def __init__(self):
bond = 1.42
sq3h = 3.**.5 * 0.5
self.sc = SuperCell(
np.array([[1.5, sq3h, 0.], [1.5, -sq3h, 0.], [0., 0., 10.]],
np.float64) * bond,
nsc=[3, 3, 1])
n = 60
rf = np.linspace(0, bond * 1.01, n)
rf = (rf, rf)
orb = SphericalOrbital(1, rf, 2.)
C = Atom(6, orb.toAtomicOrbital())
self.g = Geometry(
np.array([[0., 0., 0.], [1., 0., 0.]], np.float64) * bond,
atom=C,
sc=self.sc)
self.D = DensityMatrix(self.g)
self.DS = DensityMatrix(self.g, orthogonal=False)
def func(D, ia, idxs, idxs_xyz):
idx = D.geom.close(ia,
R=(0.1, 1.44),
idx=idxs,
idx_xyz=idxs_xyz)
ia = ia * 3
i0 = idx[0] * 3
i1 = idx[1] * 3
# on-site
p = 1.
D.D[ia, i0] = p
D.D[ia + 1, i0 + 1] = p
D.D[ia + 2, i0 + 2] = p
# nn
p = 0.1
# on-site directions
D.D[ia, ia + 1] = p
D.D[ia, ia + 2] = p
D.D[ia + 1, ia] = p
D.D[ia + 1, ia + 2] = p
D.D[ia + 2, ia] = p
D.D[ia + 2, ia + 1] = p
D.D[ia, i1 + 1] = p
D.D[ia, i1 + 2] = p
D.D[ia + 1, i1] = p
D.D[ia + 1, i1 + 2] = p
D.D[ia + 2, i1] = p
D.D[ia + 2, i1 + 1] = p
self.func = func
def __init__(self):
bond = 1.42
sq3h = 3.**.5 * 0.5
self.sc = SuperCell(np.array([[1.5, sq3h, 0.],
[1.5, -sq3h, 0.],
[0., 0., 10.]], np.float64) * bond, nsc=[3, 3, 1])
n = 60
rf = np.linspace(0, bond * 1.01, n)
rf = (rf, rf)
orb = SphericalOrbital(1, rf, 2.)
C = Atom(6, orb.toAtomicOrbital())
self.g = Geometry(np.array([[0., 0., 0.],
[1., 0., 0.]], np.float64) * bond,
atoms=C, sc=self.sc)
self.S = Overlap(self.g)
def test_wavefunction1():
N = 50
o1 = SphericalOrbital(0, (np.linspace(0, 2, N), np.exp(-np.linspace(0, 100, N))))
G = Geometry([[1] * 3, [2] * 3], Atom(6, o1), sc=[4, 4, 4])
H = Hamiltonian(G)
R, param = [0.1, 1.5], [1., 0.1]
H.construct([R, param])
ES = H.eigenstate(dtype=np.float64)
# Plot in the full thing
grid = Grid(0.1, geometry=H.geom)
grid.fill(0.)
ES.sub(0).wavefunction(grid)
def test_wavefunction_eta():
N = 50
o1 = SphericalOrbital(0, (np.linspace(0, 2, N), np.exp(-np.linspace(0, 100, N))))
G = Geometry([[1] * 3, [2] * 3], Atom(6, o1), sc=[4, 4, 4])
H = Hamiltonian(G, spin=Spin('nc'))
R, param = [0.1, 1.5], [[0., 0., 0.1, -0.1],
[1., 1., 0.1, -0.1]]
H.construct([R, param])
ES = H.eigenstate()
# Plot in the full thing
grid = Grid(0.1, dtype=np.complex128, sc=SuperCell([2, 2, 2], origo=[-1] * 3))
grid.fill(0.)
ES.sub(0).wavefunction(grid, eta=True)
def test_wavefunction2():
N = 50
o1 = SphericalOrbital(0, (np.linspace(0, 2, N), np.exp(-np.linspace(0, 100, N))))
G = Geometry([[1] * 3, [2] * 3], Atom(6, o1), sc=[4, 4, 4])
H = Hamiltonian(G)
R, param = [0.1, 1.5], [1., 0.1]
H.construct([R, param])
ES = H.eigenstate(dtype=np.float64)
# This is effectively plotting outside where no atoms exists
# (there could however still be psi weight).
grid = Grid(0.1, sc=SuperCell([2, 2, 2], origo=[2] * 3))
grid.fill(0.)
ES.sub(0).wavefunction(grid)
def test_rho2(self, setup):
bond = 1.42
sq3h = 3.**.5 * 0.5
sc = SuperCell(np.array(
[[1.5, sq3h, 0.], [1.5, -sq3h, 0.], [0., 0., 10.]], np.float64) *
bond,
nsc=[3, 3, 1])
n = 60
rf = np.linspace(0, bond * 1.01, n)
rf = (rf, rf)
orb = SphericalOrbital(1, rf, 2.)
