def scfopen(atoms, F0, nalpha, nbeta, **opts):
"SCF procedure for open-shell molecules"
verbose = opts.get("verbose", False)
D = get_guess_D(atoms)
Da = 0.5 * D
Db = 0.5 * D
Eold = 0
for i in xrange(10):
F1a = get_F1_open(atoms, Da, Db)
F1b = get_F1_open(atoms, Db, Da)
F2a = get_F2_open(atoms, Da, Db)
F2b = get_F2_open(atoms, Db, Da)
Fa = F0 + F1a + F2a
Fb = F0 + F1b + F2b
Eel = 0.5 * trace2(Da, F0 + Fa) + 0.5 * trace2(Db, F0 + Fb)
if verbose:
print i, Eel
if abs(Eel - Eold) < 0.001:
break
Eold = Eel
orbea, orbsa = eigh(Fa)
orbeb, orbsb = eigh(Fb)
Da = mkdens(orbsa, 0, nalpha)
Db = mkdens(orbsb, 0, nbeta)
return Eel
def der_oneeE(a, D, bset, atoms):
dH_dXa, dH_dYa, dH_dZa = der_Hcore_matrix(a, bset, atoms)
doneE_Xa = trace2(D, dH_dXa)
doneE_Ya = trace2(D, dH_dYa)
doneE_Za = trace2(D, dH_dZa)
#print doneE_Xa,doneE_Ya,doneE_Za
return array([doneE_Xa, doneE_Ya, doneE_Za], 'd')
def der_oneeE(a,D,bset,atoms):
dH_dXa,dH_dYa,dH_dZa = der_Hcore_matrix(a,bset,atoms)
doneE_Xa = trace2(D,dH_dXa)
doneE_Ya = trace2(D,dH_dYa)
doneE_Za = trace2(D,dH_dZa)
#print doneE_Xa,doneE_Ya,doneE_Za
return array([doneE_Xa,doneE_Ya,doneE_Za],'d')
def der_twoeE(a,D,bset):
d2Ints_dXa,d2Ints_dYa,d2Ints_dZa = der2Ints(a,bset)
Gx,Gy,Gz = der2JmK(D,d2Ints_dXa,d2Ints_dYa,d2Ints_dZa)
dtwoeE_Xa = trace2(D,Gx)
dtwoeE_Ya = trace2(D,Gy)
dtwoeE_Za = trace2(D,Gz)
#print dtwoeE_Xa,dtwoeE_Ya,dtwoeE_Za
return array([dtwoeE_Xa,dtwoeE_Ya,dtwoeE_Za],'d')
def der_twoeE(a, D, bset):
d2Ints_dXa, d2Ints_dYa, d2Ints_dZa = der2Ints(a, bset)
Gx, Gy, Gz = der2JmK(D, d2Ints_dXa, d2Ints_dYa, d2Ints_dZa)
dtwoeE_Xa = trace2(D, Gx)
dtwoeE_Ya = trace2(D, Gy)
dtwoeE_Za = trace2(D, Gz)
#print dtwoeE_Xa,dtwoeE_Ya,dtwoeE_Za
return array([dtwoeE_Xa, dtwoeE_Ya, dtwoeE_Za], 'd')
def scfclosed(atoms, F0, nclosed, **opts):
"SCF procedure for closed-shell molecules"
verbose = opts.get("verbose", False)
do_avg = opts.get("avg", False)
maxiter = opts.get("maxiter", 50)
D = get_guess_D(atoms)
Eold = 0
if do_avg:
avg = SimpleAverager(do_avg)
for i in xrange(maxiter):
if do_avg:
D = avg.getD(D)
F1 = get_F1(atoms, D)
F2 = get_F2(atoms, D)
F = F0 + F1 + F2
Eel = 0.5 * trace2(D, F0 + F)
if verbose:
print i + 1, Eel, get_Hf(atoms, Eel)
# if verbose: print i+1,Eel
if abs(Eel - Eold) < 0.001:
if verbose:
print "Exiting because converged", i + 1, Eel, Eold
break
Eold = Eel
orbe, orbs = eigh(F)
D = 2 * mkdens(orbs, 0, nclosed)
return Eel
def der_dmat(a,Qmat,bset):
"""
Looking at Szabo's equation C.12 you can see that this term results
from adding up the terms that involve derivatives of the density matrix
elements P_mu,nu. Following Szabo we compute this term as
sum_mu,nu Q_mu,nu dS_mu,nu / dRa
where the Q matrix is essentially a density matrix that is weighted by
the orbital eigenvalues. Computing the derivative of the overlap integrals
is done in the der_overlap_matrix function later in this module.
"""
dS_dXa,dS_dYa,dS_dZa = der_overlap_matrix(a,bset)
dDmat_Xa = trace2(Qmat,dS_dXa)
dDmat_Ya = trace2(Qmat,dS_dYa)
dDmat_Za = trace2(Qmat,dS_dZa)
#print dDmat_Xa,dDmat_Ya,dDmat_Za
return array([dDmat_Xa,dDmat_Ya,dDmat_Za],'d')
def der_dmat(a, Qmat, bset):
"""
Looking at Szabo's equation C.12 you can see that this term results
from adding up the terms that involve derivatives of the density matrix
elements P_mu,nu. Following Szabo we compute this term as
sum_mu,nu Q_mu,nu dS_mu,nu / dRa
where the Q matrix is essentially a density matrix that is weighted by
the orbital eigenvalues. Computing the derivative of the overlap integrals
is done in the der_overlap_matrix function later in this module.
