 0.00002
x = v[0, i, i, i] * gd.dv
E2 = xc.calculate(gd, n2, v)
n2[0, i, i, i] -= 0.00004
E2 -= xc.calculate(gd, n2, v)
x2 = E2 / 0.00004
print i, x, x2, x - x2, x / x2
equal(x, x2, 5e-12)
def initialize(self):
self.occupations = self.nlfunc.occupations
self.xc = XC(self.functional)
# Always 1 spin, no matter what calculation nspins is
self.vt_sg = self.nlfunc.finegd.empty(1)
self.e_g = self.nlfunc.finegd.empty()#.ravel()
def paired():
xc = XC('vdW-DF')
n = 0.3 * np.ones((1, N, N, N))
n += 0.01 * np.cos(np.arange(N) * 2 * pi / N)
v = 0.0 * n
xc.calculate(gd, n, v)
n2 = 1.0 * n
i = 1
n2[0, i, i, i] += 0.00002
x = v[0, i, i, i] * gd.dv
E2 = xc.calculate(gd, n2, v)
n2[0, i, i, i] -= 0.00004
E2 -= xc.calculate(gd, n2, v)
x2 = E2 / 0.00004
print(i, x, x2, x - x2, x / x2)
equal(x, x2, 2e-11)
def get_xc_difference(self, xc):
if isinstance(xc, (str, dict)):
xc = XC(xc)
xc.set_grid_descriptor(self.density.finegd)
xc.initialize(self.density, self.hamiltonian, self.wfs,
self.occupations)
xc.set_positions(self.spos_ac)
if xc.orbital_dependent:
self.converge_wave_functions()
return self.hamiltonian.get_xc_difference(xc, self.density) * Ha
def polarized():
xc = XC('vdW-DF')
n = 0.04 * np.ones((2, N, N, N))
n[1] = 0.3
n[0] += 0.02 * np.sin(np.arange(N) * 2 * pi / N)
n[1] += 0.2 * np.cos(np.arange(N) * 2 * pi / N)
v = 0.0 * n
xc.calculate(gd, n, v)
n2 = 1.0 * n
i = 1
n2[0, i, i, i] += 0.00002
x = v[0, i, i, i] * gd.dv
E2 = xc.calculate(gd, n2, v)
n2[0, i, i, i] -= 0.00004
E2 -= xc.calculate(gd, n2, v)
x2 = E2 / 0.00004
print(i, x, x2, x - x2, x / x2)
equal(x, x2, 1e-10)
def polarized():
xc = XC('vdW-DF')
n = 0.04 * np.ones((2, N, N, N))
n[1] = 0.3
n[0] += 0.02 * np.sin(np.arange(N) * 2 * pi / N)
n[1] += 0.2 * np.cos(np.arange(N) * 2 * pi / N)
v = 0.0 * n
E = xc.calculate(gd, n, v)
n2 = 1.0 * n
i = 1
n2[0, i, i, i] += 0.00002
x = v[0, i, i, i] * gd.dv
E2 = xc.calculate(gd, n2, v)
n2[0, i, i, i] -= 0.00004
E2 -= xc.calculate(gd, n2, v)
x2 = E2 / 0.00004
print i, x, x2, x - x2, x / x2
equal(x, x2, 1e-10)
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 update(self,
calculator=None,
nspins=None,
eps=0.001,
istart=0,
jend=None,
energy_range=None,
xc=None,
derivative_level=None,
numscale=0.001):
changed = False
if self.calculator != calculator or \
self.nspins != nspins or \
self.eps != eps or \
self.istart != istart or \
self.jend != jend :
changed = True
if not changed: return
self.calculator = calculator
self.nspins = nspins
self.eps = eps
self.istart = istart
self.jend = jend
self.xc = xc
self.derivative_level = derivative_level
self.numscale = numscale
self.kss = KSSingles(calculator=calculator,
nspins=nspins,
eps=eps,
istart=istart,
jend=jend,
energy_range=energy_range,
txt=self.txt)
if not self.force_ApmB:
Om = OmegaMatrix
name = 'LrTDDFT'
if self.xc:
xc = XC(self.xc)
if hasattr(xc, 'hybrid') and xc.hybrid > 0.0:
Om = ApmB
name = 'LrTDDFThyb'
else:
Om = ApmB
name = 'LrTDDFThyb'
self.Om = Om(self.calculator,
self.kss,
self.xc,
self.derivative_level,
self.numscale,
finegrid=self.finegrid,
eh_comm=self.eh_comm,
txt=self.txt)
self.name = name
def get_non_xc_total_energies(self):
"""Compile non-XC total energy contributions"""
if self.e_dft is None:
self.e_dft = self.calc.get_potential_energy()
if self.e0 is None:
from gpaw.xc.kernel import XCNull
xc_null = XC(XCNull())
self.e0 = self.e_dft + self.calc.get_xc_difference(xc_null)
assert isinstance(self.e_dft, float)
assert isinstance(self.e0, float)
def propagate_single(self, dt):
# --------------
# Predictor step
# --------------
# 1. Calculate H(t)
self.save_wfs() # kpt.C2_nM = kpt.C_nM
# 2. H_MM(t) = <M|H(t)|H>
# Solve Psi(t+dt) from (S_MM - 0.5j*H_MM(t)*dt) Psi(t+dt) =
# (S_MM + 0.5j*H_MM(t)*dt) Psi(t)
for k, kpt in enumerate(self.wfs.kpt_u):
if self.fxc is not None:
if self.time == 0.0:
kpt.deltaXC_H_MM = self.get_hamiltonian(kpt)
self.hamiltonian.xc = XC(self.fxc)
self.update_hamiltonian()
assert len(self.wfs.kpt_u) == 1
kpt.deltaXC_H_MM -= self.get_hamiltonian(kpt)
self.update_hamiltonian()
# Call registered callback functions
self.call_observers(self.niter)
for k, kpt in enumerate(self.wfs.kpt_u):
kpt.H0_MM = self.get_hamiltonian(kpt)
if self.fxc is not None:
kpt.H0_MM += kpt.deltaXC_H_MM
self.propagate_wfs(kpt.C_nM, kpt.C_nM, kpt.S_MM, kpt.H0_MM, dt)
# ---------------
# Propagator step
# ---------------
# 1. Calculate H(t+dt)
self.update_hamiltonian()
# 2. Estimate H(t+0.5*dt) ~ H(t) + H(t+dT)
for k, kpt in enumerate(self.wfs.kpt_u):
kpt.H0_MM *= 0.5
if self.fxc is not None:
# Store this to H0_MM and maybe save one extra H_MM of
# memory?
kpt.H0_MM += 0.5 * (self.get_hamiltonian(kpt) +
kpt.deltaXC_H_MM)
else:
# Store this to H0_MM and maybe save one extra H_MM of
# memory?
kpt.H0_MM += 0.5 * self.get_hamiltonian(kpt)
# 3. Solve Psi(t+dt) from
# (S_MM - 0.5j*H_MM(t+0.5*dt)*dt) Psi(t+dt)
# = (S_MM + 0.5j*H_MM(t+0.5*dt)*dt) Psi(t)
self.propagate_wfs(kpt.C2_nM, kpt.C_nM, kpt.S_MM, kpt.H0_MM, dt)
self.niter += 1
self.time += dt
def get_density(self, atom_indices=None, gridrefinement=2):
"""Get sum of atomic densities from the given atom list.
All atoms are taken if the list is not given."""
all_atoms = self.calculator.get_atoms()
if atom_indices is None:
atom_indices = range(len(all_atoms))
density = self.calculator.density
spos_ac = all_atoms.get_scaled_positions()
rank_a = self.finegd.get_ranks_from_positions(spos_ac)
density.set_positions(all_atoms.get_scaled_positions(),
AtomPartition(self.finegd.comm, rank_a))
# select atoms
atoms = []
D_asp = {}
rank_a = []
all_D_asp = self.calculator.density.D_asp
all_rank_a = self.calculator.density.atom_partition.rank_a
for a in atom_indices:
if a in all_D_asp:
D_asp[len(atoms)] = all_D_asp.get(a)
atoms.append(all_atoms[a])
rank_a.append(all_rank_a[a])
atoms = Atoms(atoms,
cell=all_atoms.get_cell(),
pbc=all_atoms.get_pbc())
spos_ac = atoms.get_scaled_positions()
Z_a = atoms.get_atomic_numbers()
par = self.calculator.parameters
setups = Setups(Z_a, par.setups, par.basis, XC(par.xc),
self.calculator.wfs.world)
# initialize
self.initialize(setups, self.calculator.timer, np.zeros(len(atoms)),
False)
self.set_mixer(None)
# FIXME nparray causes partitionong.py test to fail
self.set_positions(spos_ac, AtomPartition(self.gd.comm, rank_a))
self.D_asp = D_asp
basis_functions = BasisFunctions(
self.gd, [setup.phit_j for setup in self.setups], cut=True)
basis_functions.set_positions(spos_ac)
self.initialize_from_atomic_densities(basis_functions)
aed_sg, gd = self.get_all_electron_density(atoms, gridrefinement)
return aed_sg.sum(axis=0), gd
def mbeef_exchange_energy_contribs(self):
"""Legendre polynomial exchange contributions to mBEEF Etot"""
self.get_non_xc_total_energies()
e_x = np.zeros((self.max_order, self.max_order))
for p1 in range(self.max_order): # alpha
for p2 in range(self.max_order): # s2
pars_i = np.array([1, self.trans[0], p2, 1.0])
pars_j = np.array([1, self.trans[1], p1, 1.0])
pars = np.hstack((pars_i, pars_j))
x = XC('2D-MGGA', pars)
e_x[p1, p2] = (self.e_dft + self.calc.get_xc_difference(x) -
self.e0)
del x
return e_x
def beefvdw_energy_contribs_x(self):
"""Legendre polynomial exchange contributions to BEEF-vdW Etot"""
self.get_non_xc_total_energies()
e_pbe = (self.e_dft + self.calc.get_xc_difference('GGA_C_PBE') -
self.e0)
exch = np.zeros(30)
for p in range(30):
pars = [4, 0, p, 1.0]
bee = XC('BEE2', pars)
exch[p] = (self.e_dft + self.calc.get_xc_difference(bee) -
self.e0 - e_pbe)
del bee
return exch
def __init__(self, xc='LDA', finegrid=False, **parameters):
"""Self-Interaction Corrected Functionals (PZ-SIC).
finegrid: boolean
Use fine grid for energy functional evaluations?
"""
if isinstance(xc, str):
xc = XC(xc)
self.xc = xc
self.type = xc.type
XCFunctional.__init__(self, xc.name + '-PZ-SIC')
self.finegrid = finegrid
self.parameters = parameters
def get_xc_difference(self, xc):
if isinstance(xc, str):
xc = XC(xc)
xc.initialize(self.density, self.hamiltonian, self.wfs,
self.occupations)
xc.set_positions(self.atoms.get_scaled_positions() % 1.0)
if xc.orbital_dependent:
self.converge_wave_functions()
return self.hamiltonian.get_xc_difference(xc, self.density) * Hartree
def get_radial_potential(calc, a, ai):
"""Calculates dV/dr / r for the effective potential.
Below, f_g denotes dV/dr = minus the radial force"""
rgd = a.xc_correction.rgd
r_g = rgd.r_g
r_g[0] = 1.0e-12
dr_g = rgd.dr_g
Ns = calc.wfs.nspins
D_sp = calc.density.D_asp[ai]
B_pq = a.xc_correction.B_pqL[:, :, 0]
n_qg = a.xc_correction.n_qg
D_sq = np.dot(D_sp, B_pq)
n_sg = np.dot(D_sq, n_qg) / (4 * np.pi)**0.5
n_sg[:] += a.xc_correction.nc_g / Ns
# Coulomb force from nucleus
fc_g = a.Z / r_g**2
# Hartree force
rho_g = 4 * np.pi * r_g**2 * dr_g * np.sum(n_sg, axis=0)
fh_g = -np.array([np.sum(rho_g[:ig]) for ig in range(len(r_g))]) / r_g**2
# xc force
xc = XC(calc.get_xc_functional())
v_sg = np.zeros_like(n_sg)
xc.calculate_spherical(a.xc_correction.rgd, n_sg, v_sg)
fxc_sg = np.array([a.xc_correction.rgd.derivative(v_sg[s])
for s in range(Ns)])
fxc_g = np.sum(fxc_sg, axis=0) / Ns
# f_sg = np.tile(fc_g, (Ns, 1)) + np.tile(fh_g, (Ns, 1)) + fxc_sg
f_sg = np.tile(fc_g + fh_g + fxc_g, (Ns, 1))
return f_sg[:] / r_g
def get_density(self, atom_indicees=None):
"""Get sum of atomic densities from the given atom list.
All atoms are taken if the list is not given."""
all_atoms = self.calculator.get_atoms()
if atom_indicees is None:
atom_indicees = range(len(all_atoms))
density = self.calculator.density
density.set_positions(all_atoms.get_scaled_positions() % 1.0,
self.calculator.wfs.rank_a)
# select atoms
atoms = []
D_asp = {}
rank_a = []
all_D_asp = self.calculator.density.D_asp
all_rank_a = self.calculator.density.rank_a
for a in atom_indicees:
if a in all_D_asp:
D_asp[len(atoms)] = all_D_asp.get(a)
atoms.append(all_atoms[a])
rank_a.append(all_rank_a[a])
atoms = Atoms(atoms, cell=all_atoms.get_cell())
spos_ac = atoms.get_scaled_positions() % 1.0
Z_a = atoms.get_atomic_numbers()
par = self.calculator.input_parameters
setups = Setups(Z_a, par.setups, par.basis, par.lmax, XC(par.xc),
self.calculator.wfs.world)
self.D_asp = D_asp
# initialize
self.initialize(setups, par.stencils[1], self.calculator.timer,
[0] * len(atoms), False)
self.set_mixer(None)
self.set_positions(spos_ac, rank_a)
basis_functions = BasisFunctions(
self.gd, [setup.phit_j for setup in self.setups], cut=True)
basis_functions.set_positions(spos_ac)
self.initialize_from_atomic_densities(basis_functions)
aed_sg, gd = Density.get_all_electron_density(self,
atoms,
gridrefinement=2)
return aed_sg[0], gd
def __init__(self, xc='LDA', finegrid=False, **parameters):
"""Self-Interaction Corrected Functionals (PZ-SIC).
finegrid: boolean
Use fine grid for energy functional evaluations?
