def Coulomb_integral_ijkq(self, i, j, k, q, spin, integrals, yukawa=False):
name = self.Coulomb_integral_name(i, j, k, q, spin)
if name in integrals:
return integrals[name]
# create the Kohn-Sham singles
kss_ij = PairDensity(self.paw)
kss_ij.initialize(self.paw.wfs.kpt_u[spin], i, j)
kss_kq = PairDensity(self.paw)
kss_kq.initialize(self.paw.wfs.kpt_u[spin], k, q)
rhot_p = kss_ij.with_compensation_charges(self.finegrid != 0)
phit_p = np.zeros(rhot_p.shape, rhot_p.dtype)
if yukawa:
self.screened_poissonsolver.solve(phit_p, rhot_p, charge=None)
else:
self.poisson.solve(phit_p, rhot_p, charge=None)
if self.finegrid == 1:
phit = self.gd.zeros()
self.restrict(phit_p, phit)
else:
phit = phit_p
rhot = kss_kq.with_compensation_charges(self.finegrid == 2)
integrals[name] = self.Coulomb_integral_kss(kss_ij,
kss_kq,
phit,
rhot,
yukawa=yukawa)
return integrals[name]
def dipole_op(c, state1, state2, k=0, s=0):
# Taken from KSSingle, maybe make this accessible in
# KSSingle?
wfs = c.wfs
gd = wfs.gd
kpt = None
for i in wfs.kpt_u:
if i.k == k and i.s == s:
kpt = i
pd = PairDensity(c)
pd.initialize(kpt, state1, state2)
# coarse grid contribution
# <i|r|j> is the negative of the dipole moment (because of negative
# e- charge)
me = -gd.calculate_dipole_moment(pd.get())
# augmentation contributions
ma = np.zeros(me.shape)
pos_av = c.get_atoms().get_positions() / Bohr
for a, P_ni in kpt.P_ani.items():
Ra = pos_av[a]
Pi_i = P_ni[state1]
Pj_i = P_ni[state2]
Delta_pL = wfs.setups[a].Delta_pL
ni = len(Pi_i)
ma0 = 0
ma1 = np.zeros(me.shape)
for i in range(ni):
for j in range(ni):
pij = Pi_i[i] * Pj_i[j]
ij = packed_index(i, j, ni)
# L=0 term
ma0 += Delta_pL[ij, 0] * pij
# L=1 terms
if wfs.setups[a].lmax >= 1:
# see spherical_harmonics.py for
# L=1:y L=2:z; L=3:x
ma1 += np.array([
Delta_pL[ij, 3], Delta_pL[ij, 1], Delta_pL[ij, 2]
]) * pij
ma += sqrt(4 * pi / 3) * ma1 + Ra * sqrt(4 * pi) * ma0
gd.comm.sum(ma)
me += ma
return me * Bohr
def Coulomb_integral_ijkq(self, i, j, k, q, spin, integrals):
name = self.Coulomb_integral_name(i, j, k, q, spin)
if name in integrals:
return integrals[name]
# create the Kohn-Sham singles
kss_ij = PairDensity(self.paw)
kss_ij.initialize(self.paw.wfs.kpt_u[spin], i, j)
kss_kq = PairDensity(self.paw)
kss_kq.initialize(self.paw.wfs.kpt_u[spin], k, q)
rhot_p = kss_ij.with_compensation_charges(self.finegrid is not 0)
phit_p = np.zeros(rhot_p.shape, rhot_p.dtype)
self.poisson.solve(phit_p, rhot_p, charge=None)
if self.finegrid == 1:
phit = self.gd.zeros()
self.restrict(phit_p, phit)
else:
phit = phit_p
rhot = kss_kq.with_compensation_charges(self.finegrid is 2)
integrals[name] = self.Coulomb_integral_kss(kss_ij, kss_kq, phit, rhot)
return integrals[name]
def dipole_op(c, state1, state2, k=0, s=0):