"""
dS_dXa, dS_dYa, dS_dZa = der_overlap_matrix(a, bset)
dDmat_Xa = trace2(Qmat, dS_dXa)
dDmat_Ya = trace2(Qmat, dS_dYa)
dDmat_Za = trace2(Qmat, dS_dZa)
#print dDmat_Xa,dDmat_Ya,dDmat_Za
return array([dDmat_Xa, dDmat_Ya, dDmat_Za], 'd')
def der_twoeE_uhf(a,Da,Db,bset):
d2Ints_dXa,d2Ints_dYa,d2Ints_dZa = der2Ints(a,bset)
dJax,dJay,dJaz = derJ(Da,d2Ints_dXa,d2Ints_dYa,d2Ints_dZa)
dJbx,dJby,dJbz = derJ(Db,d2Ints_dXa,d2Ints_dYa,d2Ints_dZa)
dKax,dKay,dKaz = derK(Da,d2Ints_dXa,d2Ints_dYa,d2Ints_dZa)
dKbx,dKby,dKbz = derK(Db,d2Ints_dXa,d2Ints_dYa,d2Ints_dZa)
Dab = Da + Db
dtwoeE_Xa = 0.5*trace2(Dab,dJax+dJbx) - 0.5*(trace2(Da,dKax)+trace2(Db,dKbx))
dtwoeE_Ya = 0.5*trace2(Dab,dJay+dJby) - 0.5*(trace2(Da,dKay)+trace2(Db,dKby))
dtwoeE_Za = 0.5*trace2(Dab,dJaz+dJbz) - 0.5*(trace2(Da,dKaz)+trace2(Db,dKbz))
return array([dtwoeE_Xa,dtwoeE_Ya,dtwoeE_Za],'d')
def der_twoeE_uhf(a, Da, Db, bset):
d2Ints_dXa, d2Ints_dYa, d2Ints_dZa = der2Ints(a, bset)
dJax, dJay, dJaz = derJ(Da, d2Ints_dXa, d2Ints_dYa, d2Ints_dZa)
dJbx, dJby, dJbz = derJ(Db, d2Ints_dXa, d2Ints_dYa, d2Ints_dZa)
dKax, dKay, dKaz = derK(Da, d2Ints_dXa, d2Ints_dYa, d2Ints_dZa)
dKbx, dKby, dKbz = derK(Db, d2Ints_dXa, d2Ints_dYa, d2Ints_dZa)
Dab = Da + Db
dtwoeE_Xa = 0.5 * trace2(
Dab, dJax + dJbx) - 0.5 * (trace2(Da, dKax) + trace2(Db, dKbx))
dtwoeE_Ya = 0.5 * trace2(
Dab, dJay + dJby) - 0.5 * (trace2(Da, dKay) + trace2(Db, dKby))
dtwoeE_Za = 0.5 * trace2(
Dab, dJaz + dJbz) - 0.5 * (trace2(Da, dKaz) + trace2(Db, dKbz))
return array([dtwoeE_Xa, dtwoeE_Ya, dtwoeE_Za], 'd')
def scfopen(atoms,F0,nalpha,nbeta,**kwargs):
"SCF procedure for open-shell molecules"
verbose = kwargs.get('verbose')
D = get_guess_D(atoms)
Da = 0.5*D
Db = 0.5*D
Eold = 0
for i in xrange(10):
F1a = get_F1_open(atoms,Da,Db)
F1b = get_F1_open(atoms,Db,Da)
F2a = get_F2_open(atoms,Da,Db)
F2b = get_F2_open(atoms,Db,Da)
Fa = F0+F1a+F2a
Fb = F0+F1b+F2b
Eel = 0.5*trace2(Da,F0+Fa)+0.5*trace2(Db,F0+Fb)
if verbose: print i,Eel
if abs(Eel-Eold) < 0.001: break
Eold = Eel
orbea,orbsa = eigh(Fa)
orbeb,orbsb = eigh(Fb)
Da = mkdens(orbsa,0,nalpha)
Db = mkdens(orbsb,0,nbeta)
return Eel
def scfclosed(atoms,F0,nclosed,**kwargs):
"SCF procedure for closed-shell molecules"
verbose = kwargs.get('verbose')
do_avg = kwargs.get('avg',settings.MINDOAveraging)
maxiter = kwargs.get('maxiter',settings.MaxIter)
D = get_guess_D(atoms)
Eold = 0
if do_avg: avg = SimpleAverager(do_avg)
for i in xrange(maxiter):
if do_avg: D = avg.getD(D)
F1 = get_F1(atoms,D)
F2 = get_F2(atoms,D)
F = F0+F1+F2
Eel = 0.5*trace2(D,F0+F)
if verbose: print i+1,Eel,get_Hf(atoms,Eel)
#if verbose: print i+1,Eel
if abs(Eel-Eold) < 0.001:
if verbose:
print "Exiting because converged",i+1,Eel,Eold
break
Eold = Eel
orbe,orbs = eigh(F)
D = 2*mkdens(orbs,0,nclosed)
return Eel
def udft_fixed_occ(atoms, occa, occb, **kwargs):
"""\
occa and occb represent the orbital occupation arrays for
the calculating spin orbitals with holes
udft(atoms,**kwargs) - Unrestricted spin DFT driving routine
atoms A Molecule object containing the molecule
Options: Value Description
-------- ----- -----------
verbose False Output terse information to stdout (default)
True Print out additional information
ConvCriteria 1e-4 Convergence Criteria
MaxIter 20 Maximum SCF iterations
DoAveraging True Use DIIS for accelerated convergence (default)
False No convergence acceleration
ETemp False Use ETemp value for finite temperature DFT (default)
float Use (float) for the electron temperature
bfs None The basis functions to use. List of CGBF's
basis_data None The basis data to use to construct bfs
integrals None The one- and two-electron integrals to use
If not None, S,h,Ints
orbs None If not none, the guess orbitals
functional SVWN Use the SVWN (LDA) DFT functional (default)
S0 Use the Slater Xalpha DFT functional
BLYP Use the BLYP GGA DFT functional
PBE Use the PBE DFT functional
grid_nrad 32 Number of radial shells per atom
grid_fineness 1 Radial shell fineness. 0->coarse, 1->medium, 2->fine
"""
verbose = kwargs.get('verbose', False)
ConvCriteria = kwargs.get('ConvCriteria', 1e-4)
MaxIter = kwargs.get('MaxIter', 20)
DoAveraging = kwargs.get('DoAveraging', True)
averaging = kwargs.get('averaging', 0.5)
ETemp = kwargs.get('ETemp', False)
functional = kwargs.get('functional', 'LDA')
#default to LDA which has no correlation since that is easier
kwargs['do_grad_dens'] = need_gradients[functional]
kwargs['do_spin_polarized'] = True
bfs = kwargs.get('bfs', None)
if not bfs:
basis_data = kwargs.get('basis_data', None)
bfs = getbasis(atoms, basis_data)
integrals = kwargs.get('integrals', None)
if integrals:
S, h, Ints = integrals
else:
S, h, Ints = getints(bfs, atoms)
nel = atoms.get_nel()
enuke = atoms.get_enuke()
# default medium mesh
grid_nrad = kwargs.get('grid_nrad', 32)
grid_fineness = kwargs.get('grid_fineness', 1)
gr = MolecularGrid(atoms, grid_nrad, grid_fineness, **kwargs)
gr.set_bf_amps(bfs)
# It would be nice to have a more intelligent treatment of the guess
# so that I could pass in a density rather than a set of orbs.
orbs = kwargs.get('orbs', None)
if not orbs: orbe, orbs = geigh(h, S)
orbsa = orbsb = orbs
nalpha, nbeta = atoms.get_alphabeta()
if verbose:
print "UDFT calculation on %s using functional %s" % (atoms.name,
functional)
print "Nbf = %d" % len(bfs)
print "Nalpha = %d" % nalpha
print "Nbeta = %d" % nbeta
eold = 0.