"""
if isinstance(xc, basestring):
xc = XC(xc)
if xc.orbital_dependent:
raise ValueError('SIC does not support ' + xc.name)
self.xc = xc
XCFunctional.__init__(self, xc.name + '-PZ-SIC', xc.type)
self.finegrid = finegrid
self.parameters = parameters
def get_density(self, atom_indices=None, gridrefinement=2):
"""Get sum of atomic densities from the given atom list.
Parameters
----------
atom_indices : list_like
All atoms are taken if the list is not given.
gridrefinement : 1, 2, 4
Gridrefinement given to get_all_electron_density
Returns
-------
type
spin summed density, grid_descriptor
"""
all_atoms = self.calculator.get_atoms()
if atom_indices is None:
atom_indices = range(len(all_atoms))
# select atoms
atoms = self.calculator.get_atoms()[atom_indices]
spos_ac = atoms.get_scaled_positions()
Z_a = atoms.get_atomic_numbers()
par = self.calculator.parameters
setups = Setups(Z_a, par.setups, par.basis, XC(par.xc),
self.calculator.wfs.world)
# initialize
self.initialize(setups, self.calculator.timer, np.zeros(
(len(atoms), 3)), False)
self.set_mixer(None)
rank_a = self.gd.get_ranks_from_positions(spos_ac)
self.set_positions(spos_ac, AtomPartition(self.gd.comm, rank_a))
basis_functions = BasisFunctions(
self.gd, [setup.phit_j for setup in self.setups], cut=True)
basis_functions.set_positions(spos_ac)
self.initialize_from_atomic_densities(basis_functions)
aed_sg, gd = self.get_all_electron_density(atoms, gridrefinement)
return aed_sg.sum(axis=0), gd
def get_libvdwxc_functional(name, **kwargs):
if 'name' in kwargs:
name2 = kwargs.pop('name')
assert name == name2
funcs = {
'vdW-DF': vdw_df,
'vdW-DF2': vdw_df2,
'vdW-DF-cx': vdw_df_cx,
'optPBE-vdW': vdw_optPBE,
'optB88-vdW': vdw_optB88,
'C09-vdW': vdw_C09,
'BEEF-vdW': vdw_beef,
'mBEEF-vdW': vdw_mbeef
}
semilocal_xc = kwargs.pop('semilocal_xc', None)
if semilocal_xc is not None:
from gpaw.xc import XC
semilocal_xc = XC(semilocal_xc)
func = funcs[name](**kwargs)
if semilocal_xc is not None:
assert semilocal_xc.name == func.semilocal_xc.name
return func
def __init__(self, name, hybrid=None, xc=None, omega=None):
"""Mix standard functionals with exact exchange.
name: str
Name of hybrid functional.
hybrid: float
Fraction of exact exchange.
xc: str or XCFunctional object
Standard DFT functional with scaled down exchange.
"""
if name == 'EXX':
assert hybrid is None and xc is None
hybrid = 1.0
xc = XC(XCNull())
elif name == 'PBE0':
assert hybrid is None and xc is None
hybrid = 0.25
xc = XC('HYB_GGA_XC_PBEH')
elif name == 'B3LYP':
assert hybrid is None and xc is None
hybrid = 0.2
xc = XC('HYB_GGA_XC_B3LYP')
elif name == 'HSE03':
assert hybrid is None and xc is None and omega is None
hybrid = 0.25
omega = 0.106
xc = XC('HYB_GGA_XC_HSE03')
elif name == 'HSE06':
assert hybrid is None and xc is None and omega is None
hybrid = 0.25
omega = 0.11
xc = XC('HYB_GGA_XC_HSE06')
if isinstance(xc, str):
xc = XC(xc)
self.hybrid = float(hybrid)
self.xc = xc
self.omega = omega
self.type = xc.type
XCFunctional.__init__(self, name)
def initialize_fxc(self, niter):
self.has_fxc = self.fxc_name is not None
if not self.has_fxc:
return
self.timer.start('Initialize fxc')
# XXX: Similar functionality is available in
# paw.py: PAW.linearize_to_xc(self, newxc)
# See test/lcaotddft/fxc_vs_linearize.py
get_H_MM = self.get_hamiltonian_matrix
# Calculate deltaXC: 1. take current H_MM
if niter == 0:
self.deltaXC_H_uMM = [None] * len(self.wfs.kpt_u)
for u, kpt in enumerate(self.wfs.kpt_u):
self.deltaXC_H_uMM[u] = get_H_MM(kpt, addfxc=False)
# Update hamiltonian.xc
if self.fxc_name == 'RPA':
xc_name = 'null'
else:
xc_name = self.fxc_name
# XXX: xc is not written to the gpw file
# XXX: so we need to set it always
xc = XC(xc_name)
xc.initialize(self.density, self.hamiltonian, self.wfs,
self.occupations)
xc.set_positions(self.hamiltonian.spos_ac)
self.hamiltonian.xc = xc
self.update()
# Calculate deltaXC: 2. update with new H_MM
if niter == 0:
for u, kpt in enumerate(self.wfs.kpt_u):
self.deltaXC_H_uMM[u] -= get_H_MM(kpt, addfxc=False)
self.timer.stop('Initialize fxc')
def calculate_Kxc(gd,
nt_sG,
npw,
Gvec_Gc,
nG,
vol,
bcell_cv,
R_av,
setups,
D_asp,
functional='ALDA',
density_cut=None):
"""ALDA kernel"""
# The soft part
#assert np.abs(nt_sG[0].shape - nG).sum() == 0
if functional == 'ALDA_X':
x_only = True
A_x = -3. / 4. * (3. / np.pi)**(1. / 3.)
nspins = len(nt_sG)
assert nspins in [1, 2]
fxc_sg = nspins**(1. / 3.) * 4. / 9. * A_x * nt_sG**(-2. / 3.)
else:
assert len(nt_sG) == 1
x_only = False
fxc_sg = np.zeros_like(nt_sG)
xc = XC(functional[1:])
xc.calculate_fxc(gd, nt_sG, fxc_sg)
if density_cut is not None:
fxc_sg[np.where(nt_sG * len(nt_sG) < density_cut)] = 0.0
# FFT fxc(r)
nG0 = nG[0] * nG[1] * nG[2]
tmp_sg = [np.fft.fftn(fxc_sg[s]) * vol / nG0 for s in range(len(nt_sG))]
r_vg = gd.get_grid_point_coordinates()
Kxc_sGG = np.zeros((len(fxc_sg), npw, npw), dtype=complex)
for s in range(len(fxc_sg)):
for iG in range(npw):
for jG in range(npw):
dG_c = Gvec_Gc[iG] - Gvec_Gc[jG]
if (nG / 2 - np.abs(dG_c) > 0).all():
index = (dG_c + nG) % nG
Kxc_sGG[s, iG, jG] = tmp_sg[s][index[0],
index[1],
index[2]]
else: # not in the fft index
dG_v = np.dot(dG_c, bcell_cv)
dGr_g = gemmdot(dG_v, r_vg, beta=0.0)
Kxc_sGG[s, iG, jG] = gd.integrate(np.exp(-1j * dGr_g)
* fxc_sg[s])
# The PAW part
KxcPAW_sGG = np.zeros_like(Kxc_sGG)
dG_GGv = np.zeros((npw, npw, 3))
for iG in range(npw):
for jG in range(npw):
dG_c = Gvec_Gc[iG] - Gvec_Gc[jG]
dG_GGv[iG, jG] = np.dot(dG_c, bcell_cv)
for a, setup in enumerate(setups):
if rank == a % size:
rgd = setup.xc_correction.rgd
n_qg = setup.xc_correction.n_qg
nt_qg = setup.xc_correction.nt_qg
nc_g = setup.xc_correction.nc_g
nct_g = setup.xc_correction.nct_g
Y_nL = setup.xc_correction.Y_nL
dv_g = rgd.dv_g
D_sp = D_asp[a]
B_pqL = setup.xc_correction.B_pqL
D_sLq = np.inner(D_sp, B_pqL.T)
nspins = len(D_sp)
f_sg = rgd.empty(nspins)
ft_sg = rgd.empty(nspins)
n_sLg = np.dot(D_sLq, n_qg)
nt_sLg = np.dot(D_sLq, nt_qg)
# Add core density
n_sLg[:, 0] += np.sqrt(4. * np.pi) / nspins * nc_g
nt_sLg[:, 0] += np.sqrt(4. * np.pi) / nspins * nct_g
coefatoms_GG = np.exp(-1j * np.inner(dG_GGv, R_av[a]))
for n, Y_L in enumerate(Y_nL):
w = weight_n[n]
f_sg[:] = 0.0
n_sg = np.dot(Y_L, n_sLg)
if x_only:
f_sg = nspins * (4 / 9.) * A_x * (nspins * n_sg)**(-2 / 3.)
else:
xc.calculate_fxc(rgd, n_sg, f_sg)
ft_sg[:] = 0.0
nt_sg = np.dot(Y_L, nt_sLg)
if x_only:
ft_sg = nspins * (4 / 9.) * (A_x
* (nspins * nt_sg)**(-2 / 3.))
else:
xc.calculate_fxc(rgd, nt_sg, ft_sg)
for i in range(len(rgd.r_g)):
coef_GG = np.exp(-1j * np.inner(dG_GGv, R_nv[n])
* rgd.r_g[i])
for s in range(len(f_sg)):
KxcPAW_sGG[s] += w * np.dot(coef_GG,
(f_sg[s, i] -
ft_sg[s, i])
* dv_g[i]) * coefatoms_GG
world.sum(KxcPAW_sGG)
Kxc_sGG += KxcPAW_sGG
return Kxc_sGG / vol
def calculate_Kxc(gd, nt_sG, npw, Gvec_Gc, nG, vol,
bcell_cv, R_av, setups, D_asp):
"""LDA kernel"""
# The soft part
assert np.abs(nt_sG[0].shape - nG).sum() == 0
xc = XC('LDA')
fxc_sg = np.zeros_like(nt_sG)
xc.calculate_fxc(gd, nt_sG, fxc_sg)
fxc_g = fxc_sg[0]
# FFT fxc(r)
nG0 = nG[0] * nG[1] * nG[2]
tmp_g = np.fft.fftn(fxc_g) * vol / nG0
r_vg = gd.get_grid_point_coordinates()
Kxc_GG = np.zeros((npw, npw), dtype=complex)
for iG in range(npw):
for jG in range(npw):
dG_c = Gvec_Gc[iG] - Gvec_Gc[jG]
if (nG / 2 - np.abs(dG_c) > 0).all():
index = (dG_c + nG) % nG
Kxc_GG[iG, jG] = tmp_g[index[0], index[1], index[2]]
else: # not in the fft index
dG_v = np.dot(dG_c, bcell_cv)
dGr_g = gemmdot(dG_v, r_vg, beta=0.0)
Kxc_GG[iG, jG] = gd.integrate(np.exp(-1j*dGr_g)*fxc_g)
KxcPAW_GG = np.zeros_like(Kxc_GG)
# The PAW part
dG_GGv = np.zeros((npw, npw, 3))
for iG in range(npw):
for jG in range(npw):
dG_c = Gvec_Gc[iG] - Gvec_Gc[jG]
dG_GGv[iG, jG] = np.dot(dG_c, bcell_cv)
for a, setup in enumerate(setups):
if rank == a % size:
rgd = setup.xc_correction.rgd
n_qg = setup.xc_correction.n_qg
nt_qg = setup.xc_correction.nt_qg
nc_g = setup.xc_correction.nc_g
nct_g = setup.xc_correction.nct_g
Y_nL = setup.xc_correction.Y_nL
dv_g = rgd.dv_g
D_sp = D_asp[a]
B_pqL = setup.xc_correction.B_pqL
D_sLq = np.inner(D_sp, B_pqL.T)
nspins = len(D_sp)
assert nspins == 1
f_sg = rgd.empty(nspins)
ft_sg = rgd.empty(nspins)
n_sLg = np.dot(D_sLq, n_qg)
nt_sLg = np.dot(D_sLq, nt_qg)
# Add core density
n_sLg[:, 0] += sqrt(4 * pi) / nspins * nc_g
nt_sLg[:, 0] += sqrt(4 * pi) / nspins * nct_g
coefatoms_GG = np.exp(-1j * np.inner(dG_GGv, R_av[a]))
for n, Y_L in enumerate(Y_nL):
w = weight_n[n]
f_sg[:] = 0.0
n_sg = np.dot(Y_L, n_sLg)
xc.calculate_fxc(rgd, n_sg, f_sg)
ft_sg[:] = 0.0
nt_sg = np.dot(Y_L, nt_sLg)
xc.calculate_fxc(rgd, nt_sg, ft_sg)
coef_GGg = np.exp(-1j * np.outer(np.inner(dG_GGv, R_nv[n]),
rgd.r_g)).reshape(npw,npw,rgd.ng)
KxcPAW_GG += w * np.dot(coef_GGg, (f_sg[0]-ft_sg[0]) * dv_g) * coefatoms_GG
world.sum(KxcPAW_GG)
Kxc_GG += KxcPAW_GG
return Kxc_GG / vol
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
from __future__ import print_function
from math import pi
from gpaw.atom.radialgd import EquidistantRadialGridDescriptor
from gpaw.grid_descriptor import GridDescriptor
from gpaw.xc import XC
import numpy as np
from gpaw.test import equal
rgd = EquidistantRadialGridDescriptor(0.01, 100)
for name in ['LDA', 'PBE']:
xc = XC(name)
for nspins in [1, 2]:
n = rgd.zeros(nspins)
v = rgd.zeros(nspins)
n[:] = np.exp(-rgd.r_g**2)
n[-1] *= 2
E = xc.calculate_spherical(rgd, n, v)
i = 23
x = v[-1, i] * rgd.dv_g[i]
n[-1, i] += 0.000001
Ep = xc.calculate_spherical(rgd, n, v)
n[-1, i] -= 0.000002
Em = xc.calculate_spherical(rgd, n, v)
x2 = (Ep - Em) / 0.000002
print(name, nspins, E, x, x2, x - x2)
equal(x, x2, 1e-9)
n[-1, i] += 0.000001
if nspins == 1:
ns = rgd.empty(2)
ns[:] = n / 2
# -------------------------------------------------------------------
from gpaw.test.ut_common import ase_svnversion, shapeopt, TestCase, \
TextTestRunner, CustomTextTestRunner, defaultTestLoader, \
initialTestLoader, create_random_atoms, create_parsize_maxbands
memstats = False
if memstats:
# Developer use of this feature requires ASE 3.1.0 svn.rev. 905 or later.
assert ase_svnversion >= 905 # wasn't bug-free untill 973!
from ase.utils.memory import MemorySingleton, MemoryStatistics
# -------------------------------------------------------------------
p = InputParameters(spinpol=False)
xc = XC(p.xc)
p.setups = dict([(symbol, SetupData(symbol, xc.name)) for symbol in 'HO'])
class UTBandParallelSetup(TestCase):
"""
Setup a simple band parallel calculation."""
