def GetCoulombUJ(lmbda_eps, Rx, Ag, Bg, l, Nk, U0, J0):
(lmbda, eps) = lmbda_eps
Fk = CmpSlaterInt(lmbda, Rx, Ag, Bg, l, Nk, False)
UJs = SlaterF2J(array(Fk) / eps, l)
UH = UJs[0]
JH = sum(UJs[1:]) / len(UJs[1:])
return array([UH - U0, JH - J0])
def GetDielectricFunctions(UJ_icase,
projector_file='projectorw.dat',
options_Nk=8):
Nk = 2**options_Nk + 1
(Rx_, Ag_, Bg_, ls_) = GetWaveF(projector_file)
UlamJ = {}
for icase in UJ_icase.keys():
Rx = Rx_[icase]
Ag = Ag_[icase]
Bg = Bg_[icase]
l = ls_[icase]
lmbda = 0.000001
epsilon = 1.
if UJ_icase[icase][0] > 0:
(Uunscr, Junscr) = GetCoulombUJ(
[lmbda, epsilon], Rx, Ag, Bg, l, Nk, 0.0,
0.0) # First compute the unscreened interaction
epsilon = Uunscr / UJ_icase[icase][
0] # dielectric constant is the ration between the unscreened and screened interaction
print 'lambda=', lmbda, 'epsilon=', epsilon
Fk = CmpSlaterInt(lmbda, Rx, Ag, Bg, l, Nk, True)
Fk = array(Fk) / epsilon
UJs = SlaterF2J(Fk, l)
print 'Fk=', Fk.tolist()
print 'U,J=', UJs
UlamJ[icase] = (UJ_icase[icase][0], lmbda, epsilon, UJs[1:])
return UlamJ
def Anisimov(nocc, Fk, l, fh_info):
nd = sum(nocc)
UJ = SlaterF2J(Fk, l)
print 'U=', UJ[0], 'Js=', UJ[1:], 'n_imp=', nd
print >> fh_info, 'U=', UJ[0], 'Js=', UJ[1:], 'n_imp=', nd
n0 = int(nd + 0.1)
return (UJ[0] * (nd - 0.5) - UJ[1] / 2. * (nd - 1),
UJ[0] * (n0 - 0.5) - UJ[1] / 2. * (n0 - 1))
def AverageHartreeFock(nocc, Fk, l):
J_HF = zeros((4, 4))
J_HF[0, :1] = [1.] # s-electrons
J_HF[1, :2] = [1., 2. / 5.] # p-electrons
J_HF[2, :3] = [1., 32. / 65., 20. / 117.] # d-electrons
J_HF[3, :4] = [1., 110. / 173., 167. / 1038., 475. / 4498.] # f-electrons
nd = sum(nocc)
nd1 = nd / (2 * (2 * l + 1.))
UJ = array(SlaterF2J(Fk, l))
Vu = UJ[0] * (nd - nd1)
Vj = nd1 * sum([UJ[i] * J_HF[l, i] for i in range(1, len(UJ))])
#print 'Vu=', Vu, 'Vj=', Vj
return Vu - Vj
def GetLambdas(UJ_icase, projector_file='projectorw.dat', options_Nk=8):
Nk = 2**options_Nk + 1
(Rx_, Ag_, Bg_, ls_) = GetWaveF(projector_file)
UlamJ = {}
for icase in UJ_icase.keys():
Rx = Rx_[icase]
Ag = Ag_[icase]
Bg = Bg_[icase]
l = ls_[icase]
#lmbda = optimize.brentq(GetCoulombU, 0., 3., args=(Rx,Ag,Bg,l,Nk,U_icase[icase]))
lmbda = 0.000001
epsilon = 1.
if UJ_icase[icase][0] > 0:
lmbda = optimize.brentq(GetCoulombU,
0.,
3.,
args=(Rx, Ag, Bg, l, Nk,
UJ_icase[icase][0]))
epsilon = 1.
if UJ_icase[icase][1] > 0:
sol = optimize.root(GetCoulombUJ, [lmbda, epsilon],
args=(Rx, Ag, Bg, l, Nk,
UJ_icase[icase][0],
UJ_icase[icase][1]))
if sol.success:
(lmbda, epsilon) = sol.x
else:
print 'ERROR:', sol.message
print 'lambda=', lmbda, 'epsilon=', epsilon
Fk = CmpSlaterInt(lmbda, Rx, Ag, Bg, l, Nk, True)
Fk = array(Fk) / epsilon
UJs = SlaterF2J(Fk, l)
print 'Fk=', Fk.tolist()
print 'U,J=', UJs
UlamJ[icase] = (UJ_icase[icase][0], lmbda, epsilon, UJs[1:])
return UlamJ
def GetCoulombU(lmbda, Rx, Ag, Bg, l, Nk, U0):
Fk = CmpSlaterInt(lmbda, Rx, Ag, Bg, l, Nk, False)
UJs = SlaterF2J(Fk, l)
return UJs[0] - U0
for icase in range(len(Rx_)):
Rx = Rx_[icase]
Ag = Ag_[icase]
Bg = Bg_[icase]
l = ls_[icase]
if options.U0 > 0:
lmbda = optimize.brentq(GetCoulombU,
0.,
3.,
args=(Rx, Ag, Bg, l, Nk, options.U0))
epsilon = 1.
if options.J0 > 0:
sol = optimize.root(GetCoulombUJ, [lmbda, epsilon],
args=(Rx, Ag, Bg, l, Nk, options.U0,
options.J0))
if sol.success:
(lmbda, epsilon) = sol.x
else:
print 'ERROR:', sol.message
else:
lmbda = options.lmbda
epsilon = 1.
print 'lambda=', lmbda, 'epsilon=', epsilon
Fk = CmpSlaterInt(lmbda, Rx, Ag, Bg, l, Nk, True)
UJs = SlaterF2J(Fk, l)
print 'Fk=', (array(Fk) / epsilon).tolist()
print 'U,J=', (array(UJs) / epsilon).tolist()