# Converge the LDA density for the system:
print "Optimization of DFT density"
for i in xrange(MaxIter):
Da = mk_auger_dens(orbsa, occa)
Db = mk_auger_dens(orbsb, occb)
Dab = Da + Db
if DoAveraging:
if i:
Da = averaging * Da + (1 - averaging) * Da0
Db = averaging * Db + (1 - averaging) * Db0
Da0 = Da
Db0 = Db
Ja = getJ(Ints, Da)
Jb = getJ(Ints, Db)
#remember we must use a functional that has no correlation energy
gr.setdens(Da, Db)
exca, XCa, XCb = getXC(gr, nel, **kwargs)
Fa = h + Ja + Jb + XCa
Fb = h + Ja + Jb + XCb
orbea, orbsa = geigh(Fa, S)
orbeb, orbsb = geigh(Fb, S)
Eone = trace2(Dab, h)
Ej = 0.5 * trace2(Dab, Ja + Jb)
Exc = 0.5 * exca + 0.5 * excb
energy = Eone + Ej + Exc + enuke
print i + 1, " ", energy, " ", Ej, " ", Exc
if verbose:
print "%d %10.4f %10.4f %10.4f" % (i, energy, Ej, Exc)
if abs(energy - eold) < ConvCriteria: break
eold = energy
print "Final U%s energy for system %s is %f" % (functional, atoms.name,
energy)
return energy, (orbea, orbeb), (orbsa, orbsb)
def udft(atoms,**kwargs):
"""\
udft(atoms,**kwargs) - Unrestricted spin DFT driving routine
atoms A Molecule object containing the molecule
Options: Value Description
-------- ----- -----------
verbose False Output terse information to stdout (default)
True Print out additional information
ConvCriteria 1e-4 Convergence Criteria
MaxIter 20 Maximum SCF iterations
DoAveraging True Use DIIS for accelerated convergence (default)
False No convergence acceleration
ETemp False Use ETemp value for finite temperature DFT (default)
float Use (float) for the electron temperature
bfs None The basis functions to use. List of CGBF's
basis_data None The basis data to use to construct bfs
integrals None The one- and two-electron integrals to use
If not None, S,h,Ints
orbs None If not none, the guess orbitals
functional SVWN Use the SVWN (LDA) DFT functional (default)
S0 Use the Slater Xalpha DFT functional
BLYP Use the BLYP GGA DFT functional
PBE Use the PBE DFT functional
grid_nrad 32 Number of radial shells per atom
grid_fineness 1 Radial shell fineness. 0->coarse, 1->medium, 2->fine
"""
verbose = kwargs.get('verbose')
ConvCriteria = kwargs.get('ConvCriteria',settings.DFTConvergenceCriteria)
MaxIter = kwargs.get('MaxIter',settings.MaxIter)
DoAveraging = kwargs.get('DoAveraging',settings.DFTAveraging)
ETemp = kwargs.get('ETemp',settings.DFT.ElectronTemperature)
functional = kwargs.get('functional',settings.DFTFunctional)
kwargs['do_grad_dens'] = need_gradients[functional]
kwargs['do_spin_polarized'] = True
bfs = getbasis(atoms,**kwargs)
S,h,Ints = getints(bfs,atoms,**kwargs)
nel = atoms.get_nel()
enuke = atoms.get_enuke()
# default medium mesh
grid_nrad = kwargs.get('grid_nrad',settings.DFTGridRadii)
grid_fineness = kwargs.get('grid_fineness',settings.DFTGridFineness)
gr = MolecularGrid(atoms,grid_nrad,grid_fineness,**kwargs)
gr.set_bf_amps(bfs)
# It would be nice to have a more intelligent treatment of the guess
# so that I could pass in a density rather than a set of orbs.
orbs = kwargs.get('orbs')
if not orbs: orbe,orbs = geigh(h,S)
orbsa = orbsb = orbs
nalpha,nbeta = atoms.get_alphabeta()
if verbose:
print "UDFT calculation on %s using functional %s" \
% (atoms.name,functional)
print "Nbf = %d" % len(bfs)
print "Nalpha = %d" % nalpha
print "Nbeta = %d" % nbeta
eold = 0.
# Converge the LDA density for the system:
if verbose: print "Optimization of DFT density"
for i in xrange(MaxIter):
Da = mkdens(orbsa,0,nalpha)
Db = mkdens(orbsb,0,nbeta)
gr.setdens(Da,Db)
Ja = getJ(Ints,Da)
Jb = getJ(Ints,Db)
Exc,XCa,XCb = getXC(gr,nel,**kwargs)
Fa = h+Ja+Jb-Ka
Fb = h+Ja+Jb-Kb
orbea,orbsa = geigh(Fa,S)
orbeb,orbsb = geigh(Fb,S)
Eja = trace2(D,Ja)
Ejb = trace2(D,Jb)
Eone = 2*trace2(D,h)
energy = Eone + Eja + Ejb + Exc + enuke
if verbose:
print "%d %10.4f %10.4f %10.4f %10.4f %10.4f" % (
i,energy,Eone,Eja+Ejb,Exc,enuke)
if abs(energy-eold) < ConvCriteria: break
eold = energy
print "Final U%s energy for system %s is %f" % (
functional,atoms.name,energy)
return energy,orbe,orbs
def udft_fixed_occ(atoms,occa, occb, **kwargs):
"""\
occa and occb represent the orbital occupation arrays for
the calculating spin orbitals with holes
udft(atoms,**kwargs) - Unrestricted spin DFT driving routine
atoms A Molecule object containing the molecule
Options: Value Description
-------- ----- -----------
verbose False Output terse information to stdout (default)
True Print out additional information
ConvCriteria 1e-4 Convergence Criteria
MaxIter 20 Maximum SCF iterations
DoAveraging True Use DIIS for accelerated convergence (default)
False No convergence acceleration
ETemp False Use ETemp value for finite temperature DFT (default)
float Use (float) for the electron temperature
bfs None The basis functions to use. List of CGBF's
basis_data None The basis data to use to construct bfs
integrals None The one- and two-electron integrals to use
If not None, S,h,Ints
orbs None If not none, the guess orbitals
functional SVWN Use the SVWN (LDA) DFT functional (default)
S0 Use the Slater Xalpha DFT functional
BLYP Use the BLYP GGA DFT functional
PBE Use the PBE DFT functional
grid_nrad 32 Number of radial shells per atom
grid_fineness 1 Radial shell fineness. 0->coarse, 1->medium, 2->fine
"""
verbose = kwargs.get('verbose',False)
ConvCriteria = kwargs.get('ConvCriteria',1e-4)
MaxIter = kwargs.get('MaxIter',20)
DoAveraging = kwargs.get('DoAveraging',True)
averaging = kwargs.get('averaging',0.5)
ETemp = kwargs.get('ETemp',False)
functional = kwargs.get('functional','LDA')
#default to LDA which has no correlation since that is easier
kwargs['do_grad_dens'] = need_gradients[functional]
kwargs['do_spin_polarized'] = True
bfs = kwargs.get('bfs',None)
if not bfs:
basis_data = kwargs.get('basis_data',None)
bfs = getbasis(atoms,basis_data)
integrals = kwargs.get('integrals',None)
if integrals:
S,h,Ints = integrals
else:
S,h,Ints = getints(bfs,atoms)
nel = atoms.get_nel()
enuke = atoms.get_enuke()
# default medium mesh
grid_nrad = kwargs.get('grid_nrad',32)
grid_fineness = kwargs.get('grid_fineness',1)
gr = MolecularGrid(atoms,grid_nrad,grid_fineness,**kwargs)
gr.set_bf_amps(bfs)