# Number of bands
nbands = 36
# Spin-paired, single kpoint
nspins = 1
nibzkpts = 1
# Strided or blocked groups
def initialize_1d(self):
self.ae = self.nlfunc.ae
self.xc = XC(self.functional)
self.v_g = np.zeros(self.ae.N)
self.e_g = np.zeros(self.ae.N)
from __future__ import print_function
import numpy as np
import numpy.random as ra
from gpaw.setup import create_setup
from gpaw.xc import XC
from gpaw.test import equal
x = 0.000001
ra.seed(8)
for xc in ['LDA', 'PBE']:
print(xc)
xc = XC(xc)
s = create_setup('N', xc)
ni = s.ni
nii = ni * (ni + 1) // 2
D_p = 0.1 * ra.random(nii) + 0.2
H_p = np.zeros(nii)
E = xc.calculate_paw_correction(s, D_p.reshape(1, -1), H_p.reshape(1, -1))
dD_p = x * ra.random(nii)
dE = np.dot(H_p, dD_p) / x
D_p += dD_p
Ep = xc.calculate_paw_correction(s, D_p.reshape(1, -1))
D_p -= 2 * dD_p
Em = xc.calculate_paw_correction(s, D_p.reshape(1, -1))
print(dE, dE - 0.5 * (Ep - Em) / x)
equal(dE, 0.5 * (Ep - Em) / x, 1e-6)
Ems = xc.calculate_paw_correction(s, np.array([0.5 * D_p, 0.5 * D_p]))
print(Em - Ems)
def calculate_Kxc(pd, nt_sG, R_av, setups, D_asp, functional='ALDA',
density_cut=None):
"""ALDA kernel"""
gd = pd.gd
npw = pd.ngmax
nG = pd.gd.N_c
vol = pd.gd.volume
bcell_cv = np.linalg.inv(pd.gd.cell_cv)
G_Gv = pd.get_reciprocal_vectors()
# The soft part
#assert np.abs(nt_sG[0].shape - nG).sum() == 0
if functional == 'ALDA_X':
x_only = True
A_x = -3. / 4. * (3. / np.pi)**(1. / 3.)
nspins = len(nt_sG)
assert nspins in [1, 2]
fxc_sg = nspins**(1. / 3.) * 4. / 9. * A_x * nt_sG**(-2. / 3.)
else:
assert len(nt_sG) == 1
x_only = False
fxc_sg = np.zeros_like(nt_sG)
xc = XC(functional[1:])
xc.calculate_fxc(gd, nt_sG, fxc_sg)
if density_cut is not None:
fxc_sg[np.where(nt_sG * len(nt_sG) < density_cut)] = 0.0
# FFT fxc(r)
nG0 = nG[0] * nG[1] * nG[2]
tmp_sg = [np.fft.fftn(fxc_sg[s]) * vol / nG0 for s in range(len(nt_sG))]
r_vg = gd.get_grid_point_coordinates()
Kxc_sGG = np.zeros((len(fxc_sg), npw, npw), dtype=complex)
for s in range(len(fxc_sg)):
for iG, iQ in enumerate(pd.Q_qG[0]):
iQ_c = (np.unravel_index(iQ, nG) + nG // 2) % nG - nG // 2
for jG, jQ in enumerate(pd.Q_qG[0]):
jQ_c = (np.unravel_index(jQ, nG) + nG // 2) % nG - nG // 2
ijQ_c = (iQ_c - jQ_c)
if (abs(ijQ_c) < nG // 2).all():
Kxc_sGG[s, iG, jG] = tmp_sg[s][tuple(ijQ_c)]
# The PAW part
KxcPAW_sGG = np.zeros_like(Kxc_sGG)
dG_GGv = np.zeros((npw, npw, 3))
for v in range(3):
dG_GGv[:, :, v] = np.subtract.outer(G_Gv[:, v], G_Gv[:, v])
for a, setup in enumerate(setups):
if rank == a % size:
rgd = setup.xc_correction.rgd
n_qg = setup.xc_correction.n_qg
nt_qg = setup.xc_correction.nt_qg
nc_g = setup.xc_correction.nc_g
nct_g = setup.xc_correction.nct_g
Y_nL = setup.xc_correction.Y_nL
dv_g = rgd.dv_g
D_sp = D_asp[a]
B_pqL = setup.xc_correction.B_pqL
D_sLq = np.inner(D_sp, B_pqL.T)
nspins = len(D_sp)
f_sg = rgd.empty(nspins)
ft_sg = rgd.empty(nspins)
n_sLg = np.dot(D_sLq, n_qg)
nt_sLg = np.dot(D_sLq, nt_qg)
# Add core density
n_sLg[:, 0] += np.sqrt(4. * np.pi) / nspins * nc_g
nt_sLg[:, 0] += np.sqrt(4. * np.pi) / nspins * nct_g
coefatoms_GG = np.exp(-1j * np.inner(dG_GGv, R_av[a]))
for n, Y_L in enumerate(Y_nL):
w = weight_n[n]
f_sg[:] = 0.0
n_sg = np.dot(Y_L, n_sLg)
if x_only:
f_sg = nspins * (4 / 9.) * A_x * (nspins * n_sg)**(-2 / 3.)
else:
xc.calculate_fxc(rgd, n_sg, f_sg)
ft_sg[:] = 0.0
nt_sg = np.dot(Y_L, nt_sLg)
if x_only:
ft_sg = nspins * (4 / 9.) * (A_x
* (nspins * nt_sg)**(-2 / 3.))
else:
xc.calculate_fxc(rgd, nt_sg, ft_sg)
for i in range(len(rgd.r_g)):
coef_GG = np.exp(-1j * np.inner(dG_GGv, R_nv[n])
* rgd.r_g[i])
for s in range(len(f_sg)):
KxcPAW_sGG[s] += w * np.dot(coef_GG,
(f_sg[s, i] -
ft_sg[s, i])
* dv_g[i]) * coefatoms_GG
world.sum(KxcPAW_sGG)
Kxc_sGG += KxcPAW_sGG
return Kxc_sGG / vol
class OmegaMatrix:
"""
Omega matrix in Casidas linear response formalism
Parameters
- calculator: the calculator object the ground state calculation
- kss: the Kohn-Sham singles object
- xc: the exchange correlation approx. to use
- derivativeLevel: which level i of d^i Exc/dn^i to use
- numscale: numeric epsilon for derivativeLevel=0,1
- filehandle: the oject can be read from a filehandle
- txt: output stream or file name
- finegrid: level of fine grid to use. 0: nothing, 1 for poisson only,
2 everything on the fine grid
"""
def __init__(self,
calculator=None,
kss=None,
xc=None,
derivativeLevel=None,
numscale=0.001,
filehandle=None,
txt=None,
finegrid=2,
eh_comm=None,
):
if not txt and calculator:
txt = calculator.txt
self.txt, firsttime = initialize_text_stream(txt, mpi.rank)
if eh_comm == None:
eh_comm = mpi.serial_comm
self.eh_comm = eh_comm
if filehandle is not None:
self.kss = kss
self.read(fh=filehandle)
return None
self.fullkss = kss
self.finegrid = finegrid
if calculator is None:
return
self.paw = calculator
wfs = self.paw.wfs
# handle different grid possibilities
self.restrict = None
self.poisson = PoissonSolver(nn=self.paw.hamiltonian.poisson.nn)
if finegrid:
self.poisson.set_grid_descriptor(self.paw.density.finegd)
self.poisson.initialize()
self.gd = self.paw.density.finegd
if finegrid == 1:
self.gd = wfs.gd
else:
self.poisson.set_grid_descriptor(wfs.gd)
self.poisson.initialize()
self.gd = wfs.gd
self.restrict = Transformer(self.paw.density.finegd, wfs.gd,
self.paw.input_parameters.stencils[1]
).apply
if xc == 'RPA':
xc = None # enable RPA as keyword
if xc is not None:
self.xc = XC(xc)
self.xc.initialize(self.paw.density, self.paw.hamiltonian,
wfs, self.paw.occupations)
# check derivativeLevel
if derivativeLevel is None:
derivativeLevel= \
self.xc.get_functional().get_max_derivative_level()
self.derivativeLevel = derivativeLevel
# change the setup xc functional if needed
# the ground state calculation may have used another xc
if kss.npspins > kss.nvspins:
spin_increased = True
else:
spin_increased = False
else:
self.xc = None
self.numscale = numscale
self.singletsinglet = False
if kss.nvspins<2 and kss.npspins<2:
# this will be a singlet to singlet calculation only
self.singletsinglet=True
nij = len(kss)
self.Om = np.zeros((nij,nij))
self.get_full()
def get_full(self):
self.paw.timer.start('Omega RPA')
self.get_rpa()
self.paw.timer.stop()
if self.xc is not None:
self.paw.timer.start('Omega XC')
self.get_xc()
self.paw.timer.stop()
self.eh_comm.sum(self.Om)
self.full = self.Om
def get_xc(self):
"""Add xc part of the coupling matrix"""
# shorthands
paw = self.paw
wfs = paw.wfs
gd = paw.density.finegd
comm = gd.comm
eh_comm = self.eh_comm
fg = self.finegrid is 2
kss = self.fullkss
nij = len(kss)
Om_xc = self.Om
# initialize densities
# nt_sg is the smooth density on the fine grid with spin index
if kss.nvspins==2:
# spin polarised ground state calc.
nt_sg = paw.density.nt_sg
else:
# spin unpolarised ground state calc.
if kss.npspins==2:
# construct spin polarised densities
nt_sg = np.array([.5*paw.density.nt_sg[0],
.5*paw.density.nt_sg[0]])
else:
nt_sg = paw.density.nt_sg
# check if D_sp have been changed before
D_asp = self.paw.density.D_asp
for a, D_sp in D_asp.items():
if len(D_sp) != kss.npspins:
if len(D_sp) == 1:
D_asp[a] = np.array([0.5 * D_sp[0], 0.5 * D_sp[0]])
else:
D_asp[a] = np.array([D_sp[0] + D_sp[1]])
# restrict the density if needed
if fg:
nt_s = nt_sg
else:
nt_s = self.gd.zeros(nt_sg.shape[0])
for s in range(nt_sg.shape[0]):
self.restrict(nt_sg[s], nt_s[s])
gd = paw.density.gd
# initialize vxc or fxc
if self.derivativeLevel==0:
raise NotImplementedError
if kss.npspins==2:
v_g=nt_sg[0].copy()
else:
v_g=nt_sg.copy()
elif self.derivativeLevel==1:
pass
elif self.derivativeLevel==2:
fxc_sg = np.zeros(nt_sg.shape)
self.xc.calculate_fxc(gd, nt_sg, fxc_sg)
else:
raise ValueError('derivativeLevel can only be 0,1,2')
## self.paw.my_nuclei = []
ns=self.numscale
xc=self.xc
print >> self.txt, 'XC',nij,'transitions'
for ij in range(eh_comm.rank, nij, eh_comm.size):
print >> self.txt,'XC kss['+'%d'%ij+']'
timer = Timer()
timer.start('init')
timer2 = Timer()
if self.derivativeLevel >= 1:
# vxc is available
# We use the numerical two point formula for calculating
# the integral over fxc*n_ij. The results are
# vvt_s smooth integral
# nucleus.I_sp atom based correction matrices (pack2)
# stored on each nucleus
timer2.start('init v grids')
vp_s=np.zeros(nt_s.shape,nt_s.dtype.char)
vm_s=np.zeros(nt_s.shape,nt_s.dtype.char)
if kss.npspins == 2: # spin polarised
nv_s = nt_s.copy()
nv_s[kss[ij].pspin] += ns * kss[ij].get(fg)
xc.calculate(gd, nv_s, vp_s)
nv_s = nt_s.copy()
nv_s[kss[ij].pspin] -= ns * kss[ij].get(fg)
xc.calculate(gd, nv_s, vm_s)
else: # spin unpolarised
nv = nt_s + ns * kss[ij].get(fg)
xc.calculate(gd, nv, vp_s)
nv = nt_s - ns * kss[ij].get(fg)
xc.calculate(gd, nv, vm_s)
vvt_s = (0.5 / ns) * (vp_s - vm_s)
timer2.stop()
# initialize the correction matrices
timer2.start('init v corrections')
I_asp = {}
for a, P_ni in wfs.kpt_u[kss[ij].spin].P_ani.items():
# create the modified density matrix
Pi_i = P_ni[kss[ij].i]
Pj_i = P_ni[kss[ij].j]
P_ii = np.outer(Pi_i, Pj_i)
# we need the symmetric form, hence we can pack
P_p = pack(P_ii)
D_sp = self.paw.density.D_asp[a].copy()
D_sp[kss[ij].pspin] -= ns * P_p
setup = wfs.setups[a]
I_sp = np.zeros_like(D_sp)
self.xc.calculate_paw_correction(setup, D_sp, I_sp)
I_sp *= -1.0
D_sp = self.paw.density.D_asp[a].copy()
D_sp[kss[ij].pspin] += ns * P_p
self.xc.calculate_paw_correction(setup, D_sp, I_sp)
I_sp /= 2.0 * ns
I_asp[a] = I_sp
timer2.stop()
timer.stop()
t0 = timer.get_time('init')
timer.start(ij)
for kq in range(ij,nij):
weight = self.weight_Kijkq(ij, kq)
if self.derivativeLevel == 0:
# only Exc is available
if kss.npspins==2: # spin polarised
nv_g = nt_sg.copy()
nv_g[kss[ij].pspin] += kss[ij].get(fg)
nv_g[kss[kq].pspin] += kss[kq].get(fg)
Excpp = xc.get_energy_and_potential(
nv_g[0], v_g, nv_g[1], v_g)
nv_g = nt_sg.copy()
nv_g[kss[ij].pspin] += kss[ij].get(fg)
nv_g[kss[kq].pspin] -= kss[kq].get(fg)
Excpm = xc.get_energy_and_potential(\
nv_g[0],v_g,nv_g[1],v_g)
nv_g = nt_sg.copy()
nv_g[kss[ij].pspin] -=\
kss[ij].get(fg)
nv_g[kss[kq].pspin] +=\
kss[kq].get(fg)
Excmp = xc.get_energy_and_potential(\
nv_g[0],v_g,nv_g[1],v_g)
nv_g = nt_sg.copy()
nv_g[kss[ij].pspin] -= \
kss[ij].get(fg)
nv_g[kss[kq].pspin] -=\
kss[kq].get(fg)
Excpp = xc.get_energy_and_potential(\
nv_g[0],v_g,nv_g[1],v_g)
else: # spin unpolarised
nv_g=nt_sg + ns*kss[ij].get(fg)\
+ ns*kss[kq].get(fg)
Excpp = xc.get_energy_and_potential(nv_g,v_g)
nv_g=nt_sg + ns*kss[ij].get(fg)\
- ns*kss[kq].get(fg)
Excpm = xc.get_energy_and_potential(nv_g,v_g)
nv_g=nt_sg - ns*kss[ij].get(fg)\
+ ns*kss[kq].get(fg)
Excmp = xc.get_energy_and_potential(nv_g,v_g)
nv_g=nt_sg - ns*kss[ij].get(fg)\
- ns*kss[kq].get(fg)
Excmm = xc.get_energy_and_potential(nv_g,v_g)
Om_xc[ij,kq] += weight *\
0.25*(Excpp-Excmp-Excpm+Excmm)/(ns*ns)
elif self.derivativeLevel == 1:
# vxc is available
timer2.start('integrate')
Om_xc[ij,kq] += weight*\
self.gd.integrate(kss[kq].get(fg)*
vvt_s[kss[kq].pspin])
timer2.stop()
timer2.start('integrate corrections')
Exc = 0.
for a, P_ni in wfs.kpt_u[kss[kq].spin].P_ani.items():
# create the modified density matrix
Pk_i = P_ni[kss[kq].i]
Pq_i = P_ni[kss[kq].j]
P_ii = np.outer(Pk_i, Pq_i)
# we need the symmetric form, hence we can pack
# use pack as I_sp used pack2
P_p = pack(P_ii)
Exc += np.dot(I_asp[a][kss[kq].pspin], P_p)
Om_xc[ij, kq] += weight * self.gd.comm.sum(Exc)
timer2.stop()
elif self.derivativeLevel == 2:
# fxc is available
if kss.npspins==2: # spin polarised
Om_xc[ij,kq] += weight *\
gd.integrate(kss[ij].get(fg) *
kss[kq].get(fg) *
fxc_sg[kss[ij].pspin, kss[kq].pspin])
else: # spin unpolarised
Om_xc[ij,kq] += weight *\
gd.integrate(kss[ij].get(fg) *
kss[kq].get(fg) *
fxc_sg)
# XXX still numeric derivatives for local terms
timer2.start('integrate corrections')
Exc = 0.
for a, P_ni in wfs.kpt_u[kss[kq].spin].P_ani.items():
# create the modified density matrix
Pk_i = P_ni[kss[kq].i]
Pq_i = P_ni[kss[kq].j]
P_ii = np.outer(Pk_i, Pq_i)
# we need the symmetric form, hence we can pack
# use pack as I_sp used pack2
P_p = pack(P_ii)
Exc += np.dot(I_asp[a][kss[kq].pspin], P_p)
Om_xc[ij, kq] += weight * self.gd.comm.sum(Exc)
timer2.stop()
if ij != kq:
Om_xc[kq,ij] = Om_xc[ij,kq]
timer.stop()
## timer2.write()
if ij < (nij-1):
print >> self.txt,'XC estimated time left',\
self.time_left(timer, t0, ij, nij)
def Coulomb_integral_kss(self, kss_ij, kss_kq, phit, rhot,
timer=None):
# smooth part
if timer:
timer.start('integrate')
I = self.gd.integrate(rhot * phit)
if timer:
timer.stop()
timer.start('integrate corrections 2')
wfs = self.paw.wfs
Pij_ani = wfs.kpt_u[kss_ij.spin].P_ani
Pkq_ani = wfs.kpt_u[kss_kq.spin].P_ani
# Add atomic corrections
Ia = 0.0
for a, Pij_ni in Pij_ani.items():
Pi_i = Pij_ni[kss_ij.i]
Pj_i = Pij_ni[kss_ij.j]
Dij_ii = np.outer(Pi_i, Pj_i)
Dij_p = pack(Dij_ii)
Pk_i = Pkq_ani[a][kss_kq.i]
Pq_i = Pkq_ani[a][kss_kq.j]
Dkq_ii = np.outer(Pk_i, Pq_i)
Dkq_p = pack(Dkq_ii)
C_pp = wfs.setups[a].M_pp
# ----
# 2 > P P C P P
# ---- ip jr prst ks qt
# prst
Ia += 2.0*np.dot(Dkq_p, np.dot(C_pp, Dij_p))
I += self.gd.comm.sum(Ia)
if timer:
timer.stop()
return I
def get_rpa(self):
"""calculate RPA part of the omega matrix"""
# shorthands
kss=self.fullkss
finegrid=self.finegrid
wfs = self.paw.wfs
eh_comm = self.eh_comm
# calculate omega matrix
nij = len(kss)
print >> self.txt,'RPA',nij,'transitions'
Om = self.Om
for ij in range(eh_comm.rank, nij, eh_comm.size):
print >> self.txt,'RPA kss['+'%d'%ij+']=', kss[ij]
timer = Timer()
timer.start('init')
timer2 = Timer()
# smooth density including compensation charges
timer2.start('with_compensation_charges 0')
rhot_p = kss[ij].with_compensation_charges(
finegrid is not 0)
timer2.stop()
# integrate with 1/|r_1-r_2|
timer2.start('poisson')
phit_p = np.zeros(rhot_p.shape, rhot_p.dtype.char)
self.poisson.solve(phit_p, rhot_p, charge=None)
timer2.stop()
timer.stop()
t0 = timer.get_time('init')
timer.start(ij)
if finegrid == 1:
rhot = kss[ij].with_compensation_charges()
phit = self.gd.zeros()
## print "shapes 0=",phit.shape,rhot.shape
self.restrict(phit_p,phit)
else:
phit = phit_p
rhot = rhot_p
for kq in range(ij,nij):
if kq != ij:
# smooth density including compensation charges
timer2.start('kq with_compensation_charges')
rhot = kss[kq].with_compensation_charges(
finegrid is 2)
timer2.stop()
pre = 2 * sqrt(kss[ij].get_energy() * kss[kq].get_energy() *
kss[ij].get_weight() * kss[kq].get_weight() )
I = self.Coulomb_integral_kss(kss[ij], kss[kq],
rhot, phit, timer2)
Om[ij,kq] = pre * I
if ij == kq:
Om[ij,kq] += kss[ij].get_energy()**2
else:
Om[kq,ij]=Om[ij,kq]
timer.stop()
## timer2.write()
if ij < (nij-1):
t = timer.get_time(ij) # time for nij-ij calculations
t = .5*t*(nij-ij) # estimated time for n*(n+1)/2, n=nij-(ij+1)
print >> self.txt,'RPA estimated time left',\
self.timestring(t0*(nij-ij-1)+t)
def singlets_triplets(self):
"""Split yourself into singlet and triplet transitions"""
assert(self.fullkss.npspins == 2)
assert(self.fullkss.nvspins == 1)
# strip kss from down spins
skss = KSSingles()
tkss = KSSingles()
map = []
for ij, ks in enumerate(self.fullkss):
if ks.pspin == ks.spin:
skss.append((ks + ks) / sqrt(2))
tkss.append((ks - ks) / sqrt(2))
map.append(ij)
nkss = len(skss)
# define the singlet and the triplet omega-matrixes
sOm = OmegaMatrix(kss=skss)
sOm.full = np.empty((nkss, nkss))
tOm = OmegaMatrix(kss=tkss)
tOm.full = np.empty((nkss, nkss))
for ij in range(nkss):
for kl in range(nkss):
sOm.full[ij, kl] = (self.full[map[ij], map[kl]] +
self.full[map[ij], nkss + map[kl]])
tOm.full[ij, kl] = (self.full[map[ij], map[kl]] -
self.full[map[ij], nkss + map[kl]])
return sOm, tOm
def timestring(self, t):
ti = int(t + 0.5)
td = ti // 86400
st = ''
if td > 0:
st += '%d' % td + 'd'
ti -= td * 86400
th = ti // 3600
if th > 0:
st += '%d' % th + 'h'
ti -= th * 3600
tm = ti // 60
if tm > 0:
st += '%d' % tm + 'm'
ti -= tm * 60
st += '%d' % ti + 's'
return st
def time_left(self, timer, t0, ij, nij):
t = timer.get_time(ij) # time for nij-ij calculations
t = .5 * t * (nij - ij) # estimated time for n*(n+1)/2, n=nij-(ij+1)
return self.timestring(t0 * (nij - ij - 1) + t)
def get_map(self, istart=None, jend=None, energy_range=None):
"""Return the reduction map for the given requirements"""
self.istart = istart
self.jend = jend
if istart is None and jend is None and energy_range is None:
return None, self.fullkss
# reduce the matrix
print >> self.txt,'# diagonalize: %d transitions original'\
% len(self.fullkss)
if energy_range is None:
if istart is None: istart = self.kss.istart
if self.fullkss.istart > istart:
raise RuntimeError('istart=%d has to be >= %d' %
(istart, self.kss.istart))
if jend is None: jend = self.kss.jend
if self.fullkss.jend < jend:
raise RuntimeError('jend=%d has to be <= %d' %
(jend, self.kss.jend))
else:
try:
emin, emax = energy_range
except:
emax = energy_range
emin = 0.
emin /= Hartree
emax /= Hartree
map= []
kss = KSSingles()
for ij, k in zip(range(len(self.fullkss)), self.fullkss):
if energy_range is None:
if k.i >= istart and k.j <= jend:
kss.append(k)
map.append(ij)
else:
if k.energy >= emin and k.energy < emax:
kss.append(k)
map.append(ij)
kss.update()
print >> self.txt, '# diagonalize: %d transitions now' % len(kss)
return map, kss
def diagonalize(self, istart=None, jend=None, energy_range=None,
TDA=False):
"""Evaluate Eigenvectors and Eigenvalues:"""
if TDA:
raise NotImplementedError
map, kss = self.get_map(istart, jend, energy_range)
nij = len(kss)
if map is None:
evec = self.full.copy()
else:
evec = np.zeros((nij,nij))
for ij in range(nij):
for kq in range(nij):
evec[ij,kq] = self.full[map[ij],map[kq]]
assert(len(evec) > 0)
self.eigenvectors = evec
self.eigenvalues = np.zeros((len(kss)))
self.kss = kss
diagonalize(self.eigenvectors, self.eigenvalues)
def Kss(self, kss=None):
"""Set and get own Kohn-Sham singles"""
if kss is not None:
self.fullkss = kss
if(hasattr(self,'fullkss')):
return self.fullkss
else:
return None
def read(self, filename=None, fh=None):
"""Read myself from a file"""
if fh is None:
f = open(filename, 'r')
else:
f = fh
f.readline()
nij = int(f.readline())
full = np.zeros((nij,nij))
for ij in range(nij):
l = f.readline().split()
for kq in range(ij,nij):
full[ij,kq] = float(l[kq-ij])
full[kq,ij] = full[ij,kq]
self.full = full
if fh is None:
f.close()
def write(self, filename=None, fh=None):
"""Write current state to a file."""