# Taken from KSSingle, maybe make this accessible in
# KSSingle?
wfs = c.wfs
gd = wfs.gd
kpt = None
for i in wfs.kpt_u:
if i.k == k and i.s == s:
kpt = i
pd = PairDensity(c)
pd.initialize(kpt, state1, state2)
# coarse grid contribution
# <i|r|j> is the negative of the dipole moment (because of negative
# e- charge)
me = -gd.calculate_dipole_moment(pd.get())
# augmentation contributions
ma = np.zeros(me.shape)
pos_av = c.get_atoms().get_positions() / Bohr
for a, P_ni in kpt.P_ani.items():
Ra = pos_av[a]
Pi_i = P_ni[state1]
Pj_i = P_ni[state2]
Delta_pL = wfs.setups[a].Delta_pL
ni = len(Pi_i)
ma0 = 0
ma1 = np.zeros(me.shape)
for i in range(ni):
for j in range(ni):
pij = Pi_i[i]*Pj_i[j]
ij = packed_index(i, j, ni)
# L=0 term
ma0 += Delta_pL[ij,0]*pij
# L=1 terms
if wfs.setups[a].lmax >= 1:
# see spherical_harmonics.py for
# L=1:y L=2:z; L=3:x
ma1 += np.array([Delta_pL[ij,3], Delta_pL[ij,1],
Delta_pL[ij,2]]) * pij
ma += sqrt(4 * pi / 3) * ma1 + Ra * sqrt(4 * pi) * ma0
gd.comm.sum(ma)
me += ma
return me * Bohr
def __init__(self, paw):
paw.initialize_positions()
self.nspins = paw.wfs.nspins
self.nbands = paw.wfs.bd.nbands
self.restrict = paw.hamiltonian.restrict
self.pair_density = PairDensity(paw.density, paw.atoms, finegrid=True)
self.dv = paw.wfs.gd.dv
self.dtype = paw.wfs.dtype
self.setups = paw.wfs.setups
# Allocate space for matrices
self.nt_G = paw.wfs.gd.empty()
self.rhot_g = paw.density.finegd.empty()
self.vt_G = paw.wfs.gd.empty()
self.vt_g = paw.density.finegd.empty()
self.poisson_solve = paw.hamiltonian.poisson.solve
def __init__(self,
iidx=None,
jidx=None,
pspin=None,
kpt=None,
paw=None,
string=None,
fijscale=1):
if string is not None:
self.fromstring(string)
return None
# normal entry
PairDensity.__init__(self, paw)
wfs = paw.wfs
PairDensity.initialize(self, kpt, iidx, jidx)
self.pspin = pspin
f = kpt.f_n
self.fij = (f[iidx] - f[jidx]) * fijscale
e = kpt.eps_n
self.energy = e[jidx] - e[iidx]
# calculate matrix elements -----------
gd = wfs.gd
self.gd = gd
# length form ..........................
# course grid contribution
# <i|r|j> is the negative of the dipole moment (because of negative
# e- charge)
me = -gd.calculate_dipole_moment(self.get())
# augmentation contributions
ma = np.zeros(me.shape)
pos_av = paw.atoms.get_positions() / Bohr
for a, P_ni in kpt.P_ani.items():
Ra = pos_av[a]
Pi_i = P_ni[self.i]
Pj_i = P_ni[self.j]
Delta_pL = wfs.setups[a].Delta_pL
ni = len(Pi_i)
ma0 = 0
ma1 = np.zeros(me.shape)
for i in range(ni):
for j in range(ni):
pij = Pi_i[i] * Pj_i[j]
ij = packed_index(i, j, ni)
# L=0 term
ma0 += Delta_pL[ij, 0] * pij
# L=1 terms
if wfs.setups[a].lmax >= 1:
# see spherical_harmonics.py for
# L=1:y L=2:z; L=3:x
ma1 += np.array([
Delta_pL[ij, 3], Delta_pL[ij, 1], Delta_pL[ij, 2]
]) * pij
ma += sqrt(4 * pi / 3) * ma1 + Ra * sqrt(4 * pi) * ma0
gd.comm.sum(ma)
## print '<KSSingle> i,j,me,ma,fac=',self.i,self.j,\
## me, ma,sqrt(self.energy*self.fij)
# print 'l: me, ma', me, ma
self.me = sqrt(self.energy * self.fij) * (me + ma)
self.mur = -(me + ma)
## print '<KSSingle> mur=',self.mur,-self.fij *me
# velocity form .............................
self.muv = np.zeros(me.shape) # does not work XXX
def __init__(self, iidx=None, jidx=None, pspin=None, kpt=None,
paw=None, string=None, fijscale=1):
if string is not None:
self.fromstring(string)
return None
# normal entry
PairDensity.__init__(self, paw)
wfs = paw.wfs
PairDensity.initialize(self, kpt, iidx, jidx)
self.pspin=pspin
f = kpt.f_n
self.fij = (f[iidx] - f[jidx]) * fijscale
e = kpt.eps_n
self.energy = e[jidx] - e[iidx]