# It would be nice to have a more intelligent treatment of the guess
# so that I could pass in a density rather than a set of orbs.
orbs = kwargs.get('orbs',None)
if not orbs: orbe,orbs = geigh(h,S)
orbsa = orbsb = orbs
nalpha,nbeta = atoms.get_alphabeta()
if verbose:
print "UDFT calculation on %s using functional %s" % (
atoms.name,functional)
print "Nbf = %d" % len(bfs)
print "Nalpha = %d" % nalpha
print "Nbeta = %d" % nbeta
eold = 0.
# Converge the LDA density for the system:
print "Optimization of DFT density"
for i in xrange(MaxIter):
Da = mk_auger_dens(orbsa, occa)
Db = mk_auger_dens(orbsb, occb)
Dab = Da + Db
if DoAveraging:
if i:
Da = averaging*Da + (1-averaging)*Da0
Db = averaging*Db + (1-averaging)*Db0
Da0 = Da
Db0 = Db
Ja = getJ(Ints,Da)
Jb = getJ(Ints,Db)
#remember we must use a functional that has no correlation energy
gr.setdens(Da,Db)
exca,XCa,XCb = getXC(gr,nel,**kwargs)
Fa = h+Ja+Jb+XCa
Fb = h+Ja+Jb+XCb
orbea,orbsa = geigh(Fa,S)
orbeb,orbsb = geigh(Fb,S)
Eone = trace2(Dab,h)
Ej = 0.5*trace2(Dab,Ja+Jb)
Exc = 0.5*exca + 0.5*excb
energy = Eone + Ej + Exc + enuke
print i+1," ",energy," ",Ej," ",Exc
if verbose:
print "%d %10.4f %10.4f %10.4f" % (i,energy,Ej,Exc)
if abs(energy-eold) < ConvCriteria: break
eold = energy
print "Final U%s energy for system %s is %f" % (
functional,atoms.name,energy)
return energy,(orbea,orbeb),(orbsa,orbsb)
def dft_fixed_occ(atoms,occs,**kwargs):
"""\
dft(atoms,**kwargs) - DFT driving routine
atoms A Molecule object containing the molecule
Options: Value Description
-------- ----- -----------
verbose False Output terse information to stdout (default)
True Print out additional information
ConvCriteria 1e-4 Convergence Criteria
MaxIter 20 Maximum SCF iterations
DoAveraging True Use DIIS for accelerated convergence (default)
False No convergence acceleration
ETemp False Use ETemp value for finite temperature DFT (default)
float Use (float) for the electron temperature
bfs None The basis functions to use. List of CGBF's
basis_data None The basis data to use to construct bfs
integrals None The one- and two-electron integrals to use
If not None, S,h,Ints
orbs None If not none, the guess orbitals
functional SVWN Use the SVWN (LDA) DFT functional (default)
S0 Use the Slater Xalpha DFT functional
BLYP Use the BLYP GGA DFT functional
PBE Use the PBE DFT functional
grid_nrad 32 Number of radial shells per atom
grid_fineness 1 Radial shell fineness. 0->coarse, 1->medium, 2->fine
spin_type A Average occupation method for open shell (default)
R Restricted open shell (not implemented yet)
U Unrestricted open shell (aka spin-polarized dft)
Only A works now. Stay tuned.
"""
verbose = kwargs.get('verbose',False)
ConvCriteria = kwargs.get('ConvCriteria',1e-4)
MaxIter = kwargs.get('MaxIter',20)
DoAveraging = kwargs.get('DoAveraging',True)
ETemp = kwargs.get('ETemp',False)
functional = kwargs.get('functional','SVWN')
kwargs['do_grad_dens'] = need_gradients[functional]
bfs = kwargs.get('bfs',None)
if not bfs:
basis_data = kwargs.get('basis_data',None)
bfs = getbasis(atoms,basis_data)
integrals = kwargs.get('integrals',None)
if integrals:
S,h,Ints = integrals
else:
S,h,Ints = getints(bfs,atoms)
nel = atoms.get_nel()
enuke = atoms.get_enuke()
# default medium mesh
grid_nrad = kwargs.get('grid_nrad',32)
grid_fineness = kwargs.get('grid_fineness',1)
gr = MolecularGrid(atoms,grid_nrad,grid_fineness,**kwargs)
gr.set_bf_amps(bfs)
# It would be nice to have a more intelligent treatment of the guess
# so that I could pass in a density rather than a set of orbs.
orbs = kwargs.get('orbs',None)
if orbs is None: orbe,orbs = geigh(h,S)
nclosed,nopen = atoms.get_closedopen()
if verbose:
print "DFT calculation on %s using functional %s" % (
atoms.name,functional)
print "Nbf = %d" % len(bfs)
print "Nclosed = %d" % nclosed
print "Nopen = %d" % nclosed
if nopen: print "Using spin-averaged dft for open shell calculation"
eold = 0.