if mpi.rank == mpi.MASTER:
if fh is None:
f = open(filename, 'w')
else:
f = fh
f.write('# OmegaMatrix\n')
nij = len(self.fullkss)
f.write('%d\n' % nij)
for ij in range(nij):
for kq in range(ij,nij):
f.write(' %g' % self.full[ij,kq])
f.write('\n')
if fh is None:
f.close()
def weight_Kijkq(self, ij, kq):
"""weight for the coupling matrix terms"""
kss = self.fullkss
return 2.*sqrt( kss[ij].get_energy() * kss[kq].get_energy() *
kss[ij].get_weight() * kss[kq].get_weight() )
def __str__(self):
str='<OmegaMatrix> '
if hasattr(self,'eigenvalues'):
str += 'dimension '+ ('%d'%len(self.eigenvalues))
str += "\neigenvalues: "
for ev in self.eigenvalues:
str += ' ' + ('%f'%(sqrt(ev) * Hartree))
return str
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
import numpy as np
import numpy.random as ra
from gpaw.test import equal
from gpaw.setup import create_setup
from gpaw.grid_descriptor import GridDescriptor
from gpaw.localized_functions import create_localized_functions
from gpaw.spline import Spline
from gpaw.xc import XC
from gpaw.utilities import pack
from gpaw.mpi import serial_comm
ra.seed(8)
for name in ['LDA', 'PBE']:
xc = XC(name)
s = create_setup('N', xc)
ni = s.ni
niAO = s.niAO
wt0_j = s.phit_j
rcut = s.xc_correction.rgd.r_g[-1]
wt_j = []
for wt0 in wt0_j:
data = [wt0(r) for r in np.arange(121) * rcut / 100]
data[-1] = 0.0
l = wt0.get_angular_momentum_number()
wt_j.append(Spline(l, 1.2 * rcut, data))
a = rcut * 1.2 * 2 + 1.0
## n = 120
n = 70
def __init__(self,
calculator=None,
kss=None,
xc=None,
derivativeLevel=None,
numscale=0.001,
filehandle=None,
txt=None,
finegrid=2,
eh_comm=None,
):
if not txt and calculator:
txt = calculator.txt
self.txt, firsttime = initialize_text_stream(txt, mpi.rank)
if eh_comm == None:
eh_comm = mpi.serial_comm
self.eh_comm = eh_comm
if filehandle is not None:
self.kss = kss
self.read(fh=filehandle)
return None
self.fullkss = kss
self.finegrid = finegrid
if calculator is None:
return
self.paw = calculator
wfs = self.paw.wfs
# handle different grid possibilities
self.restrict = None
self.poisson = PoissonSolver(nn=self.paw.hamiltonian.poisson.nn)
if finegrid:
self.poisson.set_grid_descriptor(self.paw.density.finegd)
self.poisson.initialize()
self.gd = self.paw.density.finegd
if finegrid == 1:
self.gd = wfs.gd
else:
self.poisson.set_grid_descriptor(wfs.gd)
self.poisson.initialize()
self.gd = wfs.gd
self.restrict = Transformer(self.paw.density.finegd, wfs.gd,
self.paw.input_parameters.stencils[1]
).apply
if xc == 'RPA':
xc = None # enable RPA as keyword
if xc is not None:
self.xc = XC(xc)
self.xc.initialize(self.paw.density, self.paw.hamiltonian,
wfs, self.paw.occupations)
# check derivativeLevel
if derivativeLevel is None:
derivativeLevel= \
self.xc.get_functional().get_max_derivative_level()
self.derivativeLevel = derivativeLevel
# change the setup xc functional if needed
# the ground state calculation may have used another xc
if kss.npspins > kss.nvspins:
spin_increased = True
else:
spin_increased = False
else:
self.xc = None
self.numscale = numscale
self.singletsinglet = False
if kss.nvspins<2 and kss.npspins<2:
# this will be a singlet to singlet calculation only
self.singletsinglet=True
nij = len(kss)
self.Om = np.zeros((nij,nij))
self.get_full()
from __future__ import print_function
import numpy as np
import numpy.random as ra
from gpaw.setup import create_setup
from gpaw.xc.noncollinear import NonCollinearFunctional
from gpaw.xc import XC
from gpaw.test import equal
from gpaw.utilities import pack
x = 0.0000001
ra.seed(8)
for xc in ['LDA']:#, 'PBE']:
print(xc)
xc = XC(xc)
s = create_setup('N', xc)
ni = s.ni
D_sp = np.array([pack(np.outer(P_i, P_i))
for P_i in 0.2 * ra.random((2, ni)) - 0.1])
D_sp[1] += D_sp[0]
nii = ni * (ni + 1) // 2
E = xc.calculate_paw_correction(s, D_sp)
xc = NonCollinearFunctional(xc)
Dnc_sp = np.zeros((4, nii))
Dnc_sp[0] = D_sp.sum(0)
Dnc_sp[3] = D_sp[0] - D_sp[1]
Enc = xc.calculate_paw_correction(s, Dnc_sp)
def initialize(self, atoms=None):
"""Inexpensive initialization."""
if atoms is None:
atoms = self.atoms
else:
# Save the state of the atoms:
self.atoms = atoms.copy()
par = self.input_parameters
world = par.communicator
if world is None:
world = mpi.world
elif hasattr(world, 'new_communicator'):
# Check for whether object has correct type already
#
# Using isinstance() is complicated because of all the
# combinations, serial/parallel/debug...
pass
else:
# world should be a list of ranks:
world = mpi.world.new_communicator(np.asarray(world))
self.wfs.world = world
self.set_text(par.txt, par.verbose)
natoms = len(atoms)
cell_cv = atoms.get_cell() / Bohr
pbc_c = atoms.get_pbc()
Z_a = atoms.get_atomic_numbers()
magmom_av = atoms.get_initial_magnetic_moments()
# Generate new xc functional only when it is reset by set
if self.hamiltonian is None or self.hamiltonian.xc is None:
if isinstance(par.xc, str):
xc = XC(par.xc)
else:
xc = par.xc
else:
xc = self.hamiltonian.xc
mode = par.mode
if xc.orbital_dependent and mode == 'lcao':
raise NotImplementedError('LCAO mode does not support '
'orbital-dependent XC functionals.')
if mode == 'pw':
mode = PW()
if mode == 'fd' and par.usefractrans:
raise NotImplementedError('FD mode does not support '
'fractional translations.')
if mode == 'lcao' and par.usefractrans:
raise Warning('Fractional translations have not been tested '
'with LCAO mode. Use with care!')
if par.realspace is None:
realspace = not isinstance(mode, PW)
else:
realspace = par.realspace
if isinstance(mode, PW):
assert not realspace
if par.gpts is not None:
N_c = np.array(par.gpts)
else:
h = par.h
if h is not None:
h /= Bohr
N_c = get_number_of_grid_points(cell_cv, h, mode, realspace)
if par.filter is None and not isinstance(mode, PW):
gamma = 1.6
hmax = ((np.linalg.inv(cell_cv)**2).sum(0)**-0.5 / N_c).max()
def filter(rgd, rcut, f_r, l=0):
gcut = np.pi / hmax - 2 / rcut / gamma
f_r[:] = rgd.filter(f_r, rcut * gamma, gcut, l)
else:
filter = par.filter
setups = Setups(Z_a, par.setups, par.basis, par.lmax, xc,
filter, world)
if magmom_av.ndim == 1:
collinear = True
magmom_av, magmom_a = np.zeros((natoms, 3)), magmom_av
magmom_av[:, 2] = magmom_a
else:
collinear = False
magnetic = magmom_av.any()
spinpol = par.spinpol
if par.hund:
if natoms != 1:
raise ValueError('hund=True arg only valid for single atoms!')
spinpol = True
magmom_av[0] = (0, 0, setups[0].get_hunds_rule_moment(par.charge))
if spinpol is None:
spinpol = magnetic
elif magnetic and not spinpol:
raise ValueError('Non-zero initial magnetic moment for a ' +
'spin-paired calculation!')
if collinear:
nspins = 1 + int(spinpol)
ncomp = 1
else:
nspins = 1
ncomp = 2
# K-point descriptor
bzkpts_kc = kpts2ndarray(par.kpts, self.atoms)
kd = KPointDescriptor(bzkpts_kc, nspins, collinear, par.usefractrans)
width = par.width
if width is None:
if pbc_c.any():
width = 0.1 # eV
else:
width = 0.0
else:
assert par.occupations is None
if hasattr(self, 'time') or par.dtype == complex:
dtype = complex
else:
if kd.gamma:
dtype = float
else:
dtype = complex
## rbw: If usefractrans=True, kd.set_symmetry might overwrite N_c.
## This is necessary, because N_c must be dividable by 1/(fractional translation),
## f.e. fractional translations of a grid point must land on a grid point.
N_c = kd.set_symmetry(atoms, setups, magmom_av, par.usesymm, N_c, world)
nao = setups.nao
nvalence = setups.nvalence - par.charge
M_v = magmom_av.sum(0)
M = np.dot(M_v, M_v)**0.5
nbands = par.nbands
if nbands is None:
nbands = 0
for setup in setups:
nbands_from_atom = setup.get_default_nbands()
# Any obscure setup errors?
if nbands_from_atom < -(-setup.Nv // 2):
raise ValueError('Bad setup: This setup requests %d'
' bands but has %d electrons.'
% (nbands_from_atom, setup.Nv))
nbands += nbands_from_atom
nbands = min(nao, nbands)
elif nbands > nao and mode == 'lcao':
raise ValueError('Too many bands for LCAO calculation: '
'%d bands and only %d atomic orbitals!' %
(nbands, nao))
if nvalence < 0:
raise ValueError(
'Charge %f is not possible - not enough valence electrons' %
par.charge)
if nbands <= 0:
nbands = int(nvalence + M + 0.5) // 2 + (-nbands)
if nvalence > 2 * nbands:
raise ValueError('Too few bands! Electrons: %f, bands: %d'
% (nvalence, nbands))
nbands *= ncomp
if par.width is not None:
self.text('**NOTE**: please start using '
'occupations=FermiDirac(width).')
if par.fixmom:
self.text('**NOTE**: please start using '
'occupations=FermiDirac(width, fixmagmom=True).')
if self.occupations is None:
if par.occupations is None:
# Create object for occupation numbers:
self.occupations = occupations.FermiDirac(width, par.fixmom)
else:
self.occupations = par.occupations
self.occupations.magmom = M_v[2]
cc = par.convergence
if mode == 'lcao':
niter_fixdensity = 0
else:
niter_fixdensity = None
if self.scf is None:
self.scf = SCFLoop(
cc['eigenstates'] / Hartree**2 * nvalence,
cc['energy'] / Hartree * max(nvalence, 1),
cc['density'] * nvalence,
par.maxiter, par.fixdensity,
niter_fixdensity)
parsize_kpt = par.parallel['kpt']
parsize_domain = par.parallel['domain']
parsize_bands = par.parallel['band']
if not realspace:
pbc_c = np.ones(3, bool)
if not self.wfs:
if parsize_domain == 'domain only': # XXX this was silly!
parsize_domain = world.size
parallelization = mpi.Parallelization(world,
nspins * kd.nibzkpts)
ndomains = None
if parsize_domain is not None:
ndomains = np.prod(parsize_domain)
if isinstance(mode, PW):
if ndomains > 1:
raise ValueError('Planewave mode does not support '
'domain decomposition.')
ndomains = 1
parallelization.set(kpt=parsize_kpt,
domain=ndomains,
band=parsize_bands)
domain_comm, kpt_comm, band_comm = \
parallelization.build_communicators()
#domain_comm, kpt_comm, band_comm = mpi.distribute_cpus(
# parsize_domain, parsize_bands,
# nspins, kd.nibzkpts, world, par.idiotproof, mode)
kd.set_communicator(kpt_comm)
parstride_bands = par.parallel['stridebands']
# Unfortunately we need to remember that we adjusted the
# number of bands so we can print a warning if it differs
# from the number specified by the user. (The number can
# be inferred from the input parameters, but it's tricky
# because we allow negative numbers)
self.nbands_parallelization_adjustment = -nbands % band_comm.size
nbands += self.nbands_parallelization_adjustment
# I would like to give the following error message, but apparently
# there are cases, e.g. gpaw/test/gw_ppa.py, which involve
# nbands > nao and are supposed to work that way.
#if nbands > nao:
# raise ValueError('Number of bands %d adjusted for band '
# 'parallelization %d exceeds number of atomic '
# 'orbitals %d. This problem can be fixed '
# 'by reducing the number of bands a bit.'
# % (nbands, band_comm.size, nao))
bd = BandDescriptor(nbands, band_comm, parstride_bands)
if (self.density is not None and
self.density.gd.comm.size != domain_comm.size):
# Domain decomposition has changed, so we need to
# reinitialize density and hamiltonian:
if par.fixdensity:
raise RuntimeError('Density reinitialization conflict ' +
'with "fixdensity" - specify domain decomposition.')
self.density = None
self.hamiltonian = None
# Construct grid descriptor for coarse grids for wave functions:
gd = self.grid_descriptor_class(N_c, cell_cv, pbc_c,
domain_comm, parsize_domain)
# do k-point analysis here? XXX
args = (gd, nvalence, setups, bd, dtype, world, kd, self.timer)
if par.parallel['sl_auto']:
# Choose scalapack parallelization automatically
for key, val in par.parallel.items():
if (key.startswith('sl_') and key != 'sl_auto'
and val is not None):
raise ValueError("Cannot use 'sl_auto' together "
"with '%s'" % key)
max_scalapack_cpus = bd.comm.size * gd.comm.size
nprow = max_scalapack_cpus
npcol = 1
# Get a sort of reasonable number of columns/rows
while npcol < nprow and nprow % 2 == 0:
npcol *= 2
nprow //= 2
assert npcol * nprow == max_scalapack_cpus
# ScaLAPACK creates trouble if there aren't at least a few
# whole blocks; choose block size so there will always be
# several blocks. This will crash for small test systems,
# but so will ScaLAPACK in any case
blocksize = min(-(-nbands // 4), 64)
sl_default = (nprow, npcol, blocksize)
else:
sl_default = par.parallel['sl_default']
if mode == 'lcao':
# Layouts used for general diagonalizer
sl_lcao = par.parallel['sl_lcao']
if sl_lcao is None:
sl_lcao = sl_default
lcaoksl = get_KohnSham_layouts(sl_lcao, 'lcao',
gd, bd, dtype,
nao=nao, timer=self.timer)
if collinear:
self.wfs = LCAOWaveFunctions(lcaoksl, *args)
else:
from gpaw.xc.noncollinear import \
NonCollinearLCAOWaveFunctions
self.wfs = NonCollinearLCAOWaveFunctions(lcaoksl, *args)
elif mode == 'fd' or isinstance(mode, PW):
# buffer_size keyword only relevant for fdpw
buffer_size = par.parallel['buffer_size']
# Layouts used for diagonalizer
sl_diagonalize = par.parallel['sl_diagonalize']
if sl_diagonalize is None:
sl_diagonalize = sl_default
diagksl = get_KohnSham_layouts(sl_diagonalize, 'fd',
gd, bd, dtype,
buffer_size=buffer_size,
timer=self.timer)
# Layouts used for orthonormalizer
sl_inverse_cholesky = par.parallel['sl_inverse_cholesky']
if sl_inverse_cholesky is None:
sl_inverse_cholesky = sl_default
if sl_inverse_cholesky != sl_diagonalize:
message = 'sl_inverse_cholesky != sl_diagonalize ' \
'is not implemented.'
