def test_dipole_prepared_continuum():
"""
see
G. Fronzoni, M. Stener, S. Furlan, P. Decleva
Chemical Physics 273 (2001) 117-133
"""
from DFTB.LR_TDDFTB import LR_TDDFTB
from DFTB import XYZ
from DFTB.Scattering import slako_tables_scattering
# BOUND ORBITAL = H**O
atomlist = XYZ.read_xyz("./water.xyz")[0]
tddftb = LR_TDDFTB(atomlist)
tddftb.setGeometry(atomlist, charge=0)
options = {"nstates": 1}
tddftb.getEnergies(**options)
valorbs, radial_val = load_pseudo_atoms(atomlist)
H**O, LUMO = tddftb.dftb2.getFrontierOrbitals()
bound_orbs = tddftb.dftb2.getKSCoefficients()
# polarization direction of E-field
epol = np.array([0.0, 1.0, 0.0])
# according to Koopman's theorem the electron is ionized from the H**O
mo_indx = range(0, len(bound_orbs))
nmo = len(mo_indx)
for imo in range(0, nmo):
mo_bound = bound_orbs[:, mo_indx[imo]]
# CONTINUUM ORBITALS at energy E
for E in slako_tables_scattering.energies:
bs = AtomicScatteringBasisSet(atomlist, E)
SKT_bf, SKT_ff = load_slako_scattering(atomlist, E)
Dipole = ScatteringDipoleMatrix(atomlist, valorbs, SKT_bf)
# projection of dipoles onto polarization direction
Dipole_projected = np.zeros((Dipole.shape[0], Dipole.shape[1]))
for xyz in [0, 1, 2]:
Dipole_projected += Dipole[:, :, xyz] * epol[xyz]
# unnormalized coefficients of dipole-prepared continuum orbitals
mo_scatt = np.dot(mo_bound, Dipole_projected)
nrm2 = np.dot(mo_scatt, mo_scatt)
# normalized coefficients
mo_scatt /= np.sqrt(nrm2)
Cube.orbital2grid(atomlist, bs.bfs, mo_scatt, \
filename="/tmp/scattering_orbital_%d_to_%s.cube" % (imo, str(E).replace(".", "p")), dbuff=25.0)
delattr(Cube.orbital_amplitude, "cached_grid")
PAD.asymptotic_density(wavefunction2, 20.0, E)
plt.show()
# build LCAO of two atomic s-waves with PKE=5 eV
from DFTB.Scattering.SlakoScattering import AtomicScatteringBasisSet
bs = AtomicScatteringBasisSet(atomlist, E)
lcao_continuum = np.array([
+1.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
-1.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
])
lcao_continuum /= la.norm(lcao_continuum)
Cube.orbital2grid(atomlist, bs.bfs, lcao_continuum, \
filename="/tmp/h2+_lcao_continuum_orbital_%s.cube" % str(E).replace(".", "p"), dbuff=15.0, ppb=2.5)
def test_scattering_orbitals():
from DFTB.LR_TDDFTB import LR_TDDFTB
from DFTB import XYZ
atomlist = XYZ.read_xyz("h2.xyz")[0]
tddftb = LR_TDDFTB(atomlist)
tddftb.setGeometry(atomlist, charge=0)
options = {"nstates": 1}
tddftb.getEnergies(**options)
valorbs, radial_val = load_pseudo_atoms(atomlist)
E = 5.0 / 27.211
bs = AtomicScatteringBasisSet(atomlist, E)
print bs.bfs
SKT_bf, SKT_ff = load_slako_scattering(atomlist, E)
S_bb, H0_bb = tddftb.dftb2._constructH0andS()
S_bf, H0_bf = ScatteringHamiltonianMatrix(atomlist, valorbs, SKT_bf)
#
invS_bb = la.inv(S_bb)
# (H-E*S)^t . Id . (H-E*S)
HmE2 = np.dot(H0_bf.conjugate().transpose(), np.dot(invS_bb, H0_bf)) \
- E * np.dot( S_bf.conjugate().transpose(), np.dot(invS_bb, H0_bf)) \
- E * np.dot(H0_bf.conjugate().transpose(), np.dot(invS_bb, S_bf)) \
+ E**2 * np.dot(S_bf.conjugate().transpose(), np.dot(invS_bb, S_bf))
Scont = continuum_flux(atomlist, SKT_bf)
S2 = np.dot(S_bf.conjugate().transpose(), np.dot(la.inv(S_bb), S_bf))
"""
#
H2 = np.dot(H0_bf.transpose(), np.dot(la.inv(S_bb), H0_bf))
S2 = np.dot( S_bf.transpose(), np.dot(la.inv(S_bb), S_bf))
print "H2"
print H2
print "S2"
print S2
scat_orbe2, scat_orbs = sla.eig(H2) #, S2)
print "PKE = %s" % E
print "Energies^2 = %s" % scat_orbe2
scat_orbe = np.sqrt(scat_orbe2)
sort_indx = np.argsort(scat_orbe)
scat_orbe = scat_orbe[sort_indx]
scat_orbs = scat_orbs[:,sort_indx]
print "Energies of scattering orbitals: %s" % scat_orbe
orbE = np.argmin(abs(scat_orbe-E))
"""
assert np.sum(abs(HmE2.conjugate().transpose() - HmE2)) < 1.0e-10
assert np.sum(abs(S2.conjugate().transpose() - S2)) < 1.0e-10
lambdas, scat_orbs = sla.eigh(HmE2)
print "lambdas = %s" % lambdas
from DFTB.Scattering import PAD
for i in range(0, len(lambdas)):
if abs(lambdas[i]) > 1.0e-8:
print "%d lambda = %s" % (i, lambdas[i])
###
def wavefunction(grid, dV):
# evaluate orbital
amp = Cube.orbital_amplitude(grid,
bs.bfs,
scat_orbs[:, i],
cache=False)
return amp
PAD.asymptotic_density(wavefunction, 20, E)
###
for (flm, l, m) in classify_lm(bs, scat_orbs[:, i]):
if abs(flm).max() > 1.0e-4:
print " %s %s %s" % (l, m, abs(flm))
Cube.orbital2grid(atomlist, bs.bfs, scat_orbs[:,i], \
filename="/tmp/scattering_orbital_%d.cube" % i, dbuff=25.0)
delattr(Cube.orbital_amplitude, "cached_grid")