if DoAveraging:
print "Using DIIS averaging"
avg=DIIS(S)
# Converge the LDA density for the system:
if verbose: print "Optimization of DFT density"
for i in xrange(MaxIter):
#print "SCF Iteration:",i,"Starting Energy:",eold
#save the starting orbitals
oldorbs=orbs
if ETemp:
efermi = get_efermi(nel,orbe,ETemp)
occs = get_fermi_occs(efermi,orbe,ETemp)
D = mkdens_occs(orbs,occs)
entropy = get_entropy(occs,ETemp)
else:
D = mk_auger_dens(orbs, occs)
#D = mkdens_spinavg(orbs,nclosed,nopen)
gr.setdens(D)
J = getJ(Ints,D)
Exc,XC = getXC(gr,nel,**kwargs)
F = h+2*J+XC
if DoAveraging: F = avg.getF(F,D)
orbe,orbs = geigh(F,S)
#pad_out(orbs)
#save the new eigenstates of the fock operator F
neworbs=orbs
#send oldorbs and neworbs to get biorthogonalized method
#orbs = biorthog(neworbs, oldorbs, S, nel)
Ej = 2*trace2(D,J)
Eone = 2*trace2(D,h)
energy = Eone + Ej + Exc + enuke
print i+1," ",energy," ",Ej," ",Exc," ",enuke
if ETemp: energy += entropy
if verbose:
print "%d %10.4f %10.4f %10.4f %10.4f %10.4f" % (
i,energy,Eone,Ej,Exc,enuke)
if abs(energy-eold) < ConvCriteria: break
eold = energy
print "Final %s energy for system %s is %f" % (functional,atoms.name,energy)
return energy,orbe,orbs
def get_energy(h,F,D,enuke=0.,**opts):
"Form the total energy of the closed-shell wave function."
eone = trace2(D,h)
etwo = trace2(D,F)
#print "eone,etwo,enuke",(2*eone),(etwo-eone),enuke
return eone+etwo+enuke
def uhf_fixed_occ(atoms,occa, occb,**opts):
"""\
occa and occb represent the orbital occupation arrays for
the calculating spin orbitals with holes
uhf(atoms,**opts) - Unrestriced Open Shell Hartree Fock
atoms A Molecule object containing the molecule
Options: Value Description
-------- ----- -----------
ConvCriteria 1e-4 Convergence Criteria
MaxIter 20 Maximum SCF iterations
DoAveraging True Use DIIS averaging for convergence acceleration
bfs None The basis functions to use. List of CGBF's
basis_data None The basis data to use to construct bfs
integrals None The one- and two-electron integrals to use
If not None, S,h,Ints
orbs None If not None, the guess orbitals
"""
from biorthogonal import biorthogonalize,pad_out
ConvCriteria = opts.get('ConvCriteria',1e-5)
MaxIter = opts.get('MaxIter',40)
DoAveraging = opts.get('DoAveraging',True)
averaging = opts.get('averaging',0.5)
ETemp = opts.get('ETemp',False)
bfs = opts.get('bfs',None)
if not bfs:
basis_data = opts.get('basis_data',None)
bfs = getbasis(atoms,basis_data)
integrals = opts.get('integrals', None)
if integrals:
S,h,Ints = integrals
else:
S,h,Ints = getints(bfs,atoms)
nel = atoms.get_nel()
nalpha,nbeta = atoms.get_alphabeta() #pass in opts for multiplicity
S,h,Ints = getints(bfs,atoms)
orbsa = opts.get('orbsa',None)
orbsb = opts.get('orbsb',None)
if (orbsa!=None and orbsb!=None):
orbsa = orbsa
orbsb = orbsb
else:
orbe,orbs = geigh(h,S)
orbea = orbeb = orbe
orbsa = orbsb = orbs
#print "A Trial Orbital Energies:\n", orbea
print "A Trial Orbitals:\n"
pad_out(orbsa)
#print "B Trial Orbital Energies:\n",orbeb
print "B Trial Orbitals:\n"
pad_out(orbsb)
enuke = atoms.get_enuke()
eold = 0.
for i in xrange(MaxIter):
print "SCF Iteration:",i,"Starting Energy:",eold
#save the starting orbitals
oldorbs_a=orbsa
oldorbs_b=orbsb
Da = mk_auger_dens(orbsa,occa)
Db = mk_auger_dens(orbsb,occb)
#Da_std = mkdens(orbsa,0,nalpha)
#Db_std = mkdens(orbsb,0,nbeta)
#pad_out(Da - Da_std ) #use to test mk_aug_dens with ground state occupations
#pad_out(Db - Db_std )
Ja = getJ(Ints,Da)
Jb = getJ(Ints,Db)
Ka = getK(Ints,Da)
Kb = getK(Ints,Db)
Fa = h+Ja+Jb-Ka
Fb = h+Ja+Jb-Kb
orbea,orbsa = geigh(Fa,S)
orbeb,orbsb = geigh(Fb,S)
#save the new orbitals
neworbs_a=orbsa
neworbs_b=orbsb
#now we biorthogonalize the new orbitals to the old ones
#to setup occupation arrays for the next scf cycle
orbsa = biorthogonalize(neworbs_a,oldorbs_a,S,nalpha,occa)
orbsb = biorthogonalize(neworbs_b,oldorbs_b,S,nbeta,occb)
energya = get_energy(h,Fa,Da)
energyb = get_energy(h,Fb,Db)
energy = (energya+energyb)/2+enuke
Dab = Da+Db
Eone = trace2(Dab,h)
Ej = 0.5*trace2(Dab,Ja+Jb)
Ek = -0.5*(trace2(Da,Ka)+trace2(Db,Kb))
#print "%d %f %f %f %f" % (i,energy,Eone,Ej,Ek)
logging.debug("%d %f %f %f %f" % (i,energy,Eone,Ej,Ek))
if abs(energy-eold) < ConvCriteria: break
eold = energy
if i==(MaxIter-1):
print "Warning: Reached maximum number of SCF cycles may want to rerun calculation with more SCF cycles"
logger.info("Final UHF energy for system %s is %f" % (atoms.name,energy))
return energy,(orbea,orbeb),(orbsa,orbsb)
def uhf(atoms, **kwargs):
"""\
uhf(atoms,**kwargs) - Unrestriced Open Shell Hartree Fock
atoms A Molecule object containing the molecule
Options: Value Description
-------- ----- -----------
ConvCriteria 1e-4 Convergence Criteria
MaxIter 20 Maximum SCF iterations
DoAveraging True Use DIIS averaging for convergence acceleration
bfs None The basis functions to use. List of CGBF's
basis_data None The basis data to use to construct bfs
integrals None The one- and two-electron integrals to use
If not None, S,h,Ints
orbs None If not None, the guess orbitals
"""
ConvCriteria = kwargs.get('ConvCriteria', settings.ConvergenceCriteria)
MaxIter = kwargs.get('MaxIter', settings.MaxIters)
DoAveraging = kwargs.get('DoAveraging', settings.Averaging)
averaging = kwargs.get('averaging', settings.MixingFraction)
ETemp = kwargs.get('ETemp', settings.ElectronTemperature)
verbose = kwargs.get('verbose')
bfs = getbasis(atoms, **kwargs)
S, h, Ints = getints(bfs, atoms, **kwargs)
nel = atoms.get_nel()
nalpha, nbeta = atoms.get_alphabeta() #pass in kwargs for multiplicity
orbs = kwargs.get('orbs')
if orbs != None:
#orbsa = orbsb = orbs
orbsa = orbs[0]
orbsb = orbs[1]
else:
orbe, orbs = geigh(h, S)
orbea = orbeb = orbe
orbsa = orbsb = orbs
enuke = atoms.get_enuke()
eold = 0.