raise NotImplementedError(message)
orthoksl = get_KohnSham_layouts(sl_inverse_cholesky, 'fd',
gd, bd, dtype,
buffer_size=buffer_size,
timer=self.timer)
# Use (at most) all available LCAO for initialization
lcaonbands = min(nbands, nao)
try:
lcaobd = BandDescriptor(lcaonbands, band_comm,
parstride_bands)
except RuntimeError:
initksl = None
else:
# Layouts used for general diagonalizer
# (LCAO initialization)
sl_lcao = par.parallel['sl_lcao']
if sl_lcao is None:
sl_lcao = sl_default
initksl = get_KohnSham_layouts(sl_lcao, 'lcao',
gd, lcaobd, dtype,
nao=nao,
timer=self.timer)
if hasattr(self, 'time'):
assert mode == 'fd'
from gpaw.tddft import TimeDependentWaveFunctions
self.wfs = TimeDependentWaveFunctions(par.stencils[0],
diagksl, orthoksl, initksl, gd, nvalence, setups,
bd, world, kd, self.timer)
elif mode == 'fd':
self.wfs = FDWaveFunctions(par.stencils[0], diagksl,
orthoksl, initksl, *args)
else:
# Planewave basis:
self.wfs = mode(diagksl, orthoksl, initksl, *args)
else:
self.wfs = mode(self, *args)
else:
self.wfs.set_setups(setups)
if not self.wfs.eigensolver:
# Number of bands to converge:
nbands_converge = cc['bands']
if nbands_converge == 'all':
nbands_converge = nbands
elif nbands_converge != 'occupied':
assert isinstance(nbands_converge, int)
if nbands_converge < 0:
nbands_converge += nbands
eigensolver = get_eigensolver(par.eigensolver, mode,
par.convergence)
eigensolver.nbands_converge = nbands_converge
# XXX Eigensolver class doesn't define an nbands_converge property
if isinstance(xc, SIC):
eigensolver.blocksize = 1
self.wfs.set_eigensolver(eigensolver)
if self.density is None:
gd = self.wfs.gd
if par.stencils[1] != 9:
# Construct grid descriptor for fine grids for densities
# and potentials:
finegd = gd.refine()
else:
# Special case (use only coarse grid):
finegd = gd
if realspace:
self.density = RealSpaceDensity(
gd, finegd, nspins, par.charge + setups.core_charge,
collinear, par.stencils[1])
else:
self.density = ReciprocalSpaceDensity(
gd, finegd, nspins, par.charge + setups.core_charge,
collinear)
self.density.initialize(setups, self.timer, magmom_av, par.hund)
self.density.set_mixer(par.mixer)
if self.hamiltonian is None:
gd, finegd = self.density.gd, self.density.finegd
if realspace:
self.hamiltonian = RealSpaceHamiltonian(
gd, finegd, nspins, setups, self.timer, xc, par.external,
collinear, par.poissonsolver, par.stencils[1], world)
else:
self.hamiltonian = ReciprocalSpaceHamiltonian(
gd, finegd,
self.density.pd2, self.density.pd3,
nspins, setups, self.timer, xc, par.external,
collinear, world)
xc.initialize(self.density, self.hamiltonian, self.wfs,
self.occupations)
self.text()
self.print_memory_estimate(self.txt, maxdepth=memory_estimate_depth)
self.txt.flush()
self.timer.print_info(self)
if dry_run:
self.dry_run()
self.initialized = True
gd.beg_c[2] <= 3 < gd.end_c[2])
if here:
x = v[-1, 1, 2, 3] * gd.dv
n[-1, 1, 2, 3] += 0.000001
Ep = xc.calculate(gd, n, v)
if here:
n[-1, 1, 2, 3] -= 0.000002
Em = xc.calculate(gd, n, v)
x2 = (Ep - Em) / 0.000002
if here:
print(xc.name, E, x, x2, x - x2)
equal(x, x2, 1e-11)
n[-1, 1, 2, 3] += 0.000001
if 0:#xc.type == 'LDA':
xc = XC(NonCollinearLDAKernel())
else:
xc = NonCollinearFunctional(xc)
n2 = gd.zeros(4)
n2[0] = n.sum(0)
n2[3] = n[0] - n[1]
E2 = xc.calculate(gd, n2)
print(E, E2-E)
assert abs(E2 - E) < 1e-11
n2[1] = 0.1 * n2[3]
n2[2] = 0.2 * n2[3]
n2[3] *= (1 - 0.1**2 - 0.2**2)**0.5
v = n2 * 0
E2 = xc.calculate(gd, n2, v)
print(E, E2-E)
def initialize(self):
self.xc = XC(self.functional)
self.vt_sg = self.nlfunc.finegd.empty(self.nlfunc.nspins)
self.e_g = self.nlfunc.finegd.empty()
class C_GLLBScr(Contribution):
def __init__(self, nlfunc, weight, functional='GGA_X_B88', metallic=False):
Contribution.__init__(self, nlfunc, weight)
self.functional = functional
self.old_coeffs = None
self.iter = 0
self.metallic = metallic
def get_name(self):
return 'SCREENING'
def get_desc(self):
return '(' + self.functional + ')'
# Initialize GLLBScr functional
def initialize_1d(self):
self.ae = self.nlfunc.ae
self.xc = XC(self.functional)
self.v_g = np.zeros(self.ae.N)
self.e_g = np.zeros(self.ae.N)
# Calcualte the GLLB potential and energy 1d
def add_xc_potential_and_energy_1d(self, v_g):
self.v_g[:] = 0.0
self.e_g[:] = 0.0
self.xc.calculate_spherical(self.ae.rgd, self.ae.n.reshape((1, -1)),
self.v_g.reshape((1, -1)), self.e_g)
v_g += 2 * self.weight * self.e_g / (self.ae.n + 1e-10)
Exc = self.weight * np.sum(self.e_g * self.ae.rgd.dv_g)
return Exc
def initialize(self):
self.occupations = self.nlfunc.occupations
self.xc = XC(self.functional)
# Always 1 spin, no matter what calculation nspins is
self.vt_sg = self.nlfunc.finegd.empty(1)
self.e_g = self.nlfunc.finegd.empty()#.ravel()
def get_coefficient_calculator(self):
return self
def f(self, f):
return sqrt(f)
def get_coefficients(self, e_j, f_j):
homo_e = max( [ np.where(f>1e-3, e, -1000) for f,e in zip(f_j, e_j)] )
return [ f * K_G * self.f( max(0, homo_e - e)) for e,f in zip(e_j, f_j) ]
def get_coefficients_1d(self, smooth=False, lumo_perturbation = False):
homo_e = max( [ np.where(f>1e-3, e, -1000) for f,e in zip(self.ae.f_j, self.ae.e_j)])
if not smooth:
if lumo_perturbation:
lumo_e = min( [ np.where(f<1e-3, e, 1000) for f,e in zip(self.ae.f_j, self.ae.e_j)])
return np.array([ f * K_G * (self.f( max(0, lumo_e - e)) - self.f(max(0, homo_e -e)))
for e,f in zip(self.ae.e_j, self.ae.f_j) ])
else:
return np.array([ f * K_G * (self.f( max(0, homo_e - e)))
for e,f in zip(self.ae.e_j, self.ae.f_j) ])
else:
return [ [ f * K_G * self.f( max(0, homo_e - e))
for e,f in zip(e_n, f_n) ]
for e_n, f_n in zip(self.ae.e_ln, self.ae.f_ln) ]
def get_coefficients_by_kpt(self, kpt_u, lumo_perturbation=False, homolumo=None, nspins=1):
if not hasattr(kpt_u[0],'orbitals_ready'):
kpt_u[0].orbitals_ready = True
return None
#if kpt_u[0].psit_nG is None or isinstance(kpt_u[0].psit_nG,
# TarFileReference):
# if kpt_u[0].C_nM==None:
# return None
if homolumo == None:
if self.metallic:
# For metallic systems, the calculated fermi level represents
# the most accurate estimate for reference-energy
eref_lumo_s = eref_s = nspins * [ self.occupations.get_fermi_level() ]
else:
# Find h**o and lumo levels for each spin
eref_s = []
eref_lumo_s = []
for s in range(nspins):
h**o, lumo = self.occupations.get_homo_lumo_by_spin(self.nlfunc.wfs, s)
eref_s.append(h**o)
eref_lumo_s.append(lumo)
else:
eref_s, eref_lumo_s = homolumo
if not isinstance(eref_s, (list, tuple)):
eref_s = [ eref_s ]
eref_lumo_s = [ eref_lumo_s ]
# The parameter ee might sometimes be set to small thereshold value to
# achieve convergence on small systems with degenerate H**O.
if len(kpt_u) > nspins:
ee = 0.0
else:
ee = 0.05 / 27.21
if lumo_perturbation:
return [np.array([
f * K_G * (self.f( np.where(eref_lumo_s[kpt.s] - e>ee, eref_lumo_s[kpt.s]-e,0))
-self.f( np.where(eref_s[kpt.s] - e>ee, eref_s[kpt.s]-e,0)))
for e, f in zip(kpt.eps_n, kpt.f_n) ])
for kpt in kpt_u ]
else:
coeff = [ np.array([ f * K_G * self.f( np.where(eref_s[kpt.s] - e>ee, eref_s[kpt.s]-e,0))
for e, f in zip(kpt.eps_n, kpt.f_n) ])
for kpt in kpt_u ]
return coeff
def calculate_spinpaired(self, e_g, n_g, v_g):
self.e_g[:] = 0.0
self.vt_sg[:] = 0.0
self.xc.calculate(self.nlfunc.finegd, n_g[None, ...], self.vt_sg,
self.e_g)
self.e_g[:] = np.where(n_g<1e-10, 0, self.e_g)
v_g += self.weight * 2 * self.e_g / (n_g + 1e-10)
e_g += self.weight * self.e_g
def calculate_spinpolarized(self, e_g, n_sg, v_sg):
# Calculate spinpolarized exchange screening as two spin-paired calculations n=2*n_s
for n, v in [ (n_sg[0], v_sg[0]), (n_sg[1], v_sg[1]) ]:
self.e_g[:] = 0.0
self.vt_sg[:] = 0.0
self.xc.calculate(self.nlfunc.finegd, 2*n[None, ...], self.vt_sg, self.e_g)
self.e_g[:] = np.where(n<1e-10, 0, self.e_g)
v += self.weight * 2 * self.e_g / (2 * n + 1e-9)
e_g += self.weight * self.e_g / 2
def calculate_energy_and_derivatives(self, setup, D_sp, H_sp, a, addcoredensity=True):
# Get the XC-correction instance
c = setup.xc_correction
nspins = self.nlfunc.nspins
E = 0
for D_p, dEdD_p in zip(D_sp, H_sp):
D_Lq = np.dot(c.B_pqL.T, nspins*D_p)
n_Lg = np.dot(D_Lq, c.n_qg)
if addcoredensity:
n_Lg[0] += c.nc_g * sqrt(4 * pi)
nt_Lg = np.dot(D_Lq, c.nt_qg)
if addcoredensity:
nt_Lg[0] += c.nct_g * sqrt(4 * pi)
dndr_Lg = np.zeros((c.Lmax, c.ng))
dntdr_Lg = np.zeros((c.Lmax, c.ng))
for L in range(c.Lmax):
c.rgd.derivative(n_Lg[L], dndr_Lg[L])
c.rgd.derivative(nt_Lg[L], dntdr_Lg[L])
vt_g = np.zeros(c.ng)
v_g = np.zeros(c.ng)
e_g = np.zeros(c.ng)
deda2_g = np.zeros(c.ng)
for y, (w, Y_L) in enumerate(zip(weight_n, c.Y_nL)):
# Cut gradient releated coefficient to match the setup's Lmax
A_Li = rnablaY_nLv[y, :c.Lmax]
# Expand pseudo density
nt_g = np.dot(Y_L, nt_Lg)
# Expand pseudo density gradient
a1x_g = np.dot(A_Li[:, 0], nt_Lg)
a1y_g = np.dot(A_Li[:, 1], nt_Lg)
a1z_g = np.dot(A_Li[:, 2], nt_Lg)
a2_g = a1x_g**2 + a1y_g**2 + a1z_g**2
a2_g[1:] /= c.rgd.r_g[1:]**2
a2_g[0] = a2_g[1]
a1_g = np.dot(Y_L, dntdr_Lg)
a2_g += a1_g**2
vt_g[:] = 0.0
e_g[:] = 0.0
# Calculate pseudo GGA energy density (potential is discarded)
self.xc.kernel.calculate(e_g, nt_g.reshape((1, -1)),
vt_g.reshape((1, -1)),
a2_g.reshape((1, -1)),
deda2_g.reshape((1, -1)))
# Calculate pseudo GLLB-potential from GGA-energy density
vt_g[:] = 2 * e_g / (nt_g + 1e-10)
dEdD_p -= self.weight * w * np.dot(np.dot(c.B_pqL, Y_L),
np.dot(c.nt_qg, vt_g * c.rgd.dv_g))
E -= w * np.dot(e_g, c.rgd.dv_g) / nspins
# Expand density
n_g = np.dot(Y_L, n_Lg)
# Expand density gradient
a1x_g = np.dot(A_Li[:, 0], n_Lg)
a1y_g = np.dot(A_Li[:, 1], n_Lg)
a1z_g = np.dot(A_Li[:, 2], n_Lg)
a2_g = a1x_g**2 + a1y_g**2 + a1z_g**2
a2_g[1:] /= c.rgd.r_g[1:]**2
a2_g[0] = a2_g[1]
a1_g = np.dot(Y_L, dndr_Lg)
a2_g += a1_g**2
v_g[:] = 0.0
e_g[:] = 0.0
# Calculate GGA energy density (potential is discarded)
self.xc.kernel.calculate(e_g, n_g.reshape((1, -1)),
v_g.reshape((1, -1)),
a2_g.reshape((1, -1)),
deda2_g.reshape((1, -1)))
# Calculate GLLB-potential from GGA-energy density
v_g[:] = 2 * e_g / (n_g + 1e-10)
dEdD_p += self.weight * w * np.dot(np.dot(c.B_pqL, Y_L),
np.dot(c.n_qg, v_g * c.rgd.dv_g))
