def ip(symbol, fd, setup):
xc = 'LDA'
aea = AllElectronAtom(symbol, log=fd)
aea.initialize()
aea.run()
aea.refine()
aea.scalar_relativistic = True
aea.refine()
energy = aea.ekin + aea.eH + aea.eZ + aea.exc
eigs = []
for l, channel in enumerate(aea.channels):
n = l + 1
for e, f in zip(channel.e_n, channel.f_n):
if f == 0:
break
eigs.append((e, n, l))
n += 1
e0, n0, l0 = max(eigs)
aea = AllElectronAtom(symbol, log=fd)
aea.add(n0, l0, -1)
aea.initialize()
aea.run()
aea.refine()
aea.scalar_relativistic = True
aea.refine()
IP = aea.ekin + aea.eH + aea.eZ + aea.exc - energy
IP *= Ha
s = create_setup(symbol, type=setup, xc=xc)
f_ln = defaultdict(list)
for l, f in zip(s.l_j, s.f_j):
if f:
f_ln[l].append(f)
f_sln = [[f_ln[l] for l in range(1 + max(f_ln))]]
calc = AtomPAW(symbol, f_sln, xc=xc, txt=fd, setups=setup)
energy = calc.results['energy']
# eps_n = calc.wfs.kpt_u[0].eps_n
f_sln[0][l0][-1] -= 1
calc = AtomPAW(symbol, f_sln, xc=xc, charge=1, txt=fd, setups=setup)
IP2 = calc.results['energy'] - energy
return IP, IP2
'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 = s.xc_correction.calculate(xc, 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 = s.xc_correction.calculate(xc, D_p.reshape(1, -1))
print xcname, dE, (E2 - E1) / x
equal(dE, (E2 - E1) / x, 0.003)
E2s = s.xc_correction.calculate(xc,
np.array([0.5 * D_p, 0.5 * D_p]), np.array([H_p, H_p]))
'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 = s.xc_correction.calculate(xc, 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 = s.xc_correction.calculate(xc, D_p.reshape(1, -1))
print xcname, dE, (E2 - E1) / x
equal(dE, (E2 - E1) / x, 0.003)
E2s = s.xc_correction.calculate(xc, np.array([0.5 * D_p, 0.5 * D_p]),
np.array([H_p, H_p]))
import argparse
import matplotlib.pyplot as plt
from gpaw.setup import create_setup
parser = argparse.ArgumentParser(
description='Calculate approximation to the energy variation with '
'plane-wave cutoff energy. The approximation is to use the kinetic '
'energy from a PAW atom, which can be calculated efficiently on '
'a radial grid.')
parser.add_argument('-d', '--derivative', type=float, metavar='ECUT',
help='Calculate derivative of energy correction with '
'respect to plane-wave cutoff energy.')
parser.add_argument('name', help='Name of PAW dataset.')
args = parser.parse_args()
ds = create_setup(args.name)
G, de, e0 = ekin(ds)
dG = G[1]
if args.derivative:
dedecut = -dekindecut(G, de, args.derivative / Ha)
print('de/decut({}, {} eV) = {:.6f}'
.format(args.name, args.derivative, dedecut))
else:
de = (np.add.accumulate(de) - 0.5 * de[0] - 0.5 * de) * dG
ecut = 0.5 * G**2 * Ha
y = (de[-1] - de) * Ha
plt.plot(ecut, y)
plt.xlim(300, 1000)
from math import sqrt, pi
import numpy as np
from gpaw.setup import create_setup
from gpaw.grid_descriptor import GridDescriptor
from gpaw.localized_functions import create_localized_functions
from gpaw.xc import XC
n = 60 #40 /8 * 10
a = 10.0
gd = GridDescriptor((n, n, n), (a, a, a))
c_LL = np.identity(9, float)
a_Lg = gd.zeros(9)
nspins = 2
xc = XC('LDA')
for soft in [False]:
s = create_setup('Cu', xc, lmax=2)
ghat_l = s.ghat_l
ghat_Lg = create_localized_functions(ghat_l, gd, (0.54321, 0.5432, 0.543))
a_Lg[:] = 0.0
ghat_Lg.add(a_Lg, c_LL)
for l in range(3):
for m in range(2 * l + 1):
L = l**2 + m
a_g = a_Lg[L]
Q0 = gd.integrate(a_g) / sqrt(4 * pi)
Q1_m = -gd.calculate_dipole_moment(a_g) / sqrt(4 * pi / 3)
print(Q0)
if l == 0:
Q0 -= 1.0
Q1_m[:] = 0.0
elif l == 1:
from gpaw.setup import create_setup
for symbol, M, n in [('Pd', 1, 6), # 4d -> 5s
('Fe', 3, 5),
('V', 3, 5),
('Ti', 2, 5)]:
s = create_setup(symbol)
f_si = s.calculate_initial_occupation_numbers(magmom=M,
hund=False,
charge=0,
nspins=2)
print(f_si)
magmom = (f_si[0] - f_si[1]).sum()
assert abs(magmom - M) < 1e-10
N = ((f_si[0] - f_si[1]) != 0).sum()
assert n == N, 'Wrong # of values have changed'
import numpy as np
import numpy.random as ra
from gpaw.setup import create_setup
from gpaw.xc import XC
x = 0.000001
ra.seed(8)
xc = XC('LDA')
s = create_setup('H', xc)
ni = s.ni
nii = ni * (ni + 1) // 2
D_p = 0.1 * ra.random((1, nii)) + 0.2
H_p = np.zeros(nii)
def f(x):
return x
J_pp = s.xc_correction.four_phi_integrals(D_p, f)
# Check integrals using two_phi_integrals function and finite differences:
pass
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
equal(Em, Ems, 1.0e-12)
from math import sqrt, pi
import numpy as np
from gpaw.setup import create_setup
from gpaw.grid_descriptor import GridDescriptor
from gpaw.localized_functions import create_localized_functions
from gpaw.xc import XC
n = 60#40 /8 * 10
a = 10.0
gd = GridDescriptor((n, n, n), (a, a, a))
c_LL = np.identity(9, float)
a_Lg = gd.zeros(9)
nspins = 2
xc = XC('LDA')
for soft in [False]:
s = create_setup('Cu', xc, lmax=2)
ghat_l = s.ghat_l
ghat_Lg = create_localized_functions(ghat_l, gd, (0.54321, 0.5432, 0.543))
a_Lg[:] = 0.0
ghat_Lg.add(a_Lg, c_LL)
for l in range(3):
for m in range(2 * l + 1):
L = l**2 + m
a_g = a_Lg[L]
Q0 = gd.integrate(a_g) / sqrt(4 * pi)
Q1_m = -gd.calculate_dipole_moment(a_g) / sqrt(4 * pi / 3)
print Q0
if l == 0:
Q0 -= 1.0
Q1_m[:] = 0.0
elif l == 1:
import numpy as np
import numpy.random as ra
from gpaw.setup import create_setup
from gpaw.xc import XC
x = 0.000001
ra.seed(8)
xc = XC('LDA')
s = create_setup('H', xc)
ni = s.ni
nii = ni * (ni + 1) // 2
D_p = 0.1 * ra.random((1, nii)) + 0.2
H_p = np.zeros(nii)
def f(x):
return x
J_pp = s.xc_correction.four_phi_integrals(D_p, f)
# Check integrals using two_phi_integrals function and finite differences:
pass