logger.info("UHF calculation on %s" % atoms.name)
logger.info("Nbf = %d" % len(bfs))
logger.info("Nalpha = %d" % nalpha)
logger.info("Nbeta = %d" % nbeta)
logger.info("Averaging = %s" % DoAveraging)
logging.debug("Optimization of HF orbitals")
for i in xrange(MaxIter):
if verbose: print "SCF Iteration:", i, "Starting Energy:", eold
if ETemp:
# We have to multiply nalpha and nbeta by 2
# to get the Fermi energies to come out correct:
efermia = get_efermi(2.0 * nalpha, orbea, ETemp)
occsa = get_fermi_occs(efermia, orbea, ETemp)
#print "occsa = ",occsa
Da = mkdens_occs(orbsa, occsa)
efermib = get_efermi(2.0 * nbeta, orbeb, ETemp)
occsb = get_fermi_occs(efermib, orbeb, ETemp)
#print "occsb = ",occsb
Db = mkdens_occs(orbsb, occsb)
entropy = 0.5 * (get_entropy(occsa, ETemp) +
get_entropy(occsb, ETemp))
else:
Da = mkdens(orbsa, 0, nalpha)
Db = mkdens(orbsb, 0, nbeta)
if DoAveraging:
if i:
Da = averaging * Da + (1 - averaging) * Da0
Db = averaging * Db + (1 - averaging) * Db0
Da0 = Da
Db0 = Db
Ja = getJ(Ints, Da)
Jb = getJ(Ints, Db)
Ka = getK(Ints, Da)
Kb = getK(Ints, Db)
Fa = h + Ja + Jb - Ka
Fb = h + Ja + Jb - Kb
orbea, orbsa = geigh(Fa, S)
orbeb, orbsb = geigh(Fb, S)
energya = get_energy(h, Fa, Da)
energyb = get_energy(h, Fb, Db)
energy = (energya + energyb) / 2 + enuke
Dab = Da + Db
Eone = trace2(Dab, h)
Ej = 0.5 * trace2(Dab, Ja + Jb)
Ek = -0.5 * (trace2(Da, Ka) + trace2(Db, Kb))
if ETemp: energy += entropy
logger.debug("%d %f %f %f %f" % (i, energy, Eone, Ej, Ek))
if abs(energy - eold) < ConvCriteria: break
eold = energy
logger.info("Final UHF energy for system %s is %f" % (atoms.name, energy))
return energy, (orbea, orbeb), (orbsa, orbsb)
def dft_fixed_occ(atoms, occs, **kwargs):
"""\
dft(atoms,**kwargs) - DFT driving routine
atoms A Molecule object containing the molecule
Options: Value Description
-------- ----- -----------
verbose False Output terse information to stdout (default)
True Print out additional information
ConvCriteria 1e-4 Convergence Criteria
MaxIter 20 Maximum SCF iterations
DoAveraging True Use DIIS for accelerated convergence (default)
False No convergence acceleration
ETemp False Use ETemp value for finite temperature DFT (default)
float Use (float) for the electron temperature
bfs None The basis functions to use. List of CGBF's
basis_data None The basis data to use to construct bfs
integrals None The one- and two-electron integrals to use
If not None, S,h,Ints
orbs None If not none, the guess orbitals
functional SVWN Use the SVWN (LDA) DFT functional (default)
S0 Use the Slater Xalpha DFT functional
BLYP Use the BLYP GGA DFT functional
PBE Use the PBE DFT functional
grid_nrad 32 Number of radial shells per atom
grid_fineness 1 Radial shell fineness. 0->coarse, 1->medium, 2->fine
spin_type A Average occupation method for open shell (default)
R Restricted open shell (not implemented yet)
U Unrestricted open shell (aka spin-polarized dft)
Only A works now. Stay tuned.
"""
verbose = kwargs.get('verbose', False)
ConvCriteria = kwargs.get('ConvCriteria', 1e-4)
MaxIter = kwargs.get('MaxIter', 20)
DoAveraging = kwargs.get('DoAveraging', True)
ETemp = kwargs.get('ETemp', False)
functional = kwargs.get('functional', 'SVWN')
kwargs['do_grad_dens'] = need_gradients[functional]
bfs = kwargs.get('bfs', None)
if not bfs:
basis_data = kwargs.get('basis_data', None)
bfs = getbasis(atoms, basis_data)
integrals = kwargs.get('integrals', None)
if integrals:
S, h, Ints = integrals
else:
S, h, Ints = getints(bfs, atoms)
nel = atoms.get_nel()
enuke = atoms.get_enuke()
# default medium mesh
grid_nrad = kwargs.get('grid_nrad', 32)
grid_fineness = kwargs.get('grid_fineness', 1)
gr = MolecularGrid(atoms, grid_nrad, grid_fineness, **kwargs)
gr.set_bf_amps(bfs)
# It would be nice to have a more intelligent treatment of the guess
# so that I could pass in a density rather than a set of orbs.
orbs = kwargs.get('orbs', None)
if orbs is None: orbe, orbs = geigh(h, S)
nclosed, nopen = atoms.get_closedopen()
if verbose:
print "DFT calculation on %s using functional %s" % (atoms.name,
functional)
print "Nbf = %d" % len(bfs)
print "Nclosed = %d" % nclosed
print "Nopen = %d" % nclosed
if nopen: print "Using spin-averaged dft for open shell calculation"
eold = 0.