# calculate matrix elements -----------
gd = wfs.gd
self.gd = gd
# length form ..........................
# course grid contribution
# <i|r|j> is the negative of the dipole moment (because of negative
# e- charge)
me = - gd.calculate_dipole_moment(self.get())
# augmentation contributions
ma = np.zeros(me.shape)
pos_av = paw.atoms.get_positions() / Bohr
for a, P_ni in kpt.P_ani.items():
Ra = pos_av[a]
Pi_i = P_ni[self.i]
Pj_i = P_ni[self.j]
Delta_pL = wfs.setups[a].Delta_pL
ni=len(Pi_i)
ma0 = 0
ma1 = np.zeros(me.shape)
for i in range(ni):
for j in range(ni):
pij = Pi_i[i]*Pj_i[j]
ij = packed_index(i, j, ni)
# L=0 term
ma0 += Delta_pL[ij,0]*pij
# L=1 terms
if wfs.setups[a].lmax >= 1:
# see spherical_harmonics.py for
# L=1:y L=2:z; L=3:x
ma1 += np.array([Delta_pL[ij,3], Delta_pL[ij,1],
Delta_pL[ij,2]]) * pij
ma += sqrt(4 * pi / 3) * ma1 + Ra * sqrt(4 * pi) * ma0
gd.comm.sum(ma)
self.me = sqrt(self.energy * self.fij) * ( me + ma )
self.mur = - ( me + ma )
# velocity form .............................
me = np.zeros(self.mur.shape)
# get derivatives
dtype = self.wfj.dtype
dwfj_cg = gd.empty((3), dtype=dtype)
if not hasattr(gd, 'ddr'):
gd.ddr = [Gradient(gd, c, dtype=dtype).apply for c in range(3)]
for c in range(3):
gd.ddr[c](self.wfj, dwfj_cg[c], kpt.phase_cd)
me[c] = gd.integrate(self.wfi * dwfj_cg[c])
if 0:
me2 = np.zeros(self.mur.shape)
for c in range(3):
gd.ddr[c](self.wfi, dwfj_cg[c], kpt.phase_cd)
me2[c] = gd.integrate(self.wfj * dwfj_cg[c])
print me, -me2, me2+me
# augmentation contributions
ma = np.zeros(me.shape)
for a, P_ni in kpt.P_ani.items():
Pi_i = P_ni[self.i]
Pj_i = P_ni[self.j]
nabla_iiv = paw.wfs.setups[a].nabla_iiv
for c in range(3):
for i1, Pi in enumerate(Pi_i):
for i2, Pj in enumerate(Pj_i):
ma[c] += Pi * Pj * nabla_iiv[i1, i2, c]
gd.comm.sum(ma)
self.muv = - (me + ma) / self.energy
## print self.mur, self.muv, self.mur - self.muv
# magnetic transition dipole ................
magn = np.zeros(me.shape)
r_cg, r2_g = coordinates(gd)
wfi_g = self.wfi
for ci in range(3):
cj = (ci + 1) % 3
ck = (ci + 2) % 3
magn[ci] = gd.integrate(wfi_g * r_cg[cj] * dwfj_cg[ck] -
wfi_g * r_cg[ck] * dwfj_cg[cj] )
# augmentation contributions
ma = np.zeros(magn.shape)
for a, P_ni in kpt.P_ani.items():
Pi_i = P_ni[self.i]
Pj_i = P_ni[self.j]
rnabla_iiv = paw.wfs.setups[a].rnabla_iiv
for c in range(3):
for i1, Pi in enumerate(Pi_i):
for i2, Pj in enumerate(Pj_i):
ma[c] += Pi * Pj * rnabla_iiv[i1, i2, c]
gd.comm.sum(ma)
self.magn = -alpha / 2. * (magn + ma)
def __init__(self,
iidx=None,
jidx=None,
pspin=None,
kpt=None,
paw=None,
string=None,
fijscale=1,
dtype=float):
if string is not None:
self.fromstring(string, dtype)
return None
# normal entry
PairDensity.__init__(self, paw)
PairDensity.initialize(self, kpt, iidx, jidx)
self.pspin = pspin
self.energy = 0.0
self.fij = 0.0
self.me = np.zeros((3), dtype=dtype)
self.mur = np.zeros((3), dtype=dtype)
self.muv = np.zeros((3), dtype=dtype)
self.magn = np.zeros((3), dtype=dtype)
self.kpt_comm = paw.wfs.kd.comm
# leave empty if not my kpt
if kpt is None:
return
wfs = paw.wfs
gd = wfs.gd
self.energy = kpt.eps_n[jidx] - kpt.eps_n[iidx]