E += w * np.dot(e_g, c.rgd.dv_g) / nspins
return E * self.weight
def add_smooth_xc_potential_and_energy_1d(self, vt_g):
self.v_g[:] = 0.0
self.e_g[:] = 0.0
self.xc.calculate_spherical(self.ae.rgd, self.ae.nt.reshape((1, -1)),
self.v_g.reshape((1, -1)), self.e_g)
vt_g += 2 * self.weight * self.e_g / (self.ae.nt + 1e-10)
return self.weight * np.sum(self.e_g * self.ae.rgd.dv_g)
def initialize_from_atomic_orbitals(self, basis_functions):
# GLLBScr needs only density which is already initialized
pass
def add_extra_setup_data(self, dict):
# GLLBScr has not any special data
pass
def read(self, reader):
# GLLBScr has no special data to be read
pass
def write(self, writer, natoms):
# GLLBScr has no special data to be written
pass
class C_XC(Contribution):
def __init__(self, nlfunc, weight, functional = 'LDA'):
Contribution.__init__(self, nlfunc, weight)
self.functional = functional
def get_name(self):
return 'XC'
def get_desc(self):
return "("+self.functional+")"
def initialize(self):
self.xc = XC(self.functional)
self.vt_sg = self.nlfunc.finegd.empty(self.nlfunc.nspins)
self.e_g = self.nlfunc.finegd.empty()
def initialize_1d(self):
self.ae = self.nlfunc.ae
self.xc = XC(self.functional)
self.v_g = np.zeros(self.ae.N)
def calculate_spinpaired(self, e_g, n_g, v_g):
self.e_g[:] = 0.0
self.vt_sg[:] = 0.0
self.xc.calculate(self.nlfunc.finegd, n_g[None, ...], self.vt_sg,
self.e_g)
v_g += self.weight * self.vt_sg[0]
e_g += self.weight * self.e_g
def calculate_spinpolarized(self, e_g, n_sg, v_sg):
self.e_g[:] = 0.0
self.vt_sg[:] = 0.0
self.xc.calculate(self.nlfunc.finegd, n_sg, self.vt_sg, self.e_g)
#self.xc.get_energy_and_potential(na_g, self.vt_sg[0], nb_g, self.vt_sg[1], e_g=self.e_g)
v_sg[0] += self.weight * self.vt_sg[0]
v_sg[1] += self.weight * self.vt_sg[1]
e_g += self.weight * self.e_g
def calculate_energy_and_derivatives(self, setup, D_sp, H_sp, a, addcoredensity=True):
E = self.xc.calculate_paw_correction(setup, D_sp, H_sp, True, a)
E += setup.xc_correction.Exc0
print("E", E)
return E
def add_xc_potential_and_energy_1d(self, v_g):
self.v_g[:] = 0.0
Exc = self.xc.calculate_spherical(self.ae.rgd,
self.ae.n.reshape((1, -1)),
self.v_g.reshape((1, -1)))
v_g += self.weight * self.v_g
return self.weight * Exc
def add_smooth_xc_potential_and_energy_1d(self, vt_g):
self.v_g[:] = 0.0
Exc = self.xc.calculate_spherical(self.ae.rgd,
self.ae.nt.reshape((1, -1)),
self.v_g.reshape((1, -1)))
vt_g += self.weight * self.v_g
return self.weight * Exc
def initialize_from_atomic_orbitals(self, basis_functions):
# LDA needs only density, which is already initialized
pass
def add_extra_setup_data(self, dict):
# LDA has not any special data
pass
def write(self, writer, natoms):
# LDA has not any special data to be written
pass
def read(self, reader):
# LDA has not any special data to be read
pass
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
'GGA_X_B88+GGA_C_P86': 2.30508027546,
'GGA_X_B88+GGA_C_LYP': 2.28183010548,
'GGA_X_FT97_A+GGA_C_LYP': 2.26846048873,
}
libxc_set = [
'LDA_X', 'LDA_X+LDA_C_PW', 'LDA_X+LDA_C_VWN', 'LDA_X+LDA_C_PZ',
'GGA_X_PBE+GGA_C_PBE', 'GGA_X_PBE_R+GGA_C_PBE',
'GGA_X_B88+GGA_C_P86', 'GGA_X_B88+GGA_C_LYP',
'GGA_X_FT97_A+GGA_C_LYP'
]
x = 0.000001
for xcname in libxc_set:
ra.seed(8)
xc = XC(xcname)
s = create_setup('N', xc)
ni = s.ni
nii = ni * (ni + 1) // 2
D_p = 0.1 * ra.random(nii) + 0.4
H_p = np.zeros(nii)
E1 = xc.calculate_paw_correction(s, D_p.reshape(1, -1), H_p.reshape(1, -1))
dD_p = x * ra.random(nii)
D_p += dD_p
dE = np.dot(H_p, dD_p) / x
E2 = xc.calculate_paw_correction(s, D_p.reshape(1, -1))
print xcname, dE, (E2 - E1) / x
equal(dE, (E2 - E1) / x, 0.003)
E2s = xc.calculate_paw_correction(s,
def __init__(self, name, stencil=2, hybrid=None, xc=None, omega=None):
"""Mix standard functionals with exact exchange.
name: str
Name of hybrid functional.
hybrid: float
Fraction of exact exchange.
xc: str or XCFunctional object
Standard DFT functional with scaled down exchange.
"""
rsf_functionals = { # Parameters can also be taken from libxc
'CAMY-BLYP': { # Akinaga, Ten-no CPL 462 (2008) 348-351
'alpha': 0.2,
'beta': 0.8,
'omega': 0.44,
'cam': True,
'rsf': 'Yukawa',
'xc': 'HYB_GGA_XC_CAMY_BLYP'
},
'CAMY-B3LYP': { # Seth, Ziegler JCTC 8 (2012) 901-907
'alpha': 0.19,
'beta': 0.46,
'omega': 0.34,
'cam': True,
'rsf': 'Yukawa',
'xc': 'HYB_GGA_XC_CAMY_B3LYP'
},
'LCY-BLYP': { # Seth, Ziegler JCTC 8 (2012) 901-907
'alpha': 0.0,
'beta': 1.0,
'omega': 0.75,
'cam': False,
'rsf': 'Yukawa',
'xc': 'HYB_GGA_XC_LCY_BLYP'
},
'LCY-PBE': { # Seth, Ziegler JCTC 8 (2012) 901-907
'alpha': 0.0,
'beta': 1.0,
'omega': 0.75,
'cam': False,
'rsf': 'Yukawa',
'xc': 'HYB_GGA_XC_LCY_PBE'
}
}
self.omega = None
self.cam_alpha = None
self.cam_beta = None
self.is_cam = False
self.rsf = None
def _xc(name):
return {'name': name, 'stencil': stencil}
if name == 'EXX':
hybrid = 1.0
xc = XC(XCNull())
elif name == 'PBE0':
hybrid = 0.25
xc = XC(_xc('HYB_GGA_XC_PBEH'))
elif name == 'B3LYP':
hybrid = 0.2
xc = XC(_xc('HYB_GGA_XC_B3LYP'))
elif name == 'HSE03':
hybrid = 0.25
omega = 0.106
xc = XC(_xc('HYB_GGA_XC_HSE03'))
elif name == 'HSE06':
hybrid = 0.25
omega = 0.11
xc = XC(_xc('HYB_GGA_XC_HSE06'))
elif name in rsf_functionals:
rsf_functional = rsf_functionals[name]
self.cam_alpha = rsf_functional['alpha']
self.cam_beta = rsf_functional['beta']
self.omega = rsf_functional['omega']
self.is_cam = rsf_functional['cam']
self.rsf = rsf_functional['rsf']
xc = XC(rsf_functional['xc'])
hybrid = self.cam_alpha + self.cam_beta
if isinstance(xc, (basestring, dict)):
xc = XC(xc)
self.hybrid = float(hybrid)
self.xc = xc
if omega is not None:
omega = float(omega)
if self.omega is not None and self.omega != omega:
self.xc.kernel.set_omega(omega)
# Needed to tune omega for RSF
self.omega = omega
XCFunctional.__init__(self, name, xc.type)
def initialize(self, atoms=None):
"""Inexpensive initialization."""
if atoms is None:
atoms = self.atoms
else:
# Save the state of the atoms:
self.atoms = atoms.copy()
par = self.input_parameters
world = par.communicator
if world is None:
world = mpi.world
elif hasattr(world, 'new_communicator'):
# Check for whether object has correct type already
#
# Using isinstance() is complicated because of all the
# combinations, serial/parallel/debug...
pass
else:
# world should be a list of ranks:
world = mpi.world.new_communicator(np.asarray(world))
self.wfs.world = world
self.set_text(par.txt, par.verbose)
natoms = len(atoms)
pos_av = atoms.get_positions() / Bohr
cell_cv = atoms.get_cell()
pbc_c = atoms.get_pbc()
Z_a = atoms.get_atomic_numbers()
magmom_a = atoms.get_initial_magnetic_moments()
magnetic = magmom_a.any()
spinpol = par.spinpol
if par.hund:
if natoms != 1:
raise ValueError('hund=True arg only valid for single atoms!')
spinpol = True
if spinpol is None:
spinpol = magnetic
elif magnetic and not spinpol:
raise ValueError('Non-zero initial magnetic moment for a '
'spin-paired calculation!')
nspins = 1 + int(spinpol)
if isinstance(par.xc, str):
xc = XC(par.xc)
else:
xc = par.xc
setups = Setups(Z_a, par.setups, par.basis, par.lmax, xc, world)
# K-point descriptor
kd = KPointDescriptor(par.kpts, nspins)
width = par.width
if width is None:
if kd.gamma:
width = 0.0
else:
width = 0.1 # eV
else:
assert par.occupations is None
if par.gpts is not None and par.h is None:
N_c = np.array(par.gpts)
else:
if par.h is None:
self.text('Using default value for grid spacing.')
h = 0.2
else:
h = par.h
N_c = h2gpts(h, cell_cv)
cell_cv /= Bohr
if hasattr(self, 'time') or par.dtype==complex:
dtype = complex
else:
if kd.gamma:
dtype = float
else:
dtype = complex
kd.set_symmetry(atoms, setups, par.usesymm, N_c)
nao = setups.nao
nvalence = setups.nvalence - par.charge
nbands = par.nbands
if nbands is None:
nbands = nao
elif nbands > nao and par.mode == 'lcao':
raise ValueError('Too many bands for LCAO calculation: ' +
'%d bands and only %d atomic orbitals!' %
(nbands, nao))
if nvalence < 0:
raise ValueError(
'Charge %f is not possible - not enough valence electrons' %
par.charge)
M = magmom_a.sum()
if par.hund:
f_si = setups[0].calculate_initial_occupation_numbers(
magmom=0, hund=True, charge=par.charge, nspins=nspins)
Mh = f_si[0].sum() - f_si[1].sum()
if magnetic and M != Mh:
raise RuntimeError('You specified a magmom that does not'
'agree with hunds rule!')
else:
M = Mh
if nbands <= 0:
nbands = int(nvalence + M + 0.5) // 2 + (-nbands)
if nvalence > 2 * nbands:
raise ValueError('Too few bands! Electrons: %d, bands: %d'
% (nvalence, nbands))
if par.width is not None:
self.text('**NOTE**: please start using '
'occupations=FermiDirac(width).')
if par.fixmom:
self.text('**NOTE**: please start using '
'occupations=FermiDirac(width, fixmagmom=True).')
if self.occupations is None:
if par.occupations is None:
# Create object for occupation numbers:
self.occupations = occupations.FermiDirac(width, par.fixmom)
else:
self.occupations = par.occupations
self.occupations.magmom = M
cc = par.convergence
if par.mode == 'lcao':
niter_fixdensity = 0
else:
niter_fixdensity = None
if self.scf is None:
self.scf = SCFLoop(
cc['eigenstates'] * nvalence,
cc['energy'] / Hartree * max(nvalence, 1),
cc['density'] * nvalence,
par.maxiter, par.fixdensity,
niter_fixdensity)
parsize, parsize_bands = par.parallel['domain'], par.parallel['band']
if parsize_bands is None:
parsize_bands = 1
# TODO delete/restructure so all checks are in BandDescriptor
if nbands % parsize_bands != 0:
raise RuntimeError('Cannot distribute %d bands to %d processors' %
(nbands, parsize_bands))
if not self.wfs:
if parsize == 'domain only': #XXX this was silly!
parsize = world.size
domain_comm, kpt_comm, band_comm = mpi.distribute_cpus(parsize,
parsize_bands, nspins, kd.nibzkpts, world, par.idiotproof)
kd.set_communicator(kpt_comm)
parstride_bands = par.parallel['stridebands']
bd = BandDescriptor(nbands, band_comm, parstride_bands)
if (self.density is not None and
self.density.gd.comm.size != domain_comm.size):
# Domain decomposition has changed, so we need to
# reinitialize density and hamiltonian:
if par.fixdensity:
raise RuntimeError("I'm confused - please specify parsize."