if DoAveraging:
print "Using DIIS averaging"
avg = DIIS(S)
# Converge the LDA density for the system:
if verbose: print "Optimization of DFT density"
for i in xrange(MaxIter):
#print "SCF Iteration:",i,"Starting Energy:",eold
#save the starting orbitals
oldorbs = orbs
if ETemp:
efermi = get_efermi(nel, orbe, ETemp)
occs = get_fermi_occs(efermi, orbe, ETemp)
D = mkdens_occs(orbs, occs)
entropy = get_entropy(occs, ETemp)
else:
D = mk_auger_dens(orbs, occs)
#D = mkdens_spinavg(orbs,nclosed,nopen)
gr.setdens(D)
J = getJ(Ints, D)
Exc, XC = getXC(gr, nel, **kwargs)
F = h + 2 * J + XC
if DoAveraging: F = avg.getF(F, D)
orbe, orbs = geigh(F, S)
#pad_out(orbs)
#save the new eigenstates of the fock operator F
neworbs = orbs
#send oldorbs and neworbs to get biorthogonalized method
#orbs = biorthog(neworbs, oldorbs, S, nel)
Ej = 2 * trace2(D, J)
Eone = 2 * trace2(D, h)
energy = Eone + Ej + Exc + enuke
print i + 1, " ", energy, " ", Ej, " ", Exc, " ", enuke
if ETemp: energy += entropy
if verbose:
print "%d %10.4f %10.4f %10.4f %10.4f %10.4f" % (i, energy, Eone,
Ej, Exc, enuke)
if abs(energy - eold) < ConvCriteria: break
eold = energy
print "Final %s energy for system %s is %f" % (functional, atoms.name,
energy)
return energy, orbe, orbs
def get_energy(h, F, D, enuke=0., **kwargs):
"Form the total energy of the closed-shell wave function."
eone = trace2(D, h)
etwo = trace2(D, F)
#print "eone,etwo,enuke",(2*eone),(etwo-eone),enuke
return eone + etwo + enuke
def uhf_fixed_occ(atoms, occa, occb, **kwargs):
"""\
occa and occb represent the orbital occupation arrays for
the calculating spin orbitals with holes
uhf(atoms,**kwargs) - Unrestriced Open Shell Hartree Fock
atoms A Molecule object containing the molecule
Options: Value Description
-------- ----- -----------
ConvCriteria 1e-4 Convergence Criteria
MaxIter 20 Maximum SCF iterations
DoAveraging True Use DIIS averaging for convergence acceleration
bfs None The basis functions to use. List of CGBF's
basis_data None The basis data to use to construct bfs
integrals None The one- and two-electron integrals to use
If not None, S,h,Ints
orbs None If not None, the guess orbitals
"""
from biorthogonal import biorthogonalize, pad_out
ConvCriteria = kwargs.get('ConvCriteria', settings.ConvergenceCriteria)
MaxIter = kwargs.get('MaxIter', settings.MaxIters)
DoAveraging = kwargs.get('DoAveraging', settings.Averaging)
averaging = kwargs.get('averaging', settings.MixingFraction)
ETemp = kwargs.get('ETemp', settings.ElectronTemperature)
bfs = getbasis(atoms, **kwargs)
S, h, Ints = getints(bfs, atoms, **kwargs)
nel = atoms.get_nel()
nalpha, nbeta = atoms.get_alphabeta() #pass in kwargs for multiplicity
orbsa = kwargs.get('orbsa')
orbsb = kwargs.get('orbsb')
if (orbsa == None or orbsb == None):
orbe, orbs = geigh(h, S)
orbea = orbeb = orbe
orbsa = orbsb = orbs
#print "A Trial Orbital Energies:\n", orbea
print "A Trial Orbitals:\n"
pad_out(orbsa)
#print "B Trial Orbital Energies:\n",orbeb
print "B Trial Orbitals:\n"
pad_out(orbsb)
enuke = atoms.get_enuke()
eold = 0.
for i in xrange(MaxIter):
print "SCF Iteration:", i, "Starting Energy:", eold
#save the starting orbitals
oldorbs_a = orbsa
oldorbs_b = orbsb
Da = mk_auger_dens(orbsa, occa)
Db = mk_auger_dens(orbsb, occb)
#Da_std = mkdens(orbsa,0,nalpha)
#Db_std = mkdens(orbsb,0,nbeta)
#pad_out(Da - Da_std ) #use to test mk_aug_dens with ground state occupations
#pad_out(Db - Db_std )
Ja = getJ(Ints, Da)
Jb = getJ(Ints, Db)
Ka = getK(Ints, Da)
Kb = getK(Ints, Db)
Fa = h + Ja + Jb - Ka
Fb = h + Ja + Jb - Kb
orbea, orbsa = geigh(Fa, S)
orbeb, orbsb = geigh(Fb, S)
#save the new orbitals
neworbs_a = orbsa
neworbs_b = orbsb
#now we biorthogonalize the new orbitals to the old ones
#to setup occupation arrays for the next scf cycle
orbsa = biorthogonalize(neworbs_a, oldorbs_a, S, nalpha, occa)
orbsb = biorthogonalize(neworbs_b, oldorbs_b, S, nbeta, occb)
energya = get_energy(h, Fa, Da)
energyb = get_energy(h, Fb, Db)
energy = (energya + energyb) / 2 + enuke
Dab = Da + Db
Eone = trace2(Dab, h)
Ej = 0.5 * trace2(Dab, Ja + Jb)
Ek = -0.5 * (trace2(Da, Ka) + trace2(Db, Kb))
#print "%d %f %f %f %f" % (i,energy,Eone,Ej,Ek)
logging.debug("%d %f %f %f %f" % (i, energy, Eone, Ej, Ek))
if abs(energy - eold) < ConvCriteria: break
eold = energy
if i == (MaxIter - 1):
print "Warning: Reached maximum number of SCF cycles may want to rerun calculation with more SCF cycles"
logger.info("Final UHF energy for system %s is %f" % (atoms.name, energy))
return energy, (orbea, orbeb), (orbsa, orbsb)
def udft(atoms, **kwargs):
"""\
udft(atoms,**kwargs) - Unrestricted spin DFT driving routine
atoms A Molecule object containing the molecule
Options: Value Description
-------- ----- -----------
verbose False Output terse information to stdout (default)
True Print out additional information
ConvCriteria 1e-4 Convergence Criteria
MaxIter 20 Maximum SCF iterations
DoAveraging True Use DIIS for accelerated convergence (default)
False No convergence acceleration
ETemp False Use ETemp value for finite temperature DFT (default)
float Use (float) for the electron temperature
bfs None The basis functions to use. List of CGBF's
basis_data None The basis data to use to construct bfs
integrals None The one- and two-electron integrals to use
If not None, S,h,Ints
orbs None If not none, the guess orbitals
functional SVWN Use the SVWN (LDA) DFT functional (default)
S0 Use the Slater Xalpha DFT functional
BLYP Use the BLYP GGA DFT functional
PBE Use the PBE DFT functional
grid_nrad 32 Number of radial shells per atom
grid_fineness 1 Radial shell fineness. 0->coarse, 1->medium, 2->fine
"""
verbose = kwargs.get('verbose')
ConvCriteria = kwargs.get('ConvCriteria', settings.DFTConvergenceCriteria)
MaxIter = kwargs.get('MaxIter', settings.MaxIter)
DoAveraging = kwargs.get('DoAveraging', settings.DFTAveraging)
ETemp = kwargs.get('ETemp', settings.DFT.ElectronTemperature)
functional = kwargs.get('functional', settings.DFTFunctional)
kwargs['do_grad_dens'] = need_gradients[functional]
kwargs['do_spin_polarized'] = True
bfs = getbasis(atoms, **kwargs)
S, h, Ints = getints(bfs, atoms, **kwargs)
nel = atoms.get_nel()
enuke = atoms.get_enuke()
# default medium mesh
grid_nrad = kwargs.get('grid_nrad', settings.DFTGridRadii)
grid_fineness = kwargs.get('grid_fineness', settings.DFTGridFineness)
gr = MolecularGrid(atoms, grid_nrad, grid_fineness, **kwargs)
gr.set_bf_amps(bfs)
