k_G = np.array([[11., 0.2, 0.1], [10., 0., 10.]])
nkpt = k_G.shape[0]
d0 = np.zeros((nkpt, m, m), dtype=complex)
for i in range(m):
for j in range(m):
for ik in range(nkpt):
k = k_G[ik]
kk = np.sqrt(np.inner(k, k))
kr = np.inner(k, rr.T).T
expkr = np.exp(-1j * kr)
d0[ik, i, j] = gd.integrate(psi[i] * psi[j] * expkr)
# Calculate on 1d-grid < phi_i | e**(-ik.r) | phi_j >
rgd = RadialGridDescriptor(r, np.ones_like(r) * r[1])
g = [np.exp(-(r / rc * b)**2) * r**l for l in range(lmax + 1)]
l_j = range(lmax + 1)
d1 = two_phi_planewave_integrals(k_G,
rgd=rgd,
phi_jg=g,
phit_jg=np.zeros_like(g),
l_j=l_j)
d1 = d1.reshape(nkpt, m, m)
for i in range(m):
for j in range(m):
for ik in range(nkpt):
if np.abs(d0[ik, i, j] - d1[ik, i, j]) > 1e-10:
print(i, j, d0[ik, i, j] - d1[ik, i, j])
from math import pi
from gpaw.grid_descriptor import RadialGridDescriptor, GridDescriptor
from gpaw.xc import XC
import numpy as np
from gpaw.test import equal
r = 0.01 * np.arange(100)
dr = 0.01 * np.ones(100)
rgd = RadialGridDescriptor(r, dr)
for name in ['LDA', 'PBE']:
xc = XC(name)
for nspins in [1, 2]:
n = rgd.zeros(nspins)
v = rgd.zeros(nspins)
n[:] = np.exp(-r**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
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):
"""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
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 intialize_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']:
# For some reason this works better for these atoms:
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.')
g = np.arange(N, dtype=float)
self.r = beta * g / (N - g)
self.dr = beta * N / (N - g)**2
self.rgd = RadialGridDescriptor(self.r, self.dr)
self.d2gdr2 = -2 * N * beta / (beta + self.r)**3
# 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.intialize_wave_functions()
n[:] = self.calculate_density()
bar = '|------------------------------------------------|'
t(bar)
niter = 0
qOK = log(1e-10)
while True:
# calculate hartree potential
hartree(0, n * r * dr, self.beta, self.N, vHr)
# add potential from nuclear point charge (v = -Z / r)
vHr -= Z
# calculated exchange correlation potential and energy
self.vXC[:] = 0.0
if self.xc.type == 'GLLB':
# Update the potential to self.vXC an the energy to self.Exc
Exc = self.xc.get_xc_potential_and_energy_1d(self.vXC)
else:
Exc = self.xc.calculate_spherical(self.rgd,
n.reshape((1, -1)),
self.vXC.reshape((1, -1)))
# calculate new total Kohn-Sham effective potential and
# admix with old version
vr[:] = vHr + self.vXC * r
if niter > 0:
vr[:] = 0.4 * vr + 0.6 * 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 > 117:
raise RuntimeError, 'Did not converge!'
## print
tau = self.calculate_kinetic_energy_density()
## print "Ekin(tau)=",np.dot(tau *r**2 , dr) * 4*pi
## self.write(tau,'tau1')
## tau2 = self.calculate_kinetic_energy_density2()
## self.write(tau2,'tau2')
## self.write(tau-tau2,'tau12')
## print "Ekin(tau2)=",np.dot(tau2 *r**2 , dr) * 4*pi
# When iterations are over calculate the correct exchange energy
#if self.xc.is_non_local():
# from gpaw.exx import atomic_exact_exchange
# Exc = atomic_exact_exchange(self)
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
Epot = 2 * pi * np.dot(n * r * (vHr - Z), dr)
Ekin = -4 * pi * np.dot(n * vr * r, dr)
for f, e in zip(f_j, e_j):
Ekin += f * e
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
#mathiasl
# for x in range(np.size(self.r)):
# print self.r[x] , self.u_j[self.jcorehole,x]
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 >> f, r, a
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:] = float('nan')
return alpha * potential
from math import pi
from gpaw.grid_descriptor import RadialGridDescriptor, GridDescriptor
from gpaw.xc import XC
import numpy as np
from gpaw.test import equal
r = 0.01 * np.arange(100)
dr = 0.01 * np.ones(100)
rgd = RadialGridDescriptor(r, dr)
for name in ['LDA', 'PBE']:
xc = XC(name)
for nspins in [1, 2]:
n = rgd.zeros(nspins)
v = rgd.zeros(nspins)
n[:] = np.exp(-r**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
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.')
g = np.arange(N, dtype=float)
self.r = beta * g / (N - g)
self.dr = beta * N / (N - g)**2
self.rgd = RadialGridDescriptor(self.r, self.dr)
self.d2gdr2 = -2 * N * beta / (beta + self.r)**3
# 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.intialize_wave_functions()
n[:] = self.calculate_density()
bar = '|------------------------------------------------|'
t(bar)
niter = 0
qOK = log(1e-10)
while True:
# calculate hartree potential
hartree(0, n * r * dr, self.beta, self.N, vHr)
# add potential from nuclear point charge (v = -Z / r)
vHr -= Z
# calculated exchange correlation potential and energy
self.vXC[:] = 0.0
if self.xc.type == 'GLLB':
# Update the potential to self.vXC an the energy to self.Exc
Exc = self.xc.get_xc_potential_and_energy_1d(self.vXC)
else:
Exc = self.xc.calculate_spherical(self.rgd,
n.reshape((1, -1)),
self.vXC.reshape((1, -1)))
# calculate new total Kohn-Sham effective potential and
# admix with old version
vr[:] = vHr + self.vXC * r
if niter > 0:
vr[:] = 0.4 * vr + 0.6 * 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 > 117:
raise RuntimeError, 'Did not converge!'
## print
tau = self.calculate_kinetic_energy_density()
## print "Ekin(tau)=",np.dot(tau *r**2 , dr) * 4*pi
## self.write(tau,'tau1')
## tau2 = self.calculate_kinetic_energy_density2()
## self.write(tau2,'tau2')
## self.write(tau-tau2,'tau12')
## print "Ekin(tau2)=",np.dot(tau2 *r**2 , dr) * 4*pi
# When iterations are over calculate the correct exchange energy
#if self.xc.is_non_local():
# from gpaw.exx import atomic_exact_exchange
# Exc = atomic_exact_exchange(self)
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
Epot = 2 * pi * np.dot(n * r * (vHr - Z), dr)
Ekin = -4 * pi * np.dot(n * vr * r, dr)
for f, e in zip(f_j, e_j):
Ekin += f * e
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