self.fij = (kpt.f_n[iidx] - kpt.f_n[jidx]) * fijscale
# calculate matrix elements -----------
# length form ..........................
# course grid contribution
# <i|r|j> is the negative of the dipole moment (because of negative
# e- charge)
me = -gd.calculate_dipole_moment(self.get())
# augmentation contributions
ma = np.zeros(me.shape, dtype=dtype)
pos_av = paw.atoms.get_positions() / Bohr
for a, P_ni in kpt.P_ani.items():
Ra = pos_av[a]
Pi_i = P_ni[self.i].conj()
Pj_i = P_ni[self.j]
Delta_pL = wfs.setups[a].Delta_pL
ni = len(Pi_i)
ma0 = 0
ma1 = np.zeros(me.shape, dtype=me.dtype)
for i in range(ni):
for j in range(ni):
pij = Pi_i[i] * Pj_i[j]
ij = packed_index(i, j, ni)
# L=0 term
ma0 += Delta_pL[ij, 0] * pij
# L=1 terms
if wfs.setups[a].lmax >= 1:
# see spherical_harmonics.py for
# L=1:y L=2:z; L=3:x
ma1 += np.array([
Delta_pL[ij, 3], Delta_pL[ij, 1], Delta_pL[ij, 2]
]) * pij
ma += sqrt(4 * pi / 3) * ma1 + Ra * sqrt(4 * pi) * ma0
gd.comm.sum(ma)
self.me = sqrt(self.energy * self.fij) * (me + ma)
self.mur = -(me + ma)
# velocity form .............................
if self.lcao:
# XXX Velocity form not supported in LCAO
return
me = np.zeros(self.mur.shape, dtype=dtype)
# get derivatives
dtype = self.wfj.dtype
dwfj_cg = gd.empty((3), dtype=dtype)
if not hasattr(gd, 'ddr'):
gd.ddr = [Gradient(gd, c, dtype=dtype).apply for c in range(3)]
for c in range(3):
gd.ddr[c](self.wfj, dwfj_cg[c], kpt.phase_cd)
me[c] = gd.integrate(self.wfi.conj() * dwfj_cg[c])
if 0:
me2 = np.zeros(self.mur.shape)
for c in range(3):
gd.ddr[c](self.wfi, dwfj_cg[c], kpt.phase_cd)
me2[c] = gd.integrate(self.wfj * dwfj_cg[c])
print(me, -me2, me2 + me)
# augmentation contributions
ma = np.zeros(me.shape, dtype=me.dtype)
for a, P_ni in kpt.P_ani.items():
Pi_i = P_ni[self.i].conj()
Pj_i = P_ni[self.j]
nabla_iiv = paw.wfs.setups[a].nabla_iiv
for c in range(3):
for i1, Pi in enumerate(Pi_i):
for i2, Pj in enumerate(Pj_i):
ma[c] += Pi * Pj * nabla_iiv[i1, i2, c]
gd.comm.sum(ma)
self.muv = -(me + ma) / self.energy
# magnetic transition dipole ................
r_cg, r2_g = coordinates(gd)
magn = np.zeros(me.shape, dtype=dtype)
wfi_g = self.wfi.conj()
for ci in range(3):
cj = (ci + 1) % 3
ck = (ci + 2) % 3
magn[ci] = gd.integrate(wfi_g * r_cg[cj] * dwfj_cg[ck] -
wfi_g * r_cg[ck] * dwfj_cg[cj])
# augmentation contributions
ma = np.zeros(magn.shape, dtype=magn.dtype)
for a, P_ni in kpt.P_ani.items():
Pi_i = P_ni[self.i].conj()
Pj_i = P_ni[self.j]
rnabla_iiv = paw.wfs.setups[a].rnabla_iiv
for c in range(3):
for i1, Pi in enumerate(Pi_i):
for i2, Pj in enumerate(Pj_i):
ma[c] += Pi * Pj * rnabla_iiv[i1, i2, c]
gd.comm.sum(ma)
self.magn = -alpha / 2. * (magn + ma)