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
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])
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