)
self.density = None
self.hamiltonian = None
# Construct grid descriptor for coarse grids for wave functions:
gd = self.grid_descriptor_class(N_c, cell_cv, pbc_c,
domain_comm, parsize)
# do k-point analysis here? XXX
args = (gd, nvalence, setups, bd, dtype, world, kd, self.timer)
if par.mode == 'lcao':
# Layouts used for general diagonalizer
sl_lcao = par.parallel['sl_lcao']
if sl_lcao is None:
sl_lcao = par.parallel['sl_default']
lcaoksl = get_KohnSham_layouts(sl_lcao, 'lcao',
gd, bd, dtype,
nao=nao, timer=self.timer)
self.wfs = LCAOWaveFunctions(lcaoksl, *args)
elif par.mode == 'fd' or isinstance(par.mode, PW):
# buffer_size keyword only relevant for fdpw
buffer_size = par.parallel['buffer_size']
# Layouts used for diagonalizer
sl_diagonalize = par.parallel['sl_diagonalize']
if sl_diagonalize is None:
sl_diagonalize = par.parallel['sl_default']
diagksl = get_KohnSham_layouts(sl_diagonalize, 'fd',
gd, bd, dtype,
buffer_size=buffer_size,
timer=self.timer)
# Layouts used for orthonormalizer
sl_inverse_cholesky = par.parallel['sl_inverse_cholesky']
if sl_inverse_cholesky is None:
sl_inverse_cholesky = par.parallel['sl_default']
if sl_inverse_cholesky != sl_diagonalize:
message = 'sl_inverse_cholesky != sl_diagonalize ' \
'is not implemented.'
raise NotImplementedError(message)
orthoksl = get_KohnSham_layouts(sl_inverse_cholesky, 'fd',
gd, bd, dtype,
buffer_size=buffer_size,
timer=self.timer)
# Use (at most) all available LCAO for initialization
lcaonbands = min(nbands, nao)
lcaobd = BandDescriptor(lcaonbands, band_comm, parstride_bands)
assert nbands <= nao or bd.comm.size == 1
assert lcaobd.mynbands == min(bd.mynbands, nao) #XXX
# Layouts used for general diagonalizer (LCAO initialization)
sl_lcao = par.parallel['sl_lcao']
if sl_lcao is None:
sl_lcao = par.parallel['sl_default']
initksl = get_KohnSham_layouts(sl_lcao, 'lcao',
gd, lcaobd, dtype,
nao=nao,
timer=self.timer)
if par.mode == 'fd':
self.wfs = FDWaveFunctions(par.stencils[0], diagksl,
orthoksl, initksl, *args)
else:
# Planewave basis:
self.wfs = par.mode(diagksl, orthoksl, initksl,
gd, nvalence, setups, bd,
world, kd, self.timer)
else:
self.wfs = par.mode(self, *args)
else:
self.wfs.set_setups(setups)
if not self.wfs.eigensolver:
# Number of bands to converge:
nbands_converge = cc['bands']
if nbands_converge == 'all':
nbands_converge = nbands
elif nbands_converge != 'occupied':
assert isinstance(nbands_converge, int)
if nbands_converge < 0:
nbands_converge += nbands
eigensolver = get_eigensolver(par.eigensolver, par.mode,
par.convergence)
eigensolver.nbands_converge = nbands_converge
# XXX Eigensolver class doesn't define an nbands_converge property
self.wfs.set_eigensolver(eigensolver)
if self.density is None:
gd = self.wfs.gd
if par.stencils[1] != 9:
# Construct grid descriptor for fine grids for densities
# and potentials:
finegd = gd.refine()
else:
# Special case (use only coarse grid):
finegd = gd
self.density = Density(gd, finegd, nspins,
par.charge + setups.core_charge)
self.density.initialize(setups, par.stencils[1], self.timer,
magmom_a, par.hund)
self.density.set_mixer(par.mixer)
if self.hamiltonian is None:
gd, finegd = self.density.gd, self.density.finegd
self.hamiltonian = Hamiltonian(gd, finegd, nspins,
setups, par.stencils[1], self.timer,
xc, par.poissonsolver,
par.external)
xc.initialize(self.density, self.hamiltonian, self.wfs,
self.occupations)
self.text()
self.print_memory_estimate(self.txt, maxdepth=memory_estimate_depth)
self.txt.flush()
if dry_run:
self.dry_run()
self.initialized = True
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
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)
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.gd = 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])
def log(self, *args, **kwargs):
self.fd.write(kwargs.get('sep', ' ').join([str(arg) for arg in args]) +
kwargs.get('end', '\n'))
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=1000, 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
self.gd = GridDescriptor(r1=1 / alpha2**0.5 / 50, rN=rcut, N=ngpts)
self.log('Grid points: %d (%.5f, %.5f, %.5f, ..., %.3f, %.3f)' %
((self.gd.N,) + tuple(self.gd.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.gd, 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.gd, 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.gd.zeros(self.nspins)
self.vr_sg[:] = -self.Z
def solve(self):
"""Diagonalize Schrödinger equation."""
self.eeig = 0.0
for channel in self.channels:
channel.solve(self.vr_sg[channel.s])
self.eeig += channel.get_eigenvalue_sum()
def calculate_density(self):
"""Calculate elctron density and kinetic energy."""
self.n_sg = self.gd.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.gd.poisson(n_g)
self.eH = 0.5 * self.gd.integrate(n_g * self.vHr_g, -1)
self.eZ = -self.Z * self.gd.integrate(n_g, -1)
def calculate_xc_potential(self):
self.vxc_sg = self.gd.zeros(self.nspins)
self.exc = self.xc.calculate_spherical(self.gd, 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.gd.r_g
self.vr_sg += self.vHr_g
self.vr_sg -= self.Z
self.ekin = (self.eeig -
self.gd.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()
dn = self.Z
pb = ProgressBar(log(dnmax / dn), 0, 53, self.fd)
self.log()
for iter in range(maxiter):
if iter > 1:
self.vr_sg *= mix
self.vr_sg += (1 - mix) * vr_old_sg
dn = self.gd.integrate(abs(self.n_sg - n_old_sg).sum(0))
pb(log(dnmax / dn))
if dn <= dnmax:
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 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.gd.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))
self.log('=====================================================')
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.log('============================================')
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
colors = 'krgbycm'
for ch in self.channels:
for n in range(len(ch.f_n)):
fr_g = ch.basis.expand(ch.C_nb[n]) * self.gd.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.gd.integrate(n_g, 1)
gave = self.gd.get_index(rave)
fr_g *= cmp(fr_g[gave], 0)
plt.plot(self.gd.r_g, fr_g,
ls=ls, lw=lw, color=colors[n + ch.l], label=name)
plt.legend(loc='best')
plt.axis(xmax=rc)
plt.show()
def logarithmic_derivative(self, l, energies, rcut):
vr = splrep(self.gd.r_g, self.vr_sg[0])
def v(r):
return splev(r, vr) / r
def f(y, r, e):
if r == 0:
return [y[1], -2.0]
return [y[1], 2 * (v(r) - e) * y[0]]
logderivs = []
for e in energies:
u, dudr = odeint(f, [0, 1], [0, rcut], (e,))[1, :]
logderivs.append(dudr / u)
return logderivs
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'
class C_XC(Contribution):
def __init__(self, nlfunc, weight, functional = 'LDA'):
Contribution.__init__(self, nlfunc, weight)
self.functional = functional
def get_name(self):
return 'XC'
def get_desc(self):
return "("+self.functional+")"
def initialize(self):
self.xc = XC(self.functional)
self.vt_sg = self.nlfunc.finegd.empty(self.nlfunc.nspins)
self.e_g = self.nlfunc.finegd.empty()
def initialize_1d(self):
self.ae = self.nlfunc.ae
self.xc = XC(self.functional)
self.v_g = np.zeros(self.ae.N)
def calculate_spinpaired(self, e_g, n_g, v_g):
self.e_g[:] = 0.0
self.vt_sg[:] = 0.0
self.xc.calculate(self.nlfunc.finegd, n_g[None, ...], self.vt_sg,
self.e_g)
v_g += self.weight * self.vt_sg[0]
e_g += self.weight * self.e_g
def calculate_spinpolarized(self, e_g, na_g, va_g, nb_g, vb_g):
self.e_g[:] = 0.0
self.vt_sg[:] = 0.0
self.xc.get_energy_and_potential(na_g, self.vt_sg[0], nb_g, self.vt_sg[1], e_g=self.e_g)
va_g += self.weight * self.vt_sg[0]
vb_g += self.weight * self.vt_sg[1]
e_g += (self.weight * self.e_g).ravel()
def calculate_energy_and_derivatives(self, D_sp, H_sp, a):
# Get the XC-correction instance
c = self.nlfunc.setups[a].xc_correction
assert self.nlfunc.nspins == 1
D_p = D_sp[0]
dEdD_p = H_sp[0][:]
D_Lq = dot3(c.B_pqL.T, D_p)
n_Lg = np.dot(D_Lq, c.n_qg)
n_Lg[0] += c.nc_g * sqrt(4 * pi)
nt_Lg = np.dot(D_Lq, c.nt_qg)
nt_Lg[0] += c.nct_g * sqrt(4 * pi)
dndr_Lg = np.zeros((c.Lmax, c.ng))
dntdr_Lg = np.zeros((c.Lmax, c.ng))
for L in range(c.Lmax):
c.rgd.derivative(n_Lg[L], dndr_Lg[L])
c.rgd.derivative(nt_Lg[L], dntdr_Lg[L])
E = 0
vt_g = np.zeros(c.ng)
v_g = np.zeros(c.ng)
e_g = np.zeros(c.ng)
y = 0
for w, Y_L in zip(weight_n, c.Y_nL):
A_Li = rnablaY_nLv[y, :c.Lmax]
a1x_g = np.dot(A_Li[:, 0], n_Lg)
a1y_g = np.dot(A_Li[:, 1], n_Lg)
a1z_g = np.dot(A_Li[:, 2], n_Lg)
a2_g = a1x_g**2 + a1y_g**2 + a1z_g**2
a2_g[1:] /= c.rgd.r_g[1:]**2
a2_g[0] = a2_g[1]
a1_g = np.dot(Y_L, dndr_Lg)
a2_g += a1_g**2
deda2_g = np.zeros(c.ng)
v_g[:] = 0.0
e_g[:] = 0.0
n_g = np.dot(Y_L, n_Lg)
self.xc.kernel.calculate(e_g, n_g.reshape((1, -1)),
v_g.reshape((1, -1)),
a2_g.reshape((1, -1)),
deda2_g.reshape((1, -1)))
E += w * np.dot(e_g, c.rgd.dv_g)
x_g = -2.0 * deda2_g * c.rgd.dv_g * a1_g
c.rgd.derivative2(x_g, x_g)
x_g += v_g * c.rgd.dv_g
dEdD_p += self.weight * w * np.dot(dot3(c.B_pqL, Y_L),
np.dot(c.n_qg, x_g))
x_g = 8.0 * pi * deda2_g * c.rgd.dr_g
dEdD_p += w * np.dot(dot3(c.B_pqL,
A_Li[:, 0]),
np.dot(c.n_qg, x_g * a1x_g))
dEdD_p += w * np.dot(dot3(c.B_pqL,
A_Li[:, 1]),
np.dot(c.n_qg, x_g * a1y_g))
dEdD_p += w * np.dot(dot3(c.B_pqL,
A_Li[:, 2]),
np.dot(c.n_qg, x_g * a1z_g))
n_g = np.dot(Y_L, nt_Lg)
a1x_g = np.dot(A_Li[:, 0], nt_Lg)
a1y_g = np.dot(A_Li[:, 1], nt_Lg)
a1z_g = np.dot(A_Li[:, 2], nt_Lg)
a2_g = a1x_g**2 + a1y_g**2 + a1z_g**2
a2_g[1:] /= c.rgd.r_g[1:]**2
a2_g[0] = a2_g[1]
a1_g = np.dot(Y_L, dntdr_Lg)
a2_g += a1_g**2
v_g = np.zeros(c.ng)
e_g = np.zeros(c.ng)
deda2_g = np.zeros(c.ng)
v_g[:] = 0.0
e_g[:] = 0.0
self.xc.kernel.calculate(e_g, n_g.reshape((1, -1)),
v_g.reshape((1, -1)),
a2_g.reshape((1, -1)),
deda2_g.reshape((1, -1)))
E -= w * np.dot(e_g, c.dv_g)
x_g = -2.0 * deda2_g * c.dv_g * a1_g
c.rgd.derivative2(x_g, x_g)
x_g += v_g * c.dv_g
B_Lqp = c.B_pqL.T
dEdD_p -= w * np.dot(dot3(c.B_pqL, Y_L),
np.dot(c.nt_qg, x_g))
x_g = 8.0 * pi * deda2_g * c.rgd.dr_g
dEdD_p -= w * np.dot(dot3(c.B_pqL,
A_Li[:, 0]),
np.dot(c.nt_qg, x_g * a1x_g))
dEdD_p -= w * np.dot(dot3(c.B_pqL,
A_Li[:, 1]),
np.dot(c.nt_qg, x_g * a1y_g))
dEdD_p -= w * np.dot(dot3(c.B_pqL,
A_Li[:, 2]),
np.dot(c.nt_qg, x_g * a1z_g))
y += 1
return (E) * self.weight
def add_xc_potential_and_energy_1d(self, v_g):
self.v_g[:] = 0.0
Exc = self.xc.calculate_spherical(self.ae.rgd,
self.ae.n.reshape((1, -1)),
self.v_g.reshape((1, -1)))
v_g += self.weight * self.v_g
return self.weight * Exc
def add_smooth_xc_potential_and_energy_1d(self, vt_g):
self.v_g[:] = 0.0
Exc = self.xc.calculate_spherical(self.ae.rgd,
self.ae.nt.reshape((1, -1)),
self.v_g.reshape((1, -1)))
vt_g += self.weight * self.v_g
return self.weight * Exc
def initialize_from_atomic_orbitals(self, basis_functions):
# LDA needs only density, which is already initialized
pass
def add_extra_setup_data(self, dict):
# LDA has not any special data
pass
def write(self, writer, natoms):
# LDA has not any special data to be written
pass
def read(self, reader):
# LDA has not any special data to be read
pass