# It would be nice to have a more intelligent treatment of the guess
# so that I could pass in a density rather than a set of orbs.
orbs = kwargs.get('orbs')
if not orbs: orbe, orbs = geigh(h, S)
orbsa = orbsb = orbs
nalpha, nbeta = atoms.get_alphabeta()
if verbose:
print "UDFT calculation on %s using functional %s" \
% (atoms.name,functional)
print "Nbf = %d" % len(bfs)
print "Nalpha = %d" % nalpha
print "Nbeta = %d" % nbeta
eold = 0.
# Converge the LDA density for the system:
if verbose: print "Optimization of DFT density"
for i in xrange(MaxIter):
Da = mkdens(orbsa, 0, nalpha)
Db = mkdens(orbsb, 0, nbeta)
gr.setdens(Da, Db)
Ja = getJ(Ints, Da)
Jb = getJ(Ints, Db)
Exc, XCa, XCb = getXC(gr, nel, **kwargs)
Fa = h + Ja + Jb - Ka
Fb = h + Ja + Jb - Kb
orbea, orbsa = geigh(Fa, S)
orbeb, orbsb = geigh(Fb, S)
Eja = trace2(D, Ja)
Ejb = trace2(D, Jb)
Eone = 2 * trace2(D, h)
energy = Eone + Eja + Ejb + Exc + enuke
if verbose:
print "%d %10.4f %10.4f %10.4f %10.4f %10.4f" % (
i, energy, Eone, Eja + Ejb, Exc, enuke)
if abs(energy - eold) < ConvCriteria: break
eold = energy
print "Final U%s energy for system %s is %f" % (functional, atoms.name,
energy)
return energy, orbe, orbs
def uhf(atoms,**opts):
"""\
uhf(atoms,**opts) - Unrestriced Open Shell Hartree Fock
atoms A Molecule object containing the molecule
Options: Value Description
-------- ----- -----------
ConvCriteria 1e-4 Convergence Criteria
MaxIter 20 Maximum SCF iterations
DoAveraging True Use DIIS averaging for convergence acceleration
bfs None The basis functions to use. List of CGBF's
basis_data None The basis data to use to construct bfs
integrals None The one- and two-electron integrals to use
If not None, S,h,Ints
orbs None If not None, the guess orbitals
"""
ConvCriteria = opts.get('ConvCriteria',1e-5)
MaxIter = opts.get('MaxIter',40)
DoAveraging = opts.get('DoAveraging',True)
averaging = opts.get('averaging',0.5)
ETemp = opts.get('ETemp',False)
verbose = opts.get('verbose',False)
bfs = opts.get('bfs',None)
if not bfs:
basis_data = opts.get('basis_data',None)
bfs = getbasis(atoms,basis_data)
integrals = opts.get('integrals', None)
if integrals:
S,h,Ints = integrals
else:
S,h,Ints = getints(bfs,atoms)
nel = atoms.get_nel()
nalpha,nbeta = atoms.get_alphabeta() #pass in opts for multiplicity
S,h,Ints = getints(bfs,atoms)
orbs = opts.get('orbs',None)
if orbs!=None:
#orbsa = orbsb = orbs
orbsa = orbs[0]
orbsb = orbs[1]
else:
orbe,orbs = geigh(h,S)
orbea = orbeb = orbe
orbsa = orbsb = orbs
enuke = atoms.get_enuke()
eold = 0.
logger.info("UHF calculation on %s" % atoms.name)
logger.info("Nbf = %d" % len(bfs))
logger.info("Nalpha = %d" % nalpha)
logger.info("Nbeta = %d" % nbeta)
logger.info("Averaging = %s" % DoAveraging)
logging.debug("Optimization of HF orbitals")
for i in xrange(MaxIter):
if verbose: print "SCF Iteration:",i,"Starting Energy:",eold
if ETemp:
# We have to multiply nalpha and nbeta by 2
# to get the Fermi energies to come out correct:
efermia = get_efermi(2.0*nalpha,orbea,ETemp)
occsa = get_fermi_occs(efermia,orbea,ETemp)
#print "occsa = ",occsa
Da = mkdens_occs(orbsa,occsa)
efermib = get_efermi(2.0*nbeta,orbeb,ETemp)
occsb = get_fermi_occs(efermib,orbeb,ETemp)
#print "occsb = ",occsb
Db = mkdens_occs(orbsb,occsb)
entropy = 0.5*(get_entropy(occsa,ETemp)+get_entropy(occsb,ETemp))
else:
Da = mkdens(orbsa,0,nalpha)
Db = mkdens(orbsb,0,nbeta)
if DoAveraging:
if i:
Da = averaging*Da + (1-averaging)*Da0
Db = averaging*Db + (1-averaging)*Db0
Da0 = Da
Db0 = Db
Ja = getJ(Ints,Da)
Jb = getJ(Ints,Db)
Ka = getK(Ints,Da)
Kb = getK(Ints,Db)
Fa = h+Ja+Jb-Ka
Fb = h+Ja+Jb-Kb
orbea,orbsa = geigh(Fa,S)
orbeb,orbsb = geigh(Fb,S)
energya = get_energy(h,Fa,Da)
energyb = get_energy(h,Fb,Db)
energy = (energya+energyb)/2+enuke
Dab = Da+Db
Eone = trace2(Dab,h)
Ej = 0.5*trace2(Dab,Ja+Jb)
Ek = -0.5*(trace2(Da,Ka)+trace2(Db,Kb))
if ETemp: energy += entropy
logger.debug("%d %f %f %f %f" % (i,energy,Eone,Ej,Ek))
if abs(energy-eold) < ConvCriteria: break
eold = energy
logger.info("Final UHF energy for system %s is %f" % (atoms.name,energy))
return energy,(orbea,orbeb),(orbsa,orbsb)