C = Atom(6, orb)
g = Geometry(np.array([[0., 0., 0.], [1., 0., 0.]], np.float64) * bond,
atom=C,
sc=sc)
D = DensityMatrix(g)
D.construct([[0.1, bond + 0.01], [1., 0.1]])
grid = Grid(0.2, geometry=D.geom)
D.density(grid)
D = DensityMatrix(g, spin=Spin('P'))
D.construct([[0.1, bond + 0.01], [(1., 0.5), (0.1, 0.1)]])
grid = Grid(0.2, geometry=D.geom)
D.density(grid)
D.density(grid, [1., -1])
D.density(grid, 0)
D.density(grid, 1)
D = DensityMatrix(g, spin=Spin('NC'))
D.construct([[0.1, bond + 0.01],
[(1., 0.5, 0.01, 0.01), (0.1, 0.1, 0.1, 0.1)]])
grid = Grid(0.2, geometry=D.geom)
D.density(grid)
D.density(grid, [[1., 0.], [0., -1]])
D = DensityMatrix(g, spin=Spin('SO'))
D.construct([[0.1, bond + 0.01],
[(1., 0.5, 0.01, 0.01, 0.01, 0.01, 0., 0.),
(0.1, 0.1, 0.1, 0.1, 0., 0., 0., 0.)]])
grid = Grid(0.2, geometry=D.geom)
D.density(grid)
D.density(grid, [[1., 0.], [0., -1]])
D.density(grid, Spin.X)
D.density(grid, Spin.Y)
D.density(grid, Spin.Z)
def decompose_basis(l):
# Only split once
Zr, spec = l.split('-', 1)
idx = 0
for i, c in enumerate(Zr):
if c.isdigit():
idx = i
break
R = -1
if idx == 0:
Z = Zr
else:
Z = Zr[:idx]
try:
R = float(Zr[idx:])
except:
pass
# Now figure out the orbitals
orbs = []
m_order = {
0: [0],
1: [1, -1, 0], # px, py, pz
2: [0, 2, -2, 1, -1], # d3z^2-r^2, dx^2-y^2, dxy, dxz, dyz
3: [
0, 1, -1, 2, -2, 3, -3
], # f5z^2-3r^2, f5xz^2-xr^2, f5yz^2-yr^2, fzx^2-zy^2, fxyz, fx^3-3*xy^2, f3yx^2-y^3
4: [0, 1, -1, 2, -2, 3, -3, 4, -4]
}
for i, c in enumerate(spec):
try:
l = 'spdfg'.index(c)
try:
nZ = int(spec[i + 1])
except:
nZ = 1
for z in range(nZ):
orbs.extend(
SphericalOrbital(l, rf_func(R)).toAtomicOrbital(
m=m_order[l], Z=z + 1))
except:
pass
return Z, orbs
def test_rho_fail_nc(self, setup):
bond = 1.42
sq3h = 3.**.5 * 0.5
sc = SuperCell(np.array([[1.5, sq3h, 0.],
[1.5, -sq3h, 0.],
[0., 0., 10.]], np.float64) * bond, nsc=[3, 3, 1])
n = 60
rf = np.linspace(0, bond * 1.01, n)
rf = (rf, rf)
orb = SphericalOrbital(1, rf, 2.)
C = Atom(6, orb)
g = Geometry(np.array([[0., 0., 0.],
[1., 0., 0.]], np.float64) * bond,
atoms=C, sc=sc)
D = DensityMatrix(g, spin=Spin('NC'))
D.construct([[0.1, bond + 0.01], [(1., 0.5, 0.01, 0.01), (0.1, 0.1, 0.1, 0.1)]])
grid = Grid(0.2, geometry=D.geometry)
with pytest.raises(ValueError):
D.density(grid, [1., 0.])
def read_basis(self):
""" Returns a set of atoms corresponding to the basis-sets in the nc file """
if 'BASIS' not in self.groups:
return None
basis = self.groups['BASIS']
atom = [None] * len(basis.groups)
for a_str in basis.groups:
a = basis.groups[a_str]
if 'orbnl_l' not in a.variables:
# Do the easy thing.
# Get number of orbitals
label = a.Label.strip()
Z = int(a.Atomic_number)
mass = float(a.Mass)
i = int(a.ID) - 1
atom[i] = Atom(Z, [-1] * a.Number_of_orbitals,
mass=mass,
tag=label)
continue
# Retrieve values
orb_l = a.variables['orbnl_l'][:] # angular quantum number
orb_n = a.variables['orbnl_n'][:] # principal quantum number
orb_z = a.variables['orbnl_z'][:] # zeta
orb_P = a.variables[
'orbnl_ispol'][:] > 0 # polarization shell, or not
orb_q0 = a.variables['orbnl_pop'][:] # q0 for the orbitals
orb_delta = a.variables['delta'][:] # delta for the functions
orb_psi = a.variables['orb'][:, :]
# Now loop over all orbitals
orbital = []
# Number of basis-orbitals (before m-expansion)
no = len(a.dimensions['norbs'])
# All orbital data
for io in range(no):
n = orb_n[io]
l = orb_l[io]
z = orb_z[io]
P = orb_P[io]
# Grid spacing in Bohr (conversion is done later
# because the normalization is easier)
delta = orb_delta[io]
# Since the readed data has fewer significant digits we
# might as well re-create the table of the radial component.
r = aranged(orb_psi.shape[1]) * delta
# To get it per Ang**3
# TODO, check that this is correct.
# The fact that we have to have it normalized means that we need
# to convert psi /sqrt(Bohr**3) -> /sqrt(Ang**3)
# \int psi^\dagger psi == 1
psi = orb_psi[io, :] * r**l / Bohr2Ang**(3. / 2.)
# Create the sphericalorbital and then the atomicorbital
sorb = SphericalOrbital(l, (r * Bohr2Ang, psi), orb_q0[io])
# This will be -l:l (this is the way siesta does it)
orbital.extend(sorb.toAtomicOrbital(n=n, Z=z, P=P))
# Get number of orbitals
label = a.Label.strip()
Z = int(a.Atomic_number)
mass = float(a.Mass)
i = int(a.ID) - 1
atom[i] = Atom(Z, orbital, mass=mass, tag=label)
return atom
